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Будак и др.</f> <f family="Arial Cyr" charset="204" size="12">.<sp count="2"/> </f> </text> </region> <region region-id="611" left="30" top="84" width="445.5" height="71.25" align-x="30" align-y="96" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="12"> Словесное описание задачи: </f> <f family="Arial Cyr" charset="204" size="12"> Изолированный однородный электрический провод </f> <region region-id="244" left="72.75" top="99" width="51.75" height="15.75" align-x="108" align-y="110.25" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:lessOrEqual/> <ml:apply> <ml:lessOrEqual/> <ml:real>0</ml:real> <ml:id xml:space="preserve">x</ml:id> </ml:apply> <ml:id xml:space="preserve">L</ml:id> </ml:apply> </math> <rendering item-idref="2"/> </region> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> заряжен до некоторого потенциала V0=const. В начальный момент времени конец<sp count="2"/>х=0<sp count="2"/>заземляется, а конец<sp count="2"/>x=L<sp count="2"/>продолжает оставаться изолированным. Найти распределение напряжения в проводе, если самоиндукция, сопротивление и емкость единицы длины известны.</inlineAttr> </f> </text> </region> <region region-id="612" left="30" top="168.75" width="119.25" height="13.5" align-x="30" align-y="180" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="false"> <f family="Arial Cyr" charset="204" size="12"> Задание параметров. </f> </text> </region> <region region-id="599" left="30" top="192" width="151.5" height="14.25" align-x="30" align-y="204" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="12"> Независимые параметры: </f> </text> </region> <region region-id="603" left="30" top="215.25" width="432.75" height="50.25" align-x="30" align-y="228" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="12">Самоиндукция: </f> <region region-id="604" left="115.5" top="216.75" width="35.25" height="15.75" align-x="128.25" align-y="228" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedBIUnit" xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">J</ml:id> <ml:real>10</ml:real> </ml:define> </math> <rendering item-idref="3"/> </region> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> <sp/> </inlineAttr> </f> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" 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<inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false">;</inlineAttr> </f> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false">время наблюдения процесса: </inlineAttr> </f> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> <sp/> </inlineAttr> </f> <region region-id="607" left="198.75" top="233.25" width="37.5" height="15.75" align-x="213.75" align-y="244.5" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedBIUnit" xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">T</ml:id> <ml:real>15</ml:real> </ml:define> </math> <rendering item-idref="6"/> </region> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> <sp count="2"/> </inlineAttr> </f> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false">; начальнй потенциал провода: </inlineAttr> </f> <f family="Arial Cyr" charset="204" size="12"> <sp/> </f> <region region-id="608" left="33" top="249.75" width="39" height="15.75" align-x="55.5" align-y="261" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">V0</ml:id> <ml:real>1</ml:real> </ml:define> </math> <rendering item-idref="7"/> </region> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> <sp/> </inlineAttr> </f> <inlineAttr font-weight="normal" 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underline="false" line-through="false"> <f family="Arial Cyr" charset="204" size="12"> <sp count="2"/>.</f> </inlineAttr> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> <f family="Arial Cyr" charset="204" size="12"> <sp/> </f> </inlineAttr> </text> </region> <region region-id="952" left="30" top="276" width="105.75" height="14.25" align-x="30" align-y="288" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="12"> Обозначения: </f> </text> </region> <region region-id="951" left="120" top="276.75" width="37.5" height="15.75" align-x="133.5" align-y="288" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">a</ml:id> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">c</ml:id> <ml:id xml:space="preserve">J</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="9"/> </region> <region region-id="950" left="186" top="276.75" width="41.25" height="15.75" align-x="200.25" align-y="288" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">b</ml:id> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">c</ml:id> <ml:id xml:space="preserve">R</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="10"/> </region> <region region-id="843" left="30" top="304.5" width="465.75" height="59.25" align-x="30" align-y="330" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="false"> <f family="Arial Cyr" charset="204" size="12">Критерий выбора параметров: 1) если </f> <region region-id="846" left="243" top="305.25" width="63" height="45" align-x="255" align-y="330" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:greaterThan/> <ml:id xml:space="preserve">J</ml:id> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">c</ml:id> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">R</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:div/> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">L</ml:id> <ml:real>2</ml:real> </ml:apply> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">π</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:apply> </ml:apply> </math> <rendering item-idref="11"/> </region> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> , то корни комплексные для всех n</inlineAttr> </f> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false">(N<1) и<sp count="2"/>получаем решение V4(x,t)<sp count="2"/>(</inlineAttr> </f> <f family="Arial Cyr" charset="204" size="12">V5(x,t)</f> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false">). При этом kr=5.</inlineAttr> </f> </text> </region> <region region-id="844" left="30" top="377.25" width="135.75" height="45" align-x="48" align-y="402" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">kr</ml:id> <ml:apply> <ml:id xml:space="preserve">if</ml:id> <ml:sequence> <ml:apply> <ml:greaterThan/> <ml:id xml:space="preserve">J</ml:id> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">c</ml:id> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">R</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:div/> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">L</ml:id> <ml:real>2</ml:real> </ml:apply> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">π</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:apply> </ml:apply> <ml:real>5</ml:real> <ml:real>0</ml:real> </ml:sequence> </ml:apply> </ml:define> </math> <rendering item-idref="12"/> </region> <region region-id="845" left="204" top="390.75" width="39" height="15.75" align-x="221.25" align-y="402" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">kr</ml:id> <result xmlns="http://schemas.mathsoft.com/math20"> <ml:real>0</ml:real> </result> </ml:eval> </math> <rendering item-idref="13"/> </region> <region region-id="613" left="36" top="432.75" width="384.75" height="13.5" align-x="36" align-y="444" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="false"> <f family="Arial Cyr" charset="204" size="12"> Математическая модель. </f> <f family="Arial Cyr" charset="204" size="12"> <sp/> </f> <f family="Arial Cyr" charset="204" size="10">(Вывод см. в лекциях или у Пискунова, т.2, стр.367.) </f> </text> </region> <region region-id="72" left="42" top="462.75" width="111.75" height="20.25" align-x="68.25" align-y="474" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:equal/> <ml:id xml:space="preserve" subscript="xx">V</ml:id> <ml:apply> <ml:plus/> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">c</ml:id> <ml:id xml:space="preserve">J</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="tt">V</ml:id> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">c</ml:id> <ml:id xml:space="preserve">R</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="t">V</ml:id> </ml:apply> </ml:apply> </ml:apply> </math> <rendering item-idref="14"/> </region> <region region-id="92" left="216" top="462.75" width="51.75" height="15.75" align-x="251.25" align-y="474" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:lessOrEqual/> <ml:apply> <ml:lessOrEqual/> <ml:real>0</ml:real> <ml:id xml:space="preserve">x</ml:id> </ml:apply> <ml:id xml:space="preserve">L</ml:id> </ml:apply> </math> <rendering item-idref="15"/> </region> <region region-id="93" left="312" top="462.75" width="25.5" height="15.75" align-x="322.5" align-y="474" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:greaterThan/> <ml:id xml:space="preserve">t</ml:id> <ml:real>0</ml:real> </ml:apply> </math> <rendering item-idref="16"/> </region> <region region-id="130" left="474" top="462.75" width="15.75" height="15.75" align-x="480.75" align-y="474" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:parens xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:real>1</ml:real> </ml:parens> </math> <rendering item-idref="17"/> </region> <region region-id="615" left="30" top="492.75" width="450" height="13.5" align-x="30" align-y="504" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="false"> <f family="Arial Cyr" charset="204" size="12">Здесь: V(x,t) - напряжение в сечении провода с координатой х в момент времени t;</f> </text> </region> <region region-id="99" left="42" top="522" width="204.75" height="14.25" align-x="42" align-y="534" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="12"> Краевые условия: </f> </text> </region> <region region-id="100" left="42" top="546.75" width="66" height="15.75" align-x="84.75" align-y="558" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:equal/> <ml:apply> <ml:id xml:space="preserve">V</ml:id> <ml:sequence> <ml:id xml:space="preserve">x</ml:id> <ml:real>0</ml:real> </ml:sequence> </ml:apply> <ml:id xml:space="preserve">V0</ml:id> </ml:apply> </math> <rendering item-idref="18"/> </region> <region region-id="107" left="132" top="546.75" width="60.75" height="20.25" align-x="177.75" align-y="558" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:equal/> <ml:apply> <ml:id xml:space="preserve" subscript="t">V</ml:id> <ml:sequence> <ml:id xml:space="preserve">x</ml:id> <ml:real>0</ml:real> </ml:sequence> </ml:apply> <ml:real>0</ml:real> </ml:apply> </math> <rendering item-idref="19"/> </region> <region region-id="108" left="216" top="546.75" width="108.75" height="13.5" align-x="216" align-y="558" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="false"> <f family="Arial Cyr" charset="204" size="12">Начальные условия</f> </text> </region> <region region-id="129" left="474" top="570.75" width="15.75" height="15.75" align-x="480.75" align-y="582" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:parens xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:real>2</ml:real> </ml:parens> </math> <rendering item-idref="20"/> </region> <region region-id="102" left="48" top="588.75" width="55.5" height="15.75" align-x="88.5" align-y="600" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:equal/> <ml:apply> <ml:id xml:space="preserve">V</ml:id> <ml:sequence> <ml:real>0</ml:real> <ml:id xml:space="preserve">t</ml:id> </ml:sequence> </ml:apply> <ml:real>0</ml:real> </ml:apply> </math> <rendering item-idref="21"/> </region> <region region-id="103" left="120" top="588.75" width="61.5" height="20.25" align-x="166.5" align-y="600" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:equal/> <ml:apply> <ml:id xml:space="preserve" subscript="x">V</ml:id> <ml:sequence> <ml:id xml:space="preserve">L</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:sequence> </ml:apply> <ml:real>0</ml:real> </ml:apply> </math> <rendering item-idref="22"/> </region> <region region-id="110" left="216" top="588.75" width="106.5" height="13.5" align-x="216" align-y="600" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="false"> <f family="Arial Cyr" charset="204" size="12">Граничные условия</f> </text> </region> <region region-id="114" left="42" top="624" width="129" height="14.25" align-x="42" align-y="636" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="false"> <f family="Arial Cyr" charset="204" size="12"> <sp/> </f> <f family="Arial Cyr" charset="204" size="12"> Решение </f> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-style="normal" underline="false"> ищем в виде:</inlineAttr> </f> </text> </region> <region region-id="617" left="204" top="624.75" width="95.25" height="15.75" align-x="243.75" align-y="636" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:equal/> <ml:apply> <ml:id xml:space="preserve">V</ml:id> <ml:sequence> <ml:id xml:space="preserve">x</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:sequence> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:id xml:space="preserve">X</ml:id> <ml:id xml:space="preserve">x</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve">T</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> </ml:apply> </math> <rendering item-idref="23"/> </region> <region region-id="637" left="474" top="624.75" width="28.5" height="15.75" align-x="487.5" align-y="636" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:parens xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">resh</ml:id> </ml:parens> </math> <rendering item-idref="24"/> </region> <region region-id="619" left="42" top="648.75" width="352.5" height="13.5" align-x="42" align-y="660" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="false"> <f family="Arial Cyr" charset="204" size="12">Исходя из краевых условий (2), запишем следующие выражения:</f> </text> </region> <region region-id="631" left="54" top="672.75" width="80.25" height="15.75" align-x="75.75" align-y="684" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:equal/> <ml:id xml:space="preserve">V0</ml:id> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:id xml:space="preserve">X</ml:id> <ml:id xml:space="preserve">x</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve">T</ml:id> <ml:real>0</ml:real> </ml:apply> </ml:apply> </ml:apply> </math> <rendering item-idref="25"/> </region> <region region-id="632" left="156" top="672.75" width="74.25" height="15.75" align-x="169.5" align-y="684" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:equal/> <ml:real>0</ml:real> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:id xml:space="preserve">X</ml:id> <ml:id xml:space="preserve">x</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve">T'</ml:id> <ml:real>0</ml:real> </ml:apply> </ml:apply> </ml:apply> </math> <rendering item-idref="26"/> </region> <region region-id="956" left="462" top="684.75" width="21" height="15.75" align-x="471.75" align-y="696" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:parens xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:apply> <ml:mult style="auto-select"/> <ml:real>2</ml:real> <ml:id xml:space="preserve">a</ml:id> </ml:apply> </ml:parens> </math> <rendering item-idref="27"/> </region> <region region-id="625" left="54" top="720.75" width="69.75" height="15.75" align-x="67.5" align-y="732" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:equal/> <ml:real>0</ml:real> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:id xml:space="preserve">X</ml:id> <ml:real>0</ml:real> </ml:apply> <ml:apply> <ml:id xml:space="preserve">T</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> </ml:apply> </math> <rendering item-idref="28"/> </region> <region region-id="628" left="150" top="720.75" width="72.75" height="15.75" align-x="163.5" align-y="732" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:equal/> <ml:real>0</ml:real> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:id xml:space="preserve">X'</ml:id> <ml:id xml:space="preserve">L</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve">T</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> </ml:apply> </math> <rendering item-idref="29"/> </region> <region region-id="955" left="36" top="750" width="461.25" height="43.5" align-x="36" align-y="762" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="12">Из этих равенств следует, что </f> <region region-id="635" left="202.5" top="750.75" width="45.75" height="15.75" align-x="233.25" align-y="762" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:notEqual/> <ml:apply> <ml:id xml:space="preserve">X</ml:id> <ml:id xml:space="preserve">x</ml:id> </ml:apply> <ml:real>0</ml:real> </ml:apply> </math> <rendering item-idref="30"/> </region> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> и </inlineAttr> </f> <region region-id="636" left="261" top="750.75" width="42" height="15.75" align-x="288" align-y="762" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:notEqual/> <ml:apply> <ml:id xml:space="preserve">T</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> <ml:real>0</ml:real> </ml:apply> </math> <rendering item-idref="31"/> </region> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false">. В противном случае мы </inlineAttr> </f> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false">получаем </inlineAttr> </f> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false">тривиальное (нулевое) решение. Подстановка (resh) в (1) приводит </inlineAttr> </f> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> <f family="Arial Cyr" charset="204" size="12">к двум линейным дифференциальным </f> </inlineAttr> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> <f family="Arial Cyr" charset="204" size="12">уравнениям 2-го порядка:</f> </inlineAttr> </text> </region> <region region-id="649" left="42" top="822.75" width="76.5" height="13.5" align-x="42" align-y="834" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="12">Первое из них</f> </text> </region> <region region-id="648" left="138" top="807.75" width="115.5" height="44.25" align-x="238.5" align-y="834" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:equal/> <ml:apply> <ml:plus/> <ml:apply> <ml:derivative/> <ml:lambda> <ml:boundVars> <ml:id xml:space="preserve">x</ml:id> </ml:boundVars> <ml:apply> <ml:id xml:space="preserve">X</ml:id> <ml:id xml:space="preserve">x</ml:id> </ml:apply> </ml:lambda> <ml:degree> <ml:real>2</ml:real> </ml:degree> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">λ</ml:id> <ml:apply> <ml:id xml:space="preserve">X</ml:id> <ml:id xml:space="preserve">x</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:real>0</ml:real> </ml:apply> </math> <rendering item-idref="32"/> </region> <region region-id="653" left="462" top="828.75" width="15.75" height="15.75" align-x="468.75" align-y="840" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:parens xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:real>3</ml:real> </ml:parens> </math> <rendering item-idref="33"/> </region> <region region-id="650" left="42" top="864.75" width="140.25" height="13.5" align-x="42" align-y="876" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="12">с начальными условиями:</f> </text> </region> <region region-id="652" left="198" top="864.75" width="46.5" height="15.75" align-x="229.5" align-y="876" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:equal/> <ml:apply> <ml:id xml:space="preserve">X</ml:id> <ml:real>0</ml:real> </ml:apply> <ml:real>0</ml:real> </ml:apply> </math> <rendering item-idref="34"/> </region> <region region-id="651" left="276" top="864.75" width="49.5" height="15.75" align-x="310.5" align-y="876" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:equal/> <ml:apply> <ml:id xml:space="preserve">X'</ml:id> <ml:id xml:space="preserve">L</ml:id> </ml:apply> <ml:real>0</ml:real> </ml:apply> </math> <rendering item-idref="35"/> </region> <region region-id="656" left="42" top="897" width="476.25" height="70.5" align-x="42" align-y="918" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="12">позволяет найти </f> <region region-id="655" left="134.25" top="906.75" width="53.25" height="17.25" align-x="165" align-y="918" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:equal/> <ml:apply> <ml:id xml:space="preserve">X</ml:id> <ml:id xml:space="preserve">x</ml:id> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">X</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> </ml:apply> </math> <rendering item-idref="36"/> </region> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> ,<sp count="2"/>где<sp count="2"/> </inlineAttr> </f> <region region-id="657" left="224.25" top="903.75" width="84" height="20.25" align-x="245.25" align-y="918" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:equal/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">X</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve">sin</ml:id> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:sqrt/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">λ</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> </ml:apply> <ml:id xml:space="preserve">x</ml:id> </ml:apply> </ml:apply> </ml:apply> </math> <rendering item-idref="37"/> </region> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false">,<sp count="3"/> </inlineAttr> </f> <region region-id="658" left="321" top="897.75" width="96" height="34.5" align-x="350.25" align-y="918" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:equal/> <ml:apply> <ml:sqrt/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">λ</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:div/> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">π</ml:id> <ml:parens> <ml:apply> <ml:minus/> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:real>1</ml:real> </ml:apply> </ml:parens> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:id xml:space="preserve">L</ml:id> </ml:apply> </ml:apply> </ml:apply> </math> <rendering item-idref="38"/> </region> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> <sp count="2"/>.</inlineAttr> </f> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> <sp count="2"/> </inlineAttr> </f> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> <f family="Arial Cyr" charset="204" size="12">П</f> </inlineAttr> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> <f family="Arial Cyr" charset="204" size="12">оследние </f> </inlineAttr> <f family="Arial Cyr" charset="204" size="12">называют:</f> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> <sp/> </inlineAttr> </f> <region region-id="661" left="165" top="933" width="13.5" height="18" align-x="171" align-y="945" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:indexer/> <ml:id xml:space="preserve">λ</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> </math> <rendering item-idref="39"/> </region> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> <sp/> </inlineAttr> </f> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> -</inlineAttr> </f> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> <sp count="3"/> </inlineAttr> </f> <f family="Arial Cyr" charset="204" size="12">собственными значениями </f> <f family="Arial Cyr" charset="204" size="12"> и</f> <f family="Arial Cyr" charset="204" size="12"> <sp count="2"/>соответствующие им </f> <f family="Arial Cyr" charset="204" size="12">Х</f> <f family="Arial Cyr" charset="204" size="12"> n </f> <f family="Arial Cyr" charset="204" size="12">(x) - </f> <f family="Arial Cyr" charset="204" size="12">собственными функциями</f> <f family="Arial Cyr" charset="204" size="12">.</f> </text> </region> <region region-id="690" left="42" top="978.75" width="441.75" height="43.5" align-x="42" align-y="990" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="false"> <f family="Arial Cyr" charset="204" size="12">Причём {X</f> <f family="Arial Cyr" charset="204" size="12"> n </f> <f family="Arial Cyr" charset="204" size="12">} представляет систему ортогональных функций на отрезке [-2L,2L], </f> <f family="Arial Cyr" charset="204" size="12">а</f> <f family="Arial Cyr" charset="204" size="12">также на отрезках: </f> <f family="Arial Cyr" charset="204" size="12">[0,2L] или </f> <f family="Arial Cyr" charset="204" size="12">[-L,L], </f> <f family="Arial Cyr" charset="204" size="12">[0,L] или</f> <f family="Arial Cyr" charset="204" size="12"> <sp/> </f> <f family="Arial Cyr" charset="204" size="12">[-L/2,L/2] (см. файл: СистОртогФункций\</f> <f family="Arial Cyr" charset="204" size="12">СистОртогФункций.xmcd.</f> </text> </region> <region region-id="675" left="174" top="1053.75" width="101.25" height="34.5" align-x="223.5" align-y="1074" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:parens xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:apply> <ml:id xml:space="preserve">sin</ml:id> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:div/> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">π</ml:id> <ml:parens> <ml:apply> <ml:minus/> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:real>1</ml:real> </ml:apply> </ml:parens> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:id xml:space="preserve">L</ml:id> </ml:apply> </ml:apply> <ml:id xml:space="preserve">x</ml:id> </ml:apply> </ml:apply> </ml:parens> </math> <rendering item-idref="40"/> </region> <region region-id="676" left="300" top="1062.75" width="52.5" height="15.75" align-x="341.25" align-y="1074" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:sequence xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:apply> <ml:equal/> <ml:id xml:space="preserve">n</ml:id> <ml:real>1</ml:real> </ml:apply> <ml:real>2</ml:real> <ml:id xml:space="preserve" font="1">...</ml:id> </ml:sequence> </math> <rendering item-idref="41"/> </region> <region region-id="677" left="456" top="1062.75" width="15.75" height="15.75" align-x="462.75" align-y="1074" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:parens xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:real>4</ml:real> </ml:parens> </math> <rendering item-idref="42"/> </region> <region region-id="1141" left="60" top="1110.75" width="344.25" height="13.5" align-x="60" align-y="1122" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="12">Правда, для указанных выше отрезков, нормы будут разными: </f> </text> </region> <region region-id="1142" left="60" top="1140.75" width="314.25" height="61.5" align-x="83.25" align-y="1176" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:provenance expr-id="1" xmlns:ml="http://schemas.mathsoft.com/math20"> <originRef doc-id="86a18416-aebf-489a-9dbe-33607ccad11e" version-id="06502f39-6fe4-48af-acbb-790c959f320a" branch-id="00000000-0000-0000-0000-000000000000" revision-num="54" is-modified="false" region-id="0" href="C:\Documents and Settings\Konstantin\Мои документы\Компьют технол\СлушателиФПКП\ВолнУр123.xmcd" xmlns="http://schemas.mathsoft.com/provenance10"> <hash/> </originRef> <parentRef doc-id="86a18416-aebf-489a-9dbe-33607ccad11e" version-id="06502f39-6fe4-48af-acbb-790c959f320a" branch-id="00000000-0000-0000-0000-000000000000" revision-num="54" is-modified="false" region-id="0" href="C:\Documents and Settings\Konstantin\Мои документы\Компьют технол\СлушателиФПКП\ВолнУр123.xmcd" xmlns="http://schemas.mathsoft.com/provenance10"> <hash/> </parentRef> <comment xmlns="http://schemas.mathsoft.com/provenance10"/> <originComment xmlns="http://schemas.mathsoft.com/provenance10"/> <contentHash xmlns="http://schemas.mathsoft.com/provenance10">5e62e805d1fdc05a635c4584032ef08a</contentHash> <ml:define> <ml:id xml:space="preserve">nor</ml:id> <ml:symEval style="default" hide-keywords="false" hide-lhs="false"> <ml:apply> <ml:integral auto-algorithm="true"/> <ml:lambda> <ml:boundVars> <ml:id xml:space="preserve">x</ml:id> </ml:boundVars> <ml:apply> <ml:pow/> <ml:apply> <ml:id xml:space="preserve">sin</ml:id> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:mult style="default"/> <ml:parens> <ml:apply> <ml:minus/> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:real>1</ml:real> </ml:apply> </ml:parens> <ml:apply> <ml:div/> <ml:id xml:space="preserve">π</ml:id> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:id xml:space="preserve">L</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:id xml:space="preserve">x</ml:id> </ml:apply> </ml:apply> <ml:real>2</ml:real> </ml:apply> </ml:lambda> <ml:bounds> <ml:real>0</ml:real> <ml:id xml:space="preserve">L</ml:id> </ml:bounds> </ml:apply> <ml:command> <ml:sequence> <ml:id xml:space="preserve">substitute</ml:id> <ml:apply> <ml:equal/> <ml:apply> <ml:id xml:space="preserve">sin</ml:id> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">π</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> </ml:apply> <ml:real>0</ml:real> </ml:apply> </ml:sequence> </ml:command> <ml:command> <ml:id xml:space="preserve">simplify</ml:id> </ml:command> <ml:symResult> <ml:id xml:space="preserve">π</ml:id> </ml:symResult> </ml:symEval> </ml:define> </ml:provenance> </math> <rendering item-idref="43"> <element-image-map> <box left="1.5" top="0.75" width="312.75" height="60" expr-idref="1" xmlns="http://schemas.mathsoft.com/worksheet20"/> </element-image-map> </rendering> </region> <region region-id="1143" left="444" top="1164.75" width="21" height="15.75" align-x="453.75" align-y="1176" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:provenance expr-id="1" xmlns:ml="http://schemas.mathsoft.com/math20"> <originRef doc-id="86a18416-aebf-489a-9dbe-33607ccad11e" version-id="06502f39-6fe4-48af-acbb-790c959f320a" branch-id="00000000-0000-0000-0000-000000000000" revision-num="54" is-modified="false" region-id="0" href="C:\Documents and Settings\Konstantin\Мои документы\Компьют технол\СлушателиФПКП\ВолнУр123.xmcd" xmlns="http://schemas.mathsoft.com/provenance10"> <hash/> </originRef> <parentRef doc-id="86a18416-aebf-489a-9dbe-33607ccad11e" version-id="06502f39-6fe4-48af-acbb-790c959f320a" branch-id="00000000-0000-0000-0000-000000000000" revision-num="54" is-modified="false" region-id="0" href="C:\Documents and Settings\Konstantin\Мои документы\Компьют технол\СлушателиФПКП\ВолнУр123.xmcd" xmlns="http://schemas.mathsoft.com/provenance10"> <hash/> </parentRef> <comment xmlns="http://schemas.mathsoft.com/provenance10"/> <originComment xmlns="http://schemas.mathsoft.com/provenance10"/> <contentHash xmlns="http://schemas.mathsoft.com/provenance10">e65ca673c13357ad8e9c4d306c4bdf52</contentHash> <ml:parens> <ml:apply> <ml:mult style="auto-select"/> <ml:real>4</ml:real> <ml:id xml:space="preserve">a</ml:id> </ml:apply> </ml:parens> </ml:provenance> </math> <rendering item-idref="44"> <element-image-map> <box left="1.5" top="0.75" width="19.5" height="14.25" expr-idref="1" xmlns="http://schemas.mathsoft.com/worksheet20"/> </element-image-map> </rendering> </region> <region region-id="1144" left="450" top="1230.75" width="21.75" height="15.75" align-x="459.75" align-y="1242" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:provenance expr-id="1" xmlns:ml="http://schemas.mathsoft.com/math20"> <originRef doc-id="86a18416-aebf-489a-9dbe-33607ccad11e" version-id="06502f39-6fe4-48af-acbb-790c959f320a" branch-id="00000000-0000-0000-0000-000000000000" revision-num="54" is-modified="false" region-id="0" href="C:\Documents and Settings\Konstantin\Мои документы\Компьют технол\СлушателиФПКП\ВолнУр123.xmcd" xmlns="http://schemas.mathsoft.com/provenance10"> <hash/> </originRef> <parentRef doc-id="86a18416-aebf-489a-9dbe-33607ccad11e" version-id="06502f39-6fe4-48af-acbb-790c959f320a" branch-id="00000000-0000-0000-0000-000000000000" revision-num="54" is-modified="false" region-id="0" href="C:\Documents and Settings\Konstantin\Мои документы\Компьют технол\СлушателиФПКП\ВолнУр123.xmcd" xmlns="http://schemas.mathsoft.com/provenance10"> <hash/> </parentRef> <comment xmlns="http://schemas.mathsoft.com/provenance10"/> <originComment xmlns="http://schemas.mathsoft.com/provenance10"/> <contentHash xmlns="http://schemas.mathsoft.com/provenance10">2fd412f8611709532490f5ed75b7e580</contentHash> <ml:parens> <ml:real base="2">4</ml:real> </ml:parens> </ml:provenance> </math> <rendering item-idref="45"> <element-image-map> <box left="1.5" top="0.75" width="20.25" height="14.25" expr-idref="1" xmlns="http://schemas.mathsoft.com/worksheet20"/> </element-image-map> </rendering> </region> <region region-id="1145" left="60" top="1218.75" width="339" height="61.5" align-x="89.25" align-y="1254" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:provenance expr-id="1" xmlns:ml="http://schemas.mathsoft.com/math20"> <originRef doc-id="86a18416-aebf-489a-9dbe-33607ccad11e" version-id="06502f39-6fe4-48af-acbb-790c959f320a" branch-id="00000000-0000-0000-0000-000000000000" revision-num="54" is-modified="false" region-id="0" href="C:\Documents and Settings\Konstantin\Мои документы\Компьют технол\СлушателиФПКП\ВолнУр123.xmcd" xmlns="http://schemas.mathsoft.com/provenance10"> <hash/> </originRef> <parentRef doc-id="86a18416-aebf-489a-9dbe-33607ccad11e" version-id="06502f39-6fe4-48af-acbb-790c959f320a" branch-id="00000000-0000-0000-0000-000000000000" revision-num="54" is-modified="false" region-id="0" href="C:\Documents and Settings\Konstantin\Мои документы\Компьют технол\СлушателиФПКП\ВолнУр123.xmcd" xmlns="http://schemas.mathsoft.com/provenance10"> <hash/> </parentRef> <comment xmlns="http://schemas.mathsoft.com/provenance10"/> <originComment xmlns="http://schemas.mathsoft.com/provenance10"/> <contentHash xmlns="http://schemas.mathsoft.com/provenance10">4b8cb53e32d50ad9bc2f135345887aed</contentHash> <ml:define> <ml:id xml:space="preserve">nor1</ml:id> <ml:symEval style="default" hide-keywords="false" hide-lhs="false"> <ml:apply> <ml:integral auto-algorithm="true"/> <ml:lambda> <ml:boundVars> <ml:id xml:space="preserve">x</ml:id> </ml:boundVars> <ml:apply> <ml:pow/> <ml:apply> <ml:id xml:space="preserve">sin</ml:id> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:mult style="default"/> <ml:parens> <ml:apply> <ml:minus/> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:real>1</ml:real> </ml:apply> </ml:parens> <ml:apply> <ml:div/> <ml:id xml:space="preserve">π</ml:id> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:id xml:space="preserve">L</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:id xml:space="preserve">x</ml:id> </ml:apply> </ml:apply> <ml:real>2</ml:real> </ml:apply> </ml:lambda> <ml:bounds> <ml:real>0</ml:real> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:id xml:space="preserve">L</ml:id> </ml:apply> </ml:bounds> </ml:apply> <ml:command> <ml:sequence> <ml:id xml:space="preserve">substitute</ml:id> <ml:apply> <ml:equal/> <ml:apply> <ml:id xml:space="preserve">sin</ml:id> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">π</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> </ml:apply> <ml:real>0</ml:real> </ml:apply> </ml:sequence> </ml:command> <ml:command> <ml:id xml:space="preserve">simplify</ml:id> </ml:command> <ml:symResult> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:id xml:space="preserve">π</ml:id> </ml:apply> </ml:symResult> </ml:symEval> </ml:define> </ml:provenance> </math> <rendering item-idref="46"> <element-image-map> <box left="1.5" top="0.75" width="337.5" height="60" expr-idref="1" xmlns="http://schemas.mathsoft.com/worksheet20"/> </element-image-map> </rendering> </region> <region region-id="1146" left="66" top="1296.75" width="329.25" height="13.5" align-x="66" align-y="1308" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="12">Нас интересует отрезок [0,L] и соответствующая ему норма.</f> </text> </region> <region region-id="659" left="42" top="1331.25" width="462" height="18.75" align-x="42" align-y="1344" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="12">Второе из уравнений с учётом найденного значения </f> <region region-id="694" left="327" top="1332" width="13.5" height="18" align-x="333" align-y="1344" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:indexer/> <ml:id xml:space="preserve">λ</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> </math> <rendering item-idref="47"/> </region> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> будет иметь вид:</inlineAttr> </f> </text> </region> <region region-id="691" left="42" top="1359.75" width="184.5" height="44.25" align-x="211.5" align-y="1386" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:equal/> <ml:apply> <ml:plus/> <ml:apply> <ml:plus/> <ml:apply> <ml:derivative/> <ml:lambda> <ml:boundVars> <ml:id xml:space="preserve">t</ml:id> </ml:boundVars> <ml:apply> <ml:id xml:space="preserve">T</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:lambda> <ml:degree> <ml:real>2</ml:real> </ml:degree> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:div/> <ml:id xml:space="preserve">b</ml:id> <ml:id xml:space="preserve">a</ml:id> </ml:apply> <ml:parens> <ml:apply> <ml:derivative/> <ml:lambda> <ml:boundVars> <ml:id xml:space="preserve">t</ml:id> </ml:boundVars> <ml:apply> <ml:id xml:space="preserve">T</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:lambda> </ml:apply> </ml:parens> </ml:apply> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:div/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">λ</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:id xml:space="preserve">a</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve">T</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:real>0</ml:real> </ml:apply> </math> <rendering item-idref="48"/> </region> <region region-id="692" left="264" top="1374.75" width="27.75" height="15.75" align-x="276.75" align-y="1386" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:notEqual/> <ml:id xml:space="preserve">a</ml:id> <ml:real>0</ml:real> </ml:apply> </math> <rendering item-idref="49"/> </region> <region region-id="693" left="366" top="1374.75" width="15.75" height="15.75" align-x="372.75" align-y="1386" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:parens xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:real>5</ml:real> </ml:parens> </math> <rendering item-idref="50"/> </region> <region region-id="151" left="36" top="1439.25" width="439.5" height="45.75" align-x="36" align-y="1452" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="12">Находим решение (5) , которое будет зависеть от значения </f> <region region-id="159" left="361.5" top="1440" width="13.5" height="18" align-x="367.5" align-y="1452" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:indexer/> <ml:id xml:space="preserve">λ</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> </math> <rendering item-idref="51"/> </region> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false">.</inlineAttr> </f> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false">Для этого найдем корни характеристического уравнения, соответствующего уравнению (5).</inlineAttr> </f> </text> </region> <region region-id="252" left="48" top="1494" width="77.25" height="18" align-x="72.75" align-y="1506" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:equal/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">p1</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:apply> <ml:plus/> <ml:apply> <ml:neg/> <ml:id xml:space="preserve">ν</ml:id> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">Ω</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> </ml:apply> </ml:apply> </math> <rendering item-idref="52"/> </region> <region region-id="253" left="174" top="1494" width="76.5" height="18" align-x="198.75" align-y="1506" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:equal/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">p2</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:apply> <ml:minus/> <ml:apply> <ml:neg/> <ml:id xml:space="preserve">ν</ml:id> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">Ω</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> </ml:apply> </ml:apply> </math> <rendering item-idref="53"/> </region> <region region-id="254" left="294" top="1494.75" width="52.5" height="15.75" align-x="335.25" align-y="1506" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:sequence xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:apply> <ml:equal/> <ml:id xml:space="preserve">n</ml:id> <ml:real>1</ml:real> </ml:apply> <ml:real>2</ml:real> <ml:id xml:space="preserve" font="1">...</ml:id> </ml:sequence> </math> <rendering item-idref="54"/> </region> <region region-id="273" left="480" top="1494.75" width="15.75" height="15.75" align-x="486.75" align-y="1506" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:parens xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:real>6</ml:real> </ml:parens> </math> <rendering item-idref="55"/> </region> <region region-id="291" left="42" top="1548.75" width="27" height="13.5" align-x="42" align-y="1560" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="false"> <f family="Arial Cyr" charset="204" size="12">где: </f> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> <sp/> </inlineAttr> </f> </text> </region> <region region-id="299" left="78" top="1540.5" width="43.5" height="33.75" align-x="93.75" align-y="1560" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">ν</ml:id> <ml:apply> <ml:div/> <ml:id xml:space="preserve">R</ml:id> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:id xml:space="preserve">J</ml:id> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="56"/> </region> <region region-id="304" left="144" top="1533" width="198" height="47.25" align-x="167.25" align-y="1560" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:equal/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">Ω</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:div/> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">π</ml:id> <ml:parens> <ml:apply> <ml:minus/> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:real>1</ml:real> </ml:apply> </ml:parens> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:id xml:space="preserve">L</ml:id> </ml:apply> <ml:apply> <ml:sqrt/> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">c</ml:id> <ml:id xml:space="preserve">J</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:sqrt/> <ml:apply> <ml:minus/> <ml:apply> <ml:div/> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">c</ml:id> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">R</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">L</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">J</ml:id> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">π</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:pow/> <ml:parens> <ml:apply> <ml:minus/> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:real>1</ml:real> </ml:apply> </ml:parens> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:apply> <ml:real>1</ml:real> </ml:apply> </ml:apply> </ml:apply> </ml:apply> </math> <rendering item-idref="57"/> </region> <region region-id="305" left="474" top="1548.75" width="15.75" height="15.75" align-x="480.75" align-y="1560" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:parens xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:real>7</ml:real> </ml:parens> </math> <rendering item-idref="58"/> </region> <region region-id="1071" left="30" top="1608.75" width="488.25" height="27" align-x="30" align-y="1620" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="12">В зависимости от выбора параметров и, что самое главное, от значений индекса "n", корни (6) могут быть как действительными разными или равными, так и комплексными. </f> </text> </region> <region region-id="268" left="24" top="1660.5" width="406.5" height="96.75" align-x="24" align-y="1686" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="12">Поэтому найдем такое n, при котором </f> <region region-id="261" left="233.25" top="1661.25" width="117.75" height="45" align-x="336" align-y="1686" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:equal/> <ml:apply> <ml:minus/> <ml:real>1</ml:real> <ml:apply> <ml:div/> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">c</ml:id> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">R</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">L</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">J</ml:id> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">π</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:pow/> <ml:parens> <ml:apply> <ml:minus/> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:real>1</ml:real> </ml:apply> </ml:parens> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:apply> </ml:apply> <ml:real>0</ml:real> </ml:apply> </math> <rendering item-idref="59"/> </region> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false">. Или </inlineAttr> </f> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> <sp/> </inlineAttr> </f> <region region-id="267" left="27" top="1707" width="86.25" height="36.75" align-x="39.75" align-y="1728.75" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:equal/> <ml:id xml:space="preserve">n</ml:id> <ml:apply> <ml:plus/> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:div/> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">R</ml:id> <ml:id xml:space="preserve">L</ml:id> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:id xml:space="preserve">π</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:sqrt/> <ml:apply> <ml:div/> <ml:id xml:space="preserve">c</ml:id> <ml:id xml:space="preserve">J</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:div/> <ml:real>1</ml:real> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:apply> </math> <rendering item-idref="60"/> </region> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> .</inlineAttr> </f> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false">Обозначим это значение через N</inlineAttr> </f> <f family="Arial Cyr" charset="204" size="12"> <sp/> </f> </text> </region> <region region-id="266" left="132" top="1772.25" width="92.25" height="36.75" align-x="149.25" align-y="1794" show-border="false" show-highlight="true" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedBIUnit" xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">N</ml:id> <ml:apply> <ml:plus/> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:div/> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">R</ml:id> <ml:id xml:space="preserve">L</ml:id> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:id xml:space="preserve">π</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:sqrt/> <ml:apply> <ml:div/> <ml:id xml:space="preserve">c</ml:id> <ml:id xml:space="preserve">J</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:div/> <ml:real>1</ml:real> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="61"/> </region> <region region-id="577" left="264" top="1782.75" width="44.25" height="15.75" align-x="280.5" align-y="1794" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">N</ml:id> <result xmlns="http://schemas.mathsoft.com/math20"> <ml:real>13</ml:real> </result> </ml:eval> </math> <rendering item-idref="62"/> </region> <region region-id="696" left="486" top="1782.75" width="15.75" height="15.75" align-x="492.75" align-y="1794" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:parens xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:real>8</ml:real> </ml:parens> </math> <rendering item-idref="63"/> </region> <region region-id="578" left="24" top="1832.25" width="466.5" height="12" align-x="24" align-y="1842" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="false"> <f family="Arial Cyr" charset="204" size="10">Примечание. Можно подогнать R так, чтобы N было целым. Для этого R будем вычислять по формуле:</f> </text> </region> <region region-id="579" left="36" top="1862.25" width="148.5" height="36" align-x="59.25" align-y="1884" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">RR</ml:id> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:mult style="default"/> <ml:parens> <ml:apply> <ml:minus/> <ml:apply> <ml:id xml:space="preserve">ceil</ml:id> <ml:id xml:space="preserve">N</ml:id> </ml:apply> <ml:apply> <ml:div/> <ml:real>1</ml:real> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:parens> <ml:apply> <ml:div/> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:id xml:space="preserve">π</ml:id> </ml:apply> <ml:id xml:space="preserve">L</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:sqrt/> <ml:apply> <ml:div/> <ml:id xml:space="preserve">J</ml:id> <ml:id xml:space="preserve">c</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="64"/> </region> <region region-id="580" left="222" top="1872.75" width="59.25" height="15.75" align-x="244.5" align-y="1884" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">RR</ml:id> <result xmlns="http://schemas.mathsoft.com/math20"> <ml:real>12.5</ml:real> </result> </ml:eval> </math> <rendering item-idref="65"/> </region> <region region-id="581" left="30" top="1910.25" width="477" height="12" align-x="30" align-y="1920" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="false"> <f family="Arial Cyr" charset="204" size="10">Полученное значение R=RR надо подставить в исходные данные в начале листинга. Конец Примечания.</f> </text> </region> <region region-id="278" left="30" top="1944.75" width="423" height="13.5" align-x="30" align-y="1956" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="false"> <f family="Arial Cyr" charset="204" size="12">Значения (8) приводят к разбиению множества индексов n<sp count="2"/>на подмножества.</f> </text> </region> <region region-id="465" left="150" top="1974.75" width="159" height="14.25" align-x="150" align-y="1986" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="12"> Алгоритмизация решения. </f> </text> </region> <region region-id="964" left="42" top="1998.75" width="411.75" height="13.5" align-x="42" align-y="2010" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="false"> <f family="Arial Cyr" charset="204" size="12">Все задаваемые ниже параметры можно менять в интерактивном режиме.</f> </text> </region> <region region-id="961" left="42" top="2022.75" width="230.25" height="13.5" align-x="42" align-y="2034" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="12">Зададим диапазон изменения индекса "n":</f> </text> </region> <region region-id="962" left="288" top="2022.75" width="54.75" height="15.75" align-x="314.25" align-y="2034" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">NN</ml:id> <ml:real>130</ml:real> </ml:define> </math> <rendering item-idref="66"/> </region> <region region-id="963" left="360" top="2022.75" width="57.75" height="15.75" align-x="373.5" align-y="2034" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">n</ml:id> <ml:range> <ml:real>1</ml:real> <ml:id xml:space="preserve">NN</ml:id> </ml:range> </ml:define> </math> <rendering item-idref="67"/> </region> <region region-id="850" left="42" top="2045.25" width="450.75" height="17.25" align-x="42" align-y="2058" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="false"> <f family="Arial Cyr" charset="204" size="12">Погрешность округления<sp count="2"/>N до целого числа: </f> <region region-id="1002" left="288" top="2046" width="52.5" height="16.5" align-x="303" align-y="2058" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedBIFunction" xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">ε</ml:id> <ml:real>0.001</ml:real> </ml:define> </math> <rendering item-idref="68"/> </region> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false">. Её можно задать как ноль.</inlineAttr> </f> </text> </region> <region region-id="733" left="42" top="2104.5" width="105" height="39.75" align-x="63" align-y="2130" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">λ</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:apply> <ml:pow/> <ml:parens> <ml:apply> <ml:div/> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">π</ml:id> <ml:parens> <ml:apply> <ml:minus/> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:real>1</ml:real> </ml:apply> </ml:parens> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:id xml:space="preserve">L</ml:id> </ml:apply> </ml:apply> </ml:parens> <ml:real>2</ml:real> </ml:apply> </ml:define> </math> <rendering item-idref="69"/> </region> <region region-id="732" left="174" top="2103" width="200.25" height="47.25" align-x="198" align-y="2130" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedBIUnit" xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">Ω</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:div/> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">π</ml:id> <ml:parens> <ml:apply> <ml:minus/> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:real>1</ml:real> </ml:apply> </ml:parens> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:id xml:space="preserve">L</ml:id> </ml:apply> <ml:apply> <ml:sqrt/> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">c</ml:id> <ml:id xml:space="preserve">J</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:sqrt/> <ml:apply> <ml:minus/> <ml:apply> <ml:div/> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">c</ml:id> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">R</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">L</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">J</ml:id> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">π</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:pow/> <ml:parens> <ml:apply> <ml:minus/> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:real>1</ml:real> </ml:apply> </ml:parens> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:apply> <ml:real>1</ml:real> </ml:apply> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="70"/> </region> <region region-id="546" left="42" top="2169" width="198.75" height="47.25" align-x="64.5" align-y="2196" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">ω</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:div/> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">π</ml:id> <ml:parens> <ml:apply> <ml:minus/> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:real>1</ml:real> </ml:apply> </ml:parens> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:id xml:space="preserve">L</ml:id> </ml:apply> <ml:apply> <ml:sqrt/> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">c</ml:id> <ml:id xml:space="preserve">J</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:sqrt/> <ml:apply> <ml:minus/> <ml:real>1</ml:real> <ml:apply> <ml:div/> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">c</ml:id> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">R</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">L</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">J</ml:id> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">π</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:pow/> <ml:parens> <ml:apply> <ml:minus/> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:real>1</ml:real> </ml:apply> </ml:parens> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:apply> </ml:apply> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="71"/> </region> <region region-id="858" left="42" top="2231.25" width="465.75" height="62.25" align-x="42" align-y="2244" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="false"> <f family="Arial Cyr" charset="204" size="12">Для всех случаев (всех n) </f> <f family="Arial Cyr" charset="204" size="12"> <sp/> </f> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal">, в том числе для </inlineAttr> </f> <region region-id="379" left="282.75" top="2232" width="39.75" height="18" align-x="307.5" align-y="2244" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:equal/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">ω</ml:id> <ml:id xml:space="preserve">N</ml:id> </ml:apply> <ml:real>1</ml:real> </ml:apply> </math> <rendering item-idref="72"/> </region> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false">, получим</inlineAttr> </f> <f family="Arial Cyr" charset="204" size="12"> : </f> <region region-id="381" left="381" top="2232" width="90.75" height="18" align-x="456.75" align-y="2244" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:equal/> <ml:apply> <ml:minus/> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">B</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">ω</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">ν</ml:id> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">A</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:real>0</ml:real> </ml:apply> </math> <rendering item-idref="73"/> </region> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-style="normal" underline="false" line-through="false">. </inlineAttr> </f> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false">Что в свою очередь позволит вычислить B</inlineAttr> </f> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> n </inlineAttr> </f> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false">.</inlineAttr> </f> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> <sp count="2"/>Где </inlineAttr> </f> <region region-id="1073" left="281.25" top="2250.75" width="90" height="34.5" align-x="303" align-y="2270.25" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedBIUnit" xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">A</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:apply> <ml:div/> <ml:apply> <ml:mult style="default"/> <ml:real>4</ml:real> <ml:id xml:space="preserve">V0</ml:id> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">π</ml:id> <ml:parens> <ml:apply> <ml:minus/> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:real>1</ml:real> </ml:apply> </ml:parens> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="74"/> </region> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false">.</inlineAttr> </f> </text> </region> <region region-id="1080" left="48" top="2304.75" width="321.75" height="13.5" align-x="48" align-y="2316" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="12">Проверка и вывод на экран монитора численных значений:</f> </text> </region> <region region-id="1078" left="42" top="2334.75" width="425.25" height="31.5" align-x="64.5" align-y="2352" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:apply> <ml:transpose/> <ml:id xml:space="preserve">A</ml:id> </ml:apply> <result xmlns="http://schemas.mathsoft.com/math20"> <ml:matrix rows="1" cols="131"> <ml:real>0</ml:real> <ml:real>1.2732395447351628</ml:real> <ml:real>0.42441318157838759</ml:real> <ml:real>0.25464790894703254</ml:real> <ml:real>0.18189136353359467</ml:real> <ml:real>0.14147106052612921</ml:real> <ml:real>0.11574904952137845</ml:real> <ml:real>0.097941503441166353</ml:real> <ml:real>0.084882636315677523</ml:real> <ml:real>0.074896443807950741</ml:real> <ml:real>0.067012607617640149</ml:real> <ml:real>0.060630454511198223</ml:real> <ml:real>0.055358241075441864</ml:real> <ml:real>0.050929581789406507</ml:real> <ml:real>0.0471570201753764</ml:real> <ml:real>0.043904811887419404</ml:real> <ml:real>0.041072243378553641</ml:real> <ml:real>0.038583016507126144</ml:real> <ml:real>0.036378272706718937</ml:real> <ml:real>0.034411879587436828</ml:real> <ml:real>0.032647167813722122</ml:real> <ml:real>0.031054623042321046</ml:real> <ml:real>0.029610221970585181</ml:real> <ml:real>0.028294212105225838</ml:real> <ml:real>0.027090203079471544</ml:real> <ml:real>0.025984480504799241</ml:real> <ml:real>0.024965481269316917</ml:real> <ml:real>0.024023387636512503</ml:real> <ml:real>0.023149809904275686</ml:real> <ml:real>0.022337535872546718</ml:real> <ml:real>0.021580331266697676</ml:real> <ml:real>0.020872779421887915</ml:real> <ml:real>0.020210151503732742</ml:real> <ml:real>0.019588300688233275</ml:real> <ml:real>0.019003575294554667</ml:real> <ml:real>0.018452747025147286</ml:real> <ml:real>0.017932951334298067</ml:real> <ml:real>0.017441637599111819</ml:real> <ml:real>0.016976527263135505</ml:real> <ml:real>0.016535578503054062</ml:real> <ml:real>0.016116956262470415</ml:real> <ml:real>0.015719006725125467</ml:real> <ml:real>0.0153402354787369</ml:real> <ml:real>0.014979288761590149</ml:real> <ml:real>0.014634937295806469</ml:real> <ml:real>0.014306062300395087</ml:real> <ml:real>0.013991643348738052</ml:real> <ml:real>0.013690747792851213</ml:real> <ml:real>0.013402521523528029</ml:real> <ml:real>0.01312618087355838</ml:real> <ml:real>0.012861005502375381</ml:real> <ml:real>0.012606332126090721</ml:real> <ml:real>0.01236154897801129</ml:real> <ml:real>0.012126090902239645</ml:real> <ml:real>0.011899434997524886</ml:real> <ml:real>0.011681096740689567</ml:real> <ml:real>0.01147062652914561</ml:real> <ml:real>0.011267606590576662</ml:real> <ml:real>0.011071648215088371</ml:real> <ml:real>0.010882389271240706</ml:real> <ml:real>0.010699491972564394</ml:real> <ml:real>0.010522640865579858</ml:real> <ml:real>0.010351541014107015</ml:real> <ml:real>0.010185916357881302</ml:real> <ml:real>0.010025508226261123</ml:real> <ml:real>0.00987007399019506</ml:real> <ml:real>0.0097193858376729975</ml:real> <ml:real>0.0095732296596628772</ml:real> <ml:real>0.00943140403507528</ml:real> <ml:real>0.0092937193046362231</ml:real> <ml:real>0.0091599967247134</ml:real> <ml:real>0.0090300676931571837</ml:real> <ml:real>0.0089037730401060333</ml:real> <ml:real>0.00878096237748388</ml:real> <ml:real>0.0086614935015997454</ml:real> <ml:real>0.0085452318438601522</ml:real> <ml:real>0.00843204996513353</ml:real> <ml:real>0.0083218270897723046</ml:real> <ml:real>0.0082144486757107279</ml:real> <ml:real>0.0081098060174214191</ml:real> <ml:real>0.0080077958788375009</ml:real> <ml:real>0.0079083201536345512</ml:real> <ml:real>0.0078112855505224716</ml:real> <ml:real>0.0077166033014252292</ml:real> <ml:real>0.0076241888906297163</ml:real> <ml:real>0.007533961803166643</ml:real> <ml:real>0.0074458452908489053</ml:real> <ml:real>0.0073597661545385133</ml:real> <ml:real>0.0072756545413437878</ml:real> <ml:real>0.007193443755565891</ml:real> 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z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false">Введем константы N1, N2<sp count="2"/>для вычисления В</inlineAttr> </f> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> n </inlineAttr> </f> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false">, записываемых в вектор В</inlineAttr> </f> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false">.</inlineAttr> </f> </text> </region> <region region-id="449" left="48" top="2432.25" width="133.5" height="36.75" align-x="71.25" align-y="2454" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">N1</ml:id> <ml:apply> <ml:id xml:space="preserve">floor</ml:id> <ml:apply> <ml:plus/> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:div/> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">L</ml:id> <ml:id xml:space="preserve">R</ml:id> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:id xml:space="preserve">π</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:sqrt/> <ml:apply> <ml:div/> <ml:id xml:space="preserve">c</ml:id> <ml:id xml:space="preserve">J</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:div/> <ml:real>1</ml:real> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="77"/> </region> <region region-id="862" left="210" top="2442.75" width="67.5" height="15.75" align-x="233.25" align-y="2454" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">N2</ml:id> <ml:apply> <ml:id xml:space="preserve">ceil</ml:id> <ml:id xml:space="preserve">N</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="78"/> </region> <region region-id="863" left="42" top="2478.75" width="321.75" height="13.5" align-x="42" align-y="2490" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="12">Проверка и вывод на экран монитора численных значений:</f> </text> </region> <region region-id="871" left="42" top="2508.75" width="50.25" height="15.75" align-x="64.5" align-y="2520" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">N1</ml:id> <result xmlns="http://schemas.mathsoft.com/math20"> <ml:real>13</ml:real> </result> </ml:eval> </math> <rendering item-idref="79"/> </region> <region region-id="872" left="126" top="2508.75" width="50.25" height="15.75" align-x="148.5" align-y="2520" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">N2</ml:id> <result xmlns="http://schemas.mathsoft.com/math20"> <ml:real>13</ml:real> </result> </ml:eval> </math> <rendering item-idref="80"/> </region> <region region-id="873" left="210" top="2508.75" width="44.25" height="15.75" align-x="226.5" align-y="2520" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">N</ml:id> <result xmlns="http://schemas.mathsoft.com/math20"> <ml:real>13</ml:real> </result> </ml:eval> </math> <rendering item-idref="81"/> </region> <region region-id="1087" left="36" top="2534.25" width="444.75" height="36" align-x="36" align-y="2544" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="10">Можно дать следующее описание подмножеств множества индексов n, эквивалентное приведён-</f> <f family="Arial Cyr" charset="204" size="10">ному в (15) (см. файлы </f> <f family="Arial Cyr" charset="204">"ВолнУр123.xmcd", </f> <f family="Arial Cyr" charset="204">"ВолнУр123_СтараяВерс.xmcd")</f> <f family="Arial Cyr" charset="204" size="10">, если положить </f> <f family="Symbol" charset="2" size="10"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false">e</inlineAttr> </f> <f family="Arial" charset="0" size="10"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false">=0 </inlineAttr> </f> <f family="Arial Cyr" charset="204" size="10"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false">. Описание приводится в той же последовательности, что и в (15).</inlineAttr> </f> </text> </region> <region region-id="1088" left="36" top="2586" width="432.75" height="37.5" align-x="36" align-y="2598" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="10">1. Выбор параметров: </f> <region region-id="1010" left="138" top="2586.75" width="46.5" height="15.75" align-x="160.5" align-y="2598" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:notEqual/> <ml:id xml:space="preserve">N1</ml:id> <ml:id xml:space="preserve">N2</ml:id> </ml:apply> </math> <rendering item-idref="82"/> </region> <f family="Arial Cyr" charset="204" size="10"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> and </inlineAttr> </f> <region region-id="1011" left="207" top="2586.75" width="38.25" height="15.75" align-x="229.5" align-y="2598" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:greaterOrEqual/> <ml:id xml:space="preserve">N1</ml:id> <ml:real>1</ml:real> </ml:apply> </math> <rendering item-idref="83"/> </region> <f family="Arial Cyr" charset="204" size="10"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> приводит к разбиению на подмножества:</inlineAttr> </f> <region region-id="1012" left="36" top="2604" width="48.75" height="15.75" align-x="48.75" align-y="2615.25" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:equal/> <ml:id xml:space="preserve">n</ml:id> <ml:apply> <ml:mult style="auto-select"/> <ml:real>1..</ml:real> <ml:id xml:space="preserve">N1</ml:id> </ml:apply> </ml:apply> </math> <rendering item-idref="84"/> </region> <f family="Arial Cyr" charset="204" size="10"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> <sp/> </inlineAttr> </f> <f family="Arial Cyr" charset="204" size="10"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false">(корни </inlineAttr> </f> <f family="Arial Cyr" charset="204" size="10">p1</f> <f family="Arial Cyr" charset="204" size="10"> n </f> <f family="Arial Cyr" charset="204" size="10">, p2</f> <f family="Arial Cyr" charset="204" size="10"> n </f> <f family="Arial Cyr" charset="204" size="10"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> действительные разные), </inlineAttr> </f> <region region-id="1013" left="276" top="2604" width="36.75" height="15.75" align-x="288.75" align-y="2615.25" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:equal/> <ml:id xml:space="preserve">n</ml:id> <ml:id xml:space="preserve">N2</ml:id> </ml:apply> </math> <rendering item-idref="85"/> </region> <f family="Arial Cyr" charset="204" size="10"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false">..</inlineAttr> </f> <region region-id="1014" left="319.5" top="2603.25" width="9.75" height="16.5" align-x="323.25" align-y="2615.25" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:id xml:space="preserve" xmlns:ml="http://schemas.mathsoft.com/math20">∞</ml:id> </math> <rendering item-idref="86"/> </region> <f family="Arial Cyr" charset="204" size="10"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> (корни </inlineAttr> </f> <f family="Arial Cyr" charset="204">p1</f> <f family="Arial Cyr" charset="204"> n </f> <f family="Arial Cyr" charset="204">, p2</f> <f family="Arial Cyr" charset="204"> n </f> <f family="Arial Cyr" charset="204" size="10"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> комплексные).</inlineAttr> </f> </text> </region> <region region-id="1089" left="36" top="2634" width="442.5" height="57.75" align-x="36" align-y="2646" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="10">2. Выбор параметров: </f> <region region-id="1017" left="138" top="2634.75" width="46.5" height="15.75" align-x="160.5" align-y="2646" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:equal/> <ml:id xml:space="preserve">N1</ml:id> <ml:id xml:space="preserve">N2</ml:id> </ml:apply> </math> <rendering item-idref="87"/> </region> <f family="Arial Cyr" charset="204" size="10"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> and </inlineAttr> </f> <region region-id="1018" left="207" top="2634.75" width="38.25" height="15.75" align-x="229.5" align-y="2646" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:greaterOrEqual/> <ml:id xml:space="preserve">N1</ml:id> <ml:real>2</ml:real> </ml:apply> </math> <rendering item-idref="88"/> </region> <f family="Arial Cyr" charset="204" size="10"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> приводит к разбиению на подмножества:</inlineAttr> </f> <region region-id="1019" left="36" top="2651.25" width="67.5" height="15.75" align-x="48.75" align-y="2662.5" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:equal/> <ml:id xml:space="preserve">n</ml:id> <ml:apply> <ml:minus/> <ml:apply> <ml:mult style="auto-select"/> <ml:real>1..</ml:real> <ml:id xml:space="preserve">N1</ml:id> </ml:apply> <ml:real>1</ml:real> </ml:apply> </ml:apply> </math> <rendering item-idref="89"/> </region> <f family="Arial Cyr" charset="204" size="10"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> <sp/> </inlineAttr> </f> <f family="Arial Cyr" charset="204" size="10"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false">(корни </inlineAttr> </f> <f family="Arial Cyr" charset="204">p1</f> <f family="Arial Cyr" charset="204"> n </f> <f family="Arial Cyr" charset="204">, p2</f> <f family="Arial Cyr" charset="204">n</f> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> <f family="Arial Cyr" charset="204" size="10"> действительные разные), </f> </inlineAttr> <region region-id="1016" left="294.75" top="2651.25" width="36.75" height="15.75" align-x="307.5" align-y="2662.5" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:equal/> <ml:id xml:space="preserve">n</ml:id> <ml:id xml:space="preserve">N1</ml:id> </ml:apply> </math> <rendering item-idref="90"/> </region> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> <f family="Arial Cyr" charset="204" size="10"> <sp/> </f> </inlineAttr> <f family="Arial Cyr" charset="204" size="10"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false">(</inlineAttr> </f> <f family="Arial Cyr" charset="204">корни </f> <f family="Arial Cyr" charset="204">p1</f> <f family="Arial Cyr" charset="204"> n </f> <f family="Arial Cyr" charset="204">, p2</f> <f family="Arial Cyr" charset="204"> n </f> <f family="Arial Cyr" charset="204"> действительные равные),</f> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> <f family="Arial Cyr" charset="204" size="10"> <sp/> </f> </inlineAttr> <region region-id="1020" left="78" top="2672.25" width="56.25" height="15.75" align-x="90.75" align-y="2683.5" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:equal/> <ml:id xml:space="preserve">n</ml:id> <ml:apply> <ml:plus/> <ml:id xml:space="preserve">N1</ml:id> <ml:real>1</ml:real> </ml:apply> </ml:apply> </math> <rendering item-idref="91"/> </region> <f family="Arial Cyr" charset="204" size="10"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false">..</inlineAttr> </f> <region region-id="1021" left="141" top="2671.5" width="9.75" height="16.5" align-x="144.75" align-y="2683.5" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:id xml:space="preserve" xmlns:ml="http://schemas.mathsoft.com/math20">∞</ml:id> </math> <rendering item-idref="92"/> </region> <f family="Arial Cyr" charset="204" size="10"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> (корни </inlineAttr> </f> <f family="Arial Cyr" charset="204">p1</f> <f family="Arial Cyr" charset="204">n</f> <f family="Arial Cyr" charset="204">, p2</f> <f family="Arial Cyr" charset="204"> n </f> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> <f family="Arial Cyr" charset="204" size="10"> комплексные).</f> </inlineAttr> </text> </region> <region region-id="1090" left="36" top="2706" width="403.5" height="37.5" align-x="36" align-y="2718" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="10">3. Выбор параметров: </f> <region region-id="1026" left="138" top="2706.75" width="46.5" height="15.75" align-x="160.5" align-y="2718" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:equal/> <ml:id xml:space="preserve">N1</ml:id> <ml:id xml:space="preserve">N2</ml:id> </ml:apply> </math> <rendering item-idref="93"/> </region> <f family="Arial Cyr" charset="204" size="10"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> and </inlineAttr> </f> <region region-id="1027" left="207" top="2706.75" width="37.5" height="15.75" align-x="229.5" align-y="2718" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:equal/> <ml:id xml:space="preserve">N1</ml:id> <ml:real>1</ml:real> </ml:apply> </math> <rendering item-idref="94"/> </region> <f family="Arial Cyr" charset="204" size="10"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> приводит к разбиению на подмножества:</inlineAttr> </f> <region region-id="1028" left="36" top="2724" width="27.75" height="15.75" align-x="48.75" align-y="2735.25" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:equal/> <ml:id xml:space="preserve">n</ml:id> <ml:real>1</ml:real> </ml:apply> </math> <rendering item-idref="95"/> </region> <f family="Arial Cyr" charset="204" size="10"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> <sp/> </inlineAttr> </f> <f family="Arial Cyr" charset="204" size="10"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false">(корни </inlineAttr> </f> <f family="Arial Cyr" charset="204">p1</f> <f family="Arial Cyr" charset="204"> n </f> <f family="Arial Cyr" charset="204">, p2</f> <f family="Arial Cyr" charset="204"> n </f> <f family="Arial Cyr" charset="204" size="10"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> действительные равные), </inlineAttr> </f> <region region-id="1029" left="255.75" top="2724" width="27.75" height="15.75" align-x="268.5" align-y="2735.25" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:equal/> <ml:id xml:space="preserve">n</ml:id> <ml:real>2</ml:real> </ml:apply> </math> <rendering item-idref="96"/> </region> <f family="Arial Cyr" charset="204" size="10"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false">..</inlineAttr> </f> <region region-id="1030" left="290.25" top="2723.25" width="9.75" height="16.5" align-x="294" align-y="2735.25" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:id xml:space="preserve" xmlns:ml="http://schemas.mathsoft.com/math20">∞</ml:id> </math> <rendering item-idref="97"/> </region> <f family="Arial Cyr" charset="204" size="10"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> (корни </inlineAttr> </f> <f family="Arial Cyr" charset="204">p1</f> <f family="Arial Cyr" charset="204"> n </f> <f family="Arial Cyr" charset="204">, p2</f> <f family="Arial Cyr" charset="204"> n </f> <f family="Arial Cyr" charset="204" size="10"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> комплексные).</inlineAttr> </f> </text> </region> <region region-id="1091" left="36" top="2759.25" width="450" height="33" align-x="36" align-y="2772" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="10">4. Выбор параметров: </f> <f family="Arial Cyr" charset="204" size="10"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> <sp/> </inlineAttr> </f> <region region-id="1032" left="141" top="2760.75" width="37.5" height="15.75" align-x="163.5" align-y="2772" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:equal/> <ml:id xml:space="preserve">N1</ml:id> <ml:real>0</ml:real> </ml:apply> </math> <rendering item-idref="98"/> </region> <f family="Arial Cyr" charset="204" size="10"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> приводит к разбиению на подмножества:</inlineAttr> </f> <f family="Arial Cyr" charset="204" size="10"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> <sp/> </inlineAttr> </f> <region region-id="1034" left="370.5" top="2760.75" width="27.75" height="15.75" align-x="383.25" align-y="2772" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:equal/> <ml:id xml:space="preserve">n</ml:id> <ml:real>1</ml:real> </ml:apply> </math> <rendering item-idref="99"/> </region> <f family="Arial Cyr" charset="204" size="10"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false">..</inlineAttr> </f> <region region-id="1035" left="405" top="2760" width="9.75" height="16.5" align-x="408.75" align-y="2772" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:id xml:space="preserve" xmlns:ml="http://schemas.mathsoft.com/math20">∞</ml:id> </math> <rendering item-idref="100"/> </region> <f family="Arial Cyr" charset="204" size="10"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> (корни </inlineAttr> </f> <f family="Arial Cyr" charset="204">p1</f> <f family="Arial Cyr" charset="204"> n </f> <f family="Arial Cyr" charset="204">, p2</f> <f family="Arial Cyr" charset="204">n</f> <f family="Arial Cyr" charset="204" size="10"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> комплексные).</inlineAttr> </f> </text> </region> <region region-id="1092" left="36" top="2813.25" width="329.25" height="37.5" align-x="36" align-y="2826" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204">5. Выбор параметров:</f> <f family="Arial Cyr" charset="204"> <sp/> </f> <region region-id="1041" left="138" top="2814.75" width="15.75" height="15.75" align-x="144.75" align-y="2826" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:id xml:space="preserve" xmlns:ml="http://schemas.mathsoft.com/math20">N1</ml:id> </math> <rendering item-idref="101"/> </region> <f family="Arial Cyr" charset="204" size="10"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false">-></inlineAttr> </f> <region region-id="1042" left="163.5" top="2814" width="9.75" height="16.5" align-x="167.25" align-y="2826" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:id xml:space="preserve" xmlns:ml="http://schemas.mathsoft.com/math20">∞</ml:id> </math> <rendering item-idref="102"/> </region> <f family="Arial Cyr" charset="204"> <sp count="2"/>приводит к разбиению на подмножества:</f> <region region-id="1037" left="36" top="2831.25" width="48.75" height="15.75" align-x="48.75" align-y="2842.5" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:equal/> <ml:id xml:space="preserve">n</ml:id> <ml:apply> <ml:mult style="auto-select"/> <ml:real>1..</ml:real> <ml:id xml:space="preserve">N1</ml:id> </ml:apply> </ml:apply> </math> <rendering item-idref="103"/> </region> <f family="Arial Cyr" charset="204"> <sp/> </f> <f family="Arial Cyr" charset="204">(корни </f> <f family="Arial Cyr" charset="204">p1</f> <f family="Arial Cyr" charset="204"> n </f> <f family="Arial Cyr" charset="204">, p2</f> <f family="Arial Cyr" charset="204"> n </f> <f family="Arial Cyr" charset="204"> действительные разные)</f> </text> </region> <region region-id="954" left="36" top="2862.75" width="332.25" height="16.5" align-x="36" align-y="2874" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="false"> <f family="Arial Cyr" charset="204" size="12">Теперь можно приступить к вычислению коэффициентов В</f> <f family="Arial Cyr" charset="204" size="12"> n </f> <f family="Arial Cyr" charset="204" size="12">: </f> </text> </region> <region region-id="1049" left="48" top="2904.75" width="381" height="308.25" align-x="63.75" align-y="2916" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">B</ml:id> <ml:program> <ml:ifThen> <ml:apply> <ml:and/> <ml:apply> <ml:and/> <ml:apply> <ml:notEqual/> <ml:id 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<ml:real>1</ml:real> </ml:apply> </ml:parens> </ml:apply> </ml:apply> <ml:apply> <ml:div/> <ml:real>1</ml:real> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">Ω</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:localDefine> </ml:for> <ml:for> <ml:id xml:space="preserve">n</ml:id> <ml:range> <ml:id xml:space="preserve">n0</ml:id> <ml:id xml:space="preserve">n0</ml:id> </ml:range> <ml:localDefine> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">B</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:apply> <ml:div/> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">ν</ml:id> <ml:real>4</ml:real> </ml:apply> <ml:id xml:space="preserve">V0</ml:id> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">π</ml:id> <ml:parens> <ml:apply> <ml:minus/> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:real>1</ml:real> </ml:apply> </ml:parens> </ml:apply> </ml:apply> </ml:localDefine> </ml:for> <ml:for> <ml:id xml:space="preserve">n</ml:id> <ml:range> <ml:id xml:space="preserve">n2</ml:id> <ml:id xml:space="preserve">NN</ml:id> </ml:range> <ml:localDefine> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">B</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:div/> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">ν</ml:id> <ml:real>4</ml:real> </ml:apply> <ml:id xml:space="preserve">V0</ml:id> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">π</ml:id> <ml:parens> <ml:apply> <ml:minus/> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:real>1</ml:real> </ml:apply> </ml:parens> </ml:apply> </ml:apply> <ml:apply> <ml:div/> <ml:real>1</ml:real> <ml:apply> <ml:indexer/> <ml:id 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size="12">Решение задачи (1) - (2) имеет переменную структуру, зависимую от<sp count="2"/>констант </f> <f family="Arial Cyr" charset="204" size="12">N1, N2, разбивающих множество индексов n на подмножества. Каждому набору подмножеств индексов n соответствует своя формула решения с коэффициентами </f> <f family="Arial Cyr" charset="204" size="12">B</f> <f family="Arial Cyr" charset="204" size="12"> n </f> <f family="Arial Cyr" charset="204" size="12">.</f> <f family="Arial Cyr" charset="204" size="12"> <sp/> </f> </text> </region> <region region-id="935" left="36" top="3396.75" width="476.25" height="13.5" align-x="36" align-y="3408" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="12">Выпишем четыре формулы вычисления решения </f> <f family="Arial Cyr" charset="204" size="12">:</f> </text> </region> <region region-id="917" left="42" top="3432" width="453" height="16.5" align-x="42" align-y="3444" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="false"> <f family="Arial Cyr" charset="204" size="12">1. Решение для </f> <region region-id="1062" left="129" top="3432.75" width="46.5" height="15.75" align-x="151.5" align-y="3444" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:notEqual/> <ml:id xml:space="preserve">N1</ml:id> <ml:id xml:space="preserve">N2</ml:id> </ml:apply> </math> <rendering item-idref="107"/> </region> <f family="Arial Cyr" charset="204" size="12"> и<sp count="2"/> </f> <region region-id="918" left="191.25" top="3432.75" width="38.25" height="15.75" align-x="204.75" align-y="3444" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:lessOrEqual/> <ml:real>1</ml:real> <ml:id xml:space="preserve">N1</ml:id> </ml:apply> </math> <rendering item-idref="108"/> </region> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> . Корни действительные разные и комплексные.</inlineAttr> </f> </text> </region> <region region-id="423" left="48" top="3519.75" width="393" height="99" align-x="94.5" align-y="3546" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:function> <ml:id xml:space="preserve">V1</ml:id> <ml:boundVars> <ml:id xml:space="preserve">x</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:plus split="true"/> <ml:apply> <ml:summation/> <ml:lambda> <ml:boundVars> <ml:id xml:space="preserve">n</ml:id> </ml:boundVars> <ml:parens> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:mult style="default"/> <ml:parens> <ml:apply> <ml:plus/> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">A</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:apply> 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</ml:apply> <ml:apply> <ml:id xml:space="preserve">sin</ml:id> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">π</ml:id> <ml:apply> <ml:div/> <ml:apply> <ml:minus/> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:real>1</ml:real> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:id xml:space="preserve">L</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:id xml:space="preserve">x</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:parens> </ml:lambda> <ml:bounds> <ml:id xml:space="preserve">N2</ml:id> <ml:id xml:space="preserve">NN</ml:id> </ml:bounds> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="109"/> </region> <region region-id="919" left="42" top="3630" width="457.5" height="30" align-x="42" align-y="3642" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="false"> <f family="Arial Cyr" charset="204" size="12">2. Решение для<sp count="2"/> </f> <region region-id="923" left="132" top="3630.75" width="46.5" height="15.75" align-x="154.5" align-y="3642" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:equal/> <ml:id xml:space="preserve">N1</ml:id> <ml:id xml:space="preserve">N2</ml:id> </ml:apply> </math> <rendering item-idref="110"/> </region> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> and </inlineAttr> </f> <region region-id="1063" left="204.75" top="3630.75" width="38.25" height="15.75" align-x="227.25" align-y="3642" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:greaterOrEqual/> <ml:id xml:space="preserve">N1</ml:id> <ml:real>2</ml:real> </ml:apply> </math> <rendering item-idref="111"/> </region> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> .</inlineAttr> </f> <f family="Arial Cyr" charset="204" size="12"> <sp/> </f> <f family="Arial Cyr" charset="204" size="12">Корни действительные разные, комплексные</f> <f family="Arial Cyr" charset="204" size="12">и </f> <f family="Arial Cyr" charset="204" size="12">действительные равные</f> <f family="Arial Cyr" charset="204" size="12">.</f> <f family="Arial Cyr" charset="204" size="12"> <sp count="2"/> </f> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> <sp/> </inlineAttr> </f> </text> </region> <region region-id="425" left="48" top="3693.75" width="399.75" height="131.25" align-x="94.5" align-y="3720" 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<ml:apply> <ml:minus/> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:real>1</ml:real> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:id xml:space="preserve">L</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:id xml:space="preserve">x</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:parens> </ml:lambda> <ml:bounds> <ml:real>1</ml:real> <ml:apply> <ml:minus/> <ml:id xml:space="preserve">N1</ml:id> <ml:real>1</ml:real> </ml:apply> </ml:bounds> </ml:apply> <ml:apply> <ml:summation/> <ml:lambda> <ml:boundVars> <ml:id xml:space="preserve">n</ml:id> </ml:boundVars> <ml:parens> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:mult style="default"/> <ml:parens> <ml:apply> <ml:plus/> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">A</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve">cos</ml:id> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">ω</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">B</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve">sin</ml:id> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">ω</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:apply> </ml:parens> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">e</ml:id> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:neg/> <ml:id xml:space="preserve">ν</ml:id> </ml:apply> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:id xml:space="preserve">sin</ml:id> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">π</ml:id> <ml:apply> <ml:div/> <ml:apply> <ml:minus/> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:real>1</ml:real> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:id xml:space="preserve">L</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:id xml:space="preserve">x</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:parens> </ml:lambda> <ml:bounds> <ml:apply> <ml:plus/> <ml:id xml:space="preserve">N2</ml:id> <ml:real>1</ml:real> </ml:apply> <ml:id xml:space="preserve">NN</ml:id> </ml:bounds> </ml:apply> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:mult style="default"/> <ml:parens> <ml:apply> <ml:plus/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">A</ml:id> <ml:id xml:space="preserve">N1</ml:id> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">B</ml:id> <ml:id xml:space="preserve">N1</ml:id> </ml:apply> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> </ml:parens> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">e</ml:id> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:neg/> <ml:id xml:space="preserve">ν</ml:id> </ml:apply> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:id xml:space="preserve">sin</ml:id> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">π</ml:id> <ml:apply> <ml:div/> <ml:apply> <ml:minus/> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:id xml:space="preserve">N1</ml:id> </ml:apply> <ml:real>1</ml:real> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:id xml:space="preserve">L</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:id xml:space="preserve">x</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="112"/> </region> <region region-id="926" left="60" top="3840" width="423" height="30" align-x="60" align-y="3852" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="12">3. Решение для </f> <f family="Arial Cyr" charset="204" size="12"> <sp/> </f> <region region-id="1064" left="150" top="3840.75" width="46.5" height="15.75" align-x="172.5" align-y="3852" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:equal/> <ml:id xml:space="preserve">N1</ml:id> <ml:id xml:space="preserve">N2</ml:id> </ml:apply> </math> <rendering item-idref="113"/> </region> <f family="Arial Cyr" charset="204" size="12"> and </f> <region region-id="1065" left="222.75" top="3840.75" width="38.25" height="15.75" align-x="245.25" align-y="3852" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:greaterOrEqual/> <ml:id xml:space="preserve">N1</ml:id> <ml:real>1</ml:real> </ml:apply> </math> <rendering item-idref="114"/> </region> <f family="Arial Cyr" charset="204" size="12"> . </f> <f family="Arial Cyr" charset="204" size="12">Корни<sp count="2"/>комплексные и </f> <f family="Arial Cyr" charset="204" size="12">действительные равные</f> <f family="Arial Cyr" charset="204" size="12">.</f> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> <sp/> </inlineAttr> </f> </text> </region> <region region-id="426" left="54" top="3885.75" width="379.5" height="82.5" align-x="100.5" align-y="3912" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:function> <ml:id xml:space="preserve">V3</ml:id> <ml:boundVars> <ml:id xml:space="preserve">x</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:plus split="true"/> <ml:apply> <ml:summation/> <ml:lambda> <ml:boundVars> <ml:id xml:space="preserve">n</ml:id> </ml:boundVars> <ml:parens> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:mult style="default"/> <ml:parens> <ml:apply> <ml:plus/> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">A</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve">cos</ml:id> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">ω</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">B</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve">sin</ml:id> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">ω</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:apply> </ml:parens> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">e</ml:id> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:neg/> <ml:id xml:space="preserve">ν</ml:id> </ml:apply> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:id xml:space="preserve">sin</ml:id> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">π</ml:id> <ml:apply> <ml:div/> <ml:apply> <ml:minus/> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:real>1</ml:real> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:id xml:space="preserve">L</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:id xml:space="preserve">x</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:parens> </ml:lambda> <ml:bounds> <ml:real>2</ml:real> <ml:id xml:space="preserve">NN</ml:id> </ml:bounds> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:mult style="default"/> <ml:parens> <ml:apply> <ml:plus/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">A</ml:id> <ml:real>1</ml:real> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">B</ml:id> <ml:real>1</ml:real> </ml:apply> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> </ml:parens> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">e</ml:id> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:neg/> <ml:id xml:space="preserve">ν</ml:id> </ml:apply> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:id xml:space="preserve">sin</ml:id> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">π</ml:id> <ml:apply> <ml:div/> <ml:real>1</ml:real> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:id xml:space="preserve">L</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:id xml:space="preserve">x</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="115"/> </region> <region region-id="929" left="60" top="3984.75" width="240.75" height="13.5" align-x="60" align-y="3996" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="12">4. Решение для N1=0 . </f> <f family="Arial Cyr" charset="204" size="12">Корни<sp count="2"/>комплексные.</f> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> <sp/> </inlineAttr> </f> </text> </region> <region region-id="429" left="48" top="4017.75" width="366" height="50.25" align-x="94.5" align-y="4044" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:function> <ml:id xml:space="preserve">V4</ml:id> <ml:boundVars> <ml:id xml:space="preserve">x</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:summation/> <ml:lambda> <ml:boundVars> <ml:id xml:space="preserve">n</ml:id> </ml:boundVars> <ml:parens> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:mult style="default"/> <ml:parens> <ml:apply> <ml:plus/> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">A</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve">cos</ml:id> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">ω</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">B</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve">sin</ml:id> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">ω</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:apply> </ml:parens> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">e</ml:id> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:neg/> <ml:id xml:space="preserve">ν</ml:id> </ml:apply> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:id xml:space="preserve">sin</ml:id> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">π</ml:id> <ml:apply> <ml:div/> <ml:apply> <ml:minus/> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:real>1</ml:real> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:id xml:space="preserve">L</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:id xml:space="preserve">x</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:parens> </ml:lambda> <ml:bounds> <ml:real>1</ml:real> <ml:id xml:space="preserve">NN</ml:id> </ml:bounds> </ml:apply> </ml:define> </math> <rendering item-idref="116"/> </region> <region region-id="1126" left="30" top="4090.5" width="438" height="83.25" align-x="30" align-y="4116" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="12">Поледнее выражение, получаемое при </f> <region region-id="930" left="245.25" top="4091.25" width="61.5" height="45" align-x="257.25" align-y="4116" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:greaterThan/> <ml:id xml:space="preserve">J</ml:id> <ml:apply> <ml:div/> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">c</ml:id> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">R</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">L</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">π</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:apply> </math> <rendering item-idref="117"/> </region> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false">,</inlineAttr> </f> <f family="Arial Cyr" charset="204" size="12"> <sp count="2"/>можно преобразовать к виду, если ввести</f> <f family="Arial Cyr" charset="204" size="12"> <sp/> </f> <region region-id="558" left="129" top="4137" width="71.25" height="36.75" align-x="174.75" align-y="4158" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:equal/> <ml:apply> <ml:id xml:space="preserve">cot</ml:id> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">φ</ml:id> <ml:id xml:space="preserve">k</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:div/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">B</ml:id> <ml:id xml:space="preserve">k</ml:id> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">A</ml:id> <ml:id xml:space="preserve">k</ml:id> </ml:apply> </ml:apply> </ml:apply> </math> <rendering item-idref="118"/> </region> <f family="Arial Cyr" charset="204" size="12"> :</f> </text> </region> <region region-id="1138" left="48" top="4224.75" width="87" height="15.75" align-x="62.25" align-y="4236" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">k</ml:id> <ml:range> <ml:apply> <ml:plus/> <ml:id xml:space="preserve">N1</ml:id> <ml:real>1</ml:real> </ml:apply> <ml:id xml:space="preserve">NN</ml:id> </ml:range> </ml:define> </math> <rendering item-idref="119"/> </region> <region region-id="1140" left="186" top="4215.75" width="82.5" height="36.75" align-x="207" align-y="4236" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">φ</ml:id> <ml:id xml:space="preserve">k</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve">acot</ml:id> <ml:apply> <ml:div/> <ml:id xml:space="preserve">ν</ml:id> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">ω</ml:id> <ml:id xml:space="preserve">k</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="120"/> </region> <region region-id="568" left="348" top="4221.75" width="63" height="34.5" align-x="390" align-y="4242" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:lessOrEqual/> <ml:apply> <ml:lessThan/> <ml:real>0</ml:real> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">φ</ml:id> <ml:id xml:space="preserve">k</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:div/> <ml:id xml:space="preserve">π</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> </math> <rendering item-idref="121"/> </region> <region region-id="562" left="54" top="4275.75" width="406.5" height="50.25" align-x="100.5" align-y="4302" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:function> <ml:id xml:space="preserve">V5</ml:id> <ml:boundVars> <ml:id xml:space="preserve">x</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:div/> <ml:apply> <ml:mult style="default"/> <ml:real>4</ml:real> <ml:id xml:space="preserve">V0</ml:id> </ml:apply> <ml:id xml:space="preserve">π</ml:id> </ml:apply> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">e</ml:id> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:neg/> <ml:id xml:space="preserve">ν</ml:id> </ml:apply> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:summation/> <ml:lambda> <ml:boundVars> <ml:id xml:space="preserve">n</ml:id> </ml:boundVars> <ml:parens> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:div/> <ml:real>1</ml:real> <ml:apply> <ml:mult style="default"/> <ml:parens> <ml:apply> <ml:minus/> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:real>1</ml:real> </ml:apply> </ml:parens> <ml:apply> <ml:id xml:space="preserve">sin</ml:id> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">φ</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:id xml:space="preserve">sin</ml:id> <ml:apply> <ml:plus/> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">ω</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:id xml:space="preserve">t</ml:id> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">φ</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:id xml:space="preserve">sin</ml:id> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">π</ml:id> <ml:apply> <ml:div/> <ml:apply> <ml:minus/> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:real>1</ml:real> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:id xml:space="preserve">L</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:id xml:space="preserve">x</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:parens> </ml:lambda> <ml:bounds> <ml:real>1</ml:real> <ml:id xml:space="preserve">NN</ml:id> </ml:bounds> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="122"/> </region> <region region-id="1068" left="48" top="4343.25" width="323.25" height="17.25" align-x="48" align-y="4356" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="12">5. Решение при</f> <f family="Arial Cyr" charset="204" size="12"> <sp count="2"/> </f> <region region-id="1048" left="137.25" top="4344.75" width="15.75" height="15.75" align-x="144" align-y="4356" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:id xml:space="preserve" xmlns:ml="http://schemas.mathsoft.com/math20">N1</ml:id> </math> <rendering item-idref="123"/> </region> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false">-></inlineAttr> </f> <region region-id="1070" left="164.25" top="4344" width="9.75" height="16.5" align-x="168" align-y="4356" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:id xml:space="preserve" xmlns:ml="http://schemas.mathsoft.com/math20">∞</ml:id> </math> <rendering item-idref="124"/> </region> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> <sp count="2"/>. Корни действительные разные.</inlineAttr> </f> </text> </region> <region region-id="1069" left="54" top="4377.75" width="381" height="50.25" align-x="100.5" align-y="4404" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:function> <ml:id xml:space="preserve">V6</ml:id> <ml:boundVars> <ml:id xml:space="preserve">x</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:summation/> <ml:lambda> <ml:boundVars> <ml:id xml:space="preserve">n</ml:id> </ml:boundVars> <ml:parens> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:mult style="default"/> <ml:parens> <ml:apply> <ml:plus/> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">A</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve">cosh</ml:id> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">Ω</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">B</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve">sinh</ml:id> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">Ω</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:apply> </ml:parens> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">e</ml:id> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:neg/> <ml:id xml:space="preserve">ν</ml:id> </ml:apply> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:id xml:space="preserve">sin</ml:id> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">π</ml:id> <ml:apply> <ml:div/> <ml:apply> <ml:minus/> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:real>1</ml:real> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:id xml:space="preserve">L</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:id xml:space="preserve">x</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:parens> </ml:lambda> <ml:bounds> <ml:real>1</ml:real> <ml:apply> <ml:minus/> <ml:id xml:space="preserve">NN</ml:id> <ml:real>1</ml:real> </ml:apply> </ml:bounds> </ml:apply> </ml:define> </math> <rendering item-idref="125"/> </region> <region region-id="968" left="42" top="4446.75" width="396.75" height="30" align-x="42" align-y="4458" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="12">Вывод на экран монитора численных значений параметров, по которым </f> <f family="Arial Cyr" charset="204" size="12">выбирается одна из пяти формул: </f> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> <sp/> </inlineAttr> </f> <region region-id="970" left="234" top="4461" width="50.25" height="15.75" align-x="256.5" align-y="4472.25" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">N1</ml:id> <result xmlns="http://schemas.mathsoft.com/math20"> <ml:real>13</ml:real> </result> </ml:eval> </math> <rendering item-idref="126"/> </region> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false">, </inlineAttr> </f> <region region-id="1007" left="291" top="4461" width="50.25" height="15.75" align-x="313.5" align-y="4472.25" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">N2</ml:id> <result xmlns="http://schemas.mathsoft.com/math20"> <ml:real>13</ml:real> </result> </ml:eval> </math> <rendering item-idref="127"/> </region> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false">, </inlineAttr> </f> <region region-id="1107" left="348" top="4461" width="59.25" height="15.75" align-x="373.5" align-y="4472.25" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval 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disable-calc="false"> <ml:eval xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">R</ml:id> <result xmlns="http://schemas.mathsoft.com/math20"> <ml:real>12.5</ml:real> </result> </ml:eval> </math> <rendering item-idref="130"/> </region> <region region-id="1104" left="138" top="4488.75" width="57" height="15.75" align-x="152.25" align-y="4500" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">L</ml:id> <result xmlns="http://schemas.mathsoft.com/math20"> <ml:real>6.2831853071795862</ml:real> </result> </ml:eval> </math> <rendering item-idref="131"/> </region> <region region-id="1103" left="204" top="4488.75" width="43.5" height="15.75" align-x="225.75" align-y="4500" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">V0</ml:id> <result xmlns="http://schemas.mathsoft.com/math20"> <ml:real>1</ml:real> </result> </ml:eval> </math> <rendering item-idref="132"/> </region> <region region-id="1102" left="264" top="4488.75" width="40.5" height="15.75" align-x="276.75" align-y="4500" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">c</ml:id> <result xmlns="http://schemas.mathsoft.com/math20"> <ml:real>10</ml:real> </result> </ml:eval> </math> <rendering item-idref="133"/> </region> <region region-id="1101" left="318" top="4488.75" width="42" height="15.75" align-x="332.25" align-y="4500" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">T</ml:id> <result xmlns="http://schemas.mathsoft.com/math20"> <ml:real>15</ml:real> </result> </ml:eval> </math> <rendering item-idref="134"/> </region> <region region-id="571" left="54" top="4524.75" width="260.25" height="13.5" align-x="54" align-y="4536" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="false"> <f family="Arial Cyr" charset="204" size="12">Логический блок выбора одной из </f> <f family="Arial Cyr" charset="204" size="12">пяти</f> <f family="Arial Cyr" charset="204" size="12"> формул:</f> </text> </region> <region region-id="1148" left="54" top="4560.75" width="260.25" height="99.75" align-x="94.5" align-y="4572" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedBIUnit" xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:function> <ml:id xml:space="preserve">V</ml:id> <ml:boundVars> <ml:id xml:space="preserve">x</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:boundVars> </ml:function> <ml:program> <ml:ifThen> <ml:apply> <ml:and/> <ml:apply> <ml:notEqual/> <ml:id xml:space="preserve">N1</ml:id> <ml:id xml:space="preserve">N2</ml:id> </ml:apply> <ml:apply> <ml:greaterOrEqual/> <ml:apply> <ml:greaterOrEqual/> <ml:id xml:space="preserve">NN</ml:id> <ml:id xml:space="preserve">N1</ml:id> </ml:apply> <ml:real>1</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:id xml:space="preserve">V1</ml:id> <ml:sequence> <ml:id xml:space="preserve">x</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:sequence> </ml:apply> </ml:ifThen> <ml:ifThen> <ml:apply> <ml:and/> <ml:apply> <ml:equal/> <ml:id xml:space="preserve">N1</ml:id> <ml:id xml:space="preserve">N2</ml:id> </ml:apply> <ml:apply> <ml:greaterOrEqual/> <ml:apply> <ml:greaterOrEqual/> <ml:id xml:space="preserve">NN</ml:id> <ml:id xml:space="preserve">N1</ml:id> </ml:apply> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:id xml:space="preserve">V2</ml:id> <ml:sequence> <ml:id xml:space="preserve">x</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:sequence> </ml:apply> </ml:ifThen> <ml:ifThen> <ml:apply> <ml:and/> <ml:apply> <ml:equal/> <ml:id xml:space="preserve">N1</ml:id> <ml:id xml:space="preserve">N2</ml:id> </ml:apply> <ml:apply> <ml:equal/> <ml:apply> <ml:greaterOrEqual/> <ml:id xml:space="preserve">NN</ml:id> <ml:id xml:space="preserve">N1</ml:id> </ml:apply> <ml:real>1</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:id xml:space="preserve">V3</ml:id> <ml:sequence> <ml:id xml:space="preserve">x</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:sequence> </ml:apply> </ml:ifThen> <ml:ifThen> <ml:apply> <ml:equal/> <ml:id xml:space="preserve">N1</ml:id> <ml:real>0</ml:real> </ml:apply> <ml:apply> <ml:id xml:space="preserve">V5</ml:id> <ml:sequence> <ml:id xml:space="preserve">x</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:sequence> </ml:apply> </ml:ifThen> <ml:ifThen> <ml:apply> <ml:greaterThan/> <ml:id xml:space="preserve">N1</ml:id> <ml:id xml:space="preserve">NN</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve">V6</ml:id> <ml:sequence> <ml:id xml:space="preserve">x</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:sequence> </ml:apply> </ml:ifThen> </ml:program> </ml:define> </math> <rendering item-idref="135"/> </region> <region region-id="1149" left="54" top="4686.75" width="219.75" height="99.75" align-x="69" align-y="4698" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">fr</ml:id> <ml:program> <ml:ifThen> <ml:apply> <ml:and/> <ml:apply> <ml:notEqual/> <ml:id xml:space="preserve">N1</ml:id> <ml:id xml:space="preserve">N2</ml:id> </ml:apply> <ml:apply> <ml:greaterOrEqual/> <ml:apply> <ml:greaterOrEqual/> <ml:id xml:space="preserve">NN</ml:id> <ml:id xml:space="preserve">N1</ml:id> </ml:apply> <ml:real>1</ml:real> </ml:apply> </ml:apply> <ml:str xml:space="preserve">V1</ml:str> </ml:ifThen> <ml:ifThen> <ml:apply> <ml:and/> <ml:apply> <ml:equal/> <ml:id xml:space="preserve">N1</ml:id> <ml:id xml:space="preserve">N2</ml:id> </ml:apply> <ml:apply> <ml:greaterOrEqual/> <ml:apply> <ml:greaterOrEqual/> <ml:id xml:space="preserve">NN</ml:id> <ml:id xml:space="preserve">N1</ml:id> </ml:apply> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:str xml:space="preserve">V2</ml:str> </ml:ifThen> <ml:ifThen> <ml:apply> <ml:and/> <ml:apply> <ml:equal/> <ml:id xml:space="preserve">N1</ml:id> <ml:id xml:space="preserve">N2</ml:id> </ml:apply> <ml:apply> <ml:equal/> <ml:apply> <ml:greaterOrEqual/> <ml:id xml:space="preserve">NN</ml:id> <ml:id xml:space="preserve">N1</ml:id> </ml:apply> <ml:real>1</ml:real> </ml:apply> </ml:apply> <ml:str xml:space="preserve">V3</ml:str> </ml:ifThen> <ml:ifThen> <ml:apply> <ml:equal/> <ml:id xml:space="preserve">N1</ml:id> <ml:real>0</ml:real> </ml:apply> <ml:str xml:space="preserve">V5</ml:str> </ml:ifThen> <ml:ifThen> <ml:apply> <ml:greaterThan/> <ml:id xml:space="preserve">N1</ml:id> <ml:id xml:space="preserve">NN</ml:id> </ml:apply> <ml:str xml:space="preserve">V6</ml:str> </ml:ifThen> </ml:program> </ml:define> </math> <rendering item-idref="136"/> </region> <region region-id="1005" left="54" top="4818" width="213" height="16.5" align-x="54" align-y="4830" show-border="false" show-highlight="true" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="false"> <f family="Arial Cyr" charset="204" size="12">Выбрана формула решения: </f> <region region-id="1006" left="213" top="4818.75" width="53.25" height="15.75" align-x="227.25" align-y="4830" show-border="false" show-highlight="true" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">fr</ml:id> <result xmlns="http://schemas.mathsoft.com/math20"> <ml:str xml:space="preserve">V2</ml:str> </result> </ml:eval> </math> <rendering item-idref="137"/> </region> </text> </region> <region region-id="828" left="60" top="4860.75" width="198" height="13.5" align-x="60" align-y="4872" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="false"> <f family="Arial Cyr" charset="204" size="12">Возможна анимация по параметру t:</f> </text> </region> <region region-id="932" left="294" top="4852.5" width="80.25" height="33.75" align-x="305.25" align-y="4872" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">t</ml:id> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:div/> <ml:real>1</ml:real> <ml:real>10</ml:real> </ml:apply> <ml:id xml:space="preserve">FRAME</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="138"/> </region> <region region-id="934" left="408" top="4860.75" width="92.25" height="15.75" align-x="457.5" align-y="4872" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:apply> <ml:id xml:space="preserve">V</ml:id> <ml:sequence> <ml:real>1</ml:real> <ml:real>10</ml:real> </ml:sequence> </ml:apply> <result xmlns="http://schemas.mathsoft.com/math20"> <ml:real>0.99879610758821991</ml:real> </result> </ml:eval> </math> <rendering item-idref="139"/> </region> <region region-id="1150" left="54" top="4920" width="381.75" height="205.5" align-x="54" align-y="4920" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <plot disable-calc="false" item-idref="140"/> <rendering item-idref="141"/> </region> <region region-id="68" left="48" top="5184" width="135.75" height="14.25" align-x="48" align-y="5196" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="false"> <f family="Arial Cyr" charset="204" size="12">Б). </f> <f family="Arial Cyr" charset="204" size="12"> Численное решение. </f> </text> </region> <region region-id="30" left="66" top="5208.75" width="27" height="15.75" align-x="78.75" align-y="5220" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:id xml:space="preserve" xmlns:ml="http://schemas.mathsoft.com/math20">Given</ml:id> </math> <rendering item-idref="142"/> </region> <region region-id="56" left="48" top="5230.5" width="171" height="33.75" align-x="90.75" align-y="5250" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:equal/> <ml:apply> <ml:id xml:space="preserve" subscript="t">w</ml:id> <ml:sequence> <ml:id xml:space="preserve">x</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:sequence> </ml:apply> <ml:apply> <ml:minus/> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:div/> <ml:real>1</ml:real> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">c</ml:id> <ml:id xml:space="preserve">J</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:id 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Будак и др.</f> <f family="Arial Cyr" charset="204" size="12">.<sp count="2"/> </f> </text> </region> <region region-id="611" left="30" top="84" width="445.5" height="71.25" align-x="30" align-y="96" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="12"> Словесное описание задачи: </f> <f family="Arial Cyr" charset="204" size="12"> Изолированный однородный электрический провод </f> <region region-id="244" left="72.75" top="99" width="51.75" height="15.75" align-x="108" align-y="110.25" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:lessOrEqual/> <ml:apply> <ml:lessOrEqual/> <ml:real>0</ml:real> <ml:id xml:space="preserve">x</ml:id> </ml:apply> <ml:id xml:space="preserve">L</ml:id> </ml:apply> </math> <rendering item-idref="2"/> </region> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> заряжен до некоторого потенциала V0=const. В начальный момент времени конец<sp count="2"/>х=0<sp count="2"/>заземляется, а конец<sp count="2"/>x=L<sp count="2"/>продолжает оставаться изолированным. Найти распределение напряжения в проводе, если самоиндукция, сопротивление и емкость единицы длины известны.</inlineAttr> </f> </text> </region> <region region-id="612" left="30" top="168.75" width="119.25" height="13.5" align-x="30" align-y="180" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="false"> <f family="Arial Cyr" charset="204" size="12"> Задание параметров. </f> </text> </region> <region region-id="599" left="30" top="192" width="151.5" height="14.25" align-x="30" align-y="204" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="12"> Независимые параметры: </f> </text> </region> <region region-id="603" left="30" top="215.25" width="432.75" height="50.25" align-x="30" align-y="228" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="12">Самоиндукция: </f> <region region-id="604" left="115.5" top="216.75" width="35.25" height="15.75" align-x="128.25" align-y="228" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedBIUnit" xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">J</ml:id> <ml:real>10</ml:real> </ml:define> </math> <rendering item-idref="3"/> </region> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> <sp/> </inlineAttr> </f> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" 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<inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false">;</inlineAttr> </f> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false">время наблюдения процесса: </inlineAttr> </f> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> <sp/> </inlineAttr> </f> <region region-id="607" left="198.75" top="233.25" width="37.5" height="15.75" align-x="213.75" align-y="244.5" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedBIUnit" xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">T</ml:id> <ml:real>15</ml:real> </ml:define> </math> <rendering item-idref="6"/> </region> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> <sp count="2"/> </inlineAttr> </f> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false">; начальнй потенциал провода: </inlineAttr> </f> <f family="Arial Cyr" charset="204" size="12"> <sp/> </f> <region region-id="608" left="33" top="249.75" width="39" height="15.75" align-x="55.5" align-y="261" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">V0</ml:id> <ml:real>1</ml:real> </ml:define> </math> <rendering item-idref="7"/> </region> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> <sp/> </inlineAttr> </f> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> <f family="Arial Cyr" charset="204" size="12">; </f> </inlineAttr> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> <f family="Arial Cyr" charset="204" size="12">ёмкость провода: </f> </inlineAttr> <region region-id="830" left="182.25" top="249.75" width="36" height="15.75" align-x="195.75" align-y="261" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedBIUnit" xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">c</ml:id> <ml:real>10</ml:real> </ml:define> </math> <rendering item-idref="8"/> </region> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> <f family="Arial Cyr" charset="204" size="12"> <sp/> </f> </inlineAttr> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> <f family="Arial Cyr" charset="204" size="12"> <sp count="2"/>.</f> </inlineAttr> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> <f family="Arial Cyr" charset="204" size="12"> <sp/> </f> </inlineAttr> </text> </region> <region region-id="952" left="30" top="276" width="105.75" height="14.25" align-x="30" align-y="288" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="12"> Обозначения: </f> </text> </region> <region region-id="951" left="120" top="276.75" width="37.5" height="15.75" align-x="133.5" align-y="288" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">a</ml:id> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">c</ml:id> <ml:id xml:space="preserve">J</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="9"/> </region> <region region-id="950" left="186" top="276.75" width="41.25" height="15.75" align-x="200.25" align-y="288" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">b</ml:id> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">c</ml:id> <ml:id xml:space="preserve">R</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="10"/> </region> <region region-id="843" left="30" top="304.5" width="465.75" height="59.25" align-x="30" align-y="330" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="false"> <f family="Arial Cyr" charset="204" size="12">Критерий выбора параметров: 1) если </f> <region region-id="846" left="243" top="305.25" width="63" height="45" align-x="255" align-y="330" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:greaterThan/> <ml:id xml:space="preserve">J</ml:id> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">c</ml:id> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">R</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:div/> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">L</ml:id> <ml:real>2</ml:real> </ml:apply> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">π</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:apply> </ml:apply> </math> <rendering item-idref="11"/> </region> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> , то корни комплексные для всех n</inlineAttr> </f> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false">(N<1) и<sp count="2"/>получаем решение V4(x,t)<sp count="2"/>(</inlineAttr> </f> <f family="Arial Cyr" charset="204" size="12">V5(x,t)</f> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false">). При этом kr=5.</inlineAttr> </f> </text> </region> <region region-id="844" left="30" top="377.25" width="135.75" height="45" align-x="48" align-y="402" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">kr</ml:id> <ml:apply> <ml:id xml:space="preserve">if</ml:id> <ml:sequence> <ml:apply> <ml:greaterThan/> <ml:id xml:space="preserve">J</ml:id> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">c</ml:id> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">R</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:div/> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">L</ml:id> <ml:real>2</ml:real> </ml:apply> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">π</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:apply> </ml:apply> <ml:real>5</ml:real> <ml:real>0</ml:real> </ml:sequence> </ml:apply> </ml:define> </math> <rendering item-idref="12"/> </region> <region region-id="845" left="204" top="390.75" width="39" height="15.75" align-x="221.25" align-y="402" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">kr</ml:id> <result xmlns="http://schemas.mathsoft.com/math20"> <ml:real>0</ml:real> </result> </ml:eval> </math> <rendering item-idref="13"/> </region> <region region-id="613" left="36" top="432.75" width="384.75" height="13.5" align-x="36" align-y="444" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="false"> <f family="Arial Cyr" charset="204" size="12"> Математическая модель. </f> <f family="Arial Cyr" charset="204" size="12"> <sp/> </f> <f family="Arial Cyr" charset="204" size="10">(Вывод см. в лекциях или у Пискунова, т.2, стр.367.) </f> </text> </region> <region region-id="72" left="42" top="462.75" width="111.75" height="20.25" align-x="68.25" align-y="474" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:equal/> <ml:id xml:space="preserve" subscript="xx">V</ml:id> <ml:apply> <ml:plus/> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">c</ml:id> <ml:id xml:space="preserve">J</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="tt">V</ml:id> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">c</ml:id> <ml:id xml:space="preserve">R</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="t">V</ml:id> </ml:apply> </ml:apply> </ml:apply> </math> <rendering item-idref="14"/> </region> <region region-id="92" left="216" top="462.75" width="51.75" height="15.75" align-x="251.25" align-y="474" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:lessOrEqual/> <ml:apply> <ml:lessOrEqual/> <ml:real>0</ml:real> <ml:id xml:space="preserve">x</ml:id> </ml:apply> <ml:id xml:space="preserve">L</ml:id> </ml:apply> </math> <rendering item-idref="15"/> </region> <region region-id="93" left="312" top="462.75" width="25.5" height="15.75" align-x="322.5" align-y="474" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:greaterThan/> <ml:id xml:space="preserve">t</ml:id> <ml:real>0</ml:real> </ml:apply> </math> <rendering item-idref="16"/> </region> <region region-id="130" left="474" top="462.75" width="15.75" height="15.75" align-x="480.75" align-y="474" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:parens xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:real>1</ml:real> </ml:parens> </math> <rendering item-idref="17"/> </region> <region region-id="615" left="30" top="492.75" width="450" height="13.5" align-x="30" align-y="504" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="false"> <f family="Arial Cyr" charset="204" size="12">Здесь: V(x,t) - напряжение в сечении провода с координатой х в момент времени t;</f> </text> </region> <region region-id="99" left="42" top="522" width="204.75" height="14.25" align-x="42" align-y="534" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="12"> Краевые условия: </f> </text> </region> <region region-id="100" left="42" top="546.75" width="66" height="15.75" align-x="84.75" align-y="558" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:equal/> <ml:apply> <ml:id xml:space="preserve">V</ml:id> <ml:sequence> <ml:id xml:space="preserve">x</ml:id> <ml:real>0</ml:real> </ml:sequence> </ml:apply> <ml:id xml:space="preserve">V0</ml:id> </ml:apply> </math> <rendering item-idref="18"/> </region> <region region-id="107" left="132" top="546.75" width="60.75" height="20.25" align-x="177.75" align-y="558" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:equal/> <ml:apply> <ml:id xml:space="preserve" subscript="t">V</ml:id> <ml:sequence> <ml:id xml:space="preserve">x</ml:id> <ml:real>0</ml:real> </ml:sequence> </ml:apply> <ml:real>0</ml:real> </ml:apply> </math> <rendering item-idref="19"/> </region> <region region-id="108" left="216" top="546.75" width="108.75" height="13.5" align-x="216" align-y="558" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="false"> <f family="Arial Cyr" charset="204" size="12">Начальные условия</f> </text> </region> <region region-id="129" left="474" top="570.75" width="15.75" height="15.75" align-x="480.75" align-y="582" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:parens xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:real>2</ml:real> </ml:parens> </math> <rendering item-idref="20"/> </region> <region region-id="102" left="48" top="588.75" width="55.5" height="15.75" align-x="88.5" align-y="600" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:equal/> <ml:apply> <ml:id xml:space="preserve">V</ml:id> <ml:sequence> <ml:real>0</ml:real> <ml:id xml:space="preserve">t</ml:id> </ml:sequence> </ml:apply> <ml:real>0</ml:real> </ml:apply> </math> <rendering item-idref="21"/> </region> <region region-id="103" left="120" top="588.75" width="61.5" height="20.25" align-x="166.5" align-y="600" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:equal/> <ml:apply> <ml:id xml:space="preserve" subscript="x">V</ml:id> <ml:sequence> <ml:id xml:space="preserve">L</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:sequence> </ml:apply> <ml:real>0</ml:real> </ml:apply> </math> <rendering item-idref="22"/> </region> <region region-id="110" left="216" top="588.75" width="106.5" height="13.5" align-x="216" align-y="600" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="false"> <f family="Arial Cyr" charset="204" size="12">Граничные условия</f> </text> </region> <region region-id="114" left="42" top="624" width="129" height="14.25" align-x="42" align-y="636" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="false"> <f family="Arial Cyr" charset="204" size="12"> <sp/> </f> <f family="Arial Cyr" charset="204" size="12"> Решение </f> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-style="normal" underline="false"> ищем в виде:</inlineAttr> </f> </text> </region> <region region-id="617" left="204" top="624.75" width="95.25" height="15.75" align-x="243.75" align-y="636" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:equal/> <ml:apply> <ml:id xml:space="preserve">V</ml:id> <ml:sequence> <ml:id xml:space="preserve">x</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:sequence> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:id xml:space="preserve">X</ml:id> <ml:id xml:space="preserve">x</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve">T</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> </ml:apply> </math> <rendering item-idref="23"/> </region> <region region-id="637" left="474" top="624.75" width="28.5" height="15.75" align-x="487.5" align-y="636" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:parens xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">resh</ml:id> </ml:parens> </math> <rendering item-idref="24"/> </region> <region region-id="619" left="42" top="648.75" width="352.5" height="13.5" align-x="42" align-y="660" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="false"> <f family="Arial Cyr" charset="204" size="12">Исходя из краевых условий (2), запишем следующие выражения:</f> </text> </region> <region region-id="631" left="54" top="672.75" width="80.25" height="15.75" align-x="75.75" align-y="684" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:equal/> <ml:id xml:space="preserve">V0</ml:id> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:id xml:space="preserve">X</ml:id> <ml:id xml:space="preserve">x</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve">T</ml:id> <ml:real>0</ml:real> </ml:apply> </ml:apply> </ml:apply> </math> <rendering item-idref="25"/> </region> <region region-id="632" left="156" top="672.75" width="74.25" height="15.75" align-x="169.5" align-y="684" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:equal/> <ml:real>0</ml:real> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:id xml:space="preserve">X</ml:id> <ml:id xml:space="preserve">x</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve">T'</ml:id> <ml:real>0</ml:real> </ml:apply> </ml:apply> </ml:apply> </math> <rendering item-idref="26"/> </region> <region region-id="956" left="462" top="684.75" width="21" height="15.75" align-x="471.75" align-y="696" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:parens xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:apply> <ml:mult style="auto-select"/> <ml:real>2</ml:real> <ml:id xml:space="preserve">a</ml:id> </ml:apply> </ml:parens> </math> <rendering item-idref="27"/> </region> <region region-id="625" left="54" top="720.75" width="69.75" height="15.75" align-x="67.5" align-y="732" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:equal/> <ml:real>0</ml:real> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:id xml:space="preserve">X</ml:id> <ml:real>0</ml:real> </ml:apply> <ml:apply> <ml:id xml:space="preserve">T</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> </ml:apply> </math> <rendering item-idref="28"/> </region> <region region-id="628" left="150" top="720.75" width="72.75" height="15.75" align-x="163.5" align-y="732" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:equal/> <ml:real>0</ml:real> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:id xml:space="preserve">X'</ml:id> <ml:id xml:space="preserve">L</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve">T</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> </ml:apply> </math> <rendering item-idref="29"/> </region> <region region-id="955" left="36" top="750" width="461.25" height="43.5" align-x="36" align-y="762" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="12">Из этих равенств следует, что </f> <region region-id="635" left="202.5" top="750.75" width="45.75" height="15.75" align-x="233.25" align-y="762" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:notEqual/> <ml:apply> <ml:id xml:space="preserve">X</ml:id> <ml:id xml:space="preserve">x</ml:id> </ml:apply> <ml:real>0</ml:real> </ml:apply> </math> <rendering item-idref="30"/> </region> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> и </inlineAttr> </f> <region region-id="636" left="261" top="750.75" width="42" height="15.75" align-x="288" align-y="762" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:notEqual/> <ml:apply> <ml:id xml:space="preserve">T</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> <ml:real>0</ml:real> </ml:apply> </math> <rendering item-idref="31"/> </region> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false">. В противном случае мы </inlineAttr> </f> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false">получаем </inlineAttr> </f> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false">тривиальное (нулевое) решение. Подстановка (resh) в (1) приводит </inlineAttr> </f> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> <f family="Arial Cyr" charset="204" size="12">к двум линейным дифференциальным </f> </inlineAttr> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> <f family="Arial Cyr" charset="204" size="12">уравнениям 2-го порядка:</f> </inlineAttr> </text> </region> <region region-id="649" left="42" top="822.75" width="76.5" height="13.5" align-x="42" align-y="834" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="12">Первое из них</f> </text> </region> <region region-id="648" left="138" top="807.75" width="115.5" height="44.25" align-x="238.5" align-y="834" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:equal/> <ml:apply> <ml:plus/> <ml:apply> <ml:derivative/> <ml:lambda> <ml:boundVars> <ml:id xml:space="preserve">x</ml:id> </ml:boundVars> <ml:apply> <ml:id xml:space="preserve">X</ml:id> <ml:id xml:space="preserve">x</ml:id> </ml:apply> </ml:lambda> <ml:degree> <ml:real>2</ml:real> </ml:degree> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">λ</ml:id> <ml:apply> <ml:id xml:space="preserve">X</ml:id> <ml:id xml:space="preserve">x</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:real>0</ml:real> </ml:apply> </math> <rendering item-idref="32"/> </region> <region region-id="653" left="462" top="828.75" width="15.75" height="15.75" align-x="468.75" align-y="840" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:parens xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:real>3</ml:real> </ml:parens> </math> <rendering item-idref="33"/> </region> <region region-id="650" left="42" top="864.75" width="140.25" height="13.5" align-x="42" align-y="876" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="12">с начальными условиями:</f> </text> </region> <region region-id="652" left="198" top="864.75" width="46.5" height="15.75" align-x="229.5" align-y="876" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:equal/> <ml:apply> <ml:id xml:space="preserve">X</ml:id> <ml:real>0</ml:real> </ml:apply> <ml:real>0</ml:real> </ml:apply> </math> <rendering item-idref="34"/> </region> <region region-id="651" left="276" top="864.75" width="49.5" height="15.75" align-x="310.5" align-y="876" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:equal/> <ml:apply> <ml:id xml:space="preserve">X'</ml:id> <ml:id xml:space="preserve">L</ml:id> </ml:apply> <ml:real>0</ml:real> </ml:apply> </math> <rendering item-idref="35"/> </region> <region region-id="656" left="42" top="897" width="476.25" height="70.5" align-x="42" align-y="918" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="12">позволяет найти </f> <region region-id="655" left="134.25" top="906.75" width="53.25" height="17.25" align-x="165" align-y="918" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:equal/> <ml:apply> <ml:id xml:space="preserve">X</ml:id> <ml:id xml:space="preserve">x</ml:id> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">X</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> </ml:apply> </math> <rendering item-idref="36"/> </region> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> ,<sp count="2"/>где<sp count="2"/> </inlineAttr> </f> <region region-id="657" left="224.25" top="903.75" width="84" height="20.25" align-x="245.25" align-y="918" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:equal/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">X</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve">sin</ml:id> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:sqrt/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">λ</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> </ml:apply> <ml:id xml:space="preserve">x</ml:id> </ml:apply> </ml:apply> </ml:apply> </math> <rendering item-idref="37"/> </region> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false">,<sp count="3"/> </inlineAttr> </f> <region region-id="658" left="321" top="897.75" width="96" height="34.5" align-x="350.25" align-y="918" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:equal/> <ml:apply> <ml:sqrt/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">λ</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:div/> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">π</ml:id> <ml:parens> <ml:apply> <ml:minus/> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:real>1</ml:real> </ml:apply> </ml:parens> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:id xml:space="preserve">L</ml:id> </ml:apply> </ml:apply> </ml:apply> </math> <rendering item-idref="38"/> </region> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> <sp count="2"/>.</inlineAttr> </f> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> <sp count="2"/> </inlineAttr> </f> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> <f family="Arial Cyr" charset="204" size="12">П</f> </inlineAttr> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> <f family="Arial Cyr" charset="204" size="12">оследние </f> </inlineAttr> <f family="Arial Cyr" charset="204" size="12">называют:</f> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> <sp/> </inlineAttr> </f> <region region-id="661" left="165" top="933" width="13.5" height="18" align-x="171" align-y="945" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:indexer/> <ml:id xml:space="preserve">λ</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> </math> <rendering item-idref="39"/> </region> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> <sp/> </inlineAttr> </f> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> -</inlineAttr> </f> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> <sp count="3"/> </inlineAttr> </f> <f family="Arial Cyr" charset="204" size="12">собственными значениями </f> <f family="Arial Cyr" charset="204" size="12"> и</f> <f family="Arial Cyr" charset="204" size="12"> <sp count="2"/>соответствующие им </f> <f family="Arial Cyr" charset="204" size="12">Х</f> <f family="Arial Cyr" charset="204" size="12"> n </f> <f family="Arial Cyr" charset="204" size="12">(x) - </f> <f family="Arial Cyr" charset="204" size="12">собственными функциями</f> <f family="Arial Cyr" charset="204" size="12">.</f> </text> </region> <region region-id="690" left="42" top="978.75" width="441.75" height="43.5" align-x="42" align-y="990" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="false"> <f family="Arial Cyr" charset="204" size="12">Причём {X</f> <f family="Arial Cyr" charset="204" size="12"> n </f> <f family="Arial Cyr" charset="204" size="12">} представляет систему ортогональных функций на отрезке [-2L,2L], </f> <f family="Arial Cyr" charset="204" size="12">а</f> <f family="Arial Cyr" charset="204" size="12">также на отрезках: </f> <f family="Arial Cyr" charset="204" size="12">[0,2L] или </f> <f family="Arial Cyr" charset="204" size="12">[-L,L], </f> <f family="Arial Cyr" charset="204" size="12">[0,L] или</f> <f family="Arial Cyr" charset="204" size="12"> <sp/> </f> <f family="Arial Cyr" charset="204" size="12">[-L/2,L/2] (см. файл: СистОртогФункций\</f> <f family="Arial Cyr" charset="204" size="12">СистОртогФункций.xmcd.</f> </text> </region> <region region-id="675" left="174" top="1053.75" width="101.25" height="34.5" align-x="223.5" align-y="1074" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:parens xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:apply> <ml:id xml:space="preserve">sin</ml:id> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:div/> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">π</ml:id> <ml:parens> <ml:apply> <ml:minus/> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:real>1</ml:real> </ml:apply> </ml:parens> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:id xml:space="preserve">L</ml:id> </ml:apply> </ml:apply> <ml:id xml:space="preserve">x</ml:id> </ml:apply> </ml:apply> </ml:parens> </math> <rendering item-idref="40"/> </region> <region region-id="676" left="300" top="1062.75" width="52.5" height="15.75" align-x="341.25" align-y="1074" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:sequence xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:apply> <ml:equal/> <ml:id xml:space="preserve">n</ml:id> <ml:real>1</ml:real> </ml:apply> <ml:real>2</ml:real> <ml:id xml:space="preserve" font="1">...</ml:id> </ml:sequence> </math> <rendering item-idref="41"/> </region> <region region-id="677" left="456" top="1062.75" width="15.75" height="15.75" align-x="462.75" align-y="1074" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:parens xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:real>4</ml:real> </ml:parens> </math> <rendering item-idref="42"/> </region> <region region-id="1141" left="60" top="1110.75" width="344.25" height="13.5" align-x="60" align-y="1122" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="12">Правда, для указанных выше отрезков, нормы будут разными: </f> </text> </region> <region region-id="1142" left="60" top="1140.75" width="314.25" height="61.5" align-x="83.25" align-y="1176" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:provenance expr-id="1" xmlns:ml="http://schemas.mathsoft.com/math20"> <originRef doc-id="86a18416-aebf-489a-9dbe-33607ccad11e" version-id="06502f39-6fe4-48af-acbb-790c959f320a" branch-id="00000000-0000-0000-0000-000000000000" revision-num="54" is-modified="false" region-id="0" href="C:\Documents and Settings\Konstantin\Мои документы\Компьют технол\СлушателиФПКП\ВолнУр123.xmcd" xmlns="http://schemas.mathsoft.com/provenance10"> <hash/> </originRef> <parentRef doc-id="86a18416-aebf-489a-9dbe-33607ccad11e" version-id="06502f39-6fe4-48af-acbb-790c959f320a" branch-id="00000000-0000-0000-0000-000000000000" revision-num="54" is-modified="false" region-id="0" href="C:\Documents and Settings\Konstantin\Мои документы\Компьют технол\СлушателиФПКП\ВолнУр123.xmcd" xmlns="http://schemas.mathsoft.com/provenance10"> <hash/> </parentRef> <comment xmlns="http://schemas.mathsoft.com/provenance10"/> <originComment xmlns="http://schemas.mathsoft.com/provenance10"/> <contentHash xmlns="http://schemas.mathsoft.com/provenance10">5e62e805d1fdc05a635c4584032ef08a</contentHash> <ml:define> <ml:id xml:space="preserve">nor</ml:id> <ml:symEval style="default" hide-keywords="false" hide-lhs="false"> <ml:apply> <ml:integral auto-algorithm="true"/> <ml:lambda> <ml:boundVars> <ml:id xml:space="preserve">x</ml:id> </ml:boundVars> <ml:apply> <ml:pow/> <ml:apply> <ml:id xml:space="preserve">sin</ml:id> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:mult style="default"/> <ml:parens> <ml:apply> <ml:minus/> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:real>1</ml:real> </ml:apply> </ml:parens> <ml:apply> <ml:div/> <ml:id xml:space="preserve">π</ml:id> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:id xml:space="preserve">L</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:id xml:space="preserve">x</ml:id> </ml:apply> </ml:apply> <ml:real>2</ml:real> </ml:apply> </ml:lambda> <ml:bounds> <ml:real>0</ml:real> <ml:id xml:space="preserve">L</ml:id> </ml:bounds> </ml:apply> <ml:command> <ml:sequence> <ml:id xml:space="preserve">substitute</ml:id> <ml:apply> <ml:equal/> <ml:apply> <ml:id xml:space="preserve">sin</ml:id> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">π</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> </ml:apply> <ml:real>0</ml:real> </ml:apply> </ml:sequence> </ml:command> <ml:command> <ml:id xml:space="preserve">simplify</ml:id> </ml:command> <ml:symResult> <ml:id xml:space="preserve">π</ml:id> </ml:symResult> </ml:symEval> </ml:define> </ml:provenance> </math> <rendering item-idref="43"> <element-image-map> <box left="1.5" top="0.75" width="312.75" height="60" expr-idref="1" xmlns="http://schemas.mathsoft.com/worksheet20"/> </element-image-map> </rendering> </region> <region region-id="1143" left="444" top="1164.75" width="21" height="15.75" align-x="453.75" align-y="1176" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:provenance expr-id="1" xmlns:ml="http://schemas.mathsoft.com/math20"> <originRef doc-id="86a18416-aebf-489a-9dbe-33607ccad11e" version-id="06502f39-6fe4-48af-acbb-790c959f320a" branch-id="00000000-0000-0000-0000-000000000000" revision-num="54" is-modified="false" region-id="0" href="C:\Documents and Settings\Konstantin\Мои документы\Компьют технол\СлушателиФПКП\ВолнУр123.xmcd" xmlns="http://schemas.mathsoft.com/provenance10"> <hash/> </originRef> <parentRef doc-id="86a18416-aebf-489a-9dbe-33607ccad11e" version-id="06502f39-6fe4-48af-acbb-790c959f320a" branch-id="00000000-0000-0000-0000-000000000000" revision-num="54" is-modified="false" region-id="0" href="C:\Documents and Settings\Konstantin\Мои документы\Компьют технол\СлушателиФПКП\ВолнУр123.xmcd" xmlns="http://schemas.mathsoft.com/provenance10"> <hash/> </parentRef> <comment xmlns="http://schemas.mathsoft.com/provenance10"/> <originComment xmlns="http://schemas.mathsoft.com/provenance10"/> <contentHash xmlns="http://schemas.mathsoft.com/provenance10">e65ca673c13357ad8e9c4d306c4bdf52</contentHash> <ml:parens> <ml:apply> <ml:mult style="auto-select"/> <ml:real>4</ml:real> <ml:id xml:space="preserve">a</ml:id> </ml:apply> </ml:parens> </ml:provenance> </math> <rendering item-idref="44"> <element-image-map> <box left="1.5" top="0.75" width="19.5" height="14.25" expr-idref="1" xmlns="http://schemas.mathsoft.com/worksheet20"/> </element-image-map> </rendering> </region> <region region-id="1144" left="450" top="1230.75" width="21.75" height="15.75" align-x="459.75" align-y="1242" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:provenance expr-id="1" xmlns:ml="http://schemas.mathsoft.com/math20"> <originRef doc-id="86a18416-aebf-489a-9dbe-33607ccad11e" version-id="06502f39-6fe4-48af-acbb-790c959f320a" branch-id="00000000-0000-0000-0000-000000000000" revision-num="54" is-modified="false" region-id="0" href="C:\Documents and Settings\Konstantin\Мои документы\Компьют технол\СлушателиФПКП\ВолнУр123.xmcd" xmlns="http://schemas.mathsoft.com/provenance10"> <hash/> </originRef> <parentRef doc-id="86a18416-aebf-489a-9dbe-33607ccad11e" version-id="06502f39-6fe4-48af-acbb-790c959f320a" branch-id="00000000-0000-0000-0000-000000000000" revision-num="54" is-modified="false" region-id="0" href="C:\Documents and Settings\Konstantin\Мои документы\Компьют технол\СлушателиФПКП\ВолнУр123.xmcd" xmlns="http://schemas.mathsoft.com/provenance10"> <hash/> </parentRef> <comment xmlns="http://schemas.mathsoft.com/provenance10"/> <originComment xmlns="http://schemas.mathsoft.com/provenance10"/> <contentHash xmlns="http://schemas.mathsoft.com/provenance10">2fd412f8611709532490f5ed75b7e580</contentHash> <ml:parens> <ml:real base="2">4</ml:real> </ml:parens> </ml:provenance> </math> <rendering item-idref="45"> <element-image-map> <box left="1.5" top="0.75" width="20.25" height="14.25" expr-idref="1" xmlns="http://schemas.mathsoft.com/worksheet20"/> </element-image-map> </rendering> </region> <region region-id="1145" left="60" top="1218.75" width="339" height="61.5" align-x="89.25" align-y="1254" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:provenance expr-id="1" xmlns:ml="http://schemas.mathsoft.com/math20"> <originRef doc-id="86a18416-aebf-489a-9dbe-33607ccad11e" version-id="06502f39-6fe4-48af-acbb-790c959f320a" branch-id="00000000-0000-0000-0000-000000000000" revision-num="54" is-modified="false" region-id="0" href="C:\Documents and Settings\Konstantin\Мои документы\Компьют технол\СлушателиФПКП\ВолнУр123.xmcd" xmlns="http://schemas.mathsoft.com/provenance10"> <hash/> </originRef> <parentRef doc-id="86a18416-aebf-489a-9dbe-33607ccad11e" version-id="06502f39-6fe4-48af-acbb-790c959f320a" branch-id="00000000-0000-0000-0000-000000000000" revision-num="54" is-modified="false" region-id="0" href="C:\Documents and Settings\Konstantin\Мои документы\Компьют технол\СлушателиФПКП\ВолнУр123.xmcd" xmlns="http://schemas.mathsoft.com/provenance10"> <hash/> </parentRef> <comment xmlns="http://schemas.mathsoft.com/provenance10"/> <originComment xmlns="http://schemas.mathsoft.com/provenance10"/> <contentHash xmlns="http://schemas.mathsoft.com/provenance10">4b8cb53e32d50ad9bc2f135345887aed</contentHash> <ml:define> <ml:id xml:space="preserve">nor1</ml:id> <ml:symEval style="default" hide-keywords="false" hide-lhs="false"> <ml:apply> <ml:integral auto-algorithm="true"/> <ml:lambda> <ml:boundVars> <ml:id xml:space="preserve">x</ml:id> </ml:boundVars> <ml:apply> <ml:pow/> <ml:apply> <ml:id xml:space="preserve">sin</ml:id> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:mult style="default"/> <ml:parens> <ml:apply> <ml:minus/> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:real>1</ml:real> </ml:apply> </ml:parens> <ml:apply> <ml:div/> <ml:id xml:space="preserve">π</ml:id> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:id xml:space="preserve">L</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:id xml:space="preserve">x</ml:id> </ml:apply> </ml:apply> <ml:real>2</ml:real> </ml:apply> </ml:lambda> <ml:bounds> <ml:real>0</ml:real> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:id xml:space="preserve">L</ml:id> </ml:apply> </ml:bounds> </ml:apply> <ml:command> <ml:sequence> <ml:id xml:space="preserve">substitute</ml:id> <ml:apply> <ml:equal/> <ml:apply> <ml:id xml:space="preserve">sin</ml:id> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">π</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> </ml:apply> <ml:real>0</ml:real> </ml:apply> </ml:sequence> </ml:command> <ml:command> <ml:id xml:space="preserve">simplify</ml:id> </ml:command> <ml:symResult> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:id xml:space="preserve">π</ml:id> </ml:apply> </ml:symResult> </ml:symEval> </ml:define> </ml:provenance> </math> <rendering item-idref="46"> <element-image-map> <box left="1.5" top="0.75" width="337.5" height="60" expr-idref="1" xmlns="http://schemas.mathsoft.com/worksheet20"/> </element-image-map> </rendering> </region> <region region-id="1146" left="66" top="1296.75" width="329.25" height="13.5" align-x="66" align-y="1308" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="12">Нас интересует отрезок [0,L] и соответствующая ему норма.</f> </text> </region> <region region-id="659" left="42" top="1331.25" width="462" height="18.75" align-x="42" align-y="1344" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="12">Второе из уравнений с учётом найденного значения </f> <region region-id="694" left="327" top="1332" width="13.5" height="18" align-x="333" align-y="1344" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:indexer/> <ml:id xml:space="preserve">λ</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> </math> <rendering item-idref="47"/> </region> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> будет иметь вид:</inlineAttr> </f> </text> </region> <region region-id="691" left="42" top="1359.75" width="184.5" height="44.25" align-x="211.5" align-y="1386" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:equal/> <ml:apply> <ml:plus/> <ml:apply> <ml:plus/> <ml:apply> <ml:derivative/> <ml:lambda> <ml:boundVars> <ml:id xml:space="preserve">t</ml:id> </ml:boundVars> <ml:apply> <ml:id xml:space="preserve">T</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:lambda> <ml:degree> <ml:real>2</ml:real> </ml:degree> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:div/> <ml:id xml:space="preserve">b</ml:id> <ml:id xml:space="preserve">a</ml:id> </ml:apply> <ml:parens> <ml:apply> <ml:derivative/> <ml:lambda> <ml:boundVars> <ml:id xml:space="preserve">t</ml:id> </ml:boundVars> <ml:apply> <ml:id xml:space="preserve">T</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:lambda> </ml:apply> </ml:parens> </ml:apply> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:div/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">λ</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:id xml:space="preserve">a</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve">T</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:real>0</ml:real> </ml:apply> </math> <rendering item-idref="48"/> </region> <region region-id="692" left="264" top="1374.75" width="27.75" height="15.75" align-x="276.75" align-y="1386" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:notEqual/> <ml:id xml:space="preserve">a</ml:id> <ml:real>0</ml:real> </ml:apply> </math> <rendering item-idref="49"/> </region> <region region-id="693" left="366" top="1374.75" width="15.75" height="15.75" align-x="372.75" align-y="1386" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:parens xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:real>5</ml:real> </ml:parens> </math> <rendering item-idref="50"/> </region> <region region-id="151" left="36" top="1439.25" width="439.5" height="45.75" align-x="36" align-y="1452" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="12">Находим решение (5) , которое будет зависеть от значения </f> <region region-id="159" left="361.5" top="1440" width="13.5" height="18" align-x="367.5" align-y="1452" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:indexer/> <ml:id xml:space="preserve">λ</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> </math> <rendering item-idref="51"/> </region> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false">.</inlineAttr> </f> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false">Для этого найдем корни характеристического уравнения, соответствующего уравнению (5).</inlineAttr> </f> </text> </region> <region region-id="252" left="48" top="1494" width="77.25" height="18" align-x="72.75" align-y="1506" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:equal/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">p1</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:apply> <ml:plus/> <ml:apply> <ml:neg/> <ml:id xml:space="preserve">ν</ml:id> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">Ω</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> </ml:apply> </ml:apply> </math> <rendering item-idref="52"/> </region> <region region-id="253" left="174" top="1494" width="76.5" height="18" align-x="198.75" align-y="1506" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:equal/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">p2</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:apply> <ml:minus/> <ml:apply> <ml:neg/> <ml:id xml:space="preserve">ν</ml:id> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">Ω</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> </ml:apply> </ml:apply> </math> <rendering item-idref="53"/> </region> <region region-id="254" left="294" top="1494.75" width="52.5" height="15.75" align-x="335.25" align-y="1506" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:sequence xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:apply> <ml:equal/> <ml:id xml:space="preserve">n</ml:id> <ml:real>1</ml:real> </ml:apply> <ml:real>2</ml:real> <ml:id xml:space="preserve" font="1">...</ml:id> </ml:sequence> </math> <rendering item-idref="54"/> </region> <region region-id="273" left="480" top="1494.75" width="15.75" height="15.75" align-x="486.75" align-y="1506" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:parens xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:real>6</ml:real> </ml:parens> </math> <rendering item-idref="55"/> </region> <region region-id="291" left="42" top="1548.75" width="27" height="13.5" align-x="42" align-y="1560" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="false"> <f family="Arial Cyr" charset="204" size="12">где: </f> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> <sp/> </inlineAttr> </f> </text> </region> <region region-id="299" left="78" top="1540.5" width="43.5" height="33.75" align-x="93.75" align-y="1560" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">ν</ml:id> <ml:apply> <ml:div/> <ml:id xml:space="preserve">R</ml:id> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:id xml:space="preserve">J</ml:id> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="56"/> </region> <region region-id="304" left="144" top="1533" width="198" height="47.25" align-x="167.25" align-y="1560" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:equal/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">Ω</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:div/> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">π</ml:id> <ml:parens> <ml:apply> <ml:minus/> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:real>1</ml:real> </ml:apply> </ml:parens> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:id xml:space="preserve">L</ml:id> </ml:apply> <ml:apply> <ml:sqrt/> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">c</ml:id> <ml:id xml:space="preserve">J</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:sqrt/> <ml:apply> <ml:minus/> <ml:apply> <ml:div/> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">c</ml:id> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">R</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">L</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">J</ml:id> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">π</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:pow/> <ml:parens> <ml:apply> <ml:minus/> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:real>1</ml:real> </ml:apply> </ml:parens> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:apply> <ml:real>1</ml:real> </ml:apply> </ml:apply> </ml:apply> </ml:apply> </math> <rendering item-idref="57"/> </region> <region region-id="305" left="474" top="1548.75" width="15.75" height="15.75" align-x="480.75" align-y="1560" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:parens xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:real>7</ml:real> </ml:parens> </math> <rendering item-idref="58"/> </region> <region region-id="1071" left="30" top="1608.75" width="488.25" height="27" align-x="30" align-y="1620" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="12">В зависимости от выбора параметров и, что самое главное, от значений индекса "n", корни (6) могут быть как действительными разными или равными, так и комплексными. </f> </text> </region> <region region-id="268" left="24" top="1660.5" width="406.5" height="96.75" align-x="24" align-y="1686" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="12">Поэтому найдем такое n, при котором </f> <region region-id="261" left="233.25" top="1661.25" width="117.75" height="45" align-x="336" align-y="1686" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:equal/> <ml:apply> <ml:minus/> <ml:real>1</ml:real> <ml:apply> <ml:div/> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">c</ml:id> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">R</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">L</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">J</ml:id> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">π</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:pow/> <ml:parens> <ml:apply> <ml:minus/> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:real>1</ml:real> </ml:apply> </ml:parens> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:apply> </ml:apply> <ml:real>0</ml:real> </ml:apply> </math> <rendering item-idref="59"/> </region> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false">. Или </inlineAttr> </f> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> <sp/> </inlineAttr> </f> <region region-id="267" left="27" top="1707" width="86.25" height="36.75" align-x="39.75" align-y="1728.75" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:equal/> <ml:id xml:space="preserve">n</ml:id> <ml:apply> <ml:plus/> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:div/> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">R</ml:id> <ml:id xml:space="preserve">L</ml:id> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:id xml:space="preserve">π</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:sqrt/> <ml:apply> <ml:div/> <ml:id xml:space="preserve">c</ml:id> <ml:id xml:space="preserve">J</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:div/> <ml:real>1</ml:real> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:apply> </math> <rendering item-idref="60"/> </region> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> .</inlineAttr> </f> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false">Обозначим это значение через N</inlineAttr> </f> <f family="Arial Cyr" charset="204" size="12"> <sp/> </f> </text> </region> <region region-id="266" left="132" top="1772.25" width="92.25" height="36.75" align-x="149.25" align-y="1794" show-border="false" show-highlight="true" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedBIUnit" xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">N</ml:id> <ml:apply> <ml:plus/> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:div/> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">R</ml:id> <ml:id xml:space="preserve">L</ml:id> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:id xml:space="preserve">π</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:sqrt/> <ml:apply> <ml:div/> <ml:id xml:space="preserve">c</ml:id> <ml:id xml:space="preserve">J</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:div/> <ml:real>1</ml:real> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="61"/> </region> <region region-id="577" left="264" top="1782.75" width="44.25" height="15.75" align-x="280.5" align-y="1794" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">N</ml:id> <result xmlns="http://schemas.mathsoft.com/math20"> <ml:real>13</ml:real> </result> </ml:eval> </math> <rendering item-idref="62"/> </region> <region region-id="696" left="486" top="1782.75" width="15.75" height="15.75" align-x="492.75" align-y="1794" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:parens xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:real>8</ml:real> </ml:parens> </math> <rendering item-idref="63"/> </region> <region region-id="578" left="24" top="1832.25" width="466.5" height="12" align-x="24" align-y="1842" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="false"> <f family="Arial Cyr" charset="204" size="10">Примечание. Можно подогнать R так, чтобы N было целым. Для этого R будем вычислять по формуле:</f> </text> </region> <region region-id="579" left="36" top="1862.25" width="148.5" height="36" align-x="59.25" align-y="1884" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">RR</ml:id> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:mult style="default"/> <ml:parens> <ml:apply> <ml:minus/> <ml:apply> <ml:id xml:space="preserve">ceil</ml:id> <ml:id xml:space="preserve">N</ml:id> </ml:apply> <ml:apply> <ml:div/> <ml:real>1</ml:real> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:parens> <ml:apply> <ml:div/> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:id xml:space="preserve">π</ml:id> </ml:apply> <ml:id xml:space="preserve">L</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:sqrt/> <ml:apply> <ml:div/> <ml:id xml:space="preserve">J</ml:id> <ml:id xml:space="preserve">c</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="64"/> </region> <region region-id="580" left="222" top="1872.75" width="59.25" height="15.75" align-x="244.5" align-y="1884" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">RR</ml:id> <result xmlns="http://schemas.mathsoft.com/math20"> <ml:real>12.5</ml:real> </result> </ml:eval> </math> <rendering item-idref="65"/> </region> <region region-id="581" left="30" top="1910.25" width="477" height="12" align-x="30" align-y="1920" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="false"> <f family="Arial Cyr" charset="204" size="10">Полученное значение R=RR надо подставить в исходные данные в начале листинга. Конец Примечания.</f> </text> </region> <region region-id="278" left="30" top="1944.75" width="423" height="13.5" align-x="30" align-y="1956" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="false"> <f family="Arial Cyr" charset="204" size="12">Значения (8) приводят к разбиению множества индексов n<sp count="2"/>на подмножества.</f> </text> </region> <region region-id="465" left="150" top="1974.75" width="159" height="14.25" align-x="150" align-y="1986" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="12"> Алгоритмизация решения. </f> </text> </region> <region region-id="964" left="42" top="1998.75" width="411.75" height="13.5" align-x="42" align-y="2010" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="false"> <f family="Arial Cyr" charset="204" size="12">Все задаваемые ниже параметры можно менять в интерактивном режиме.</f> </text> </region> <region region-id="961" left="42" top="2022.75" width="230.25" height="13.5" align-x="42" align-y="2034" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="12">Зададим диапазон изменения индекса "n":</f> </text> </region> <region region-id="962" left="288" top="2022.75" width="54.75" height="15.75" align-x="314.25" align-y="2034" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">NN</ml:id> <ml:real>130</ml:real> </ml:define> </math> <rendering item-idref="66"/> </region> <region region-id="963" left="360" top="2022.75" width="57.75" height="15.75" align-x="373.5" align-y="2034" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">n</ml:id> <ml:range> <ml:real>1</ml:real> <ml:id xml:space="preserve">NN</ml:id> </ml:range> </ml:define> </math> <rendering item-idref="67"/> </region> <region region-id="850" left="42" top="2045.25" width="450.75" height="17.25" align-x="42" align-y="2058" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="false"> <f family="Arial Cyr" charset="204" size="12">Погрешность округления<sp count="2"/>N до целого числа: </f> <region region-id="1002" left="288" top="2046" width="52.5" height="16.5" align-x="303" align-y="2058" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedBIFunction" xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">ε</ml:id> <ml:real>0.001</ml:real> </ml:define> </math> <rendering item-idref="68"/> </region> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false">. Её можно задать как ноль.</inlineAttr> </f> </text> </region> <region region-id="733" left="42" top="2104.5" width="105" height="39.75" align-x="63" align-y="2130" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">λ</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:apply> <ml:pow/> <ml:parens> <ml:apply> <ml:div/> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">π</ml:id> <ml:parens> <ml:apply> <ml:minus/> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:real>1</ml:real> </ml:apply> </ml:parens> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:id xml:space="preserve">L</ml:id> </ml:apply> </ml:apply> </ml:parens> <ml:real>2</ml:real> </ml:apply> </ml:define> </math> <rendering item-idref="69"/> </region> <region region-id="732" left="174" top="2103" width="200.25" height="47.25" align-x="198" align-y="2130" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedBIUnit" xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">Ω</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:div/> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">π</ml:id> <ml:parens> <ml:apply> <ml:minus/> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:real>1</ml:real> </ml:apply> </ml:parens> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:id xml:space="preserve">L</ml:id> </ml:apply> <ml:apply> <ml:sqrt/> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">c</ml:id> <ml:id xml:space="preserve">J</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:sqrt/> <ml:apply> <ml:minus/> <ml:apply> <ml:div/> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">c</ml:id> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">R</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">L</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">J</ml:id> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">π</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:pow/> <ml:parens> <ml:apply> <ml:minus/> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:real>1</ml:real> </ml:apply> </ml:parens> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:apply> <ml:real>1</ml:real> </ml:apply> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="70"/> </region> <region region-id="546" left="42" top="2169" width="198.75" height="47.25" align-x="64.5" align-y="2196" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">ω</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:div/> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">π</ml:id> <ml:parens> <ml:apply> <ml:minus/> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:real>1</ml:real> </ml:apply> </ml:parens> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:id xml:space="preserve">L</ml:id> </ml:apply> <ml:apply> <ml:sqrt/> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">c</ml:id> <ml:id xml:space="preserve">J</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:sqrt/> <ml:apply> <ml:minus/> <ml:real>1</ml:real> <ml:apply> <ml:div/> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">c</ml:id> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">R</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">L</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">J</ml:id> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">π</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:pow/> <ml:parens> <ml:apply> <ml:minus/> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:real>1</ml:real> </ml:apply> </ml:parens> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:apply> </ml:apply> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="71"/> </region> <region region-id="858" left="42" top="2231.25" width="465.75" height="62.25" align-x="42" align-y="2244" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="false"> <f family="Arial Cyr" charset="204" size="12">Для всех случаев (всех n) </f> <f family="Arial Cyr" charset="204" size="12"> <sp/> </f> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal">, в том числе для </inlineAttr> </f> <region region-id="379" left="282.75" top="2232" width="39.75" height="18" align-x="307.5" align-y="2244" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:equal/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">ω</ml:id> <ml:id xml:space="preserve">N</ml:id> </ml:apply> <ml:real>1</ml:real> </ml:apply> </math> <rendering item-idref="72"/> </region> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false">, получим</inlineAttr> </f> <f family="Arial Cyr" charset="204" size="12"> : </f> <region region-id="381" left="381" top="2232" width="90.75" height="18" align-x="456.75" align-y="2244" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:equal/> <ml:apply> <ml:minus/> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">B</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">ω</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">ν</ml:id> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">A</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:real>0</ml:real> </ml:apply> </math> <rendering item-idref="73"/> </region> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-style="normal" underline="false" line-through="false">. </inlineAttr> </f> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false">Что в свою очередь позволит вычислить B</inlineAttr> </f> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> n </inlineAttr> </f> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false">.</inlineAttr> </f> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> <sp count="2"/>Где </inlineAttr> </f> <region region-id="1073" left="281.25" top="2250.75" width="90" height="34.5" align-x="303" align-y="2270.25" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedBIUnit" xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">A</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:apply> <ml:div/> <ml:apply> <ml:mult style="default"/> <ml:real>4</ml:real> <ml:id xml:space="preserve">V0</ml:id> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">π</ml:id> <ml:parens> <ml:apply> <ml:minus/> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:real>1</ml:real> </ml:apply> </ml:parens> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="74"/> </region> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false">.</inlineAttr> </f> </text> </region> <region region-id="1080" left="48" top="2304.75" width="321.75" height="13.5" align-x="48" align-y="2316" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="12">Проверка и вывод на экран монитора численных значений:</f> </text> </region> <region region-id="1078" left="42" top="2334.75" width="425.25" height="31.5" align-x="64.5" align-y="2352" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:apply> <ml:transpose/> <ml:id xml:space="preserve">A</ml:id> </ml:apply> <result xmlns="http://schemas.mathsoft.com/math20"> <ml:matrix rows="1" cols="131"> <ml:real>0</ml:real> <ml:real>1.2732395447351628</ml:real> <ml:real>0.42441318157838759</ml:real> <ml:real>0.25464790894703254</ml:real> <ml:real>0.18189136353359467</ml:real> <ml:real>0.14147106052612921</ml:real> <ml:real>0.11574904952137845</ml:real> <ml:real>0.097941503441166353</ml:real> <ml:real>0.084882636315677523</ml:real> <ml:real>0.074896443807950741</ml:real> <ml:real>0.067012607617640149</ml:real> <ml:real>0.060630454511198223</ml:real> <ml:real>0.055358241075441864</ml:real> <ml:real>0.050929581789406507</ml:real> <ml:real>0.0471570201753764</ml:real> <ml:real>0.043904811887419404</ml:real> <ml:real>0.041072243378553641</ml:real> <ml:real>0.038583016507126144</ml:real> <ml:real>0.036378272706718937</ml:real> <ml:real>0.034411879587436828</ml:real> <ml:real>0.032647167813722122</ml:real> <ml:real>0.031054623042321046</ml:real> <ml:real>0.029610221970585181</ml:real> <ml:real>0.028294212105225838</ml:real> <ml:real>0.027090203079471544</ml:real> <ml:real>0.025984480504799241</ml:real> <ml:real>0.024965481269316917</ml:real> <ml:real>0.024023387636512503</ml:real> <ml:real>0.023149809904275686</ml:real> <ml:real>0.022337535872546718</ml:real> <ml:real>0.021580331266697676</ml:real> <ml:real>0.020872779421887915</ml:real> <ml:real>0.020210151503732742</ml:real> <ml:real>0.019588300688233275</ml:real> <ml:real>0.019003575294554667</ml:real> <ml:real>0.018452747025147286</ml:real> <ml:real>0.017932951334298067</ml:real> <ml:real>0.017441637599111819</ml:real> <ml:real>0.016976527263135505</ml:real> <ml:real>0.016535578503054062</ml:real> <ml:real>0.016116956262470415</ml:real> <ml:real>0.015719006725125467</ml:real> <ml:real>0.0153402354787369</ml:real> <ml:real>0.014979288761590149</ml:real> <ml:real>0.014634937295806469</ml:real> <ml:real>0.014306062300395087</ml:real> <ml:real>0.013991643348738052</ml:real> <ml:real>0.013690747792851213</ml:real> <ml:real>0.013402521523528029</ml:real> <ml:real>0.01312618087355838</ml:real> <ml:real>0.012861005502375381</ml:real> <ml:real>0.012606332126090721</ml:real> <ml:real>0.01236154897801129</ml:real> <ml:real>0.012126090902239645</ml:real> <ml:real>0.011899434997524886</ml:real> <ml:real>0.011681096740689567</ml:real> <ml:real>0.01147062652914561</ml:real> <ml:real>0.011267606590576662</ml:real> <ml:real>0.011071648215088371</ml:real> <ml:real>0.010882389271240706</ml:real> <ml:real>0.010699491972564394</ml:real> <ml:real>0.010522640865579858</ml:real> <ml:real>0.010351541014107015</ml:real> <ml:real>0.010185916357881302</ml:real> <ml:real>0.010025508226261123</ml:real> <ml:real>0.00987007399019506</ml:real> <ml:real>0.0097193858376729975</ml:real> <ml:real>0.0095732296596628772</ml:real> <ml:real>0.00943140403507528</ml:real> <ml:real>0.0092937193046362231</ml:real> <ml:real>0.0091599967247134</ml:real> <ml:real>0.0090300676931571837</ml:real> <ml:real>0.0089037730401060333</ml:real> <ml:real>0.00878096237748388</ml:real> <ml:real>0.0086614935015997454</ml:real> <ml:real>0.0085452318438601522</ml:real> <ml:real>0.00843204996513353</ml:real> <ml:real>0.0083218270897723046</ml:real> <ml:real>0.0082144486757107279</ml:real> <ml:real>0.0081098060174214191</ml:real> <ml:real>0.0080077958788375009</ml:real> <ml:real>0.0079083201536345512</ml:real> <ml:real>0.0078112855505224716</ml:real> <ml:real>0.0077166033014252292</ml:real> <ml:real>0.0076241888906297163</ml:real> <ml:real>0.007533961803166643</ml:real> <ml:real>0.0074458452908489053</ml:real> <ml:real>0.0073597661545385133</ml:real> <ml:real>0.0072756545413437878</ml:real> <ml:real>0.007193443755565891</ml:real> 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z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false">Введем константы N1, N2<sp count="2"/>для вычисления В</inlineAttr> </f> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> n </inlineAttr> </f> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false">, записываемых в вектор В</inlineAttr> </f> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false">.</inlineAttr> </f> </text> </region> <region region-id="449" left="48" top="2432.25" width="133.5" height="36.75" align-x="71.25" align-y="2454" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">N1</ml:id> <ml:apply> <ml:id xml:space="preserve">floor</ml:id> <ml:apply> <ml:plus/> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:div/> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">L</ml:id> <ml:id xml:space="preserve">R</ml:id> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:id xml:space="preserve">π</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:sqrt/> <ml:apply> <ml:div/> <ml:id xml:space="preserve">c</ml:id> <ml:id xml:space="preserve">J</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:div/> <ml:real>1</ml:real> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="77"/> </region> <region region-id="862" left="210" top="2442.75" width="67.5" height="15.75" align-x="233.25" align-y="2454" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">N2</ml:id> <ml:apply> <ml:id xml:space="preserve">ceil</ml:id> <ml:id xml:space="preserve">N</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="78"/> </region> <region region-id="863" left="42" top="2478.75" width="321.75" height="13.5" align-x="42" align-y="2490" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="12">Проверка и вывод на экран монитора численных значений:</f> </text> </region> <region region-id="871" left="42" top="2508.75" width="50.25" height="15.75" align-x="64.5" align-y="2520" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">N1</ml:id> <result xmlns="http://schemas.mathsoft.com/math20"> <ml:real>13</ml:real> </result> </ml:eval> </math> <rendering item-idref="79"/> </region> <region region-id="872" left="126" top="2508.75" width="50.25" height="15.75" align-x="148.5" align-y="2520" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">N2</ml:id> <result xmlns="http://schemas.mathsoft.com/math20"> <ml:real>13</ml:real> </result> </ml:eval> </math> <rendering item-idref="80"/> </region> <region region-id="873" left="210" top="2508.75" width="44.25" height="15.75" align-x="226.5" align-y="2520" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">N</ml:id> <result xmlns="http://schemas.mathsoft.com/math20"> <ml:real>13</ml:real> </result> </ml:eval> </math> <rendering item-idref="81"/> </region> <region region-id="1087" left="36" top="2534.25" width="444.75" height="36" align-x="36" align-y="2544" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="10">Можно дать следующее описание подмножеств множества индексов n, эквивалентное приведён-</f> <f family="Arial Cyr" charset="204" size="10">ному в (15) (см. файлы </f> <f family="Arial Cyr" charset="204">"ВолнУр123.xmcd", </f> <f family="Arial Cyr" charset="204">"ВолнУр123_СтараяВерс.xmcd")</f> <f family="Arial Cyr" charset="204" size="10">, если положить </f> <f family="Symbol" charset="2" size="10"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false">e</inlineAttr> </f> <f family="Arial" charset="0" size="10"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false">=0 </inlineAttr> </f> <f family="Arial Cyr" charset="204" size="10"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false">. Описание приводится в той же последовательности, что и в (15).</inlineAttr> </f> </text> </region> <region region-id="1088" left="36" top="2586" width="432.75" height="37.5" align-x="36" align-y="2598" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="10">1. Выбор параметров: </f> <region region-id="1010" left="138" top="2586.75" width="46.5" height="15.75" align-x="160.5" align-y="2598" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:notEqual/> <ml:id xml:space="preserve">N1</ml:id> <ml:id xml:space="preserve">N2</ml:id> </ml:apply> </math> <rendering item-idref="82"/> </region> <f family="Arial Cyr" charset="204" size="10"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> and </inlineAttr> </f> <region region-id="1011" left="207" top="2586.75" width="38.25" height="15.75" align-x="229.5" align-y="2598" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:greaterOrEqual/> <ml:id xml:space="preserve">N1</ml:id> <ml:real>1</ml:real> </ml:apply> </math> <rendering item-idref="83"/> </region> <f family="Arial Cyr" charset="204" size="10"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> приводит к разбиению на подмножества:</inlineAttr> </f> <region region-id="1012" left="36" top="2604" width="48.75" height="15.75" align-x="48.75" align-y="2615.25" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:equal/> <ml:id xml:space="preserve">n</ml:id> <ml:apply> <ml:mult style="auto-select"/> <ml:real>1..</ml:real> <ml:id xml:space="preserve">N1</ml:id> </ml:apply> </ml:apply> </math> <rendering item-idref="84"/> </region> <f family="Arial Cyr" charset="204" size="10"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> <sp/> </inlineAttr> </f> <f family="Arial Cyr" charset="204" size="10"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false">(корни </inlineAttr> </f> <f family="Arial Cyr" charset="204" size="10">p1</f> <f family="Arial Cyr" charset="204" size="10"> n </f> <f family="Arial Cyr" charset="204" size="10">, p2</f> <f family="Arial Cyr" charset="204" size="10"> n </f> <f family="Arial Cyr" charset="204" size="10"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> действительные разные), </inlineAttr> </f> <region region-id="1013" left="276" top="2604" width="36.75" height="15.75" align-x="288.75" align-y="2615.25" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:equal/> <ml:id xml:space="preserve">n</ml:id> <ml:id xml:space="preserve">N2</ml:id> </ml:apply> </math> <rendering item-idref="85"/> </region> <f family="Arial Cyr" charset="204" size="10"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false">..</inlineAttr> </f> <region region-id="1014" left="319.5" top="2603.25" width="9.75" height="16.5" align-x="323.25" align-y="2615.25" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:id xml:space="preserve" xmlns:ml="http://schemas.mathsoft.com/math20">∞</ml:id> </math> <rendering item-idref="86"/> </region> <f family="Arial Cyr" charset="204" size="10"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> (корни </inlineAttr> </f> <f family="Arial Cyr" charset="204">p1</f> <f family="Arial Cyr" charset="204"> n </f> <f family="Arial Cyr" charset="204">, p2</f> <f family="Arial Cyr" charset="204"> n </f> <f family="Arial Cyr" charset="204" size="10"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> комплексные).</inlineAttr> </f> </text> </region> <region region-id="1089" left="36" top="2634" width="442.5" height="57.75" align-x="36" align-y="2646" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="10">2. Выбор параметров: </f> <region region-id="1017" left="138" top="2634.75" width="46.5" height="15.75" align-x="160.5" align-y="2646" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:equal/> <ml:id xml:space="preserve">N1</ml:id> <ml:id xml:space="preserve">N2</ml:id> </ml:apply> </math> <rendering item-idref="87"/> </region> <f family="Arial Cyr" charset="204" size="10"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> and </inlineAttr> </f> <region region-id="1018" left="207" top="2634.75" width="38.25" height="15.75" align-x="229.5" align-y="2646" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:greaterOrEqual/> <ml:id xml:space="preserve">N1</ml:id> <ml:real>2</ml:real> </ml:apply> </math> <rendering item-idref="88"/> </region> <f family="Arial Cyr" charset="204" size="10"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> приводит к разбиению на подмножества:</inlineAttr> </f> <region region-id="1019" left="36" top="2651.25" width="67.5" height="15.75" align-x="48.75" align-y="2662.5" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:equal/> <ml:id xml:space="preserve">n</ml:id> <ml:apply> <ml:minus/> <ml:apply> <ml:mult style="auto-select"/> <ml:real>1..</ml:real> <ml:id xml:space="preserve">N1</ml:id> </ml:apply> <ml:real>1</ml:real> </ml:apply> </ml:apply> </math> <rendering item-idref="89"/> </region> <f family="Arial Cyr" charset="204" size="10"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> <sp/> </inlineAttr> </f> <f family="Arial Cyr" charset="204" size="10"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false">(корни </inlineAttr> </f> <f family="Arial Cyr" charset="204">p1</f> <f family="Arial Cyr" charset="204"> n </f> <f family="Arial Cyr" charset="204">, p2</f> <f family="Arial Cyr" charset="204">n</f> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> <f family="Arial Cyr" charset="204" size="10"> действительные разные), </f> </inlineAttr> <region region-id="1016" left="294.75" top="2651.25" width="36.75" height="15.75" align-x="307.5" align-y="2662.5" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:equal/> <ml:id xml:space="preserve">n</ml:id> <ml:id xml:space="preserve">N1</ml:id> </ml:apply> </math> <rendering item-idref="90"/> </region> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> <f family="Arial Cyr" charset="204" size="10"> <sp/> </f> </inlineAttr> <f family="Arial Cyr" charset="204" size="10"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false">(</inlineAttr> </f> <f family="Arial Cyr" charset="204">корни </f> <f family="Arial Cyr" charset="204">p1</f> <f family="Arial Cyr" charset="204"> n </f> <f family="Arial Cyr" charset="204">, p2</f> <f family="Arial Cyr" charset="204"> n </f> <f family="Arial Cyr" charset="204"> действительные равные),</f> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> <f family="Arial Cyr" charset="204" size="10"> <sp/> </f> </inlineAttr> <region region-id="1020" left="78" top="2672.25" width="56.25" height="15.75" align-x="90.75" align-y="2683.5" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:equal/> <ml:id xml:space="preserve">n</ml:id> <ml:apply> <ml:plus/> <ml:id xml:space="preserve">N1</ml:id> <ml:real>1</ml:real> </ml:apply> </ml:apply> </math> <rendering item-idref="91"/> </region> <f family="Arial Cyr" charset="204" size="10"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false">..</inlineAttr> </f> <region region-id="1021" left="141" top="2671.5" width="9.75" height="16.5" align-x="144.75" align-y="2683.5" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:id xml:space="preserve" xmlns:ml="http://schemas.mathsoft.com/math20">∞</ml:id> </math> <rendering item-idref="92"/> </region> <f family="Arial Cyr" charset="204" size="10"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> (корни </inlineAttr> </f> <f family="Arial Cyr" charset="204">p1</f> <f family="Arial Cyr" charset="204">n</f> <f family="Arial Cyr" charset="204">, p2</f> <f family="Arial Cyr" charset="204"> n </f> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> <f family="Arial Cyr" charset="204" size="10"> комплексные).</f> </inlineAttr> </text> </region> <region region-id="1090" left="36" top="2706" width="403.5" height="37.5" align-x="36" align-y="2718" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="10">3. Выбор параметров: </f> <region region-id="1026" left="138" top="2706.75" width="46.5" height="15.75" align-x="160.5" align-y="2718" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:equal/> <ml:id xml:space="preserve">N1</ml:id> <ml:id xml:space="preserve">N2</ml:id> </ml:apply> </math> <rendering item-idref="93"/> </region> <f family="Arial Cyr" charset="204" size="10"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> and </inlineAttr> </f> <region region-id="1027" left="207" top="2706.75" width="37.5" height="15.75" align-x="229.5" align-y="2718" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:equal/> <ml:id xml:space="preserve">N1</ml:id> <ml:real>1</ml:real> </ml:apply> </math> <rendering item-idref="94"/> </region> <f family="Arial Cyr" charset="204" size="10"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> приводит к разбиению на подмножества:</inlineAttr> </f> <region region-id="1028" left="36" top="2724" width="27.75" height="15.75" align-x="48.75" align-y="2735.25" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:equal/> <ml:id xml:space="preserve">n</ml:id> <ml:real>1</ml:real> </ml:apply> </math> <rendering item-idref="95"/> </region> <f family="Arial Cyr" charset="204" size="10"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> <sp/> </inlineAttr> </f> <f family="Arial Cyr" charset="204" size="10"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false">(корни </inlineAttr> </f> <f family="Arial Cyr" charset="204">p1</f> <f family="Arial Cyr" charset="204"> n </f> <f family="Arial Cyr" charset="204">, p2</f> <f family="Arial Cyr" charset="204"> n </f> <f family="Arial Cyr" charset="204" size="10"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> действительные равные), </inlineAttr> </f> <region region-id="1029" left="255.75" top="2724" width="27.75" height="15.75" align-x="268.5" align-y="2735.25" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:equal/> <ml:id xml:space="preserve">n</ml:id> <ml:real>2</ml:real> </ml:apply> </math> <rendering item-idref="96"/> </region> <f family="Arial Cyr" charset="204" size="10"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false">..</inlineAttr> </f> <region region-id="1030" left="290.25" top="2723.25" width="9.75" height="16.5" align-x="294" align-y="2735.25" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:id xml:space="preserve" xmlns:ml="http://schemas.mathsoft.com/math20">∞</ml:id> </math> <rendering item-idref="97"/> </region> <f family="Arial Cyr" charset="204" size="10"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> (корни </inlineAttr> </f> <f family="Arial Cyr" charset="204">p1</f> <f family="Arial Cyr" charset="204"> n </f> <f family="Arial Cyr" charset="204">, p2</f> <f family="Arial Cyr" charset="204"> n </f> <f family="Arial Cyr" charset="204" size="10"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> комплексные).</inlineAttr> </f> </text> </region> <region region-id="1091" left="36" top="2759.25" width="450" height="33" align-x="36" align-y="2772" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="10">4. Выбор параметров: </f> <f family="Arial Cyr" charset="204" size="10"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> <sp/> </inlineAttr> </f> <region region-id="1032" left="141" top="2760.75" width="37.5" height="15.75" align-x="163.5" align-y="2772" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:equal/> <ml:id xml:space="preserve">N1</ml:id> <ml:real>0</ml:real> </ml:apply> </math> <rendering item-idref="98"/> </region> <f family="Arial Cyr" charset="204" size="10"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> приводит к разбиению на подмножества:</inlineAttr> </f> <f family="Arial Cyr" charset="204" size="10"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> <sp/> </inlineAttr> </f> <region region-id="1034" left="370.5" top="2760.75" width="27.75" height="15.75" align-x="383.25" align-y="2772" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:equal/> <ml:id xml:space="preserve">n</ml:id> <ml:real>1</ml:real> </ml:apply> </math> <rendering item-idref="99"/> </region> <f family="Arial Cyr" charset="204" size="10"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false">..</inlineAttr> </f> <region region-id="1035" left="405" top="2760" width="9.75" height="16.5" align-x="408.75" align-y="2772" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:id xml:space="preserve" xmlns:ml="http://schemas.mathsoft.com/math20">∞</ml:id> </math> <rendering item-idref="100"/> </region> <f family="Arial Cyr" charset="204" size="10"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> (корни </inlineAttr> </f> <f family="Arial Cyr" charset="204">p1</f> <f family="Arial Cyr" charset="204"> n </f> <f family="Arial Cyr" charset="204">, p2</f> <f family="Arial Cyr" charset="204">n</f> <f family="Arial Cyr" charset="204" size="10"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> комплексные).</inlineAttr> </f> </text> </region> <region region-id="1092" left="36" top="2813.25" width="329.25" height="37.5" align-x="36" align-y="2826" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204">5. Выбор параметров:</f> <f family="Arial Cyr" charset="204"> <sp/> </f> <region region-id="1041" left="138" top="2814.75" width="15.75" height="15.75" align-x="144.75" align-y="2826" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:id xml:space="preserve" xmlns:ml="http://schemas.mathsoft.com/math20">N1</ml:id> </math> <rendering item-idref="101"/> </region> <f family="Arial Cyr" charset="204" size="10"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false">-></inlineAttr> </f> <region region-id="1042" left="163.5" top="2814" width="9.75" height="16.5" align-x="167.25" align-y="2826" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:id xml:space="preserve" xmlns:ml="http://schemas.mathsoft.com/math20">∞</ml:id> </math> <rendering item-idref="102"/> </region> <f family="Arial Cyr" charset="204"> <sp count="2"/>приводит к разбиению на подмножества:</f> <region region-id="1037" left="36" top="2831.25" width="48.75" height="15.75" align-x="48.75" align-y="2842.5" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:equal/> <ml:id xml:space="preserve">n</ml:id> <ml:apply> <ml:mult style="auto-select"/> <ml:real>1..</ml:real> <ml:id xml:space="preserve">N1</ml:id> </ml:apply> </ml:apply> </math> <rendering item-idref="103"/> </region> <f family="Arial Cyr" charset="204"> <sp/> </f> <f family="Arial Cyr" charset="204">(корни </f> <f family="Arial Cyr" charset="204">p1</f> <f family="Arial Cyr" charset="204"> n </f> <f family="Arial Cyr" charset="204">, p2</f> <f family="Arial Cyr" charset="204"> n </f> <f family="Arial Cyr" charset="204"> действительные разные)</f> </text> </region> <region region-id="954" left="36" top="2862.75" width="332.25" height="16.5" align-x="36" align-y="2874" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="false"> <f family="Arial Cyr" charset="204" size="12">Теперь можно приступить к вычислению коэффициентов В</f> <f family="Arial Cyr" charset="204" size="12"> n </f> <f family="Arial Cyr" charset="204" size="12">: </f> </text> </region> <region region-id="1049" left="48" top="2904.75" width="381" height="308.25" align-x="63.75" align-y="2916" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">B</ml:id> <ml:program> <ml:ifThen> <ml:apply> <ml:and/> <ml:apply> <ml:and/> <ml:apply> <ml:notEqual/> <ml:id 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<ml:real>1</ml:real> </ml:apply> </ml:parens> </ml:apply> </ml:apply> <ml:apply> <ml:div/> <ml:real>1</ml:real> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">Ω</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:localDefine> </ml:for> <ml:for> <ml:id xml:space="preserve">n</ml:id> <ml:range> <ml:id xml:space="preserve">n0</ml:id> <ml:id xml:space="preserve">n0</ml:id> </ml:range> <ml:localDefine> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">B</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:apply> <ml:div/> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">ν</ml:id> <ml:real>4</ml:real> </ml:apply> <ml:id xml:space="preserve">V0</ml:id> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">π</ml:id> <ml:parens> <ml:apply> <ml:minus/> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:real>1</ml:real> </ml:apply> </ml:parens> </ml:apply> </ml:apply> </ml:localDefine> </ml:for> <ml:for> <ml:id xml:space="preserve">n</ml:id> <ml:range> <ml:id xml:space="preserve">n2</ml:id> <ml:id xml:space="preserve">NN</ml:id> </ml:range> <ml:localDefine> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">B</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:div/> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">ν</ml:id> <ml:real>4</ml:real> </ml:apply> <ml:id xml:space="preserve">V0</ml:id> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">π</ml:id> <ml:parens> <ml:apply> <ml:minus/> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:real>1</ml:real> </ml:apply> </ml:parens> </ml:apply> </ml:apply> <ml:apply> <ml:div/> <ml:real>1</ml:real> <ml:apply> <ml:indexer/> <ml:id 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size="12">Решение задачи (1) - (2) имеет переменную структуру, зависимую от<sp count="2"/>констант </f> <f family="Arial Cyr" charset="204" size="12">N1, N2, разбивающих множество индексов n на подмножества. Каждому набору подмножеств индексов n соответствует своя формула решения с коэффициентами </f> <f family="Arial Cyr" charset="204" size="12">B</f> <f family="Arial Cyr" charset="204" size="12"> n </f> <f family="Arial Cyr" charset="204" size="12">.</f> <f family="Arial Cyr" charset="204" size="12"> <sp/> </f> </text> </region> <region region-id="935" left="36" top="3396.75" width="476.25" height="13.5" align-x="36" align-y="3408" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="12">Выпишем четыре формулы вычисления решения </f> <f family="Arial Cyr" charset="204" size="12">:</f> </text> </region> <region region-id="917" left="42" top="3432" width="453" height="16.5" align-x="42" align-y="3444" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="false"> <f family="Arial Cyr" charset="204" size="12">1. Решение для </f> <region region-id="1062" left="129" top="3432.75" width="46.5" height="15.75" align-x="151.5" align-y="3444" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:notEqual/> <ml:id xml:space="preserve">N1</ml:id> <ml:id xml:space="preserve">N2</ml:id> </ml:apply> </math> <rendering item-idref="107"/> </region> <f family="Arial Cyr" charset="204" size="12"> и<sp count="2"/> </f> <region region-id="918" left="191.25" top="3432.75" width="38.25" height="15.75" align-x="204.75" align-y="3444" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:lessOrEqual/> <ml:real>1</ml:real> <ml:id xml:space="preserve">N1</ml:id> </ml:apply> </math> <rendering item-idref="108"/> </region> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> . Корни действительные разные и комплексные.</inlineAttr> </f> </text> </region> <region region-id="423" left="48" top="3519.75" width="393" height="99" align-x="94.5" align-y="3546" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:function> <ml:id xml:space="preserve">V1</ml:id> <ml:boundVars> <ml:id xml:space="preserve">x</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:plus split="true"/> <ml:apply> <ml:summation/> <ml:lambda> <ml:boundVars> <ml:id xml:space="preserve">n</ml:id> </ml:boundVars> <ml:parens> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:mult style="default"/> <ml:parens> <ml:apply> <ml:plus/> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">A</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:apply> 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</ml:apply> <ml:apply> <ml:id xml:space="preserve">sin</ml:id> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">π</ml:id> <ml:apply> <ml:div/> <ml:apply> <ml:minus/> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:real>1</ml:real> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:id xml:space="preserve">L</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:id xml:space="preserve">x</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:parens> </ml:lambda> <ml:bounds> <ml:id xml:space="preserve">N2</ml:id> <ml:id xml:space="preserve">NN</ml:id> </ml:bounds> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="109"/> </region> <region region-id="919" left="42" top="3630" width="457.5" height="30" align-x="42" align-y="3642" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="false"> <f family="Arial Cyr" charset="204" size="12">2. Решение для<sp count="2"/> </f> <region region-id="923" left="132" top="3630.75" width="46.5" height="15.75" align-x="154.5" align-y="3642" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:equal/> <ml:id xml:space="preserve">N1</ml:id> <ml:id xml:space="preserve">N2</ml:id> </ml:apply> </math> <rendering item-idref="110"/> </region> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> and </inlineAttr> </f> <region region-id="1063" left="204.75" top="3630.75" width="38.25" height="15.75" align-x="227.25" align-y="3642" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:greaterOrEqual/> <ml:id xml:space="preserve">N1</ml:id> <ml:real>2</ml:real> </ml:apply> </math> <rendering item-idref="111"/> </region> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> .</inlineAttr> </f> <f family="Arial Cyr" charset="204" size="12"> <sp/> </f> <f family="Arial Cyr" charset="204" size="12">Корни действительные разные, комплексные</f> <f family="Arial Cyr" charset="204" size="12">и </f> <f family="Arial Cyr" charset="204" size="12">действительные равные</f> <f family="Arial Cyr" charset="204" size="12">.</f> <f family="Arial Cyr" charset="204" size="12"> <sp count="2"/> </f> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> <sp/> </inlineAttr> </f> </text> </region> <region region-id="425" left="48" top="3693.75" width="399.75" height="131.25" align-x="94.5" align-y="3720" 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<ml:apply> <ml:minus/> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:real>1</ml:real> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:id xml:space="preserve">L</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:id xml:space="preserve">x</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:parens> </ml:lambda> <ml:bounds> <ml:real>1</ml:real> <ml:apply> <ml:minus/> <ml:id xml:space="preserve">N1</ml:id> <ml:real>1</ml:real> </ml:apply> </ml:bounds> </ml:apply> <ml:apply> <ml:summation/> <ml:lambda> <ml:boundVars> <ml:id xml:space="preserve">n</ml:id> </ml:boundVars> <ml:parens> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:mult style="default"/> <ml:parens> <ml:apply> <ml:plus/> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">A</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve">cos</ml:id> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">ω</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">B</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve">sin</ml:id> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">ω</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:apply> </ml:parens> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">e</ml:id> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:neg/> <ml:id xml:space="preserve">ν</ml:id> </ml:apply> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:id xml:space="preserve">sin</ml:id> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">π</ml:id> <ml:apply> <ml:div/> <ml:apply> <ml:minus/> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:real>1</ml:real> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:id xml:space="preserve">L</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:id xml:space="preserve">x</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:parens> </ml:lambda> <ml:bounds> <ml:apply> <ml:plus/> <ml:id xml:space="preserve">N2</ml:id> <ml:real>1</ml:real> </ml:apply> <ml:id xml:space="preserve">NN</ml:id> </ml:bounds> </ml:apply> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:mult style="default"/> <ml:parens> <ml:apply> <ml:plus/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">A</ml:id> <ml:id xml:space="preserve">N1</ml:id> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">B</ml:id> <ml:id xml:space="preserve">N1</ml:id> </ml:apply> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> </ml:parens> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">e</ml:id> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:neg/> <ml:id xml:space="preserve">ν</ml:id> </ml:apply> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:id xml:space="preserve">sin</ml:id> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">π</ml:id> <ml:apply> <ml:div/> <ml:apply> <ml:minus/> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:id xml:space="preserve">N1</ml:id> </ml:apply> <ml:real>1</ml:real> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:id xml:space="preserve">L</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:id xml:space="preserve">x</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="112"/> </region> <region region-id="926" left="60" top="3840" width="423" height="30" align-x="60" align-y="3852" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="12">3. Решение для </f> <f family="Arial Cyr" charset="204" size="12"> <sp/> </f> <region region-id="1064" left="150" top="3840.75" width="46.5" height="15.75" align-x="172.5" align-y="3852" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:equal/> <ml:id xml:space="preserve">N1</ml:id> <ml:id xml:space="preserve">N2</ml:id> </ml:apply> </math> <rendering item-idref="113"/> </region> <f family="Arial Cyr" charset="204" size="12"> and </f> <region region-id="1065" left="222.75" top="3840.75" width="38.25" height="15.75" align-x="245.25" align-y="3852" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:greaterOrEqual/> <ml:id xml:space="preserve">N1</ml:id> <ml:real>1</ml:real> </ml:apply> </math> <rendering item-idref="114"/> </region> <f family="Arial Cyr" charset="204" size="12"> . </f> <f family="Arial Cyr" charset="204" size="12">Корни<sp count="2"/>комплексные и </f> <f family="Arial Cyr" charset="204" size="12">действительные равные</f> <f family="Arial Cyr" charset="204" size="12">.</f> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> <sp/> </inlineAttr> </f> </text> </region> <region region-id="426" left="54" top="3885.75" width="379.5" height="82.5" align-x="100.5" align-y="3912" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:function> <ml:id xml:space="preserve">V3</ml:id> <ml:boundVars> <ml:id xml:space="preserve">x</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:plus split="true"/> <ml:apply> <ml:summation/> <ml:lambda> <ml:boundVars> <ml:id xml:space="preserve">n</ml:id> </ml:boundVars> <ml:parens> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:mult style="default"/> <ml:parens> <ml:apply> <ml:plus/> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">A</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve">cos</ml:id> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">ω</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">B</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve">sin</ml:id> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">ω</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:apply> </ml:parens> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">e</ml:id> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:neg/> <ml:id xml:space="preserve">ν</ml:id> </ml:apply> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:id xml:space="preserve">sin</ml:id> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">π</ml:id> <ml:apply> <ml:div/> <ml:apply> <ml:minus/> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:real>1</ml:real> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:id xml:space="preserve">L</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:id xml:space="preserve">x</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:parens> </ml:lambda> <ml:bounds> <ml:real>2</ml:real> <ml:id xml:space="preserve">NN</ml:id> </ml:bounds> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:mult style="default"/> <ml:parens> <ml:apply> <ml:plus/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">A</ml:id> <ml:real>1</ml:real> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">B</ml:id> <ml:real>1</ml:real> </ml:apply> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> </ml:parens> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">e</ml:id> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:neg/> <ml:id xml:space="preserve">ν</ml:id> </ml:apply> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:id xml:space="preserve">sin</ml:id> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">π</ml:id> <ml:apply> <ml:div/> <ml:real>1</ml:real> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:id xml:space="preserve">L</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:id xml:space="preserve">x</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="115"/> </region> <region region-id="929" left="60" top="3984.75" width="240.75" height="13.5" align-x="60" align-y="3996" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="12">4. Решение для N1=0 . </f> <f family="Arial Cyr" charset="204" size="12">Корни<sp count="2"/>комплексные.</f> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> <sp/> </inlineAttr> </f> </text> </region> <region region-id="429" left="48" top="4017.75" width="366" height="50.25" align-x="94.5" align-y="4044" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:function> <ml:id xml:space="preserve">V4</ml:id> <ml:boundVars> <ml:id xml:space="preserve">x</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:summation/> <ml:lambda> <ml:boundVars> <ml:id xml:space="preserve">n</ml:id> </ml:boundVars> <ml:parens> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:mult style="default"/> <ml:parens> <ml:apply> <ml:plus/> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">A</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve">cos</ml:id> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">ω</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">B</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve">sin</ml:id> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">ω</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:apply> </ml:parens> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">e</ml:id> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:neg/> <ml:id xml:space="preserve">ν</ml:id> </ml:apply> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:id xml:space="preserve">sin</ml:id> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">π</ml:id> <ml:apply> <ml:div/> <ml:apply> <ml:minus/> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:real>1</ml:real> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:id xml:space="preserve">L</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:id xml:space="preserve">x</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:parens> </ml:lambda> <ml:bounds> <ml:real>1</ml:real> <ml:id xml:space="preserve">NN</ml:id> </ml:bounds> </ml:apply> </ml:define> </math> <rendering item-idref="116"/> </region> <region region-id="1126" left="30" top="4090.5" width="438" height="83.25" align-x="30" align-y="4116" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="12">Поледнее выражение, получаемое при </f> <region region-id="930" left="245.25" top="4091.25" width="61.5" height="45" align-x="257.25" align-y="4116" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:greaterThan/> <ml:id xml:space="preserve">J</ml:id> <ml:apply> <ml:div/> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">c</ml:id> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">R</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">L</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">π</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:apply> </math> <rendering item-idref="117"/> </region> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false">,</inlineAttr> </f> <f family="Arial Cyr" charset="204" size="12"> <sp count="2"/>можно преобразовать к виду, если ввести</f> <f family="Arial Cyr" charset="204" size="12"> <sp/> </f> <region region-id="558" left="129" top="4137" width="71.25" height="36.75" align-x="174.75" align-y="4158" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:equal/> <ml:apply> <ml:id xml:space="preserve">cot</ml:id> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">φ</ml:id> <ml:id xml:space="preserve">k</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:div/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">B</ml:id> <ml:id xml:space="preserve">k</ml:id> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">A</ml:id> <ml:id xml:space="preserve">k</ml:id> </ml:apply> </ml:apply> </ml:apply> </math> <rendering item-idref="118"/> </region> <f family="Arial Cyr" charset="204" size="12"> :</f> </text> </region> <region region-id="1138" left="48" top="4224.75" width="87" height="15.75" align-x="62.25" align-y="4236" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">k</ml:id> <ml:range> <ml:apply> <ml:plus/> <ml:id xml:space="preserve">N1</ml:id> <ml:real>1</ml:real> </ml:apply> <ml:id xml:space="preserve">NN</ml:id> </ml:range> </ml:define> </math> <rendering item-idref="119"/> </region> <region region-id="1140" left="186" top="4215.75" width="82.5" height="36.75" align-x="207" align-y="4236" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">φ</ml:id> <ml:id xml:space="preserve">k</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve">acot</ml:id> <ml:apply> <ml:div/> <ml:id xml:space="preserve">ν</ml:id> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">ω</ml:id> <ml:id xml:space="preserve">k</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="120"/> </region> <region region-id="568" left="348" top="4221.75" width="63" height="34.5" align-x="390" align-y="4242" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:lessOrEqual/> <ml:apply> <ml:lessThan/> <ml:real>0</ml:real> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">φ</ml:id> <ml:id xml:space="preserve">k</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:div/> <ml:id xml:space="preserve">π</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> </math> <rendering item-idref="121"/> </region> <region region-id="562" left="54" top="4275.75" width="406.5" height="50.25" align-x="100.5" align-y="4302" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:function> <ml:id xml:space="preserve">V5</ml:id> <ml:boundVars> <ml:id xml:space="preserve">x</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:div/> <ml:apply> <ml:mult style="default"/> <ml:real>4</ml:real> <ml:id xml:space="preserve">V0</ml:id> </ml:apply> <ml:id xml:space="preserve">π</ml:id> </ml:apply> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">e</ml:id> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:neg/> <ml:id xml:space="preserve">ν</ml:id> </ml:apply> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:summation/> <ml:lambda> <ml:boundVars> <ml:id xml:space="preserve">n</ml:id> </ml:boundVars> <ml:parens> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:div/> <ml:real>1</ml:real> <ml:apply> <ml:mult style="default"/> <ml:parens> <ml:apply> <ml:minus/> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:real>1</ml:real> </ml:apply> </ml:parens> <ml:apply> <ml:id xml:space="preserve">sin</ml:id> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">φ</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:id xml:space="preserve">sin</ml:id> <ml:apply> <ml:plus/> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">ω</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:id xml:space="preserve">t</ml:id> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">φ</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:id xml:space="preserve">sin</ml:id> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">π</ml:id> <ml:apply> <ml:div/> <ml:apply> <ml:minus/> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:real>1</ml:real> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:id xml:space="preserve">L</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:id xml:space="preserve">x</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:parens> </ml:lambda> <ml:bounds> <ml:real>1</ml:real> <ml:id xml:space="preserve">NN</ml:id> </ml:bounds> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="122"/> </region> <region region-id="1068" left="48" top="4343.25" width="323.25" height="17.25" align-x="48" align-y="4356" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="12">5. Решение при</f> <f family="Arial Cyr" charset="204" size="12"> <sp count="2"/> </f> <region region-id="1048" left="137.25" top="4344.75" width="15.75" height="15.75" align-x="144" align-y="4356" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:id xml:space="preserve" xmlns:ml="http://schemas.mathsoft.com/math20">N1</ml:id> </math> <rendering item-idref="123"/> </region> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false">-></inlineAttr> </f> <region region-id="1070" left="164.25" top="4344" width="9.75" height="16.5" align-x="168" align-y="4356" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:id xml:space="preserve" xmlns:ml="http://schemas.mathsoft.com/math20">∞</ml:id> </math> <rendering item-idref="124"/> </region> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> <sp count="2"/>. Корни действительные разные.</inlineAttr> </f> </text> </region> <region region-id="1069" left="54" top="4377.75" width="381" height="50.25" align-x="100.5" align-y="4404" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:function> <ml:id xml:space="preserve">V6</ml:id> <ml:boundVars> <ml:id xml:space="preserve">x</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:summation/> <ml:lambda> <ml:boundVars> <ml:id xml:space="preserve">n</ml:id> </ml:boundVars> <ml:parens> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:mult style="default"/> <ml:parens> <ml:apply> <ml:plus/> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">A</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve">cosh</ml:id> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">Ω</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">B</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve">sinh</ml:id> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">Ω</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:apply> </ml:parens> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">e</ml:id> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:neg/> <ml:id xml:space="preserve">ν</ml:id> </ml:apply> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:id xml:space="preserve">sin</ml:id> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">π</ml:id> <ml:apply> <ml:div/> <ml:apply> <ml:minus/> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:real>1</ml:real> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:id xml:space="preserve">L</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:id xml:space="preserve">x</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:parens> </ml:lambda> <ml:bounds> <ml:real>1</ml:real> <ml:apply> <ml:minus/> <ml:id xml:space="preserve">NN</ml:id> <ml:real>1</ml:real> </ml:apply> </ml:bounds> </ml:apply> </ml:define> </math> <rendering item-idref="125"/> </region> <region region-id="968" left="42" top="4446.75" width="396.75" height="30" align-x="42" align-y="4458" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="12">Вывод на экран монитора численных значений параметров, по которым </f> <f family="Arial Cyr" charset="204" size="12">выбирается одна из пяти формул: </f> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> <sp/> </inlineAttr> </f> <region region-id="970" left="234" top="4461" width="50.25" height="15.75" align-x="256.5" align-y="4472.25" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">N1</ml:id> <result xmlns="http://schemas.mathsoft.com/math20"> <ml:real>13</ml:real> </result> </ml:eval> </math> <rendering item-idref="126"/> </region> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false">, </inlineAttr> </f> <region region-id="1007" left="291" top="4461" width="50.25" height="15.75" align-x="313.5" align-y="4472.25" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">N2</ml:id> <result xmlns="http://schemas.mathsoft.com/math20"> <ml:real>13</ml:real> </result> </ml:eval> </math> <rendering item-idref="127"/> </region> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false">, </inlineAttr> </f> <region region-id="1107" left="348" top="4461" width="59.25" height="15.75" align-x="373.5" align-y="4472.25" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval 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disable-calc="false"> <ml:eval xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">R</ml:id> <result xmlns="http://schemas.mathsoft.com/math20"> <ml:real>12.5</ml:real> </result> </ml:eval> </math> <rendering item-idref="130"/> </region> <region region-id="1104" left="138" top="4488.75" width="57" height="15.75" align-x="152.25" align-y="4500" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">L</ml:id> <result xmlns="http://schemas.mathsoft.com/math20"> <ml:real>6.2831853071795862</ml:real> </result> </ml:eval> </math> <rendering item-idref="131"/> </region> <region region-id="1103" left="204" top="4488.75" width="43.5" height="15.75" align-x="225.75" align-y="4500" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">V0</ml:id> <result xmlns="http://schemas.mathsoft.com/math20"> <ml:real>1</ml:real> </result> </ml:eval> </math> <rendering item-idref="132"/> </region> <region region-id="1102" left="264" top="4488.75" width="40.5" height="15.75" align-x="276.75" align-y="4500" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">c</ml:id> <result xmlns="http://schemas.mathsoft.com/math20"> <ml:real>10</ml:real> </result> </ml:eval> </math> <rendering item-idref="133"/> </region> <region region-id="1101" left="318" top="4488.75" width="42" height="15.75" align-x="332.25" align-y="4500" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">T</ml:id> <result xmlns="http://schemas.mathsoft.com/math20"> <ml:real>15</ml:real> </result> </ml:eval> </math> <rendering item-idref="134"/> </region> <region region-id="571" left="54" top="4524.75" width="260.25" height="13.5" align-x="54" align-y="4536" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="false"> <f family="Arial Cyr" charset="204" size="12">Логический блок выбора одной из </f> <f family="Arial Cyr" charset="204" size="12">пяти</f> <f family="Arial Cyr" charset="204" size="12"> формул:</f> </text> </region> <region region-id="1148" left="54" top="4560.75" width="260.25" height="99.75" align-x="94.5" align-y="4572" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedBIUnit" xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:function> <ml:id xml:space="preserve">V</ml:id> <ml:boundVars> <ml:id xml:space="preserve">x</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:boundVars> </ml:function> <ml:program> <ml:ifThen> <ml:apply> <ml:and/> <ml:apply> <ml:notEqual/> <ml:id xml:space="preserve">N1</ml:id> <ml:id xml:space="preserve">N2</ml:id> </ml:apply> <ml:apply> <ml:greaterOrEqual/> <ml:apply> <ml:greaterOrEqual/> <ml:id xml:space="preserve">NN</ml:id> <ml:id xml:space="preserve">N1</ml:id> </ml:apply> <ml:real>1</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:id xml:space="preserve">V1</ml:id> <ml:sequence> <ml:id xml:space="preserve">x</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:sequence> </ml:apply> </ml:ifThen> <ml:ifThen> <ml:apply> <ml:and/> <ml:apply> <ml:equal/> <ml:id xml:space="preserve">N1</ml:id> <ml:id xml:space="preserve">N2</ml:id> </ml:apply> <ml:apply> <ml:greaterOrEqual/> <ml:apply> <ml:greaterOrEqual/> <ml:id xml:space="preserve">NN</ml:id> <ml:id xml:space="preserve">N1</ml:id> </ml:apply> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:id xml:space="preserve">V2</ml:id> <ml:sequence> <ml:id xml:space="preserve">x</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:sequence> </ml:apply> </ml:ifThen> <ml:ifThen> <ml:apply> <ml:and/> <ml:apply> <ml:equal/> <ml:id xml:space="preserve">N1</ml:id> <ml:id xml:space="preserve">N2</ml:id> </ml:apply> <ml:apply> <ml:equal/> <ml:apply> <ml:greaterOrEqual/> <ml:id xml:space="preserve">NN</ml:id> <ml:id xml:space="preserve">N1</ml:id> </ml:apply> <ml:real>1</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:id xml:space="preserve">V3</ml:id> <ml:sequence> <ml:id xml:space="preserve">x</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:sequence> </ml:apply> </ml:ifThen> <ml:ifThen> <ml:apply> <ml:equal/> <ml:id xml:space="preserve">N1</ml:id> <ml:real>0</ml:real> </ml:apply> <ml:apply> <ml:id xml:space="preserve">V5</ml:id> <ml:sequence> <ml:id xml:space="preserve">x</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:sequence> </ml:apply> </ml:ifThen> <ml:ifThen> <ml:apply> <ml:greaterThan/> <ml:id xml:space="preserve">N1</ml:id> <ml:id xml:space="preserve">NN</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve">V6</ml:id> <ml:sequence> <ml:id xml:space="preserve">x</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:sequence> </ml:apply> </ml:ifThen> </ml:program> </ml:define> </math> <rendering item-idref="135"/> </region> <region region-id="1149" left="54" top="4686.75" width="219.75" height="99.75" align-x="69" align-y="4698" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">fr</ml:id> <ml:program> <ml:ifThen> <ml:apply> <ml:and/> <ml:apply> <ml:notEqual/> <ml:id xml:space="preserve">N1</ml:id> <ml:id xml:space="preserve">N2</ml:id> </ml:apply> <ml:apply> <ml:greaterOrEqual/> <ml:apply> <ml:greaterOrEqual/> <ml:id xml:space="preserve">NN</ml:id> <ml:id xml:space="preserve">N1</ml:id> </ml:apply> <ml:real>1</ml:real> </ml:apply> </ml:apply> <ml:str xml:space="preserve">V1</ml:str> </ml:ifThen> <ml:ifThen> <ml:apply> <ml:and/> <ml:apply> <ml:equal/> <ml:id xml:space="preserve">N1</ml:id> <ml:id xml:space="preserve">N2</ml:id> </ml:apply> <ml:apply> <ml:greaterOrEqual/> <ml:apply> <ml:greaterOrEqual/> <ml:id xml:space="preserve">NN</ml:id> <ml:id xml:space="preserve">N1</ml:id> </ml:apply> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:str xml:space="preserve">V2</ml:str> </ml:ifThen> <ml:ifThen> <ml:apply> <ml:and/> <ml:apply> <ml:equal/> <ml:id xml:space="preserve">N1</ml:id> <ml:id xml:space="preserve">N2</ml:id> </ml:apply> <ml:apply> <ml:equal/> <ml:apply> <ml:greaterOrEqual/> <ml:id xml:space="preserve">NN</ml:id> <ml:id xml:space="preserve">N1</ml:id> </ml:apply> <ml:real>1</ml:real> </ml:apply> </ml:apply> <ml:str xml:space="preserve">V3</ml:str> </ml:ifThen> <ml:ifThen> <ml:apply> <ml:equal/> <ml:id xml:space="preserve">N1</ml:id> <ml:real>0</ml:real> </ml:apply> <ml:str xml:space="preserve">V5</ml:str> </ml:ifThen> <ml:ifThen> <ml:apply> <ml:greaterThan/> <ml:id xml:space="preserve">N1</ml:id> <ml:id xml:space="preserve">NN</ml:id> </ml:apply> <ml:str xml:space="preserve">V6</ml:str> </ml:ifThen> </ml:program> </ml:define> </math> <rendering item-idref="136"/> </region> <region region-id="1005" left="54" top="4818" width="213" height="16.5" align-x="54" align-y="4830" show-border="false" show-highlight="true" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="false"> <f family="Arial Cyr" charset="204" size="12">Выбрана формула решения: </f> <region region-id="1006" left="213" top="4818.75" width="53.25" height="15.75" align-x="227.25" align-y="4830" show-border="false" show-highlight="true" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">fr</ml:id> <result xmlns="http://schemas.mathsoft.com/math20"> <ml:str xml:space="preserve">V2</ml:str> </result> </ml:eval> </math> <rendering item-idref="137"/> </region> </text> </region> <region region-id="828" left="60" top="4860.75" width="198" height="13.5" align-x="60" align-y="4872" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="false"> <f family="Arial Cyr" charset="204" size="12">Возможна анимация по параметру t:</f> </text> </region> <region region-id="932" left="294" top="4852.5" width="80.25" height="33.75" align-x="305.25" align-y="4872" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">t</ml:id> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:div/> <ml:real>1</ml:real> <ml:real>10</ml:real> </ml:apply> <ml:id xml:space="preserve">FRAME</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="138"/> </region> <region region-id="934" left="408" top="4860.75" width="92.25" height="15.75" align-x="457.5" align-y="4872" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:apply> <ml:id xml:space="preserve">V</ml:id> <ml:sequence> <ml:real>1</ml:real> <ml:real>10</ml:real> </ml:sequence> </ml:apply> <result xmlns="http://schemas.mathsoft.com/math20"> <ml:real>0.99879610758821991</ml:real> </result> </ml:eval> </math> <rendering item-idref="139"/> </region> <region region-id="1150" left="54" top="4920" width="381.75" height="205.5" align-x="54" align-y="4920" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <plot disable-calc="false" item-idref="140"/> <rendering item-idref="141"/> </region> <region region-id="68" left="48" top="5184" width="135.75" height="14.25" align-x="48" align-y="5196" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="false"> <f family="Arial Cyr" charset="204" size="12">Б). </f> <f family="Arial Cyr" charset="204" size="12"> Численное решение. </f> </text> </region> <region region-id="30" left="66" top="5208.75" width="27" height="15.75" align-x="78.75" align-y="5220" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:id xml:space="preserve" xmlns:ml="http://schemas.mathsoft.com/math20">Given</ml:id> </math> <rendering item-idref="142"/> </region> <region region-id="56" left="48" top="5230.5" width="171" height="33.75" align-x="90.75" align-y="5250" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:equal/> <ml:apply> <ml:id xml:space="preserve" subscript="t">w</ml:id> <ml:sequence> <ml:id xml:space="preserve">x</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:sequence> </ml:apply> <ml:apply> <ml:minus/> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:div/> <ml:real>1</ml:real> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">c</ml:id> <ml:id xml:space="preserve">J</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:id 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