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374 KiB
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374 KiB
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{"componentChunkName":"component---src-pages-projects-math-js","path":"/ru/projects/math/","result":{"data":{"ru_projects":{"edges":[{"node":{"html":"<p>Одной из задач, решаемых группой, является популяризация и развитие метода статистической регуляризации, созданного В.Ф. Турчинным в 70-х годах XX века.</p>\n<p>Типичной некорректной обратной задачей, возникающей в физике, является уравнение Фредгольма I рода: </p>\n<span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\"><math><semantics><mrow><mi>f</mi><mo>(</mo><mi>y</mi><mo>)</mo><mo>=</mo><munderover><mo>∫</mo><mi>a</mi><mi>b</mi></munderover><mi>d</mi><mi>x</mi><mi>K</mi><mo>(</mo><mi>x</mi><mo separator=\"true\">,</mo><mi>y</mi><mo>)</mo><mi>φ</mi><mo>(</mo><mi>x</mi><mo>)</mo></mrow><annotation encoding=\"application/x-tex\">f(y) = \\int \\limits_a^b dx K(x,y)\\varphi(x)</annotation></semantics></math></span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"strut\" style=\"height:1em;vertical-align:-0.25em;\"></span><span class=\"mord mathdefault\" style=\"margin-right:0.10764em;\">f</span><span class=\"mopen\">(</span><span class=\"mord mathdefault\" style=\"margin-right:0.03588em;\">y</span><span class=\"mclose\">)</span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"></span><span class=\"mrel\">=</span><span class=\"mspace\" style=\"margin-right:0.2777777777777778em;\"></span></span><span class=\"base\"><span class=\"strut\" style=\"height:3.7083579999999996em;vertical-align:-1.561125em;\"></span><span class=\"mop op-limits\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:2.1472329999999995em;\"><span style=\"top:-1.8988750000000003em;margin-left:-0.44445em;\"><span class=\"pstrut\" style=\"height:3.3600000000000003em;\"></span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">a</span></span></span><span style=\"top:-3.361125em;\"><span class=\"pstrut\" style=\"height:3.3600000000000003em;\"></span><span><span class=\"mop op-symbol large-op\" style=\"margin-right:0.44445em;\">∫</span></span></span><span style=\"top:-4.921125em;margin-left:0.44445em;\"><span class=\"pstrut\" style=\"height:3.3600000000000003em;\"></span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">b</span></span></span></span><span class=\"vlist-s\"></span></span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:1.561125em;\"><span></span></span></span></span></span><span class=\"mspace\" style=\"margin-right:0.16666666666666666em;\"></span><span class=\"mord mathdefault\">d</span><span class=\"mord mathdefault\">x</span><span class=\"mord mathdefault\" style=\"margin-right:0.07153em;\">K</span><span class=\"mopen\">(</span><span class=\"mord mathdefault\">x</span><span class=\"mpunct\">,</span><span class=\"mspace\" style=\"margin-right:0.16666666666666666em;\"></span><span class=\"mord mathdefault\" style=\"margin-right:0.03588em;\">y</span><span class=\"mclose\">)</span><span class=\"mord mathdefault\">φ</span><span class=\"mopen\">(</span><span class=\"mord mathdefault\">x</span><span class=\"mclose\">)</span></span></span></span></span>\n<p>Фактически, это уравнение описывает следующее: аппаратная функция прибора <span class=\"katex\"><span class=\"katex-mathml\"><math><semantics><mrow><mi>K</mi><mo>(</mo><mi>x</mi><mo separator=\"true\">,</mo><mi>y</mi><mo>)</mo></mrow><annotation encoding=\"application/x-tex\">K(x,y)</annotation></semantics></math></span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"strut\" style=\"height:1em;vertical-align:-0.25em;\"></span><span class=\"mord mathdefault\" style=\"margin-right:0.07153em;\">K</span><span class=\"mopen\">(</span><sp
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