Download Life on the Highest Plane: A Study of the Spiritual Nature by Ruth Paxson PDF

By Ruth Paxson

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Additional resources for Life on the Highest Plane: A Study of the Spiritual Nature and Needs of Man

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1. 4. 7) стабилизируемо, если значение σ достаточно велико. 4 из п. 3 заставляют задуматься о причинах «загадочной» стабилизирующей роли большой дисперсии. Пусть теперь условия среды изменяются периодически во времени. 9) где гладкая функция роста f монотонно убывает по переменной x и является T -периодической по переменной t. : Ильичев, 1998а): если средняя скорость роста положительна, т. е. 7) существует положительное T -периодическое решение, которое глобально устойчиво. Ниже в качестве иллюстрации рассмотрим действие температуры среды (θ) на характер биологических процессов водорослей.

7) f (x) = a + ib. Согласно методологии предыдущей главы было бы заманчиво рассмотреть сначала «базисные элементы» семейства W (дельта-функции), затем их выпуклые комбинации и т. д. 8) при a > 0 установлено следующее утверждение. 3. 8) реализуются следующие случаи: 1) «слабо» колебательная неустойчивость неустранима, т. е. при | b |/a π/2 нулевое равновесие остается неустойчивым при любых p > 0 и T > 0; 2) «сильно» колебательная неустойчивость устранима, т. е. при | b |/a > π/2 нулевое равновесие становится устойчивым при подходящем выборе p и T .

5 гл. 1) рассмотрим две функции ∞ f (z) = z − (a − p) − ib и g(z) = p exp (−zt) m(t) dt. 1). Функция + f (z) не имеет в DR корней, поскольку a − p < 0 (см. 2)). При + выполняется неравенство | f | > | g |. Тобольших σ на границе DR + гда согласно теореме Руше в области DR функции f и f + g будут иметь одинаковое число корней. 1) будет устойчиво. 5. 13) индуцирует гладкое сдвиг-отображение за период T (отображение Пуанкаре): P : (x0 , s0 ) → (xT , sT ). 13). Очевидно, P (C ∗ ) = C ∗ .

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