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. . 《Ukrainian Mathematical Journal》1997,49(8):1137-1142
Для скалярного лінійлого звичайпого диференціалыюго рівняння другого порядку, коефіцієнт при другій похідній якого, набуваючи
нульового значешя, може змішовати знак, одержано достатни умови існування періодичного розв'язку для довільюї неоднорідности.
We consider a scalar linear ordinary differential equation of second order, whose coefficient of the second derivative may change the sign when vanishing. For this equation, we obtain sufficient conditions for the existence of a periodic solution in the case of arbitrary periodic nonhomogeneity.相似文献
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. . . . 《Ukrainian Mathematical Journal》1997,49(8):1042-1054
Запропоновано нову процедуру для перевірки гіпотез за допомогою оптимальних статистичних критеріїв.
A new procedure is suggested for the test of hypothesis by using optimal statistical criteria.相似文献
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The tensor product of graphs , and is defined by and Let be the fractional chromatic number of a graph . In this paper, we prove that if one of the three graphs , and is a circular clique, 相似文献
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Let A be an n×n complex matrix. For a suitable subspace of Cn the Schur compression A and the (generalized) Schur complement A/ are defined. If A is written in the form according to the decomposition and if B is invertible, then and The commutativity rule for Schur complements is proved: This unifies Crabtree and Haynsworth's quotient formula for (classical) Schur complements and Anderson's commutativity rule for shorted operators. Further, the absorption rule for Schur compressions is proved: . 相似文献
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This paper investigates the existence and asymptotic behavior of nodal solutions to the following gauged nonlinear Schrödinger equation where , and is the so-called Chern–Simons term. We prove that for any positive integer k, the problem has a sign-changing solution which changes sign exactly k times. Moreover, the energy of is strictly increasing in k, and for any sequence , there exists a subsequence , such that converges in to as , where also changes sign exactly k times and solves the following equation 相似文献