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Generic saddle-node bifurcation for cascade second order ODEs on manifolds

100%

Medveď M.

1998

tom 68

nr 3

211-225

Cascade second order ODEs on manifolds are defined. These objects are locally represented by coupled second order ODEs such that any solution of one of them can represent an external force for the other one. A generic saddle-node bifurcation theorem for 1-parameter families of cascade second order ODEs is proved.

Идеал женской красоты в Оде красавице Федора Дмитриева-Мамонова

86%

Warda A.

Slavica Wratislaviensia

2011

tom 153

233-239

The article discusses the ideal of female beauty presented in Ode to the Beauty by F.I. Dmitriev-Mamonov. The object of the panegiric praise is a beautiful woman, which had not been the case earlier. The addressee of the ode is praised for the qualities of her body which is described in detail. Preserving the convention typical of the panegiric ode, the author creates the image of his addressee, while employing mythologisms, sacralization and idealisation. The description also clearly indicates the influences of the physiognomical theory of J.K. Lavater and of tendencies dominating in the Russian painting in the second part of the 18th century.

Comparison ODE theorems related to the method of lines

72%

Leszczyński H.

Journal of Applied Analysis

2011

tom Vol. 17, nr 1

137-154

We prove a comparison theorem for an ODE and DAE system which arises from the method of lines. Under a Perron comparison condition on the functional dependence and a specific Lipschitz and (W+) condition on the classical argument, we obtain strong uniqueness criteria.