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pro vyhledávání: '"Sakhnovich, Lev"'
Autor:
Sakhnovich, Lev
Ordinary differential equations of the first order on the torus have been investigated in detail by H. Poincar\'e and A. Denjoy. The long-standing problem of generalising these results for the equations of the order $k>1$ (or for the systems of equat
Externí odkaz:
http://arxiv.org/abs/2404.15887
Autor:
Sakhnovich, Lev
The oscillations described by periodic functions play an important role in many areas. In the present paper, we study periodic functions which belong to the class of the $n$-member chains. The self-intersection and local singular points of these peri
Externí odkaz:
http://arxiv.org/abs/2304.09940
Autor:
Sakhnovich, Lev
In the present paper, we study the limit sets of the almost periodic functions $f(x)$. It is interesting that the values $r=\inf|f(x)|$ and $R=\sup|f(x)|$ may be expressed in the exact form. We show that the ring $r\leq |z|\leq R$ is the limit set of
Externí odkaz:
http://arxiv.org/abs/2110.14321
Autor:
Sakhnovich, Lev
In the present paper, we consider the integral operator, which acts in Hilbert space and has sine kernel. This operator generates two operator identities and two corresponding canonical differential systems. We find the asymptotics of the correspondi
Externí odkaz:
http://arxiv.org/abs/2106.02389
Autor:
Sakhnovich, Lev
The area related to M. Liv\v{s}ic's characteristic matrix functions is too vast to be discussed in one paper and we selected for this article the problems which are close to our scientific interests. We discuss M.Liv\v{s}ic's results connected with c
Externí odkaz:
http://arxiv.org/abs/2104.12694
Autor:
Sakhnovich, Lev
We present some basic inequalities between the classical and quantum values of free energy, entropy and mean energy. We investigate the transition from the deterministic case (classical mechanics) to the probabilistic case (quantum mechanics). In the
Externí odkaz:
http://arxiv.org/abs/2006.11329
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Autor:
Sakhnovich, Lev
In this paper, we consider two types of the scattering problems (relativistic case), namely, the stationary scattering problem, where the distance $r$ tends to infinity, and the dynamical scattering problem, where the time $t$ tends to infinity. Usin
Externí odkaz:
http://arxiv.org/abs/1910.03682
Autor:
Sakhnovich, Lev
Stationary scattering problem (when the distance $r$ tends to infinity) and dynamical scattering problem (when the time $t$ tends to infinity) are considered for the 3D Schr\"odinger equation. A simple interconnection between the scattering amplitude
Externí odkaz:
http://arxiv.org/abs/1905.07608