Visnyk of V.N.Karazin Kharkiv National University. Ser. Mathematics, Applied Mathematics and Mechanics

Open access journal                   ISSN 2523-4641 (Online), ISSN 2221-5646 (Print)

Contents and Abstracts

Volume 86, 2017


Ця сторінка Українською / This page in Ukrainian

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A.L. Vyshnevetskiy, Random walks on finite groups with conjugate class probability: algebraic approach. P. 4-9.

Under well known conditions an $n$-fold convolution of probability on finite group $G$ converges to the uniform probability on $G$ ($n\rightarrow\infty$). A lot of works estimate a rate of that convergence. The aim of the article is to obtain estimates of the rate for the probabilities that are constant on classes of conjugate elements of finite groups.

Keywords: probability; finite group; convergency.

2010 Mathematics Subject Classification: 20D99; 60B15; 60B10.   [ Full-text available (PDF) ]   Top of the page.

D.V. Sysoev, A сondition for the existence of a unique equilibrium position of the Cauchy problem for linear matrix differential-algebraic equations. P. 10-17.

Sufficient conditions for the existence of a unique equilibrium position of the Cauchy problem for differential-algebraic equations are proposed. The paper proposes a constructive scheme of the equilibrium position in the Cauchy problem in the general case, when a linear operator $L,$ corresponding to homogeneous of the equation, has no inverse.

Keywords: differential-algebraic matrix equation; pseudoinverse matrix.

2010 Mathematics Subject Classification: 15A24; 34В15; 34C25.   [ Full-text available (PDF) ]   Top of the page.

A.Ya. Khrystiyanyn, Dz.V. Lukivska, Some generalizations of $p$-loxodromic functions. P. 18-25.

The functional equation of the form $f(qz) = p(z)f(z), z \in \mathbb{C} \backslash \{0\}, q \in \mathbb{C} \backslash \{0\}, |q|<1.$ is considered. For certain fixed elementary functions $p(z)$, meromorphic solutions of this equation are found. These solutions are some generalizations of $p$-loxodromic functions and can be represented via the Schottky-Klein prime function as well as classic $p$-loxodromic functions.

Keywords: loxodromic function; $p$-loxodromic function; the Schottky-Klein prime function.

2010 Mathematics Subject Classification: 30D30.   [ Full-text available (PDF) ]   Top of the page.

B.O. Chornomaz, Lower bound on the number of meet-irreducible elements in extremal lattices, P. 26-48.

Extremal lattices are lattices maximal in size with respect to the number $n$ of their join-irreducible elements with bounded Vapnik-Chervonekis dimension $k$. It is natural, however, to estimate the size of a lattice also with respect to the number of its meet-irreducible elements. Although this number may differ for nonequivalent $(n, k+1)$-extremal lattices, we show that each $(n,k+1)$-extremal lattice has $k$ disjoint chains of meet-irreducible elements, each of length $n-k+2$.

Keywords: Extremal lattices; Vapnik-Chervonekis dimension; meet-irreducible elements.

2010 Mathematics Subject Classification: 06B05; 05D99.   [ Full-text available (PDF) ]   Top of the page.

Abdon E. Choque-Rivero, The Kharitonov theorem and robust stabilization via orthogonal polynomials, P. 49-68.

Kharitonov's theorem for interval polynomials is given in terms of orthogonal polynomials on $[0,+\infty)$ and their second kind polynomials. A family of robust stabilizing controls for the canonical system is proposed.

Keywords: Kharitonov theorem; orthogonal polynomials; Hurwitz polynomials; stabilization of control systems.

2010 Mathematics Subject Classification: 34D20; 42C05; 30E05; 93D21.   [ Full-text available (PDF) ]   Top of the page.

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Visnyk Kharkivs'koho natsional'noho universytetu imeni V. N. Karazina, Seriya «Matematyka, prykladna matematyka i mekhanika»

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