https://vestnmath.dnu.dp.ua/index.php/rim/issue/feedResearches in Mathematics2024-01-07T12:30:33+00:00Editorial Mediatorvestmath@mmf.dnu.edu.uaOpen Journal Systems<table><tbody><tr><td><img src="/files/pics/gen_issue_cover.png" alt="" width="100px" height="150px" /></td><td style="padding-left: 16px; vertical-align: top;"><p>The journal publishes, semiannually, research articles in basic areas of theoretical and applied mathematics, including, but not limited to: analysis, algebra, geometry, topology, probability theory and mathematical statistics, differential equations and mathematical physics.</p><p>The journal was published annually from 1963 to 1997 under the title “Researches on modern problems of summation and approximation of functions and their applications” and from 1998 to 2018 under the title “Dnipro University Mathematics Bulletin”.</p><p>Since 2022, the journal has been included to Scopus.</p><p><em>Attention:</em> The template of the submission (.tex and .cls files) was updated on 28.05.2023. Please proceed to <a href="/index.php/rim/about/submissions#authorGuidelines">Author Guidelines</a> to download and use the latest version.</p></td></tr></tbody></table>https://vestnmath.dnu.dp.ua/index.php/rim/article/view/402Preamble2023-12-26T21:05:16+00:00Editors Editorsdnuvestmath@gmail.com2023-12-26T17:03:48+00:00Copyright (c) 2023 Editors Editorshttps://vestnmath.dnu.dp.ua/index.php/rim/article/view/403A Countable Intersection Like Characterization of Star-Lindelöf Spaces2023-12-26T21:05:17+00:00P. Balbalprasenjit177@gmail.comThere have been various studies on star-Lindelöfness but they always explain it in terms of open coverings. So, we have demonstrated in this study a connection between star-Lindelöfness and the family of closed sets that resembles countable intersection property of Lindelöf space. We show that a topological space $$$X$$$ is star-Lindelöf if and only if every closed subset's family of $$$X$$$ not having the modified non-countable intersection property have non-empty intersection.2023-12-26T17:03:49+00:00Copyright (c) 2023 P. Balhttps://vestnmath.dnu.dp.ua/index.php/rim/article/view/404Matroids related to groups and semigroups2023-12-26T21:05:17+00:00D.I. Bezushchakbezushchak@gmail.comMatroid is defined as a pair $$$(X,\mathcal{I})$$$, where $$$X$$$ is a nonempty finite set, and $$$\mathcal{I}$$$ is a nonempty set of subsets of $$$X$$$ that satisfies the Hereditary Axiom and the Augmentation Axiom. The paper investigates for which semigroups (primarily finite) $$$S$$$, the pair $$$(\widehat{S}, \mathcal{I})$$$ will be a matroid.2023-12-26T17:03:49+00:00Copyright (c) 2023 D.I. Bezushchakhttps://vestnmath.dnu.dp.ua/index.php/rim/article/view/405Derivations of rings of infinite matrices2023-12-26T21:05:17+00:00O.O. Bezushchakbezushchak@knu.uaWe describe derivations of several important associative and Lie rings of infinite matrices over general rings of coefficients.2023-12-26T17:03:49+00:00Copyright (c) 2023 O.O. Bezushchakhttps://vestnmath.dnu.dp.ua/index.php/rim/article/view/406On the domains of convergence of the branched continued fraction expansion of ratio $$$H_4(a,d+1;c,d;\mathbf{z})/H_4(a,d+2;c,d+1;\mathbf{z})$$$2023-12-26T21:05:17+00:00R.I. Dmytryshyndmytryshynr@hotmail.comI.-A.V. Lutsivlutsiv.ilona@gmail.comO.S. Bodnarbodnarotern@ukr.net<p>The paper considers the problem of establishing the convergence criteria of the branched continued fraction expansion of the ratio of Horn's hypergeometric functions $$$H_4$$$. To solve it, the technique of expanding the domain of convergence of the branched continued fraction from the known small domain of convergence to a wider domain of convergence is used. For the real and complex parameters of the Horn hypergeometric function $$$H_4$$$, a number of convergence criteria of the branched continued fraction expansion under certain conditions to its coefficients in various unbounded domains of the space have been established.</p>2023-12-26T17:03:50+00:00Copyright (c) 2023 R.I. Dmytryshyn, I.-A.V. Lutsiv, O.S. Bodnarhttps://vestnmath.dnu.dp.ua/index.php/rim/article/view/407On maximality of some solvable and locally nilpotent subalgebras of the Lie algebra $$$W_n(K)$$$2023-12-26T21:05:17+00:00D.I. Efimovdanil.efimov@yahoo.comM.S. Sydorovsmsidorov95@gmail.comK.Ya. Sysaksysakkya@gmail.comLet $$$K$$$ be an algebraically closed field of characteristic zero, $$$P_n=K[x_1,\ldots ,x_n]$$$ the polynomial ring, and $$$W_n(K)$$$ the Lie algebra of all $$$K$$$-derivations on $$$P_n$$$. One of the most important subalgebras of $$$W_n(K)$$$ is the triangular subalgebra $$$u_n(K) = P_0\partial_1+\cdots+P_{n-1}\partial_n$$$, where $$$\partial_i:=\partial/\partial x_i$$$ are partial derivatives on $$$P_n$$$ and $$$P_0=K.$$$ This subalgebra consists of locally nilpotent derivations on $$$P_n.$$$ Such derivations define automorphisms of the ring $$$P_n$$$ and were studied by many authors. The subalgebra $$$u_n(K) $$$ is contained in another interesting subalgebra $$$s_n(K)=(P_0+x_1P_0)\partial_1+\cdots +(P_{n-1}+x_nP_{n-1})\partial_n,$$$ which is solvable of the derived length $$$ 2n$$$ that is the maximum derived length of solvable subalgebras of $$$W_n(K).$$$ It is proved that $$$u_n(K)$$$ is a maximal locally nilpotent subalgebra and $$$s_n(K)$$$ is a maximal solvable subalgebra of the Lie algebra $$$W_n(K)$$$.2023-12-26T17:03:50+00:00Copyright (c) 2023 D.I. Efimov, M.S. Sydorov, K.Ya. Sysakhttps://vestnmath.dnu.dp.ua/index.php/rim/article/view/408Norm attaining bilinear forms of $$${\mathcal L}(^2 d_{*}(1, w)^2)$$$ at given vectors2023-12-26T21:05:17+00:00S.G. Kimsgk317@knu.ac.kr<p>For given unit vectors $$$x_1, \cdots, x_n$$$ of a real Banach space $$$E,$$$ we define $$NA({\mathcal L}(^nE))(x_1, \cdots, x_n)=\{T\in {\mathcal L}(^nE): |T(x_1, \cdots, x_n)|=\|T\|=1\},$$ where $$${\mathcal L}(^nE)$$$ denotes the Banach space of all continuous $$$n$$$-linear forms on $$$E$$$ endowed with the norm $$$\|T\|=\sup_{\|x_k\|=1, 1\leq k\leq n}{|T(x_1, \ldots, x_n)|}$$$.<br />In this paper, we classify $$$NA({\mathcal L}(^2 d_{*}(1, w)^2))(Z_1, Z_2)$$$ for unit vectors $$$Z_1, Z_2\in d_{*}(1, w)^2,$$$ where $$$d_{*}(1, w)^2=\mathbb{R}^2$$$ with the norm of weight $$$0<w<1$$$ endowed with $$$\|(x, y)\|_{d_*(1, w)}=\max\Big\{|x|, |y|, \frac{|x|+|y|}{1+w}\Big\}$$$.</p>2023-12-26T17:03:51+00:00Copyright (c) 2023 S.G. Kimhttps://vestnmath.dnu.dp.ua/index.php/rim/article/view/409Free groups defined by finite $$$p$$$-automata2024-01-07T12:30:33+00:00A.P. Krenevychkrenevych@knu.uaA.S. Oliynykaolijnyk@gmail.comFor every odd prime $$$p$$$ we construct two $$$p$$$-automata with 14 inner states and prove that the group generated by 2 automaton permutations defined at their states is a free group of rank 2.2023-12-26T17:03:51+00:00Copyright (c) 2023 A.P. Krenevych, A.S. Oliynykhttps://vestnmath.dnu.dp.ua/index.php/rim/article/view/410On invariant ideals in group rings of torsion-free minimax nilpotent groups2023-12-26T21:05:17+00:00A.V. TushevAnatolii.Tushev@math.uni-giessen.deLet $$$k$$$ be a field and let $$$N$$$ be a nilpotent minimax torsion-free group acted by a solvable group of operators $$$G$$$ of finite rank. In the presented paper we study properties of some types of $$$G$$$-invariant ideals of the group ring $$$kN$$$.2023-12-26T17:03:51+00:00Copyright (c) 2023 A.V. Tushevhttps://vestnmath.dnu.dp.ua/index.php/rim/article/view/411A Note on Sequence of Functions associated with the Generalized Jacobi polynomial2023-12-26T21:05:17+00:00D. Wagheladivyarwaghela@gmail.comS.B. Raosnehal.b.rao-appmath@msubaroda.ac.inAn attempt is made to introduce and use operational techniques to study about a new sequence of functions containing generalized Jacobi polynomial. Some generating relations, finite summation formulae, explicit representation of a sequence of function $$$S_{n,\tau ,k}^{(\alpha ,\beta ,\gamma ,\delta )} (x;a,u,v)$$$ associated with the generalized Jacobi polynomial $$$P_{n,\,\tau }^{\left( {\alpha ,\,\gamma ,\,\beta } \right)} (x)$$$ have been deduced.2023-12-26T17:03:52+00:00Copyright (c) 2023 D. Waghela, S.B. Rao