Ukrains’kyi Matematychnyi Zhurnal
type: channel
description: Ukrains’kyi Matematychnyi Zhurnal (Ukrainian Mathematical Journal) Editor-in-Chief: A. N. Timokha ISSN: 0041-6053, 1027-3190 Ukrainian Mathematical Journal is published by Springer Nature and Institute of Mathematics of the National Academy of Sciences of Ukraine (est. 1934). The journal is a comprehensive international platform whose aim consists of publishing original research and review articles across various branches of pure and applied mathematics. Submitted manuscripts can be written in either English or Ukrainian. Their single-blind peer review is handled by the Editorial Board. After being accepted, Ukrains’kyi Matematychnyi Zhurnal (est. 1949) publishes the full-scale Ukrainian-language articles and abstracts of English submissions, whereas Ukrainian Mathematical Journal collects and issues, in full, the accepted English-language articles together with the Ukrainian-language manuscript translations. The journal scopes cover but not restricted to the eight main heading: Algebra; ODE & Dynamical Systems; Geometry, Topology & Fractals; Functional Analysis, Operator Theory & PDEs; Theory of Functions; Mathematical Physics; Probability & Statistics; Numerical & Applied Mathematics The authors are obligated to mention one of these heading and the corresponding editor when submitting the manuscript. UMZh indexed in: MathSciNet, zbMATH, Scopus, Web of Science, Google Scholar.
publisher: Institute of Mathematics, NAS of Ukraine
language: en
publication name: Ukrains’kyi Matematychnyi Zhurnal
issn: 1027-3190
items: Kazdan–Warner equation on hypergraphs
items: On the forgotten topological index of signed graphs
items: Coefficient estimates in new subclasses of analytic and bi-univalent functions defined by the combinations of the $q$-derivative and the Sǎlǎgean derivative operator
items: On certain geometric properties and Hardy spaces of generalized Bessel–Wright function
items: PS-lifting modules
items: Carleson measures on Hardy spaces with bicomplex scalars
items: Units in the group algebra $FS_{3}$
items: https://umj.imath.kiev.ua/index.php/umj/article/view/9259
items: Stability of Caputo fractional hyperbolic systems
items: Solutions of a time-asymmetric boundary-value problem for a third-order equation with variable coefficients
items: On the Grüss type inequalities within $p$-disks with applications
items: On the behavior of the modulus of $m$-th derivatives of the algebraic polynomials in the whole complex plane without recurrence formula in the weighted Bergman space
items: Zinbiel superalgebras and superbialgebras
items: Automorphisms and endomorphisms of partitions of topological spaces
items: Groups, rings, and algebras: common strategic approaches and mutual influences
items: Asymptotic behaviour of rapidly varying solutions of a differential equation with rapidly varying nonlinearity
items: Actions of Lie algebra $\mathfrak{sl}_2$ on symmetric polynomials and on Young diagrams
items: Spectral analysis of self-adjoint momentum operators with nonlocal potentials
items: On some classes of non-commutative dimonoids
items: Fusion and specialization for type ADE shuffle algebras
items: Bohr's inequalities associated with the set of all sequences of nonnegative continuous functions
items: Sharp bound for the second Hankel determinant for a $q$-starlike function associated with the $q$-exponential function
items: VITALII PAVLOVYCH MOTORNYI (28.07.1940–21.07.2025)
items: On some properties of the Gram operator
items: Supplement to the article by Douak and Maroni (2020) on a new class of 2-orthogonal polynomials
items: Solvability of linear boundary-value problems for ordinary differential systems in the space $C^{n}$
items: A quadratic completely integrated Burgers-type nonlinear model: conservation laws and Poisson structures
items: Characteristics of equilibrium states in the models of struggle between alternative opponents in the presence of external assistance only to individual players
items: On dynamics of $\lambda + \tan z^2 $
items: Moment inequality, central limit theorem, and the invariance principle for linearly positive quadrant dependent random fields

Kazdan–Warner equation on hypergraphs
type: item
description: UDC 519.17. 519.951 Let $H=(V, E)$ be a connected finite hypergraph, which is an extension of the graph theory in which the edges may connect more than two vertices and form hyperedges. We study the Kazdan-Warner equation\begin{gather*}\Delta \phi=c-he^{\phi}\end{gather*} on $H,$ where $c$ is a constant and $h$ is a known function defined on $H$. Based on the work by Grigor'yan, Lin, and Yang [A. Grigor'yan, Y. Lin, Y. Yang, Kazdan–Warner equation on graph, Calc. Var. Partial Differential Equations, 55, № 4, Article 92 (2016)], we employ the variational calculus to extend the main results concerning the solutions to the Kazdan-Warner equation from finite graphs to hypergraphs. We obtain similar results for the cases where $c>0$ and $c<0$ provided that $h$ satisfies certain conditions on hypergraphs. However, for the case where $c=0,$ we cannot get the same results.
subject: Research articles
  topic: section
subject: Kazdan-Warner equation
  topic: keywords
subject: hypergraph
  topic: keywords
subject: calculus of variations
  topic: keywords
subject: Kazdan-Warner equation
  topic: subjects
subject: hypergraph
  topic: subjects
subject: calculus of variations
  topic: subjects
creator: Haigang Zhang
creator: Juan Zhao
rights: Copyright (c) 2026 Haigang Zhang, Juan Zhao http://creativecommons.org/licenses/by/4.0
date: 2026-01-26
publication date: 2026-01-26
starting page: 91
ending page: 91
doi: 10.3842/umzh.v78i1-2.9163

On the forgotten topological index of signed graphs
type: item
description: UDC 519.17 The forgotten topological index denoted by $F(G)$ of a graph $G=(V,E)$ is defined as follows: $F(G)=\displaystyle\sum\nolimits_{i=1}^{n}\!d_v^3,$ where $d_v$ denotes the degree of the vertex $v.$ We extend the notion of forgotten topological index to signed graphs and introduce the $MS$-index of a signed graph. Moreover, we determine the forgotten topological index for the tensor product, Cartesian product, lexicographic product, strong product, symmetric difference, and the joint of the graphs $G_1$ and $G_2$ in terms of the forgotten topological index, the first Zagreb index, and the $M\kern-1ptS$-index of signed graphs $\Sigma_1=(G_1,\sigma_1)$ and $\Sigma_2=(G_2,\sigma_2),$ along with their sizes and orders.
subject: Research articles
  topic: section
subject: Signed graph
  topic: keywords
subject: graph products
  topic: keywords
subject: first Zagreb index
  topic: keywords
subject: $F$-index
  topic: keywords
subject: $MS$-index
  topic: keywords
subject: $Y$-index
  topic: keywords
creator: Shariefuddin Pirzada
creator: Mir Riyaz Ul Rashid
rights: Copyright (c) 2026 Shariefuddin Pirzada, Mir Riyaz ul Rashid http://creativecommons.org/licenses/by/4.0
date: 2026-01-26
publication date: 2026-01-26
starting page: 89
ending page: 90
doi: 10.3842/umzh.v78i1-2.8298

Coefficient estimates in new subclasses of analytic and bi-univalent functions defined by the combinations of the $q$-derivative and the Sǎlǎgean derivative operator
type: item
description: UDC 517.53 We introduce and study two new subclasses of the function class $\Sigma $ of bi-univalent functions defined in the open unit disk and associated with the Sǎlǎgean and $q$-derivative operators. Furthermore, we find estimates for the Taylor–Maclaurin coefficients $|a_{2}|$ and $|a_{3}|$ of the functions from these new subclasses. The accumulated results are quite interesting and new.
subject: Research articles
  topic: section
subject: Analytic functions
  topic: keywords
subject: Univalent functions
  topic: keywords
subject: Bi-univalent function
  topic: keywords
subject: Coefficient bounds and coefficient estimates
  topic: keywords
subject: q-derivative operator
  topic: keywords
subject: Salagean derivative operator
  topic: keywords
creator: Halit Orhan
rights: Copyright (c) 2026 Halit Orhan http://creativecommons.org/licenses/by/4.0
date: 2026-01-26
publication date: 2026-01-26
starting page: 88
ending page: 88
doi: 10.3842/umzh.v78i1-2.9261

On certain geometric properties and Hardy spaces of generalized Bessel–Wright function
type: item
description: UDC 517.53, 517.58 The main objective of the present research is to examine a specific sufficiency criterion for the pre-starlikeness, strong starlikeness, strong convexity, starlikeness, and convexity of the generalized Bessel–Wright function. Furthermore, we determine the conditions for the generalized Bessel–Wright functions to be included in the Hardy spaces, as well as bounded analytic functions. These applications are given in the form of examples and corollaries.
subject: Research articles
  topic: section
subject: Generalized Bessel-Wright
  topic: keywords
subject: gamma function
  topic: keywords
subject: starlike functions
  topic: keywords
subject: convex functions
  topic: keywords
subject: prestarlike functions
  topic: keywords
subject: strongly starlike functions
  topic: keywords
subject: strongly convex functions
  topic: keywords
subject: Hardy spaces
  topic: keywords
subject: 33C10
  topic: subjects
subject: 30C45
  topic: subjects
subject: 30C50
  topic: subjects
subject: 30H10
  topic: subjects
creator: Muhammad Umar Nawaz
creator: Mohsan Raza
creator: Khaled Mehrez
rights: Copyright (c) 2026 M. U. Nawaz, Mohsan Raza, K. Mehrez http://creativecommons.org/licenses/by/4.0
date: 2026-01-26
publication date: 2026-01-26
starting page: 86
ending page: 87
doi: 10.3842/umzh.v78i1-2.9233

PS-lifting modules
type: item
description: UDC 512.55 Let $R$ be a ring and let $M$ be a left $R$-module. We say that $M$ is {\it ps-lifting} if every submodule $N$ of $M$ contains a direct summand $X$ of $M$ such that $\dfrac{N}{X}$ is projective semisimple. We present some properties of these modules. It is shown that: (1) if a projective module is ps-lifting, then it is hereditary; (2) for a ring $R,$ every left $R$-module is ps-lifting if and only if every $R$-module is a direct sum of an injective module and a projective semisimple module; (3) $_{R}R$ is ps-lifting if and only if $\dfrac{R}{\rm Soc(R)}$ is semisimple and $R$ is hereditary.
subject: Research articles
  topic: section
subject: projective semisimple module, lifting module, projective module
  topic: keywords
subject: Primary 16D10, 16D40, 16D50 16D60, 19a13; Secondary 16D90.
  topic: subjects
creator: Engin Kaynar
rights: Copyright (c) 2026 Engin Kaynar http://creativecommons.org/licenses/by/4.0
date: 2026-01-26
publication date: 2026-01-26
starting page: 84
ending page: 85
doi: 10.3842/umzh.v78i1-2.9247

Carleson measures on Hardy spaces with bicomplex scalars
type: item
description: UDC 517.53 We explore Carleson measures given on the Hardy spaces defined over the bicomplex space and investigate the properties of the bicomplex Toeplitz operator. In the first section, we provide a comprehensive introduction and formulate the key definitions necessary for the subsequent analysis. In the second section, we present the results for $\mathbb{D}$-Carleson measures and establish their relationship with bicomplex Hardy spaces. Finally, in the last section, we extend the concept of the Toeplitz operator to the bicomplex space, thus offering broader prospects.
subject: Research articles
  topic: section
subject: Bicomplex numbers, Carleson measures, Hardy spaces, Holomorphic functions
  topic: keywords
subject: 30G35, 32A30, 32A10
  topic: subjects
creator: Stanzin Dolkar
creator: Sanjay Kumar
rights: Copyright (c) 2026 Stanzin Dolkar, Sanjay Kumar http://creativecommons.org/licenses/by/4.0
date: 2026-01-26
publication date: 2026-01-26
starting page: 82
ending page: 82
doi: 10.3842/umzh.v78i1-2.8614

Units in the group algebra $FS_{3}$
type: item
description: UDC 512.552 We explicitly describe each unit of a group algebra $Z_{p} S_{3}$ for each positive prime $p \geq 5$ by using a characterization of the group algebra of the metacyclic group $G= \langle x,c\colon x^{3}=1,\ c^{n}=1,\ cxc^{-1 } = x^{-1} \rangle$ over the finite field $F$ of characteristic $p,$ where $p$ is a positive prime such that $p \nmid 3n.$ Based on our findings, we pose a conjecture on the number of roots of some explicit polynomials over the prime field $\mathbb{Z}_{p}$ for further academic explorations.
subject: Research articles
  topic: section
subject: Group rings; Unit group; Prime fields; Polynomials.
  topic: keywords
subject: Primary 16U60; Secondary 20C05, 16S34
  topic: subjects
creator: Abhinay Kumar Gupta
creator: R. K. Sharma
rights: Copyright (c) 2026 Abhinay Kumar Gupta, R. K. Sharma http://creativecommons.org/licenses/by/4.0
date: 2026-01-26
publication date: 2026-01-26
starting page: 83
ending page: 83
doi: 10.3842/umzh.v78i1-2.9213

https://umj.imath.kiev.ua/index.php/umj/article/view/9259
type: item
title: Characterization and classification of sigmoid function and generalized discrete probability distributions series defined by Awolere–Oladipo derivative operator in the analytic univalent function space
description: UDC 517.53 The sigmoid function is a special function emulating biological neurons in terms of signal processing or sending alerts to various departments of the brain for responses. It is also good for machine learning, while the generalized discrete probability distribution series is useful for modeling infectious diseases, genetic modeling, clinical trials, risk analysis, optimal pricing, ecological and climatic modeling, and conservation biology. We explore the convex combination and several other types of behaviors of the sigmoid function associated with the generalized discrete probability distribution series in the space of univalent function theory. This is done by introducing and studying a new derivative operator. Several coefficient inequalities and consequences of various choices of the parameters involved are discussed. Graphically, by using the Python software, various convex combinations of $K_{\phi}$ and $g_{\phi}$ are presented in terms of disease and intervention, policy and policy intervention, investment return, disease spread, infection and intervention, free market and intervention, and cost and efficiency relations.
subject: Research articles
  topic: section
subject: Analytic function
  topic: keywords
subject: Generalized distribution series
  topic: keywords
subject: Python
  topic: keywords
subject: Complex Analysis
  topic: subjects
creator: Ibrahim Tunji Awolere
creator: Adeniyi Musibau Gbolagade
creator: Adeniyi Ayeni
creator: Abiodun Tinuoye Oladipo
creator: Şahsene Altınkaya
rights: Copyright (c) 2026 Ibrahim Tunji Awolere, Adeniyi Musibau Gbolagade, Adeniyi Ayeni, Abiodun Tinuoye Oladipo, Şahsene Altınkaya http://creativecommons.org/licenses/by/4.0
date: 2026-01-26
publication date: 2026-01-26
starting page: 80
ending page: 81
doi: 10.3842/umzh.v78i1-2.9259

Stability of Caputo fractional hyperbolic systems
type: item
description: UDC 517.95 We study the problems of well-posedness and stability for fractional linear hyperbolic systems (FLHS) with the Caputo time-fractional derivative. First, the existence and uniqueness are established for the global solution of the FLHS. Then we obtain some polynomial stability results for the FLHS in different Hilbert spaces. Finally, some numerical examples are presented to confirm the theoretical results.
subject: Research articles
  topic: section
subject: Hyperbolic system, Caputo fractional derivative, Polynomial stability, Finite difference scheme
  topic: keywords
creator: Hassen Arfaoui
rights: Copyright (c) 2026 Hassen Arfaoui http://creativecommons.org/licenses/by/4.0
date: 2026-01-26
publication date: 2026-01-26
starting page: 79
ending page: 79
doi: 10.3842/umzh.v78i1-2.7937

Solutions of a time-asymmetric boundary-value problem for a third-order equation with variable coefficients
type: item
description: UDC 517.951 We study a boundary-value problem with asymmetric time conditions for a third-order inhomogeneous equation with multiple characteristics of lowest-order terms. The unique solvability of the problem is proved by the energy-integral method. It is shown that if the uniqueness condition is violated, then the homogeneous problem has a nontrivial solution. The existence is proved by the Fourier method. The solution of the stated problem is obtained in the explicit form by using the constructed Green's function. The uniform convergence of the solutions and their derivatives contained in the equation is proved.
subject: Research articles
  topic: section
subject: Differential equation, third order, multiple characteristics, asymmetric boundary value problem, regular solution, uniqueness, existence, Green’s function.
  topic: keywords
creator: Yusupjon Apakov
creator: Raxmatilla Umarov
rights: Copyright (c) 2026 Yusupjon Apakov, Raxmatilla Umarov http://creativecommons.org/licenses/by/4.0
date: 2026-01-26
publication date: 2026-01-26
starting page: 77
ending page: 78
doi: 10.3842/umzh.v78i1-2.8975

On the Grüss type inequalities within $p$-disks with applications
type: item
description: UDC 517.5 We extend the classical Gr\"{u}ss inequality from Euclidean disks in $\mathbb{R}^2$ to generalized $p$-disks and present rigorous formulations for functions satisfying H\"{o}lder-type conditions. Several new Gr\"{u}ss-type inequalities are established and applied to establish bounds for the covariance of random variables defined either by probability density functions or by joint distributions.
subject: Research articles
  topic: section
subject: Gr\
  topic: keywords
subject: p-circle
  topic: keywords
subject: Generalized Trigonometric Functions
  topic: keywords
subject: Analysis
  topic: subjects
subject: Inequalities
  topic: subjects
subject: Function Teory
  topic: subjects
creator: Mohammad W. Alomari
rights: Copyright (c) 2026 Mohammad W. Alomari http://creativecommons.org/licenses/by/4.0
date: 2026-01-26
publication date: 2026-01-26
starting page: 75
ending page: 76
doi: 10.3842/umzh.v78i1-2.6690

On the behavior of the modulus of $m$-th derivatives of the algebraic polynomials in the whole complex plane without recurrence formula in the weighted Bergman space
type: item
description: UDC 517.5 We study the problem of growth of the $m$th derivatives of an arbitrary algebraic polynomial in weighted Bergman spaces in unbounded domains of the complex plane, without using the recurrence relation. We consider $k$-quasidisks and quasidisks with some additional functional conditions. These conditions enable us to combine several known classes of curves into a single class and obtain estimates for the growth of $m$th derivatives in this common class. By using similar estimates obtained for bounded quasidisks, we also provide estimates valid in the whole complex plane.
subject: Research articles
  topic: section
subject: Bernstein-Markoff inequality, Walsh inequality, Algebraic polynomial, Quasiconformal mapping, Quasicircle,
  topic: keywords
subject: 30C30, 30E10, 30C70.
  topic: subjects
creator: F. G. Abdullayev
creator: M. Imashkyzy
rights: Copyright (c) 2026 F. G. Abdullayev, M. Imashkyzy http://creativecommons.org/licenses/by/4.0
date: 2026-01-26
publication date: 2026-01-26
starting page: 71
ending page: 72
doi: 10.3842/umzh.v78i1-2.8778

Zinbiel superalgebras and superbialgebras
type: item
description: UDC 512.5 In the present paper, we propose and study a new structure of the Zinbiel superalgebras. Moreover, we define dual bimodules and matched pairs. In addition, we establish a relationship between the dual bimodules of Zinbiel superalgebras and the matched pairs of Lie speralgebras. Furthermore, we examine the Manin triples of Zinbiel superalgebras. Finally, we present the theorem that establishes the links between the matched pairs of Zinbiel superalgebras, the Zinbiel superbialgebras, and the matched pairs of subadjacent Lie superalgebras.
subject: Research articles
  topic: section
subject: Zinbiel superalgebras; Lie supercoalgebras; bialgebras; Bimodule;Matched pair.
  topic: keywords
creator: Boujemaa Agrebaoui
creator: Imed Basdouri
creator: Jebli Mohamed Eljoudi
rights: Copyright (c) 2026 Boujemaa Agrebaoui, Imed Basdouri, Jebli Mohamed Eljoudi http://creativecommons.org/licenses/by/4.0
date: 2026-01-26
publication date: 2026-01-26
starting page: 73
ending page: 74
doi: 10.3842/umzh.v78i1-2.7938

Automorphisms and endomorphisms of partitions of topological spaces
type: item
description: UDC 515.1 Let $X$ be a topological space, let $\Delta$ be a partition of $X$, and let $Y =X/\Delta$ be a quotient space with the corresponding quotient topology. Then the automorphism group $\mathcal{H}(\Delta)$ of $\Delta$ (i.e., the homeomorphisms of $X,$ which permute the elements of partition) acts in a natural way upon $Y$ by homeomorphisms. We determine the cases in which the corresponding homomorphism of the action $\psi\colon\mathcal{H}(\Delta) \to \mathcal{H}(Y)$ into the group of homeomorphisms of $Y$ is continuous with respect to the compact-open topologies. The obtained results have applications to the foliation theory.
subject: Research articles
  topic: section
subject: фактор-простір
  topic: keywords
subject: компактно-відкрита топологія
  topic: keywords
subject: точка розгалуження
  topic: keywords
subject: компактно-накриваюче відображення
  topic: keywords
subject: локальна компактність
  topic: keywords
subject: гомоморфізм дії
  topic: keywords
creator: S. Maksymenko
creator: E. Polulyakh
rights: Copyright (c) 2026 S. Maksymenko, E. Polulyakh http://creativecommons.org/licenses/by/4.0
date: 2026-01-26
publication date: 2026-01-26
starting page: 47
ending page: 70
doi: 10.3842/umzh.v78i1-2.8932

Groups, rings, and algebras: common strategic approaches and mutual influences
type: item
description: UDC 512.5 We focus on recent promising trends in the application of the key concepts and approaches from the classical infinite-group theory to various branches of algebra, such as modules over group rings, infinite-dimensional linear groups, Leibniz algebras, other generalizations of the Lie algebras, and braces. The efficacy of these trends has been well-documented in a series of recent books from reputable publishers. In our article, we present a concise overview of these emerging trends. The analysis of the mutual influence of algebraic systems promotes deeper understanding of their individual and collective significance and illustrates the unity and diversity typical of contemporary mathematics. We believe that the subsequent development of investigations in this field would promote the appearance of new discoveries and innovations clarifying the fundamental role played by the groups, rings, algebras and other algebraic structures in modern mathematics.
subject: Research articles
  topic: section
subject: algebra
  topic: keywords
subject: brace
  topic: keywords
subject: group
  topic: keywords
subject: ring
  topic: keywords
subject: module
  topic: keywords
creator: M. Dixon
creator: M. Semko
creator: I. Subbotin
rights: Copyright (c) 2026 M. Dixon, M. Semko, I. Subbotin http://creativecommons.org/licenses/by/4.0
date: 2026-01-26
publication date: 2026-01-26
starting page: 38
ending page: 46
doi: 10.3842/umzh.v78i1-2.8953

Asymptotic behaviour of rapidly varying solutions of a differential equation with rapidly varying nonlinearity
type: item
description: UDC 517.925 We study the asymptotic behavior of one class of solutions for a two-term nonautonomous ordinary differential equation of the fourth order with rapidly varying nonlinearity.
subject: Research articles
  topic: section
subject: неавтономні диференціальні рівняння, експоненціальна нелінійність, $P_\omega(Y_0,\lambda_0)$- розв'язки, асимптотична поведінка $P_\omega(Y_0,\lambda_0)$- розв'язків
  topic: keywords
subject: Диференціальні рівняння
  topic: subjects
creator: S. Golubev
rights: Copyright (c) 2026 S. Golubev http://creativecommons.org/licenses/by/4.0
date: 2026-01-26
publication date: 2026-01-26
starting page: 22
ending page: 37
doi: 10.3842/umzh.v78i1-2.9005

Actions of Lie algebra $\mathfrak{sl}_2$ on symmetric polynomials and on Young diagrams
type: item
description: UDC 512.81 We propose two realizations of representations of the complex Lie algebra $\mathfrak{sl}_2$ on the algebra of symmetric polynomials $\Lambda_n$ by differential operators. For each of these realizations, the actions on Schur polynomials are determined and the decomposition of $\Lambda_n$ into irreducible representations is obtained. By using the $\mathfrak{sl}_2$-isomorphism between $\Lambda_n$ and the vector space of Young diagrams $\mathbb{Q}\mathcal{Y}_n$ with at most $n$ rows, these representations are transferred to $\mathbb{Q}\mathcal{Y}_n.$
subject: Research articles
  topic: section
subject: Lie algebra $\mathfrak{sl}_2$
  topic: keywords
subject: representations of $\mathfrak{sl}_2$
  topic: keywords
subject: symmetric polynomials
  topic: keywords
subject: Schur polynomials
  topic: keywords
subject: Young diagrams
  topic: keywords
creator: L. Bedratyuk
rights: Copyright (c) 2026 L. Bedratyuk http://creativecommons.org/licenses/by/4.0
date: 2026-01-26
publication date: 2026-01-26
starting page: 3
ending page: 21
doi: 10.3842/umzh.v78i1-2.8860

Spectral analysis of self-adjoint momentum operators with nonlocal potentials
type: item
description: UDC 517.98 Dedicated with great pleasure to Prof. Leonid P. Nizhnik on the occasion of his 90th birthday. We construct and present a detailed study of self-adjoint operators of momentum and their perturbations by nonlocal potentials on the entire axis with one limit point and on a finite interval. The domain of definition of these perturbed self-adjoint operators is described by extended homogeneous boundary conditions, which contain not only boundary values of the function but also linear functionals of functions in the entire domain of their definition. The spectral properties of exactly solvable models of this kind are investigated.
subject: Research articles
  topic: section
subject: condition for self--adjointness, resolvent structure, eigenvalues
  topic: keywords
subject: momentum operator, differential operator,
  topic: keywords
subject: condition for self--adjointness, resolvent structure, eigenvalues
  topic: subjects
subject: momentum operator, differential operator
  topic: subjects
creator: K. Dȩbowska
creator: I. Nizhnik
rights: Copyright (c) 2025 Каміла Дембовська, Ірина Нижник http://creativecommons.org/licenses/by/4.0
date: 2025-11-14
publication date: 2025-11-14
starting page: 715
ending page: 742
doi: 10.3842/umzh.v77i12.9415

On some classes of non-commutative dimonoids
type: item
description: UDC 512.53 We study dimonoids, i.e., algebraic structures with two associative binary operations satisfying a given system of axioms. We analyze the properties of dual dimonoids. In the class of non-commutative dimonoids, we construct numerous Abelian, non-Abelian, and rectangular dimonoids. The structure of these objects is analyzed, their automorphism groups and halos are computed.
subject: Research articles
  topic: section
subject: напівгрупа, дімоноїд, група автоморфізмів
  topic: keywords
subject: напівгрупа, дімоноїд, група автоморфізмів
  topic: subjects
creator: V. Gavrylkiv
rights: Copyright (c) 2025 Володимир Гаврилків http://creativecommons.org/licenses/by/4.0
date: 2025-11-14
publication date: 2025-11-14
starting page: 703
ending page: 714
doi: 10.3842/umzh.v77i12.9209

Fusion and specialization for type ADE shuffle algebras
type: item
description: UDC 512.5 Root vectors in quantum groups (of finite type) are generalized to fused currents in quantum loop groups [J. Ding, S. Khoroshkin, Transform. Groups, 5, №1, 35–59 (2000)]. We construct fused currents as duals to specialization maps of the corresponding shuffle algebras [B. Enriquez, Transform. Groups, 5, №2, 111–120 (2000), B. Enriquez, J. Lie Theory, 13, №1, 21–64 (2003), and B. Feigin, A. Odesskii, NATO Sci., Ser. II, Math. Phys. Chem., 35 (2001)] for the ADE types; an approach, which has a potential for generalization to arbitrary Kac–Moody types. Both root vectors and fused currents depend on a convex order of the positive roots and, in the present paper, we choose the Auslander–Reiten order [C. Ringel, J. reine und angew. Math., 470, 51–88 (1996)] corresponding to the orientation of the ADE-type Dynkin diagram.
subject: Research articles
  topic: section
subject: quantum groups
  topic: keywords
subject: fused currents
  topic: keywords
subject: shuffle algebras
  topic: keywords
subject: quantum groups
  topic: subjects
subject: Hall algebras
  topic: subjects
subject: shuffle algebras
  topic: subjects
subject: fused currents
  topic: subjects
subject: Auslander-Reiten order
  topic: subjects
creator: Andrei Neguţ
creator: Alexander Tsymbaliuk
rights: Copyright (c) 2025 Andrei Neguţ, Alexander Tsymbaliuk http://creativecommons.org/licenses/by/4.0
date: 2025-11-14
publication date: 2025-11-14
starting page: 746
ending page: 747
doi: 10.3842/umzh.v77i12.9264

Bohr's inequalities associated with the set of all sequences of nonnegative continuous functions
type: item
description: UDC 517.5 We establish several sharp versions of Bohr's inequalities for the class of $K$-quasiconformal sense-preserving harmonic mappings on the unit disk $\mathbb{D} := \{z \in \mathbb{C}\colon |z| < 1\}$ by using a sequence $\{\Psi_n(r)\}_{n=0}^\infty$ of nonnegative continuous functions defined on $[0,1)$ and such that the series $\sum_{n=0}^\infty \Psi_n(r)$ converges locally uniformly in $[0,1).$ As an application, we deduce several well-known results, as well as numerous improved and refined Bohr's inequalities for harmonic mappings in the unit disk $\mathbb{D}.$
subject: Research articles
  topic: section
subject: Harmonic mappings
  topic: keywords
subject: locally univalent functions
  topic: keywords
subject: Bohr inequality
  topic: keywords
subject: K-quasiconformal mappings
  topic: keywords
subject: 30B10
  topic: subjects
subject: 30C62
  topic: subjects
subject: 30C75
  topic: subjects
subject: 40A30
  topic: subjects
subject: 30A10
  topic: subjects
creator: Raju Biswas
creator: Rajib Mandal
rights: Copyright (c) 2025 Raju Biswas, Rajib Mandal http://creativecommons.org/licenses/by/4.0
date: 2025-11-14
publication date: 2025-11-14
starting page: 743
ending page: 744
doi: 10.3842/umzh.v77i12.9269

Sharp bound for the second Hankel determinant for a $q$-starlike function associated with the $q$-exponential function
type: item
description: UDC 517.5 We determine the sharp bound of the second-order Hankel determinant $H_{2,2}(f)$ and the coefficient functional for functions from the class of $q$-starlike functions $ \mathcal{S}^*(\mathcal{L},q)$ by refining the results obtained in [Srivastava et al., Upper bound of the third Hankel determinant for a subclass of $q$-starlike functions associated with the $q$-exponential function, Bull. Sci. Math., 167 (2021); https://doi.org/10.1016/j.bulsci.2020.102942]. Moreover, we obtain sharp estimates for the Fekete–Szegö functional and the coefficient differences for the analyzed class of functions.
subject: Research articles
  topic: section
subject: Analytic functions
  topic: keywords
subject: q-derivative
  topic: keywords
subject: Hankel determinant
  topic: keywords
subject: q starlike functions
  topic: keywords
subject: q-exponential function.
  topic: keywords
subject: 30C45
  topic: subjects
subject: 30C50
  topic: subjects
creator: Karri Sanjay Kumar
rights: Copyright (c) 2025 Karri Sanjay Kumar http://creativecommons.org/licenses/by/4.0
date: 2025-11-14
publication date: 2025-11-14
starting page: 745
ending page: 745
doi: 10.3842/umzh.v77i12.9106

VITALII PAVLOVYCH MOTORNYI (28.07.1940–21.07.2025)
type: item
subject: Research articles
  topic: section
subject: -
  topic: keywords
creator: O. M. Tymokha, V. L. Makarov, I. O. Shevchuk, V. Ya. Gutlyanskii, V. F. Babenko, S. B. Vakarchuk, O. V. Davydov, V. A. Kofanov, N. V. Parfinovych, A. S. Romanyuk, A. S. Serdyuk, I. V. Sokolenko
rights: Copyright (c) 2026 O. M. Tymokha, V. L. Makarov, I. O. Shevchuk, V. Ya. Gutlyanskii, V. F. Babenko, S. B. Vakarchuk, O. V. Davydov, V. A. Kofanov, N. V. Parfinovych, A. S. Romanyuk, A. S. Serdyuk, I. V. Sokolenko http://creativecommons.org/licenses/by/4.0
license: http://creativecommons.org/licenses/by/4.0
date: 2026-01-26
publication date: 2026-01-26
starting page: 92
ending page: 96
doi: 10.3842/umzh.v78i1-2.9700

On some properties of the Gram operator
type: item
description: UDC 512.552.4 The $G$-construction allows us to obtain a system of subspaces using an abstract Gram operator. Any system of subspaces is unitarily equivalent to a system constructed by using this method. We propose another construction of a system of subspaces with the same property, provide criteria for the unitary equivalence of a pair of systems of subspaces in terms of the corresponding Gram operators, and study the problem of irreducibility of a system of subspaces in terms of the corresponding Gram operator. In addition, we provide an example illustrating how the obtained results apply to the study of a certain class of the systems of subspaces.
subject: Research articles
  topic: section
subject: systems of subspaces
  topic: keywords
subject: Gram operator
  topic: keywords
subject: Hilbert space
  topic: keywords
subject: orthogonal projector
  topic: keywords
creator: O. Strilets
rights: Copyright (c) 2025 O. Strilets http://creativecommons.org/licenses/by/4.0
date: 2025-11-07
publication date: 2025-11-07
starting page: 214
ending page: 227
doi: 10.3842/umzh.v77i3.8685

Supplement to the article by Douak and Maroni (2020) on a new class of 2-orthogonal polynomials
type: item
description: UDC 510 We consider some issues related to the 2-orthogonal polynomials (2-OP). The answers to these issues can be regarded a supplement to the article [K. Douak, P. Maroni, On a new class of 2-orthogonal polynomials, I: The recurrence relations and some properties, Integral Transform and Special Functions (2020)]. The conditions imposed on the parameters of two original recurrence relations (the first of these conditions is for the 2-OP, while the second condition is for their normalized derivatives) and guaranteeing the ``"classical" nature of the 2-OP in Hahn's sense are clarified. It is constructively proved that these recurrence relations do not cover all possible "classical" 2-OPs. An example of ``"classical" 2-OP generated by the generating function constructed by using a Bessel function of the first kind of order zero is presented. These OPs are unique because their properties are similar to the classical OPs. In particular, this concerns the fact that their zeros are real and their location. The analysis of the available literature and our own numerous numerical-analytic experiments reveals the absence of other examples of the ``"classical" 2-OPs with similar properties.
subject: Research articles
  topic: section
subject: 2-orthogonal polynomials, 2-orthogonal polynomials, generating function, recurrence relation, ``classical'' 2-orthogonal polynomials, differential equation, zeros of orthogonal polynomials.
  topic: keywords
creator: V. Makarov
rights: Copyright (c) 2025 V. Makarov http://creativecommons.org/licenses/by/4.0
date: 2025-11-07
publication date: 2025-11-07
starting page: 200
ending page: 205
doi: 10.3842/umzh.v77i3.8898

Solvability of linear boundary-value problems for ordinary differential systems in the space $C^{n}$
type: item
description: UDC 517.927 We study linear boundary-value problems for systems of first-order ordinary differential equations with the most general boundary conditions in the normed spaces of continuously differentiable functions on a finite closed interval. The boundary conditions are allowed to be overdetermined or underdetermined with respect to the differential system and may contain arbitrary derivatives of the unknown functions. We prove that the problem operator is Fredholm on appropriate pairs of normed spaces, find its index and $d$-characteristics, and prove the limit theorems for sequences of characteristic matrices of the investigated boundary-value problems and $d$-characteristics of the corresponding Fredholm operators.
subject: Research articles
  topic: section
subject: Inhomogeneous boundary-value problems
  topic: keywords
subject: Fredholm operator
  topic: keywords
subject: Fredholm numbers of an operator
  topic: keywords
subject: spaces of smooth functions
  topic: keywords
creator: V. Soldatov
rights: Copyright (c) 2025 V. Soldatov http://creativecommons.org/licenses/by/4.0
date: 2025-11-07
publication date: 2025-11-07
starting page: 206
ending page: 213
doi: 10.3842/umzh.v77i3.8940

A quadratic completely integrated Burgers-type nonlinear model: conservation laws and Poisson structures
type: item
description: UDC 517.9 We study the complete integrability of a Burgers-type nonlinear quadratic dynamical system on a functional manifold. For this system, we prove the existence of an infinite hierarchy of functionally independent and involutive conservation laws and determine a compatible pair of Poisson operators, which allows us to rewrite the analyzed system in the bi-Hamiltonian form. We also construct a recursion operator generating an infinite hierarchy of commuting vector fields on a functional manifold.
subject: Research articles
  topic: section
subject: нелiнiйна динамiчна система, закони збереження, асимптотичний аналiз, пуассоновi структури, бiгамiльтоновiсть, iнтегровнiсть, рекурсiйний оператор.
  topic: keywords
creator: Ya. Kokovska
creator: M. Prytula
rights: Copyright (c) 2025 Ya. Kokovska, M. Prytula http://creativecommons.org/licenses/by/4.0
date: 2025-11-07
publication date: 2025-11-07
starting page: 187
ending page: 199
doi: 10.3842/umzh.v77i3.8670

Characteristics of equilibrium states in the models of struggle between alternative opponents in the presence of external assistance only to individual players
type: item
description: UDC 517.9 We determine the characteristics (type, number, position in the phase portrait, and stability) of the equilibrium states of a dynamical system simulating the competition between individuals in an abstract society a part of which receives external assistance. By analyzing a system with three individuals as an example, we determine the detailed description of the dependence of phase portrait of the system on the values of the parameter of assistance and its bifurcation thresholds for two cases where assistance is provided only to one or to two players. For possible applications, we propose an interpretation of the equilibrium states as compromises in the conflict competition of social clusters.
subject: Research articles
  topic: section
subject: dynamical system, equilibrium states, difference equations, stability
  topic: keywords
creator: T. Karataieva
creator: V. Koshmanenko
rights: Copyright (c) 2025 T. Karataieva, V. Koshmanenko http://creativecommons.org/licenses/by/4.0
date: 2025-11-07
publication date: 2025-11-07
starting page: 163
ending page: 186
doi: 10.3842/umzh.v77i3.8711

On dynamics of $\lambda + \tan z^2 $
type: item
description: UDC 517.9 We propose a new family of transcendental meromorphic functions $\lambda + \tan z^2$ for $ \lambda \in \mathbb C$ and study the dynamics of the family of functions. We explore both the dynamical plane ($z$-plane) and the parameter plane ($\lambda$-plane). We show that, in the dynamical plane, there are no Herman rings, and the Julia set forms a Cantor set when the parameter lies within the unbounded hyperbolic components. In addition, it is proved that these unbounded hyperbolic components are the only available components distributed over the four quadrants of the parameter space in the complex plane. Conversely, it is shown that the Julia set is connected for the maps whose parameter lies within the remaining hyperbolic components of the parameter space. We also perform the comprehensive analysis of the combinatorial structure of both the parameter space and the dynamical plane for this family of transcendental meromorphic maps.
subject: Research articles
  topic: section
subject: Primary 37F10 , Secondary 30D05
  topic: keywords
creator: Santanu Nandi
rights: Copyright (c) 2025 Santanu Nandi http://creativecommons.org/licenses/by/4.0
date: 2025-11-07
publication date: 2025-11-07
starting page: 235
ending page: 236
doi: 10.3842/umzh.v77i3.8365

Moment inequality, central limit theorem, and the invariance principle for linearly positive quadrant dependent random fields
type: item
description: UDC 519.21 We obtain the moment inequality by considering the central limit theorem for the sums of linearly positive quadrant dependent random fields when the covariance satisfies certain conditions. Applying this moment inequality, we prove the invariance principle.
subject: Research articles
  topic: section
subject: moment inequality, central limit theorem, linearly positive quadrant dependent random fields, invariance principle.
  topic: keywords
creator: Abdurakhman Mukhamedov
rights: Copyright (c) 2025 Abdurakhman Mukhamedov http://creativecommons.org/licenses/by/4.0
date: 2025-11-07
publication date: 2025-11-07
starting page: 234
ending page: 234
doi: 10.3842/umzh.v77i3.8385