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: A method for the construction of exact solutions to the nonlinear heat equation $u_t = \left(F(u)u_x \right)_x +G(u)u_x +H(u)$
items: A problem of extreme decomposition of the complex plane with free poles
items: On the stability of the equilibrium state of a rigid body with a multilayer ideal fluid separated by elastic plates
items: A note on variational formalism for sloshing with rotational flows in a rigid tank with an unprescribed motion
items: Mathematical problems of thermomechanics for deformable bodies under thermal irradiation
items: Integral equation of elastic medium containing a deformable thread-like inclusion
items: Reduction of the two-dimensional thermoelasticity problems for solids with corner points to key integrodifferential equations
items: On a particular case of motion in the three-body problem
items: Asymptotic stabilization of a flexible beam with an attached mass
items: Review of researches on mathematical problems of mechanics and control theory at Institute of Mathematics NAS of Ukraine
items: Structure of integrals of equations of oscillations of a conical shell closed at a vertex
items: Weighted damping of external and initial disturbances in descriptor control systems
items: Fatou and Julia like sets
items: On $\Pi$-permutable subgroups in finite groups
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: 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: Carleson measures on Hardy spaces with bicomplex scalars
items: PS-lifting modules
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

A method for the construction of exact solutions to the nonlinear heat equation $u_t = \left(F(u)u_x \right)_x +G(u)u_x +H(u)$
type: item
description: UDC 517.9 We propose a method for the construction of exact solutions to the nonlinear heat equation based on the classical method of separation of variables and its generalization. We consider substitutions used to reduce the nonlinear heat equation to a system of two ordinary differential equations and construct the classes of exact solutions by the method of generalized separation of variables.
subject: Research articles
  topic: section
creator: T. A. Barannyk
creator: A. F. Barannyk
creator: I. I. Yuryk
rights: Copyright (c) 2019 Barannyk T. A.; Barannyk A. F.; Yuryk I. I.
date: 2026-02-09
publication date: 2026-02-09
starting page: 1443
ending page: 1454
doi: 10.3842/umzh.v71i11.1527

A problem of extreme decomposition of the complex plane with free poles
type: item
description: UDC 517.54 We study a problem of nonoverlapping domains with free poles on radial systems. Our main results strengthen and generalize several known results obtained in the investigation of this problem.
subject: Research articles
  topic: section
creator: A. K. Bakhtin
rights: Copyright (c) 2019 Bakhtin A. K.
date: 2026-02-09
publication date: 2026-02-09
starting page: 1299
ending page: 1320
doi: 10.3842/umzh.v71i10.1516

On the stability of the equilibrium state of a rigid body with a multilayer ideal fluid separated by elastic plates
type: item
description: UDC 531.36:531.38:533.6.013.42 L. N. Stretensky’s problem and the problem of physical pendulum oscillations are generalized to the case of a multilayer ideal fluid separated by elastic plates. Assuming the positive definiteness of the potential energy (L. N. Stretensky’s problem) and changed potential energy (the physical pendulum), we obtain the conditions of stability for the equilibrium state in these problems. A more detailed study is performed in the case of a cylindrical cavity of arbitrary cross-section. We show that for the stability of the equilibrium state in L. N. Stretensky’s problem it is necessary and sufficient that there exists a stable equilibrium state of the elastic plates and liquid in the stationary rigid body and it is sufficient that a heavier liquid is located below a lighter one. For the stability of the equilibrium state in the problem of physical pendulum oscillations, it is also necessary that there is a stable equilibrium state of the elastic plates and liquid in the stationary rigid body. It is also shown that we can use pre-tensioning of plates to stabilize an unstable equilibrium position of the physical pendulum.
subject: Research articles
  topic: section
subject: багатошарова ідеальна рідина, пружні пластини, стійкість положення рівноваги
  topic: keywords
creator: Yu. M. Kononov
rights: Copyright (c) 2021 Юрій Микитович Кононов
date: 2026-02-09
publication date: 2026-02-09
starting page: 1342
ending page: 1354
doi: 10.37863/umzh.v73i10.6840

A note on variational formalism for sloshing with rotational flows in a rigid tank with an unprescribed motion
type: item
description: UDC 517.9 The Bateman – Luke-type variational formulation of the free-boundary ‘sloshing’ problem is generalized to irrotational flows and unprescribed tank motions, i.e., to the case where both the tank and liquid motions should be found simultaneously for a given set of external forces applied to fixed points of the rigid tank body. We prove that the variational equation, which corresponds to the formulated problem, implies both the dynamic (force and moment) equations of the rigid body and the free-boundary problem, which describes sloshing in terms of the Clebsch potentials.
subject: Research articles
  topic: section
subject: sloshing
  topic: keywords
subject: rotational flows
  topic: keywords
subject: variational formalism
  topic: keywords
creator: I. A. Lukovsky
creator: A. N. Timokha
rights: Copyright (c) 2021 Олександр Миколайович Тимоха, Іван Олександрович Луковський
date: 2026-02-09
publication date: 2026-02-09
starting page: 1368
ending page: 1376
doi: 10.37863/umzh.v73i10.6795

Mathematical problems of thermomechanics for deformable bodies under thermal irradiation
type: item
description: UDC 535.51, 535.55, 539.3 It is a review of the results of researches in the field of mathematical problems of the thermomechanics of magnetizable and polarizable electroconductive deformable bodies under electromagnetic irradiation, which are carried out at Ya. S. Pidstryhach Institute for Applied Problems of Mechanics and Mathematics, NAS of Ukraine. In this paper, we formulate the problems of mathematical physics that describe the thermal and thermal stress state in such bodies taking into account the peculiarities of electromagnetic action in different frequency ranges and analyze the methods of study of the thermomechanical behavior of bodies (in particular, of different transparency, as semitransparent as well as opaque) in these ranges under thermal irradiation.
subject: Research articles
  topic: section
subject: deformable body
  topic: keywords
subject: electromagnetic field
  topic: keywords
subject: thermal radiation
  topic: keywords
subject: magnetization
  topic: keywords
subject: polarization
  topic: keywords
subject: radiation heat transfer
  topic: keywords
subject: thermal stresses
  topic: keywords
subject: mathematical problems
  topic: keywords
creator: O. R. Hachkevych
creator: R. M. Kushnir
creator: R. F. Terletskii
rights: Copyright (c) 2021 О. Р. Гачкевич , Р. М. Кушнір , Р. Ф. Терлецький
date: 2026-02-09
publication date: 2026-02-09
starting page: 1317
ending page: 1329
doi: 10.37863/umzh.v73i10.6787

Integral equation of elastic medium containing a deformable thread-like inclusion
type: item
description: UDC 517.968.23: 539.3 In this study, we propose a method of mathematical modeling of deformable thread-like (wire) inclusions based on replacing their influence on the elastic medium with the tension/compression forces distributed along their axis. We derive a regularized integral equation of the problem, which is external with respect to the inhomogeneity, and also a mathematical model of inhomogeneity, which, taking into account the contact conditions, makes it possible to determine the desired distribution of forces along the axis of inhomogeneity. An approach to solving these equations is proposed. For the case of a rectilinear elastic thread-like inclusion, an approximate solution of the problem is obtained in a close analytical form.
subject: Research articles
  topic: section
subject: thread-like inclusion
  topic: keywords
subject: integral equation
  topic: keywords
subject: regularization
  topic: keywords
creator: Ia. M. Pasternak
creator: H. T. Sulym
rights: Copyright (c) 2021 Ярослав Пастернак, Георгій Сулим
date: 2026-02-09
publication date: 2026-02-09
starting page: 1391
ending page: 1403
doi: 10.37863/umzh.v73i10.6785

Reduction of the two-dimensional thermoelasticity problems for solids with corner points to key integrodifferential equations
type: item
description: UDK 539.3 A generalization of the direct integration method is given with regard to solving the original equations of two-dimensional thermoelasticity problems for solids with corner points (i.e., plane problems for a rectangular domain and an annular sector and the axisymmetric problem for a solid cylinder of finite length). The problems are thereby reduced to a governing integrodifferential equation for a key function, which is unique for each problem. By making use of equilibrium equations, the expressions for stress-tensor components are derived in terms of the key function, while the complete sets of boundary conditions are identically reduced to the corresponding sets of integral conditions for the key function. The algorithms for separating variables in the derived governing equations are suggested by utilizing the complete sets of the eigen- and associated functions in order to construct the solutions to the formulated problems in the form of explicit dependencies on thermal loading in view of the boundary conditions.
subject: Research articles
  topic: section
subject: direct integration method
  topic: keywords
subject: analytical solutions
  topic: keywords
subject: two-dimensional problems
  topic: keywords
subject: rectangular domain
  topic: keywords
subject: annular sector
  topic: keywords
subject: finite-length cylinder
  topic: keywords
subject: integro-differential equations
  topic: keywords
creator: R. M. Kushnir
creator: Yu. V. Tokovyi
creator: M. Y. Yuzvyak
creator: A. V. Yasinskyi
rights: Copyright (c) 2021 Роман Кушнір, Yuriy Tokovyy, Микола Юзв'як, Анатолій Ясінський
date: 2026-02-09
publication date: 2026-02-09
starting page: 1355
ending page: 1367
doi: 10.37863/umzh.v73i10.6784

On a particular case of motion in the three-body problem
type: item
description: UDC 531.36; 531.011 We study the three-body problem in a particular case where two bodies have equal masses, which implies the existence of a manifold of symmetric motions. We are looking for the conditions of existence of bounded (unbounded) symmetric motions. Our analysis of boundedness (unboundedness) of motions shows that both the structure of the manifold of symmetrical motions and the integrals of energy and angular momentum are essential.
subject: Research articles
  topic: section
subject: Symmetrical motion, a Hill stable pair, distal motion, bounded motion
  topic: keywords
creator: S. P. Sosnyts’kyi
rights: Copyright (c) 2021 Stepan
date: 2026-02-09
publication date: 2026-02-09
starting page: 1404
ending page: 1413
doi: 10.37863/umzh.v73i10.6756

Asymptotic stabilization of a flexible beam with an attached mass
type: item
description: UDC 517.977 A mathematical model of a simply supported Euler – Bernoulli beam with attached spring-mass system is considered. The model is controlled by distributed piezo actuators and a lumped force. We address the issue of asymptotic behavior of solutions of this system driven by a linear feedback law. The precompactness of trajectories is established for the operator formulation of the closed-loop dynamics. Sufficient conditions for strong asymptotic stability of the trivial equilibrium are obtained.
subject: Research articles
  topic: section
subject: Euler--Bernoulli beam; stabilization; asymptotic stability; Lyapunov functional
  topic: keywords
creator: J. I. Kalosha
creator: A. L. Zuyev
rights: Copyright (c) 2021 Юлія Калоша, Олександр Леонідович Зуєв
date: 2026-02-09
publication date: 2026-02-09
starting page: 1330
ending page: 1341
doi: 10.37863/umzh.v73i10.6750

Review of researches on mathematical problems of mechanics and control theory at Institute of Mathematics NAS of Ukraine
type: item
description: We present a review of researches on mathematical problems of mechanics and control theory conducted at Institute of Mathematics NAS of Ukraine from the beginning of its foundation.
subject: Research articles
  topic: section
subject: mathematical problems of mechanics
  topic: keywords
creator: I. A. Lukovsky
creator: A. G. Mazko
creator: A. N. Timokha
rights: Copyright (c) 2021 О. М. Тимоха, І. О. Луковський, О. Г. Мазко
date: 2026-02-09
publication date: 2026-02-09
starting page: 1301
ending page: 1316
doi: 10.37863/umzh.v73i10.6704

Structure of integrals of equations of oscillations of a conical shell closed at a vertex
type: item
description: We consider a system of differential equations, which describes the free oscillations of a thin-walled conical shell of rotation with a vertex. Based on the analytical theory of systems of differential equations with a small parameter at the highest derivative and equations with a regular singular point, we establish the formal structure of regular integrals of the original equations.
subject: Research articles
  topic: section
subject: варіаційні метроди, сингулярно збурені крайові задачі, тонкостінні оболонки обертання
  topic: keywords
creator: V. A. Trotsenko
creator: Yu. V. Trotsenko
rights: Copyright (c) 2021 Юрій Троценко
date: 2026-02-09
publication date: 2026-02-09
starting page: 1414
ending page: 1422
doi: 10.37863/umzh.v73i10.6702

Weighted damping of external and initial disturbances in descriptor control systems
type: item
description: UDC 517.925.51; 681.5.03 We investigate the problem of $H_{∞}$ -control of a generalized type for a class of linear descriptor systems and suggest a criterion and sufficient conditions for the existence of control laws ensuring that the closed-loop system is regular, stable and impulse-free with a desired estimate for the weighted damping level of external and initial disturbances. The main computational procedures for the synthesis of regulators are reduced to solving linear and quadratic matrix inequalities that have no rank constraints. An example of robust stabilization of a hydraulic system with three tanks is given.
subject: Research articles
  topic: section
subject: Descriptor system
  topic: keywords
subject: bounded disturbances
  topic: keywords
subject: robust stability
  topic: keywords
creator: A. G. Mazko
rights: Copyright (c) 2021 Олексій Григорович Мазко
date: 2026-02-09
publication date: 2026-02-09
starting page: 1377
ending page: 1390
doi: 10.37863/umzh.v73i10.6698

Fatou and Julia like sets
type: item
description: UDC 517.5 For a familiy of holomorphic functions on an arbitrary domain, we introduce Fatou and Julia like sets, and establish some of their interesting properties.
subject: Short communications
  topic: section
subject: Normal families
  topic: keywords
subject: Holomorphic and entire functions
  topic: keywords
subject: Fatou and Julia sets
  topic: keywords
creator: K. S. Charak
creator: A. Singh
creator: M. Kumar
rights: Copyright (c) 2021 Manish Kumar
date: 2026-02-09
publication date: 2026-02-09
starting page: 1432
ending page: 1438
doi: 10.37863/umzh.v73i10.802

On $\Pi$-permutable subgroups in finite groups
type: item
description: UDC 512.542 Let $\sigma =\{\sigma_{i} | i\in I\}$ be some partition of the set of all primes $\Bbb{P}$ and let $\Pi$ be a nonempty subset of the set $\sigma.$ A set ${\cal H}$ of subgroups of a finite group $G$ is said to be a \emph{complete Hall $\Pi$-set} of $G$ if every member of ${\cal H}$ is a Hall $\sigma _{i}$-subgroup of $G$ for some $\sigma _{i}\in \Pi$ and ${\cal H}$ contains exactly one Hall $\sigma_{i}$-subgroup of $G$ for every $\sigma _{i}\in \Pi$ such that $\sigma_i\cap\pi(G)\neq\varnothing.$ A subgroup $A$ of $G$ is called (i) {${\cal H}^{G}$-permutable} if $AH^{x}=H^{x}A$ for $H\in {\cal H}$ and $x\in G$; (ii) {$\Pi$-permutable in $G$} if $A$ is ${\cal H}^{G}$-permutable for some complete Hall $\Pi$-set $\cal H$ of $G.$ We study the influence of $\Pi$-permutable subgroups on the structure of $G.$ In particular, we prove that if $\pi= \displaystyle\bigcup\nolimits_{\sigma_{i}\in \Pi} \sigma_{i}$ and $G =AB,$ where $A$ and $B$ are ${\cal H}^{G}$-permutable $\pi$-separable (respectively, $\pi$-closed) subgroups of $G,$ then $G$ is also $\pi$-separable (respectively, $\pi$-closed). Some known results are generalized.
subject: Short communications
  topic: section
subject: .
  topic: keywords
creator: B. Hu
creator: J. Huang
creator: N. M. Adarchenko
rights: Copyright (c) 2021 Цзяньхун Хуан, Бин Ху, Никита М. Адарченко
date: 2026-02-09
publication date: 2026-02-09
starting page: 1423
ending page: 1431
doi: 10.37863/umzh.v73i10.768

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
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
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
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
date: 2026-01-26
publication date: 2026-01-26
starting page: 3
ending page: 21
doi: 10.3842/umzh.v78i1-2.8860

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
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
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
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
date: 2026-01-26
publication date: 2026-01-26
starting page: 86
ending page: 87
doi: 10.3842/umzh.v78i1-2.9233

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
date: 2026-01-26
publication date: 2026-01-26
starting page: 82
ending page: 82
doi: 10.3842/umzh.v78i1-2.8614

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
date: 2026-01-26
publication date: 2026-01-26
starting page: 84
ending page: 85
doi: 10.3842/umzh.v78i1-2.9247

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
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
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
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
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
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
date: 2026-01-26
publication date: 2026-01-26
starting page: 71
ending page: 72
doi: 10.3842/umzh.v78i1-2.8778