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: 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: Supplement to the article by Douak and Maroni (2020) on a new class of 2-orthogonal polynomials
items: On some properties of the Gram operator
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
items: Application of the even-type delayed mean in the approximation of functions from the generalized Zygmund class with weight
items: Bicomplex Green's theorem and its application
items: Timelike Bonnet surfaces in the Lorentzian 3-space
items: Bergman theory induced by a quaternionic perturbed fractional $\psi$-Fueter operator
items: Topological structure of simple pro-Hamiltonian flows on the Möbius strip
items: On the domain of analytic continuation of Lauricella–Saran’s hypergeometric functions $F_M$ and their ratios
items: Lax–Sato integrable dispersionless systems on supermanifolds related to a centrally extended generalization of the loop superconformal Lie algebra
items: A version of Cartan–Nochka's theorem for non-Archimedean holomorphic curves with integrated reduced counting functions
items: Embedded trapped modes for water waves in an infinite channel
items: $(p,q)$-Analytic functions and a complex $(p,q)$-binomial formula
items: Casorati curvatures of pointwise slant submanifolds in para-complex space forms
items: On $\mathit{G}$-derivations of Lie–Yamaguti superalgebras
items: Evaluation of the growth of solutions of systems of linear differential equations of the $n$th order
items: Classical solutions of time-fractional quasilinear reaction-diffusion systems
items: Riemann operator function. Cayley’s transformation
items: New forms of the Lopatynsky condition
items: Averaged characteristics of smoothness in $L_2$ and estimations for the widths values of function classes
items: Some inequalities for a certain subclass of Bazilevič functions involving multiplicative calculus

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

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

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

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

Application of the even-type delayed mean in the approximation of functions from the generalized Zygmund class with weight
type: item
description: UDC 517.5 We introduce a new class of functions, namely, the generalized Zygmund class with weight. Moreover, we determine the degree of approximation for functions belonging to this class. The degree of approximation is expressed in terms of two moduli of continuity of the second order $w_1$ and $w_2$ such that $w_1/w_2$ is positive and nondecreasing. To realize this task, for approximation we use the even-type delayed mean of their Fourier series.
subject: Research articles
  topic: section
subject: Degree of approximation, Fourier series, Zygmund class with weight, modulus of continuity, even-delayed mean.
  topic: keywords
creator: Xhevat Z. Krasniqi
rights: Copyright (c) 2025 Xhevat Z. Krasniqi http://creativecommons.org/licenses/by/4.0
date: 2025-11-07
publication date: 2025-11-07
starting page: 233
ending page: 233
doi: 10.3842/umzh.v77i3.7670

Bicomplex Green's theorem and its application
type: item
description: UDC 517.9 We consider a bicomplex extension of Green's theorem, which is a key result in the integral calculus. By its application, we illustrate the bicomplex Cauchy–Goursat theorem and employ the bicomplex version of Green's theorem in order to efficiently determine numerous integrals involving various forms of bicomplex functions.
subject: Research articles
  topic: section
subject: Green’s theorem,
  topic: keywords
subject: Idempotent representation
  topic: keywords
subject: Bicomplex holomorphic functions
  topic: keywords
subject: Bicomplex integration
  topic: keywords
creator: Mahesh Puri Goswami
creator: Raj Kumar
rights: Copyright (c) 2025 Mahesh Puri Goswami, Raj Kumar http://creativecommons.org/licenses/by/4.0
date: 2025-11-07
publication date: 2025-11-07
starting page: 230
ending page: 231
doi: 10.3842/umzh.v77i3.8094

Timelike Bonnet surfaces in the Lorentzian 3-space
type: item
description: UDC 519.11 We generalize the criteria proposed by Z. Soyu\c{c}ok in the 3-dimensional Euclidean space to the Lorentz 3-space for the timelike surfaces. With an aid of this criterion we investigate nonisothermic timelike Bonnet surfaces and their associate surfaces. Finally, we consider the classification of helicoids proposed by Beneki, et al. We present nonisothermic timelike helicoids as examples illustrating our results. Thus, they satisfy the conditions as timelike Bonnet surfaces. In addition, we present the isothermic timelike minimal helicoids.
subject: Research articles
  topic: section
subject: Bonnet surface, timelike surface, timelike helicoid, associate surface, A-net
  topic: keywords
subject: geometry
  topic: subjects
creator: Filiz Kanbay
creator: Burcu Yüksekdağ
rights: Copyright (c) 2025 Filiz Kanbay, Burcu Yüksekdağ http://creativecommons.org/licenses/by/4.0
date: 2025-11-07
publication date: 2025-11-07
starting page: 232
ending page: 232
doi: 10.3842/umzh.v77i3.8383

Bergman theory induced by a quaternionic perturbed fractional $\psi$-Fueter operator
type: item
description: UDC 517.5 A useful tool proved in the present paper is the Borel–Pompeiu formula for the resulting function class of null solutions of the quaternionic perturbed fractional $\psi$-Fueter operator. Motivated by this formula, we developed major steps of the associated Bergman theory.
subject: Research articles
  topic: section
subject: Quaternionic analysis
  topic: keywords
subject: Borel-Pompeiu formulas
  topic: keywords
subject: Bergman theory
  topic: keywords
subject: perturbed fractional $\psi$-Fueter operator
  topic: keywords
creator: José O. González Cervantes
creator: Marco A. Pérez de la Rosa
creator: Juan Bory Reyes
rights: Copyright (c) 2025 José O. González Cervantes, Marco A. Pérez de la Rosa, Juan Bory Reyes http://creativecommons.org/licenses/by/4.0
date: 2025-11-07
publication date: 2025-11-07
starting page: 228
ending page: 229
doi: 10.3842/umzh.v77i3.8381

Topological structure of simple pro-Hamiltonian flows on the Möbius strip
type: item
description: UDC 515.1 We investigate the topological properties of flows on the Möbius strip, whose lift to a double cover, which is a cylinder, consists of Hamiltonian flows with a Hamiltonian that is a Morse function, constant on the boundary components. We construct a topological classification of such simple flows using distinguishing graphs made up of rooted trees, which are Reeb graphs. The resulting recursive formula calculates the number of topologically non-equivalent flows with a given number of saddles.
subject: Research articles
  topic: section
subject: Morse function
  topic: keywords
subject: Hamiltonian flow
  topic: keywords
subject: topological equivalence
  topic: keywords
subject: Reeb graph
  topic: keywords
creator: O. Prishlyak
creator: S. Stas’
rights: Copyright (c) 2025 Олександр Пришляк, Сергій Стась http://creativecommons.org/licenses/by/4.0
date: 2025-11-06
publication date: 2025-11-06
starting page: 584
ending page: 589
doi: 10.3842/umzh.v77i9.9029

On the domain of analytic continuation of Lauricella–Saran’s hypergeometric functions $F_M$ and their ratios
type: item
description: UDC 517.5 We consider the problem of extending the Lauricella-Saran's hypergeometric functions $F_M$ by branched continued fractions. In three-dimensional complex space, the domain of analytical continuation of the Lauricella-Saran's hypergeometric functions $F_M$ and their ratios is established.
subject: Research articles
  topic: section
subject: hypergeometric function
  topic: keywords
subject: branched continued fraction
  topic: keywords
subject: holomorphic function
  topic: keywords
subject: approximation by rational functions
  topic: keywords
subject: convergence
  topic: keywords
subject: Теорія функцій
  topic: subjects
creator: R. Dmytryshyn
creator: I. Nyzhnyk
rights: Copyright (c) 2025 Роман Дмитришин, Іван Нижник http://creativecommons.org/licenses/by/4.0
date: 2025-11-06
publication date: 2025-11-06
starting page: 573
ending page: 583
doi: 10.3842/umzh.v77i9.9105

Lax–Sato integrable dispersionless systems on supermanifolds related to a centrally extended generalization of the loop superconformal Lie algebra
type: item
description: UDC 517.9 We propose a new Lie-algebraic approach to the construction of Lax–Sato integrable dispersionless systems on functional supermanifolds by means of the centrally extended semidirect sum of the loop Lie algebra of superconformal vector fields on a supertorus and its regular dual space, which is based on the general Adler–Kostant–Symes Lie-algebraic scheme. By using this approach, we obtain the Lax–Sato integrable superanalogs for some systems of Mikhalev–Pavlov-type dispersionless equations given on functional supermanifolds of four commuting and numerous anticommuting independent variables and find the left gradients of the Casimir invariant reduced to the orbits of the coadjoint action of the central extension, related to these systems, as well as the associated pairs of compatible Poisson operators.
subject: Research articles
  topic: section
subject: dispersionless systems
  topic: keywords
subject: Lax-Sato integrability
  topic: keywords
subject: superconformal vector fields
  topic: keywords
subject: semi-direct sum
  topic: keywords
subject: Adler-Kostant-Symes theory
  topic: keywords
subject: Casimir invariant
  topic: keywords
creator: O. Hentosh
rights: Copyright (c) 2025 Оксана Гентош http://creativecommons.org/licenses/by/4.0
date: 2025-11-06
publication date: 2025-11-06
starting page: 555
ending page: 572
doi: 10.3842/umzh.v77i9.7950

A version of Cartan–Nochka's theorem for non-Archimedean holomorphic curves with integrated reduced counting functions
type: item
description: UDC 517.5 Let $\mathbb{K}$ be an algebraically closed field of characteristic $0,$ completed with respect to a non-Archimedean absolute value and let $\mathbb{P}^n(\mathbb{K})$ be an $n$-dimensional projective space over $\mathbb{K}.$ A collection $\mathcal H = \{H_1,\ldots,H_q\} \in \mathbb{P}^n(\mathbb{K}),$ $q \geq N+1,$ is said to be in $N$-subgeneral position if, for any $1\leq i_1<\ldots<i_{N+1}\leq q,$ we have $\bigcap_{j=1}^{N+1} H_{i_j} = \varnothing.$ We prove a version of the second main theorem for non-Archimedean holomorphic curves intersecting hyperplanes in $N$-subgeneral position with integrated reduced counting functions.
subject: Research articles
  topic: section
subject: Holomorphic curves, $p$-adic value distribution, $p$-adic Nevanlinna-Cartan theory
  topic: keywords
creator: Ha Tran Phuong
creator: Bui The Hung
creator: Padaphet Inthavichit
rights: Copyright (c) 2025 Ha Tran Phuong, Bui The Hung, Padaphet Inthavichit http://creativecommons.org/licenses/by/4.0
date: 2025-11-06
publication date: 2025-11-06
starting page: 595
ending page: 596
doi: 10.3842/umzh.v77i9.8755

Embedded trapped modes for water waves in an infinite channel
type: item
description: UDC 517.9 We present a simple perturbation scheme for calculating the frequencies of water waves trapped by a small obstruction of the water bed. The corresponding solutions describe embedded trapped modes that are localized at the obstruction and decay at infinity. A simple formula for their frequencies is obtained.
subject: Research articles
  topic: section
subject: Trapped modes
  topic: keywords
subject: water waves
  topic: keywords
creator: M. I. Romero Rodríguez
rights: Copyright (c) 2025 M. I. Romero Rodríguez http://creativecommons.org/licenses/by/4.0
date: 2025-11-06
publication date: 2025-11-06
starting page: 594
ending page: 594
doi: 10.3842/umzh.v77i9.8874

$(p,q)$-Analytic functions and a complex $(p,q)$-binomial formula
type: item
description: UDC 517.5 We introduce the notions of $(p,q)$-differential for complex discrete functions and $(p,q)$-complex differential operators in a sense of Pashaev. The $(p,q)$-analog of the $q$-binomial formula is presented and the $(p,q)$-Taylor expansion is constructed for $(p,q)$-analytic functions. These results provide a generalized framework for $(p,q)$-calculus, contributing to its applications in mathematical analysis and related fields.
subject: Research articles
  topic: section
subject: (p,q)-analyticity
  topic: keywords
subject: complex (p,q)-binomial
  topic: keywords
subject: (p,q)-Taylor expansion
  topic: keywords
creator: İlker Gençtürk
rights: Copyright (c) 2025 İlker Gençtürk http://creativecommons.org/licenses/by/4.0
date: 2025-11-06
publication date: 2025-11-06
starting page: 593
ending page: 593
doi: 10.3842/umzh.v77i9.8966

Casorati curvatures of pointwise slant submanifolds in para-complex space forms
type: item
description: UDC 515.1 We define and study pointwise slant and pointwise semi-slant submanifolds in para-Kaehler manifolds. Some theorems, characterizations, and examples are obtained for pointwise slant and pointwise semi-slant submanifolds. We also obtain some results concerning the Casorati curvature for a pointwise slant submanifold in the para-Kaehler space form.
subject: Research articles
  topic: section
subject: Para-Kaehler manifold,
  topic: keywords
subject: pointwise semi-slant submanifold,
  topic: keywords
subject: para-complex space form.
  topic: keywords
subject: 2020 Mathematic Subject Classification. 53C43,53C15,53C40.
  topic: subjects
creator: Sedat Ayaz
rights: Copyright (c) 2025 Sedat Ayaz http://creativecommons.org/licenses/by/4.0
date: 2025-11-06
publication date: 2025-11-06
starting page: 591
ending page: 592
doi: 10.3842/umzh.v77i9.8956

On $\mathit{G}$-derivations of Lie–Yamaguti superalgebras
type: item
description: UDC 512.5 Let $\mathit{G}$ be an automorphism group. We study $\mathit{G}$-derivations associated with the Lie–Yamaguti superalgebras. The concept of $\mathit{G}$-derivation, which is a derivation under both bilinear and trilinear operations is defined for the Lie–Yamaguti superalgebras. We also study some important properties of $\mathit{G}$-derivations, as well as with their relationship with other derivations of the Lie–Yamaguti superalgebras.
subject: Research articles
  topic: section
subject: Lie-Yamaguti superalgebra; Derivation; Quasi-derivation
  topic: keywords
creator: Meher Abdaoui
creator: Jamel Boujelben
rights: Copyright (c) 2025 Meher Abdaoui, Jamel Boujelben http://creativecommons.org/licenses/by/4.0
date: 2025-11-06
publication date: 2025-11-06
starting page: 590
ending page: 590
doi: 10.3842/umzh.v77i9.8857

Evaluation of the growth of solutions of systems of linear differential equations of the $n$th order
type: item
description: UDC 517.925.7 For a system of linear differential equations of the $m$th order with coefficients holomorphic in a neighborhood of $\infty,$ we obtain an a priori estimate of growth for the $n$-valued ($n \in \mathbb{N}$) analytic vector solutions of the system via the estimate for the order of growth of its coefficients.
subject: Research articles
  topic: section
subject: systems of ordinary differential equations
  topic: keywords
subject: analytic functions
  topic: keywords
subject: branch point
  topic: keywords
subject: analytical continuation
  topic: keywords
subject: Riemann surface
  topic: keywords
subject: maximum of absolute value
  topic: keywords
subject: theory of distribution of values ​​of meromorphic functions
  topic: subjects
creator: A. Mokhon’ko
creator: O. Mokhon’ko
rights: Copyright (c) 2025 Анатолій Мохонько, Олексій Мохонько http://creativecommons.org/licenses/by/4.0
date: 2025-11-04
publication date: 2025-11-04
starting page: 144
ending page: 151
doi: 10.3842/umzh.v77i2.8406

Classical solutions of time-fractional quasilinear reaction-diffusion systems
type: item
description: UDC 517.9 We analyze a quasilinear reaction-diffusion system with the time-fractional Caputo derivative. We prove the existence and uniqueness result to initial-boundary problems with Dirichlet and Robin (Neumann) boundary conditions under suitable assumptions on the given data. The existence of the solution to our problem is proved by the Leray–Schauder fixed-point theorem. Positivity property allows us to apply the method of upper-lower solutions. We provide an example of upper and lower solutions to some specific time-fractional reaction-diffusion system.
subject: Research articles
  topic: section
subject: Caputo derivative, Holder spaces, classical solution
  topic: keywords
creator: M. Krasnoschok
rights: Copyright (c) 2025 Микола Краснощок http://creativecommons.org/licenses/by/4.0
date: 2025-11-04
publication date: 2025-11-04
starting page: 123
ending page: 138
doi: 10.3842/umzh.v77i2.1147

Riemann operator function. Cayley’s transformation
type: item
description: UDC 510 We study a new class of special functions called Laguerre–Bessel polynomials (PLBs), which play the same role as Laguerre polynomials in the case of application of the Cayley transformation to the evaluation of the operator exponent. The generating function for PLBs is a Bessel operator function of the first kind of zero order obtained by replacing its operator argument by its Cayley transformation. It is shown that the PLBs coincide with a new class of 2-orthogonal polynomials with an accuracy of up to a linear transformation. It is shown that the PLBs are classical in the Hahn–Maroni sense because their normalized derivatives also form a class of 2-orthogonal polynomials with an accuracy of up to a linear transformation. We determine the following characteristics traditional for the polynomial classes: explicit representation, recurrence relations, and the differential equations of the minimal third order.
subject: Research articles
  topic: section
subject: 2-orthogonal polynomials, Laguerre--Ceyley polynomials, recurrent relation, Hahn property, classical $d$-orthogonal polynomials, monic polynomials, differential equation
  topic: keywords
creator: V. Makarov
rights: Copyright (c) 2025 Володимир Макаров http://creativecommons.org/licenses/by/4.0
date: 2025-11-04
publication date: 2025-11-04
starting page: 139
ending page: 143
doi: 10.3842/umzh.v77i2.8859

New forms of the Lopatynsky condition
type: item
description: UDC 517.956.223+512.64 We present known forms of the Lopatynsky condition of ellipticity of a problem for a linear regularly elliptic system of equations and determine new forms of this condition. Several examples of its application to various elliptic systems of equations are considered.
subject: Research articles
  topic: section
subject: еліптичні системи, еліптичні задачі, умова Лопатинського, розклад матричного многочлена
  topic: keywords
creator: V. Il’kiv
rights: Copyright (c) 2025 Володимир Ільків http://creativecommons.org/licenses/by/4.0
date: 2025-11-04
publication date: 2025-11-04
starting page: 107
ending page: 122
doi: 10.3842/umzh.v77i2.8534

Averaged characteristics of smoothness in $L_2$ and estimations for the widths values of function classes
type: item
description: UDC 517.5 In the space of $2\pi$-periodic functions $L_2,$ we investigate the characteristic of smoothness $\omega^{*}_{\mathcal{M}}(f,t):=$ $(1/t) \displaystyle\int\nolimits_0^t \omega_{\mathcal{M}}(f,\tau) d \tau $ obtained as a result of averaging of the generalized modulus of continuity $\omega_{\mathcal{M}}(f)$ formed by using a generalized finite-difference operator $\Delta^{\mathcal{M}}_h \colon L_2 \to L_2.$ We also study some properties of the functions $\omega_{\mathcal{M}}(f)$ and $\omega^{*}_{\mathcal{M}}(f).$ For the classes of functions $W(\omega^{*}_{\mathcal{M}}, \Phi),$ where $\Phi$ is a majorant, we determine the lower and upper estimates for the values of a series of $n$-widths and the establish the condition for $\Phi$ under which we obtain the exact values of these estimates. Several exact results are illustrated by specific examples.
subject: Research articles
  topic: section
subject: generalized finite difference operator, generalized smoothness characteristic of function, Fourier series, Fourier coefficients, majorant, widths of function classes.
  topic: keywords
creator: S. Vakarchuk
creator: V. Zabutna
creator: M. Vakarchuk
rights: Copyright (c) 2025 Сергій Вакарчук, Валентина Забутна, Михайло Вакарчук http://creativecommons.org/licenses/by/4.0
date: 2025-11-04
publication date: 2025-11-04
starting page: 83
ending page: 106
doi: 10.3842/umzh.v77i2.8794

Some inequalities for a certain subclass of Bazilevič functions involving multiplicative calculus
type: item
description: UDC 517.5 We define a new class of functions expressed as a convex combination of differential characterizations affected by the multiplicative derivative. Multiplicative derivative is defined in a domain, which excludes zero. Hence, in this case, the defined subclass does not involve replacing the ordinary derivative with a multiplicative derivative. However, we have used the motivation behind the purpose of this restrictive calculus given by the circumstances that we have a more versatile calculus of Newton and Euler. Estimates involving the initial coefficients of the functions, which have Maclaurin series and belong to the given function class are our main results. Some examples, along with the graphs, are used to establish the inclusion and the closure properties. Moreover, we obtain the logarithmic and inverse coefficients for the analyzed function class.
subject: Research articles
  topic: section
subject: univalent function
  topic: keywords
subject: multiplicative calculus
  topic: keywords
subject: starlike
  topic: keywords
subject: Bazilevic
  topic: keywords
subject: subordination
  topic: keywords
subject: Geometric function theory
  topic: subjects
creator: Kadhavoor R. Karthikeyan
creator: Sakkarai Lakshmi
creator: Seetharam Varadharajan
rights: Copyright (c) 2025 Kadhavoor R. Karthikeyan, Sakkarai Lakshmi, Seetharam Varadharajan http://creativecommons.org/licenses/by/4.0
date: 2025-11-04
publication date: 2025-11-04
starting page: 157
ending page: 158
doi: 10.3842/umzh.v77i2.8288