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Schmidt Rank and Singularities Ukr. Math. J. (IF 0.5) Pub Date : 2024-02-20 David Kazhdan, Amichai Lampert, Alexander Polishchuk
We revisit Schmidt’s theorem connecting the Schmidt rank of a tensor with the codimension of a certain variety and adapt the proof to the case of arbitrary characteristic. We also establish a sharper result for this kind for homogeneous polynomials, assuming that the characteristic does not divide the degree. Further, we use this to relate the Schmidt rank of a homogeneous polynomial (resp., a collection
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Smooth Rigidity for Higher-Dimensional Contact Anosov Flows Ukr. Math. J. (IF 0.5) Pub Date : 2024-02-20
We apply the technique of matching functions in the setting of contact Anosov flows satisfying a bunching assumption. This allows us to generalize the 3-dimensional rigidity result of Feldman and Ornstein [Ergodic Theory Dynam. Syst., 7, No. 1, 49–72 (1987)]. Namely, we show that if two Anosov flow of this kind are C0 conjugate, then they are Cr conjugate for some r ∈ [1, 2) or even C∞ conjugate under
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Cohomology and Formal Deformations of n-Hom–Lie Color Algebras Ukr. Math. J. (IF 0.5) Pub Date : 2024-02-20 K. Abdaoui, R. Gharbi, S. Mabrouk, A. Makhlouf
We provide a cohomology of n-Hom–Lie color algebras, in particular, a cohomology governing oneparameter formal deformations. Then we also study formal deformations of the n-Hom–Lie color algebras and introduce the notion of Nijenhuis operator on an n-Hom–Lie color algebra, which may give rise to infinitesimally trivial (n − 1)th-order deformations. Furthermore, in connection with Nijenhuis operators
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Convergence of Baum–Katz Series for Sums Whose Terms are Elements of a Linear mth Order Autoregressive Sequence Ukr. Math. J. (IF 0.5) Pub Date : 2024-02-20 Maryna Ilienko, Anastasiia Polishchuk
We establish necessary and sufficient conditions for the convergence of the Baum–Katz series for the sums of elements of linear mth order autoregressive sequences of random variables.
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On the Theory of Moduli Of The Surfaces Ukr. Math. J. (IF 0.5) Pub Date : 2024-02-20
We continue the development of the theory of moduli of the families of surfaces, in particular, of strings of various dimensions m = 1, 2, . . . ,n − 1 in Euclidean spaces \({\mathbb{R}}^{n}\) , n ≥ 2. On the basis of the proof of the lemma on the relationships between the moduli and Lebesgue measures, we prove the corresponding analog of the Fubini theorem in terms of moduli that extends the well-known
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New Quantum Hermite–Hadamard-Type Inequalities for p-Convex Functions Involving Recently Defined Quantum Integrals Ukr. Math. J. (IF 0.5) Pub Date : 2024-02-20 Ghazala Gulshan, Hüseyin Budak, Rashida Hussain, Muhammad Aamir Ali
We develop new Hermite–Hadamard-type integral inequalities for p-convex functions in the context of q-calculus by using the concept of recently defined Tq-integrals. Then the obtained Hermite–Hadamard inequality for p-convex functions is used to get a new Hermite–Hadamard inequality for coordinated p-convex functions. Furthermore, we present some examples to demonstrate the validity of our main results
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Jordan Homoderivation Behavior of Generalized Derivations in Prime Rings Ukr. Math. J. (IF 0.5) Pub Date : 2024-02-20 Nripendu Bera, Basudeb Dhara
Suppose that R is a prime ring with char(R) ≠ 2 and f(ξ1, . . . , ξn) is a noncentral multilinear polynomial over C(= Z(U)), where U is the Utumi quotient ring of R. An additive mapping h : R ⟶ R is called homoderivation if h(ab) = h(a)h(b)+h(a)b+ah(b) for all a, b ∈ R. We investigate the behavior of three generalized derivations F, G, and H of R satisfying the condition \(F\left({\xi }^{2}\right)=G\left({\xi
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Some Tauberian Theorems for the Weighted Mean Method of Summability of Double Sequences Ukr. Math. J. (IF 0.5) Pub Date : 2024-02-20
Let p = (pj) and q = (qk) be real sequences of nonnegative numbers with the property that \(\begin{array}{ccccccc}{P}_{m}=\sum_{j=0}^{m}{p}_{j}\ne 0& {\text{and}}& {Q}_{m}=\sum_{k=0}^{n}{q}_{k}\ne 0& \mathrm{for all}& m& {\text{and}}& n.\end{array}\) Also let (Pm) and (Qn) be regularly varying positive indices. Assume that (umn) is a double sequence of complex (real) numbers, which is ( \(\overline{N
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Bounds on the Parameters of Non-L-Borderenergetic Graphs Ukr. Math. J. (IF 0.5) Pub Date : 2024-02-20 Cahit Dede, Ayşe Dilek Maden
We consider graphs whose Laplacian energy is equivalent to the Laplacian energy of the complete graph of the same order, which is called an L-borderenergetic graph. First, we study the graphs with degree sequence consisting of at most three distinct integers and give new bounds for the number of vertices of these graphs to be non-L-borderenergetic. Second, by using Koolen–Moulton and McClelland inequalities
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A Modulus of Smoothness for Some Banach Function Spaces Ukr. Math. J. (IF 0.5) Pub Date : 2023-12-11 Ramazan Akgün
Based on the Steklov operator, we consider a modulus of smoothness for functions in some Banach function spaces, which can be not translation invariant, and establish its main properties. A constructive characterization of the Lipschitz class is obtained with the help of the Jackson-type direct theorem and the inverse theorem on trigonometric approximation. As an application, we present several examples
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Adomian’s Decomposition Method in the Theory of Nonlinear Autonomous Boundary-Value Problems Ukr. Math. J. (IF 0.5) Pub Date : 2023-12-11 Oleksandr Boichuk, Serhii Chuiko, Dar’ya Diachenko
For a nonlinear autonomous boundary-value problem posed for an ordinary differential equation in the critical case, we establish constructive conditions for its solvability and propose a scheme for the construction of solutions based on the use of Adomian’s decomposition method.
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Embeddings Into Countably Compact Hausdorff Spaces Ukr. Math. J. (IF 0.5) Pub Date : 2023-12-11 Taras Banakh, Serhii Bardyla, Alex Ravsky
We consider the problem of characterization of topological spaces embedded into countably compact Hausdorff topological spaces. We study the separation axioms for subspaces of Hausdorff countably compact topological spaces and construct an example of a regular separable scattered topological space that cannot be embedded into an Urysohn countably compact topological space.
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S-Colocalization and Adams Cocompletion Ukr. Math. J. (IF 0.5) Pub Date : 2023-12-08 Snigdha Bharati Choudhury, A. Behera
A relationship between the S-colocalization of an object and the Adams cocompletion of the same object in a complete small 𝒰 -category (𝒰 is a fixed Grothendieck universe) is established together with a specific set of morphisms S.
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Stochastic Bernoulli Equation on the Algebra of Generalized Functions Ukr. Math. J. (IF 0.5) Pub Date : 2023-12-08 Hafedh Rguigui
Based on the topological dual space \({\mathcal{F}}_{\theta }^{*}\left({\mathcal{S}{\prime}}_{\mathbb{C}}\right)\) of the space of entire functions with θ-exponential growth of finite type, we introduce a generalized stochastic Bernoulli–Wick differential equation (or a stochastic Bernoulli equation on the algebra of generalized functions) by using the Wick product of elements in \({\mathcal{F}}_{\theta
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On Exponential Dichotomy for Abstract Differential Equations with Delayed Argument Ukr. Math. J. (IF 0.5) Pub Date : 2023-12-08 Andrii Chaikovs’kyi, Oksana Lagoda
We consider linear differential equations of the first order with delayed arguments in a Banach space. We establish conditions for the operator coefficients necessary for the existence of exponential dichotomy on the real axis. It is proved that the analyzed differential equation is equivalent to a difference equation in a certain space. It is shown that, under the conditions of existence and uniqueness
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A Class of Fractional Integral Operators Involving a Certain General Multiindex Mittag-Leffler Function Ukr. Math. J. (IF 0.5) Pub Date : 2023-12-08 H. M. Srivastava, Manish Kumar Bansal, Priyanka Harjule
The paper is essentially motivated by the demonstrated potential for applications of the presented results in numerous widespread research areas, such as the mathematical, physical, engineering, and statistical sciences. The main object is to introduce and investigate a class of fractional integral operators involving a certain general family of multiindex Mittag-Leffler functions in their kernel.
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Generalized Weakly Demicompact and S-Demicompact Linear Relations and Their Spectral Properties Ukr. Math. J. (IF 0.5) Pub Date : 2023-12-08 Majed Fakhfakh, Aref Jeribi
We extend the concept of generalized weakly demicompact and relatively weakly demicompact operators on linear relations and present some outstanding results. Moreover, we address the theory of Fredholm and upper semi-Fredholm relations and make an attempt to establish connections with these operators.
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On the Variational Statement of One Boundary-Value Problem with Free Interface Ukr. Math. J. (IF 0.5) Pub Date : 2023-12-08 Aleksander Timokha
With the help of Clebsch’s potentials, we propose a Bateman–Luke-type variational principle for a boundary- value problem with a free (unknown) interface between two ideal compressible barotropic fluids (liquid and gas) admitting rotational flows.
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Determination of Some Properties of Starlike and Close-to-Convex Functions According to Subordinate Conditions with Convexity of a Certain Analytic Function Ukr. Math. J. (IF 0.5) Pub Date : 2023-11-28 Hasan Şahin, İsmet Yildiz
Investigation of the theory of complex functions is one of the most fascinating aspects of the theory of complex analytic functions of one variable. It has a huge impact on all areas of mathematics. Numerous mathematical concepts are explained when viewed through the theory of complex functions. Let \(f\left(z\right)\in A, f\left(z\right)=z+{\sum }_{n\ge 2}^{\infty }{a}_{n}{z}^{n},\) be an analytic
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Uncertainty Principles for the q-Hankel–Stockwell Transform Ukr. Math. J. (IF 0.5) Pub Date : 2023-11-28 Kamel Brahim, Hédi Ben Elmonser
By using the q-Jackson integral and some elements of the q-harmonic analysis associated with the q-Hankel transform, we introduce and study a q-analog of the Hankel–Stockwell transform. We present some properties from harmonic analysis (Plancherel formula, inversion formula, reproducing kernel, etc.). Furthermore, we establish a version of Heisenberg’s uncertainty principles. Finally, we study the
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Normal Properties of Numbers in Terms of their Representation by the Perron Series Ukr. Math. J. (IF 0.5) Pub Date : 2023-11-28 Mykola Moroz
We study the representation of real numbers by Perron series (P-representation) given by $$\left(\left.0;1\right]\ni x=\sum_{n=0}^{\infty }\frac{{r}_{0}{r}_{1}\dots {r}_{n}}{\left({p}_{1}-1\right){p}_{1}\dots \left({p}_{n}-1\right){p}_{n}{p}_{n+1}}={\Delta }_{{p}_{1}{p}_{2}\dots }^{P}\right.,$$ where rn, pn ∈ ℕ, pn+1 ≥ rn + 1, and its transcoding (\(\overline{P }\)-representation) $${x=\Delta }_{{g}_{1}{g}_{2}\dots
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A Tangent Inequality Over Primes Ukr. Math. J. (IF 0.5) Pub Date : 2023-11-28 S. I. Dimitrov
We introduce a new Diophantine inequality with prime numbers. Let \(1 1, every sufficiently large positive number N, and a small constant ε > 0, the tangent inequality $$\left|{p}_{1}^{c} {\mathrm{tan}}^{\theta }\left(\mathrm{log}{p}_{1}\right)+{p}_{2}^{c} {\mathrm{tan}}^{\theta }\left(\mathrm{log}{p}_{2}\right)+{p}_{3}^{c} {\mathrm{tan}}^{\theta }\left(\mathrm{log}{p}_{3}\right)-N\right|<\varepsilon
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Weighted Discrete Hardy’s Inequalities Ukr. Math. J. (IF 0.5) Pub Date : 2023-11-28 Pascal Lefèvre
We give a short proof of a weighted version of the discrete Hardy inequality. This includes the known case of classical monomial weights with optimal constant. The proof is based on the ideas of the short direct proof given recently in [P. Lefèvre, Arch. Math. (Basel), 114, No. 2, 195–198 (2020)].
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Approximation of Generalized Poisson Integrals by Interpolating Trigonometric Polynomials Ukr. Math. J. (IF 0.5) Pub Date : 2023-11-25 Anatolii Serdyuk, Tetyana Stepanyuk
We establish asymptotically unimprovable interpolation analogs of Lebesgue-type inequalities for 2π-periodic functions f that can be represented in the form of generalized Poisson integrals of functions φ from the space Lp, 1 ≤ p ≤ ∞. In these inequalities, the moduli of deviations of the interpolation Lagrange polynomials \(\left|f\left(x\right)-{\widetilde{S}}_{n-1}\left(f;x\right)\right|\) for every
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Univalence Criteria for Locally Univalent Analytic Functions Ukr. Math. J. (IF 0.5) Pub Date : 2023-11-25 Zhenyong Hu, Jinhua Fan, Xiaoyuan Wang
Suppose that p(z) = 1 + zϕ″(z)/ϕ′(z), where ϕ(z) is a locally univalent analytic function in the unit disk D with ϕ(0) = ϕ′(1) − 1 = 0. We establish the lower and upper bounds for the best constants σ0 and σ1 such that \({e}^{{-\sigma }_{0}/2}<\left|p\left(z\right)\right|<{e}^{{\sigma }_{0}/2}\) and |p(w)/p(z)| < \({e}^{{\sigma }_{1}}\) for z, w ∈ D, respectively, imply the univalence of ϕ(z) in D
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Almost Everywhere Convergence of T Means with Respect to the Vilenkin System of Integrable Functions Ukr. Math. J. (IF 0.5) Pub Date : 2023-11-25 N. Nadirashvili
We prove and discuss some new weak-type (1,1) inequalities for the maximal operators of T means with respect to the Vilenkin system generated by monotonic coefficients. We also apply the accumulated results to prove that these T means are almost everywhere convergent. As applications, we present both some well-known and new results.
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Time-Dependent Source Identification Problem for a Fractional Schrödinger Equationwith the Riemann–Liouville Derivative Ukr. Math. J. (IF 0.5) Pub Date : 2023-11-25 Ravshan Ashurov, Marjona Shakarova
We consider a Schrödinger equation \(i{\partial }_{t}^{\rho }u\left(x,t\right)-{u}_{xx}\left(x,t\right)=p\left(t\right)q\left(x\right)+f\left(x,t\right),0
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Impulsive Dirac System on Time Scales Ukr. Math. J. (IF 0.5) Pub Date : 2023-11-11 Bilender P. Allahverdiev, Hüseyin Tuna
We consider an impulsive Dirac system on Sturmian time scales and present an existence theorem for this system. Maximal, minimal, and self-adjoint operators generated by the impulsive dynamic Dirac system are constructed. We also construct the Green function for this problem. Finally, an eigenfunction expansion is obtained.
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Some Refinements of the Hermite–Hadamard Inequality with the Help of Weighted Integrals Ukr. Math. J. (IF 0.5) Pub Date : 2023-11-11 B. Bayraktar, J. E. Nápoles, F. Rabossi
By using the definition of modified (h, m, s)-convex functions of the second type, we present various refinements of the classical Hermite–Hadamard inequality obtained within the framework of weighted integrals. Throughout the paper, we show that various known results available from the literature can be obtained as particular cases of our results.
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Evolutionary Pseudodifferential Equations with Smooth Symbols in S-Type Spaces Ukr. Math. J. (IF 0.5) Pub Date : 2023-11-11 Vasyl Horodets’kyi, Roman Petryshyn, Olha Martynyuk
We study an evolutionary equation with an operator (i∂/∂x), where φ is a smooth function satisfying certain conditions. As special cases of this equation, we get a partial differential equation of parabolic type with derivatives of finite and infinite orders and an equation with certain operators of fractional differentiation. It is shown that the restriction of the operator (i∂/∂x) to some spaces
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The Concept of Topological Well-Ordered Space Ukr. Math. J. (IF 0.5) Pub Date : 2023-11-10 Mustafa Burç Kandemir, Dilan Başak Uludağ
Since the general definition of topology is based on the characteristics of the standard Euclidean topology, the relationships between the ordering on real numbers and its topology have been generalized over time and studied in numerous aspects. The compatibility of partially ordered sets with the topology on these sets was studied by many researchers. On the other hand, well-orderedness is an important
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On the Mean Value of the Generalized Dedekind Sum and Certain Generalized Hardy Sums Weighted by the Kloosterman Sum Ukr. Math. J. (IF 0.5) Pub Date : 2023-11-11 Muhammet Cihat Dağlı, Hamit Sever
We study a hybrid mean-value problem related to the generalized Dedekind sum, certain generalized Hardy sums, and Kloosterman sum and obtain several meaningful conclusions with the help of the analytic method and the properties of the sum of characters and the Gauss sum.
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Multiple Solutions to Boundary-Value Problems for Fourth-Order Elliptic Equations Ukr. Math. J. (IF 0.5) Pub Date : 2023-11-09 Duong Trong Luyen, Mai Thi Thu Trang
We study the existence of multiple solutions for a biharmonic problem $$\begin{array}{l}{\Delta }^{2}u=f\left(x,u\right)+g\left(x,u\right)\mathrm{ in \Omega },\\ u={\partial }_{v}u=0\mathrm{ on }\partial\Omega ,\end{array}$$ where Ω is a bounded domain with smooth boundary in ℝN, N > 4, f(x, ξ) is odd in ξ, and g(x, ξ) is a perturbation term. Under certain growth conditions on f and g, we show that
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Complex Hessian-Type Equations in the Weighted m-Subharmonic Class Ukr. Math. J. (IF 0.5) Pub Date : 2023-11-10 Mohamed Zaway, Jawhar Hbil
We study the existence of a solution to a general type of complex Hessian equation on some Cegrell classes. For a given measure μ defined on an m-hyperconvex domain Ω ⊂ ℂn, under suitable conditions, we prove that the equation χ(.)Hm(.) = μ has a solution that belongs to the class ℰm,χ(Ω).
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Quaternionic Davis–Wielandt Shell in a Right Quaternionic Hilbert Space Ukr. Math. J. (IF 0.5) Pub Date : 2023-11-09 Aref Jeribi, Kamel Mahfoudhi
We derive some results concerning the quaternionic Davis–Wielandt shell for a bounded right linear operator in a right quaternionic Hilbert space. The relations between the geometric properties of the quaternionic Davis–Wielandt shells and the algebraic properties of quaternionic operators are obtained.
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Periodic and Weakly Periodic Ground States Corresponding to the Subgroups of Index Three for the Ising Model on the Cayley Tree of Order Three Ukr. Math. J. (IF 0.5) Pub Date : 2023-11-09 Dilshod O. Egamov
We determine periodic and weakly periodic ground states with subgroups of index three for the Ising model on the Cayley tree of order three.
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Finite A2-Continued Fractions in the Problems of Rational Approximations of Real Numbers Ukr. Math. J. (IF 0.5) Pub Date : 2023-11-09 M. Pratsiovytyi, Ya. Goncharenko, I. Lysenko, S. Ratushnyak
We consider finite continued fractions whose elements are numbers \(\frac{1}{2}\) and 1 (the so-called A2-continued fractions): 1/a1+1/a2+. . .+1/an = [0; a1,a2, . . . ,an], ai ∈ \({A}_{2}=\left\{\frac{1}{2},1\right\}.\) We study the structure of the set F of values of all these fractions and the problem of the number of representations of numbers from the segment \(\left[\frac{1}{2};1\right]\) by
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More on Stability of Two Functional Equations Ukr. Math. J. (IF 0.5) Pub Date : 2023-11-08 Longfa Sun, Yunbai Dong
We prove the generalized stability of the functional equations $$\Vert f\left(x+y\right)\Vert =\Vert f\left(x\right)+f\left(y\right)\Vert \mathrm{ and }\Vert f\left(x-y\right)\Vert =\Vert f\left(x\right)-f\left(y\right)\Vert $$ in p-uniformly convex spaces with p ≥ 1.
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The Forcing Metric Dimension of a Total Graph of Nonzero Annihilating Ideals Ukr. Math. J. (IF 0.5) Pub Date : 2023-11-08 M. Pazoki
Let R be a commutative ring with identity, which is not an integral domain. An ideal I of a ring R is called an annihilating ideal if there exists r ∈ R − {0} such that Ir = (0). The total graph of nonzero annihilating ideals of R, denoted by Ω(R), is a graph with the vertex set A(R)* and the set of all nonzero annihilating ideals of R in which two distinct vertices I and J are joined if and only if
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Local Distance Antimagic Chromatic Number for the Union of Star and Double Star Graphs Ukr. Math. J. (IF 0.5) Pub Date : 2023-10-31 V. Priyadharshini, M. Nalliah
Let G=(V,E) be a graph on p vertices without isolated vertices. A bijection f from V to {1, 2, . . . ,p} is called a local distance antimagic labeling if, for any two adjacent vertices u and v, we get distinct weights (colors), where a vertex x has the weight w(x) = ΣvϵN(x) f(v). The local distance antimagic chromatic number χlda (G) is defined as the least number of colors used in any local distance
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Coefficient Estimates for Starlike and Convex Functions Related to Sigmoid Functions Ukr. Math. J. (IF 0.5) Pub Date : 2023-10-28 M. Raza, D. K. Thomas, A. Riaz
We give sharp coefficient bounds for starlike and convex functions related to modified sigmoid functions. We also provide some sharp coefficient bounds for the inverse functions and sharp bounds for the initial logarithmic coefficients and some coefficient differences.
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On Local Properties of Singular Integrals Ukr. Math. J. (IF 0.5) Pub Date : 2023-10-28 J. I. Mamedkhanov, S. Z. Jafarov
Let γ be a regular curve. We study the local properties of singular integrals in the class of functions \({H}_{\alpha }^{\alpha +\beta }\left({t}_{0},\upgamma \right).\) We obtain a strengthening of the Plemelj–Privalov theorem for functions from the class \({H}_{\alpha }^{\alpha +\beta }\left({t}_{0},\upgamma \right).\) It is proved that, at the point t0 of increased smoothness for α+β < 1, there
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Practical Semiglobal Uniform Exponential Stability Of Nonlinear Nonautonomous Systems Ukr. Math. J. (IF 0.5) Pub Date : 2023-10-28 A. Kicha, M. A. Hammami, I. -E. Abbes
We solve the following twofold problem: In the first part, we deduce Lyapunov sufficient conditions for the practical uniform exponential stability of nonlinear perturbed systems under different conditions for the perturbed term. The second part presents a converse Lyapunov theorem for the notion of semiglobal uniform exponential stability for parametrized nonlinear time-varying systems. We establish
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Study of the Analytic Function Related to the Le-Roy-Type Mittag-Leffler Function Ukr. Math. J. (IF 0.5) Pub Date : 2023-10-28 K. Mehrez
We study some geometric properties (such as univalence, starlikeness, convexity, and close-to-convexity) of Le-Roy-type Mittag-Leffler function. In order to solve the posed problem, we use new two-sided inequalities for the digamma function. Some examples are also provided to illustrate the obtained results. Interesting consequences are deduced to show that these results improve several results available
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A Weighted Weak-Type Inequality for One-Sided Maximal Operators Ukr. Math. J. (IF 0.5) Pub Date : 2023-10-28 J. Wang, Y. Ren, E. Zhang
We obtain necessary and sufficient conditions for a weighted weak-type inequality of the form \(\underset{\left\{{M}_{g}^{+}\left(f\right)>\uplambda \right\}}{\overset{}{\int }}\widetilde{\varphi }\left(\frac{\uplambda }{{\omega }_{3}\left(x\right){\omega }_{4}\left(x\right)}\right){\omega }_{4}\left(x\right)dx\le {C}_{1}\underset{-\infty }{\overset{+\infty }{\int }}\widetilde{\varphi }\left(\frac
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On Virial Expansions of Correlation Functions. Canonical Ensemble Ukr. Math. J. (IF 0.5) Pub Date : 2023-10-28 Yu. Pogorelov, A. Rebenko
We present a brief survey of works of the Kyiv School of Mathematicians published in Soviet journals in the 1940–70s. The main results are formulated in the language of contemporary methods of infinitedimensional analysis, which significantly simplifies their proofs. Nonlinear (in the density parameter) Kirkwood–Salzburg-type equations are obtained for the correlation functions of the canonical ensemble
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General Local Cohomology Modules in View of Low Points and High Points Ukr. Math. J. (IF 0.5) Pub Date : 2023-10-28 M. Y. Sadeghi, Kh. Ahmadi Amoli, M. Chaghamirza
Let R be a commutative Noetherian ring, let Φ be a system of ideals of R, let M be a finitely generated R-module, and let t be a nonnegative integer. We first show that a general local cohomology module \({H}_{{\Phi }_{\mathfrak{p}}}^{i}\left({M}_{\mathfrak{p}}\right)\) is a finitely generated R-module for all i < t if and only if \({\mathrm{Ass}}_{R}\left({H}_{{\Phi }_{\mathfrak{p}}}^{i}\left({M}
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Legendre Superconvergent Degenerate Kernel and Nyström Methods for Nonlinear Integral Equations Ukr. Math. J. (IF 0.5) Pub Date : 2023-10-28 C. Allouch, M. Arrai, H. Bouda, M. Tahrichi
We study polynomially based superconvergent collocation methods for the approximation of solutions to nonlinear integral equations. The superconvergent degenerate kernel method is chosen for the approximation of solutions of Hammerstein equations, while a superconvergent Nyström method is used to solve Urysohn equations. By applying interpolatory projections based on the Legendre polynomials of degree
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Robin Boundary-Value Problem for the Beltrami Equation Ukr. Math. J. (IF 0.5) Pub Date : 2023-10-05 İ. Gençtürk
We study the unique solution of the Robin boundary-value problem for the Beltrami equation with constant coefficients in a unit disc by using a technique based on a singular integral operator defined on Lp(𝔻) for all p > 2.
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Stochastic Navier–Stokes Variational Inequalities with Unilateral Boundary Conditions: Probabilistic Weak Solvability Ukr. Math. J. (IF 0.5) Pub Date : 2023-10-06 M. Sango
We initiate the investigation of stochastic Navier–Stokes variational inequalities involving unilateral boundary conditions and nonlinear forcings driven by the Wiener processes for which we establish the existence of a probabilistic weak (or martingale) solution. Our approach involves an intermediate penalized problem whose weak solution is obtained by means of Galerkin’s method in combination with
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Uniform Approximations by Fourier Sums on the Sets of Convolutions of Periodic Functions of High Smoothness Ukr. Math. J. (IF 0.5) Pub Date : 2023-10-06 A. Serdyuk, T. Stepanyuk
On the sets of 2π-periodic functions f specified by the (ψ, β)-integrals of functions φ from L1, we establish Lebesgue-type inequalities in which the uniform norms of deviations of the Fourier sums are expressed via the best approximations of the functions φ by trigonometric polynomials in the mean. It is shown that obtained estimates are asymptotically unimprovable in the case where the sequences
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On Hölder Continuity of Solutions to the Beltrami Equations Ukr. Math. J. (IF 0.5) Pub Date : 2023-10-06 V. Ryazanov, R. Salimov, E. Sevost’yanov
We study the problem of local behavior of solutions to the Beltrami equations in arbitrary domains and establish sufficient conditions for the complex coefficient of the Beltrami equation guaranteeing the existence of its Hölder-continuous solution in an arbitrary domain. These results can be used both for the investigation of boundary-value problems for the Beltrami equation and in the problems of
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On the Polyconvolution with Weight Function γ(y) = cos y for Hartley Integral Transforms $${\mathcal{H}}_{1}$$ , $${\mathcal{H}}_{2}$$ , $${\mathcal{H}}_{1}$$ and Integral Equations Ukr. Math. J. (IF 0.5) Pub Date : 2023-10-06 N. M. Khoa, T. V. Thang
We construct and study a new polyconvolution with weight function γ(y) = cos y for Hartley integral transforms \({\mathcal{H}}_{1}\), \({\mathcal{H}}_{2}\), \({\mathcal{H}}_{1}\) and apply it to the solution of integral equations and a system of integral equations of polyconvolution type.
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d-Gaussian Fibonacci, d-Gaussian Lucas Polynomials, and their Matrix Representations Ukr. Math. J. (IF 0.5) Pub Date : 2023-10-05 E. Özkan, M. Uysal
We define d-Gaussian Fibonacci polynomials and d-Gaussian Lucas polynomials and present matrix representations of these polynomials. By using the Riordan method, we obtain the factorizations of the Pascal matrix, including polynomials. In addition, we define the infinite d-Gaussian Fibonacci polynomial matrix and the d-Gaussian Lucas polynomial matrix and present their inverses.
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σ-Centralizers of Triangular Algebras Ukr. Math. J. (IF 0.5) Pub Date : 2023-10-05 M. Ashraf, M. A. Ansari
We present a characterization of the Lie (Jordan) σ-centralizers of triangular algebras. More precisely, it is proved that, under certain conditions, every Lie σ-centralizer of a triangular algebra can be represented as the sum of a σ-centralizer and a central-valued mapping. It is also shown that every Jordan σ-centralizer of a triangular algebra is a σ-centralizer.
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Some Limit Theorems for the Critical Galton–Watson Branching Processes Ukr. Math. J. (IF 0.5) Pub Date : 2023-10-05 Kh. Kudratov, Ya. Khusanbaev
We consider the critical Galton–Watson processes starting from a random number of particles and determine the effect of the mean value of initial state on the asymptotic state of the process. For processes starting from large numbers of particles and satisfying condition (S), we prove the limit theorem similar to the result obtained by W. Feller. We also prove the theorem under the condition W(n) >
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Nonexistence Results for a System of Nonlinear Fractional Integrodifferential Equations Ukr. Math. J. (IF 0.5) Pub Date : 2023-10-05 A. Mugbil
We study the nonexistence of (nontrivial) global solutions for a system of nonlinear fractional equations. Each equation involves n fractional derivatives, a subfirst-order ordinary derivative, and a nonlinear source term. The fractional derivatives are of the Caputo type and their order lies between 0 and 1. The nonlinear sources have the form of the convolution of a function of state with (possibly
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Some Commutativity Criteria for Prime Rings with Involution Involving Symmetric and Skew Symmetric Elements Ukr. Math. J. (IF 0.5) Pub Date : 2023-10-05 N. A. Dar, S. Ali, A. Abbasi, M. Ayedh
We study the Posner second theorem [Proc. Amer. Math. Soc., 8, 1093–1100 (1957)] and strong commutativity preserving problem for symmetric and skew symmetric elements involving generalized derivations on prime rings with involution. The obtained results cover numerous known theorems. We also provide examples showing that the obtained results hold neither in the case of involution of the first kind
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On Mean Cartan Torsion of Finsler Metrics Ukr. Math. J. (IF 0.5) Pub Date : 2023-08-25 A. Dehghan Nezhad, S. Beizavi
We prove that Finsler manifolds with unbounded mean Cartan torsion cannot be isometrically imbedded into any Minkowski space. We also study the generalized Randers metrics obtained by the Rizza structure and show that any generalized Randers metric has an unbounded mean Cartan torsion. Then the generalized Randers metrics cannot be isometrically imbedded into any Minkowski space. Further, we prove
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Cospectral Quantum Graphs with Dirichlet Conditions at Pendant Vertices Ukr. Math. J. (IF 0.5) Pub Date : 2023-08-25 Vyacheslav Pivovarchik, Anastasia Chernyshenko
We consider spectral problems generated by the Sturm–Liouville equation on connected simple equilateral graphs with Neumann and Dirichlet boundary conditions imposed at pendant vertices and the conditions of continuity and Kirchhoff conditions imposed at the inner vertices. We describe the cases where the first and the second terms of the asymptotics of eigenvalues unambiguously determine the shape