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Some properties of the Hermite polynomials Georgian Math. J. (IF 0.5) Pub Date : 2021-01-15 Feng Qi; Bai-Ni Guo
In this paper, by the Faà di Bruno formula and properties of Bell polynomials of the second kind, the authors reconsider the generating functions of Hermite polynomials and their squares, find an explicit formula for higher-order derivatives of the generating function of Hermite polynomials, and derive explicit formulas and recurrence relations for Hermite polynomials and their squares.
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The consistent criteria for hypotheses testing Georgian Math. J. (IF 0.5) Pub Date : 2021-01-12 Omar Purtukhia; Zurab Zerakidze
In this paper, we define consistent criteria for hypotheses testing, such that the probability of any kind of error is zero for a given criterion. The necessary and sufficient conditions for the existence of such criteria are given.
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On a class of nonlinear elliptic problems with obstacle Georgian Math. J. (IF 0.5) Pub Date : 2020-12-16 Lahsen Aharouch; Mohammed Kbiri Alaoui; Giuseppe Di Fazio; Mohamed Altanji
This paper deals with the existence and regularity of some unilateral problem associated to a nonlinear equation of type -div(a(x,u,∇u))+H(x,u,∇u)=f.
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m-potent commutators of skew derivations on Lie ideals Georgian Math. J. (IF 0.5) Pub Date : 2020-12-11 Mohd Arif Raza; Shakir Ali; Husain Alhazmi
The purpose of this paper is to investigate the behavior of prime rings involving skew derivations with m-potent commutators on Lie ideals. In addition, we provide an example that shows that we cannot expect the same conclusion in case of semiprime rings. Also, we prove some other related results and present some open problems.
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On the generalized nonmeasurability of Vitali sets and Bernstein sets Georgian Math. J. (IF 0.5) Pub Date : 2020-11-20 Alexander Kharazishvili
It is shown that the cardinality of the continuum is not real-valued measurable if and only if there exists no nonzero σ-finite diffused measure μ on the real line such that all Vitali sets (respectively all Bernstein sets) are μ-measurable.
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On “On derivations and commutativity of prime rings with involution” Georgian Math. J. (IF 0.5) Pub Date : 2020-11-07 Fuad Ali Ahmed Almahdi
In this note, we indicate some errors in [S. Ali, N. A. Dar and M. Asci, On derivations and commutativity of prime rings with involution, Georgian Math. J. 23 2016, 1, 9–14] and present the correct versions of the erroneous results.
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Localized boundary-domain singular integral equations of the Robin type problem for self-adjoint second-order strongly elliptic PDE systems Georgian Math. J. (IF 0.5) Pub Date : 2020-11-12 Otar Chkadua; Sergey Mikhailov; David Natroshvili
The paper deals with the three-dimensional Robin type boundary-value problem (BVP) for a second-order strongly elliptic system of partial differential equations in the divergence form with variable coefficients. The problem is studied by the localized parametrix based potential method. By using Green’s representation formula and properties of the localized layer and volume potentials, the BVP under
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Hecke **-algebras on locally compact hypergroups Georgian Math. J. (IF 0.5) Pub Date : 2020-11-07 Seyyed Mohammad Tabatabaie; Bentolhoda Sadathoseyni
In this paper, for a discrete hypergroup K and its subhypergroup H, we initiate the related Hecke *-algebra which is an extension of the classical one, and study its basic properties. Especially, we give a necessary and sufficient condition (named (β)) for this algebra to be associative. Also, we show that this new structure is an associative *-algebra if and only if K is a locally compact group.
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On the Skitovich–Darmois theorem for complex and quaternion random variables Georgian Math. J. (IF 0.5) Pub Date : 2020-11-07 Gennadiy Feldman
We prove the following theorem. Let α=a+ib be a nonzero complex number. Then the following statements hold: (i) Let either b≠0 or b=0 and a>0. Let ξ1 and ξ2 be independent complex random variables. Assume that the linear forms L1=ξ1+ξ2 and L2=ξ1+αξ2 are independent. Then ξj are degenerate random variables. (ii) Let b=0 and a<0. Then there exist complex Gaussian random variables in the wide sense
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A note on the trace inequality for Riesz potentials Georgian Math. J. (IF 0.5) Pub Date : 2020-11-07 Giorgi Imerlishvili; Alexander Meskhi
We establish a necessary and sufficient condition on a non-negative locally integrable function v guaranteeing the (trace) inequality
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On functions continuous with respect to a density type strong generalized topology Georgian Math. J. (IF 0.5) Pub Date : 2020-11-07 Jacek Hejduk; Anna Loranty
In the paper, some properties of functions continuous with respect to a density type strong generalized topology are presented. In particular, it is proved that each real function is approximately continuous with respect to this generalized topology almost everywhere. Moreover, some separation axioms for this generalized topological space are investigated.
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𝑞-Tricomi functions and quantum algebra representations Georgian Math. J. (IF 0.5) Pub Date : 2020-10-21 Mumtaz Riyasat; Tabinda Nahid; Subuhi Khan
The quantum groups nowadays attract a considerable interest of mathematicians and physicists. The theory of 𝑞-special functions has received a group-theoretic interpretation using the techniques of quantum groups and quantum algebras. This paper focuses on introducing the 𝑞-Tricomi functions and 2D 𝑞-Tricomi functions through the generating function and series expansion and for the first time establishing
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Frontmatter Georgian Math. J. (IF 0.5) Pub Date : 2020-12-01
Journal Name: Georgian Mathematical Journal Volume: 27 Issue: 4 Pages: i-iv
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The uniform convergence of a double sequence of functions at a point and Korovkin-type approximation theorems Georgian Math. J. (IF 0.5) Pub Date : 2020-10-22 Fadime Dirik; Kamil Demirci; Sevda Yıldız; Ana Maria Acu
In this paper, we introduce an interesting kind of convergence for a double sequence called the uniform convergence at a point. We give an example and demonstrate a Korovkin-type approximation theorem for a double sequence of functions using the uniform convergence at a point. Then we show that our result is stronger than the Korovkin theorem given by Volkov and present several graphs. Finally, in
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Mixed type boundary value problems for Laplace–Beltrami equation on a surface with the Lipschitz boundary Georgian Math. J. (IF 0.5) Pub Date : 2020-08-11 Roland Duduchava
The purpose of the present research is to investigate a general mixed type boundary value problem for the Laplace–Beltrami equation on a surface with the Lipschitz boundary 𝒞 in the non-classical setting when solutions are sought in the Bessel potential spaces Hps(C), 1p
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Frontmatter Georgian Math. J. (IF 0.5) Pub Date : 2020-09-01
Journal Name: Georgian Mathematical Journal Volume: 27 Issue: 3 Pages: i-iv
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Regular Hom-algebras admitting a multiplicative basis Georgian Math. J. (IF 0.5) Pub Date : 2020-07-16 Antonio J. Calderón Martín
Let (ℌ,μ,α) be a regular Hom-algebra of arbitrary dimension and over an arbitrary base field 𝔽. A basis ℬ={ei}i∈I of ℌ is called multiplicative if for any i,j∈I, we have that μ(ei,ej)∈𝔽ek and α(ei)∈𝔽ep for some k,p∈I. We show that if ℌ admits a multiplicative basis, then it decomposes as the direct sum ℌ=⊕rℑr of well-described ideals admitting each one a multiplicative basis. Also, the minimality
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m-potent commutators involving skew derivations and multilinear polynomials Georgian Math. J. (IF 0.5) Pub Date : 2020-07-16 Mohammad Ashraf; Sajad Ahmad Pary; Mohd Arif Raza
Let ℛ be a prime ring, 𝒬r the right Martindale quotient ring of ℛ and 𝒞 the extended centroid of ℛ. In this paper, we discuss the relationship between the structure of prime rings and the behavior of skew derivations on multilinear polynomials. More precisely, we investigate the m-potent commutators of skew derivations involving multilinear polynomials, i.e.,
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On some higher order equations admitting meromorphic solutions in a given domain Georgian Math. J. (IF 0.5) Pub Date : 2020-08-11 Grigor Barsegian; Fanning Meng
This paper relates to a recent trend in complex differential equations which studies solutions in a given domain. The classical settings in complex equations were widely studied for meromorphic solutions in the complex plane. For functions in the complex plane, we have a lot of results of general nature, in particular, the classical value distributions theory describing numbers of a-points. Many of
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Weighted grand mixed-norm Lebesgue spaces and boundedness criteria for integral operators Georgian Math. J. (IF 0.5) Pub Date : 2020-08-11 Vakhtang Kokilashvili
A new scale of weighted grand mixed norm Lebesgue spaces Lw1p1,φ1(Lw2p2,φ2) is introduced and the boundedness criteria for multiple singular operators are established.
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Admissible Galois Structures on the categories dual to some varieties of universal algebras Georgian Math. J. (IF 0.5) Pub Date : 2020-08-04 Dali Zangurashvili
The subject of the paper is suggested by G. Janelidze and motivated by his earlier result giving a positive answer to the question posed by S. MacLane whether the Galois theory of homogeneous linear ordinary differential equations over a differential field (which is Kolchin–Ritt theory and an algebraic version of Picard–Vessiot theory) can be obtained as a particular case of G. Janelidze’s Galois theory
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Asymptotic behavior of solutions of half-linear differential equations and generalized Karamata functions Georgian Math. J. (IF 0.5) Pub Date : 2020-08-06 Kusano Takaŝi; Jelena V. Manojlović
We study the asymptotic behavior of eventually positive solutions of the second-order half-linear differential equation
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On the capability of Leibniz algebras Georgian Math. J. (IF 0.5) Pub Date : 2020-07-16 Emzar Khmaladze; Revaz Kurdiani; Manuel Ladra
We study the capability property of Leibniz algebras via the non-abelian exterior product.
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Continuous abstract wavelet transform on homogeneous spaces Georgian Math. J. (IF 0.5) Pub Date : 2020-07-16 Jyoti Sharma; Ajay Kumar
The support of a wavelet transform associated with a square integrable irreducible representation of a homogeneous space is shown to have infinite measure. Assumptions are illustrated and supported by examples. The pointwise homogeneous approximation property for a wavelet transform has been investigated. An analogue of Heisenberg type inequality is also obtained for a wavelet transform on a wavelet
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Singular integral operators in some variable exponent Lebesgue spaces Georgian Math. J. (IF 0.5) Pub Date : 2020-07-16 Vakhtang Kokilashvili; Mieczysław Mastyło; Alexander Meskhi
The paper deals with the exploration of those subclasses of the variable exponent Lebesgue space Lp(⋅) with minp(⋅)=1, which are invariant with respect to Cauchy singular integral operators.
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Higher-order commutators with power central values on rings and algebras involving generalized derivations Georgian Math. J. (IF 0.5) Pub Date : 2020-06-11 Shakir Ali; Husain Alhazmi; Abdul Nadim Khan; Mohd Arif Raza
Let ℜ be a ring with center Z(ℜ). In this paper, we study the higher-order commutators with power central values on rings and algebras involving generalized derivations. Motivated by [A. Alahmadi, S. Ali, A. N. Khan and M. Salahuddin Khan, A characterization of generalized derivations on prime rings, Comm. Algebra 44 2016, 8, 3201–3210], we characterize generalized derivations and related maps that
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Asymptotic relations involving 𝑑-orthogonal polynomials Georgian Math. J. (IF 0.5) Pub Date : 2020-06-11 Imed Lamiri; Jihen Weslati
In this paper, we consider a natural extension in the context of d-orthogonality for asymptotic analysis of orthogonal polynomials. We introduce, for several d-orthogonal polynomials, asymptotic expansions in terms of d-Hermite ones. From these expansions, several limits between d-orthogonal polynomials are obtained.
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Some properties of an odd-dimensional space Georgian Math. J. (IF 0.5) Pub Date : 2020-06-01 Vakhtang Tsagareishvili
In this paper, we investigate the absolute convergence of Fourier series of functions in several variables for an odd-dimensional space when these functions have continuous partial derivatives. It should be noted that similar properties for an even-dimensional space were given in [L. D. Gogoladze and V. S. Tsagareishvili, On absolute convergence of multiple Fourier series (in Russian), Izv. Vyssh.
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Fixed fuzzy point results of generalized Suzuki type F-contraction mappings in ordered metric spaces Georgian Math. J. (IF 0.5) Pub Date : 2020-06-01 Naeem Saleem; Mujahid Abbas; Zahid Raza
The aim of this paper is to introduce generalized Suzuki type F-contraction fuzzy mappings and to prove the existence of fixed fuzzy points for such mappings in the setup of complete ordered metric spaces. An example is provided to show the validity of our results, followed by couple of remarks about the comparison of obtained results with the existing results in the literature. An application of our
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Representations for the image-kernel (p,q)-inverses of block matrices in rings Georgian Math. J. (IF 0.5) Pub Date : 2020-06-01 Dijana Mosić
We present the conditions for a block matrix of a ring to have the image-kernel (p,q)-inverse in the generalized Banachiewicz–Schur form. We give representations for the image-kernel inverses of the sum and the product of two block matrices. Some characterizations of the image-kernel (p,q)-inverse in a ring with involution are investigated too.
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Relative h-preinvex functions and integral inequalities Georgian Math. J. (IF 0.5) Pub Date : 2020-06-01 Marian Matłoka
In this paper, we consider a new class of convex functions, called relative h-preivex functions. Seven new inequalities of Hermite–Hadamard type for relative h-preinvex functions are established using different approaches.
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Weighted boundedness of multilinear singular integral operators with non-smooth kernels for the extreme cases Georgian Math. J. (IF 0.5) Pub Date : 2020-06-01 Weiping Kuang
The weighted boundedness properties of multilinear operators associated to singular integral operators with non-smooth kernels for extreme cases are obtained.
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On finite sums of periodic functions Georgian Math. J. (IF 0.5) Pub Date : 2020-06-01 Alexander Kharazishvili
It is shown that any function acting from the real line ℝ into itself can be expressed as a pointwise limit of finite sums of periodic functions. At the same time, the real analytic function x→exp(x2) cannot be represented as a uniform limit of finite sums of periodic functions and, simultaneously, this function is a locally uniform limit of finite sums of periodic functions. The latter fact needs
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A quasistatic frictional contact problem for viscoelastic materials with long memory Georgian Math. J. (IF 0.5) Pub Date : 2020-06-01 Abderrezak Kasri; Arezki Touzaline
The aim of this paper is to study a quasistatic frictional contact problem for viscoelastic materials with long-term memory. The contact boundary conditions are governed by Tresca’s law, involving a slip dependent coefficient of friction. We focus our attention on the weak solvability of the problem within the framework of variational inequalities. The existence of a solution is obtained under a smallness
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p(x)p(x)-biharmonic operator involving the p(x)p(x)-Hardy inequality Georgian Math. J. (IF 0.5) Pub Date : 2020-06-01 Abdelouahed El Khalil; Mostafa El Moumni; Moulay Driss Morchid Alaoui; Abdelfattah Touzani
In this work, we investigate the spectrum denoted by Λ for the p(x)-biharmonic operator involving the Hardy term. We prove the existence of at least one non-decreasing sequence of positive eigenvalues of this problem such that supΛ=+∞. Moreover, we prove that infΛ>0 if and only if the domain Ω satisfies the p(x)-Hardy inequality.
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Extended Mittag-Leffler function and associated fractional calculus operators Georgian Math. J. (IF 0.5) Pub Date : 2020-06-01 Junesang Choi; Rakesh K. Parmar; Purnima Chopra
Motivated mainly by certain interesting recent extensions of the generalized hypergeometric function [H. M. Srivastava, A. Çetinkaya and I. Onur Kıymaz, A certain generalized Pochhammer symbol and its applications to hypergeometric functions, Appl. Math. Comput. 226 2014, 484–491] by means of the generalized Pochhammer symbol, we introduce here a new extension of the generalized Mittag-Leffler function
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A variation on Nθ ward continuity Georgian Math. J. (IF 0.5) Pub Date : 2020-06-01 Huseyin Cakalli; Mikail Et; Hacer Şengül
The main purpose of this paper is to introduce the concept of strongly ideal lacunary quasi-Cauchyness of sequences of real numbers. Strongly ideal lacunary ward continuity is also investigated. Interesting results are obtained.
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d-orthogonality of a generalization of both Laguerre and Hermite polynomials Georgian Math. J. (IF 0.5) Pub Date : 2020-06-01 Mongi Blel; Youssèf Ben Cheikh
In this work, we give a unification and generalization of Laguerre and Hermite polynomials for which the orthogonal property is replaced by d-orthogonality. We state some properties of these new polynomials.
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On the main oscillational properties of fractional differential equations Georgian Math. J. (IF 0.5) Pub Date : 2020-06-01 Temirkhan S. Aleroev; Hedi T. Aleroeva; Oleg A. Kovalchuk; Yifa Tang
The paper establishes the basic oscillational properties of differential equations of fractional order. It is also shown that the so-called fractional oscillational equation does not have the basic oscillational properties.
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On the solutions of a higher order difference equation Georgian Math. J. (IF 0.5) Pub Date : 2020-06-01 Raafat Abo-Zeid
In this paper, we determine the forbidden set, introduce an explicit formula for the solutions and discuss the global behavior of solutions of the difference equation
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Frontmatter Georgian Math. J. (IF 0.5) Pub Date : 2020-06-01
Journal Name: Georgian Mathematical Journal Volume: 27 Issue: 2 Pages: i-iv
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Ulam type stability for non-instantaneous impulsive Caputo fractional differential equations with finite state dependent delay Georgian Math. J. (IF 0.5) Pub Date : 2020-04-21 Ravi Agarwal; Snezhana Hristova; Donal O’Regan
Four Ulam type stability concepts for non-instantaneous impulsive fractional differential equations with state dependent delay are introduced. Two different approaches to the interpretation of solutions are investigated. We study the case of an unchangeable lower bound of the Caputo fractional derivative and the case of a lower bound coinciding with the point of jump for the solution. In both cases
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A note on the strong summability of two-dimensional Walsh–Fourier series Georgian Math. J. (IF 0.5) Pub Date : 2020-04-15 George Tephnadze
In this paper, we investigate the strong summability of two-dimensional Walsh–Fourier series obtained in [F. Weisz, Strong convergence theorems for two-parameter Walsh–Fourier and trigonometric-Fourier series, Studia Math. 117 1996, 2, 173–194] (see Theorem ) and prove the sharpness of this result.
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Some remarks on Sierpiński–Zygmund functions in the strong sense Georgian Math. J. (IF 0.5) Pub Date : 2020-04-15 Alexander Kharazishvili
For certain families of topologies, the existence of a common Sierpiński–Zygmund function (of a common Sierpiński–Zygmund function in the strong sense) is established. In this connection, the notion of a Sierpiński–Zygmund space (of a Sierpiński–Zygmund space in the strong sense) is introduced and examined. The behavior of such spaces under some standard topological operations is considered.
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On n-Hom-Leibniz algebras and cohomology Georgian Math. J. (IF 0.5) Pub Date : 2020-04-15 Abdenacer Makhlouf; Anita Naolekar
The purpose of this paper is to provide a cohomology of n-Hom-Leibniz algebras. Moreover, we study some higher operations on cohomology spaces and deformations.
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Weighted higher order exponential type inequalities in metric spaces and applications Georgian Math. J. (IF 0.5) Pub Date : 2020-04-15 Huiju Wang; Pengcheng Niu
In this paper, we establish weighted higher order exponential type inequalities in the geodesic space (X,d,μ) by proposing an abstract higher order Poincaré inequality. These are also new in the non-weighted case. As applications, we obtain a weighted Trudinger’s theorem in the geodesic setting and weighted higher order exponential type estimates for functions in Folland–Stein type Sobolev spaces defined
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Local variation formulas of solutions for nonlinear controlled functional differential equations with constant delays and the discontinuous initial condition Georgian Math. J. (IF 0.5) Pub Date : 2020-01-17 Tea Shavadze
For the nonlinear controlled functional differential equations with several constant delays, the local variation formulas of solutions are proved, in which the effects of the discontinuous initial condition and perturbations of delays and the initial moment are detected.
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W(Lp,Lq) boundedness of localization operators associated with the Stockwell transform Georgian Math. J. (IF 0.5) Pub Date : 2020-01-17 Ahmet Turan Gürkanlı; Yaşar Nuri Sevgen
In this paper we study the boundedness of localization operators associated with the Stockwell transform with symbol in Lp acting on the Wiener amalgam space W(Lp,Lq)(ℝ).
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Trigonometric identities inspired by the atomic form factor Georgian Math. J. (IF 0.5) Pub Date : 2020-01-17 Abhijit Sen; Zurab K. Silagadze
We prove some trigonometric identities involving Chebyshev polynomials of the second kind. The identities were inspired by atomic form factor calculations. Generalizations of these identities, if found, will help to increase the numerical stability of atomic form factor calculations for highly excited states.
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Averaged semi-discrete scheme of sum-approximation for one nonlinear multi-dimensional integro-differential parabolic equation Georgian Math. J. (IF 0.5) Pub Date : 2019-11-26 Temur Jangveladze; Zurab Kiguradze
The paper is devoted to the construction and study of the additive averaged semi-discrete scheme for one nonlinear multi-dimensional integro-differential equation of parabolic type. The studied equation is based on the well-known Maxwell’s system arising in mathematical simulation of electromagnetic field penetration into a substance.
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Oscillation of first-order differential equations with several non-monotone retarded arguments Georgian Math. J. (IF 0.5) Pub Date : 2019-10-15 Huseyin Bereketoglu; Fatma Karakoc; Gizem S. Oztepe; Ioannis P. Stavroulakis
Consider the first-order linear differential equation with several non-monotone retarded arguments x′(t)+∑i=1mpi(t)x(τi(t))=0, t≥t0, where the functions pi,τi∈C([t0,∞),ℝ+), for every i=1,2,…,m, τi(t)≤t for t≥t0 and limt→∞τi(t)=∞. New oscillation criteria which essentially improve the known results in the literature are established. An example illustrating the results is given.
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Mixed boundary value problems for the Helmholtz equation in a model 2D angular domain Georgian Math. J. (IF 0.5) Pub Date : 2019-07-12 Roland Duduchava; Medea Tsaava
The purpose of the present research is to investigate model mixed boundary value problems (BVPs) for the Helmholtz equation in a planar angular domain Ωα⊂ℝ2 of magnitude α. These problems are considered in a non-classical setting when a solution is sought in the Bessel potential spaces ℍps(Ωα), s>1p, 1
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Idempotent matrices with invertible transpose Georgian Math. J. (IF 0.5) Pub Date : 2019-06-13 Grigore Călugăreanu
We prove that if the transpose of every 2×2 idempotent matrix over a division ring D, different from the identity matrix, is not invertible, then D is commutative.
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The method of finite differences for nonlinear functional differential equations of the first order Georgian Math. J. (IF 0.5) Pub Date : 2019-05-10 Elżbieta Puźniakowska-Gałuch
Nonlinear functional partial differential equations with initial conditions are considered on the cone. The weak convergence of a sequence of successive approximations is proved. The proof is given by the duality principle.
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Approximation by modified Jain–Baskakov operators Georgian Math. J. (IF 0.5) Pub Date : 2019-02-16 Vishnu Narayan Mishra; Preeti Sharma; Marius Mihai Birou
In the present paper, we discuss the approximation properties of Jain–Baskakov operators with parameter c. The paper deals with the modified forms of the Baskakov basis functions. Some direct results are established, which include the asymptotic formula, error estimation in terms of the modulus of continuity and weighted approximation. Also, we construct the King modification of these operators, which
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Construction of Green’s functional for a third order ordinary differential equation with general nonlocal conditions and variable principal coefficient Georgian Math. J. (IF 0.5) Pub Date : 2019-02-15 Kemal Özen
In this work, the solvability of a generally nonlocal problem is investigated for a third order linear ordinary differential equation with variable principal coefficient. A novel adjoint problem and Green’s functional are constructed for a completely nonhomogeneous problem. Several illustrative applications for the theoretical results are provided.
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L2L^{2} boundedness for commutators of fractional differential type Marcinkiewicz integral with rough variable kernel and BMO Sobolev spaces Georgian Math. J. (IF 0.5) Pub Date : 2019-02-15 Yanping Chen; Yong Ding; Kai Zhu
In this paper, for 0<γ<1 and b∈Iγ(BMO), the authors give the L2(ℝn) boundedness of μγ;b, the commutator of a fractional differential type Marcinkiewicz integral with rough variable kernel, which is an extension of some known results.
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General Tauberian theorems for the Cesàro integrability of functions Georgian Math. J. (IF 0.5) Pub Date : 2019-02-15 Ümit Totur; İbrahim Çanak
For a locally integrable function f on [0,∞), we define
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Solutions to Neumann boundary value problems with a generalized 𝑝-Laplacian Georgian Math. J. (IF 0.5) Pub Date : 2019-01-30 Katarzyna Szymańska-Dȩbowska
The purpose of this work is to investigate the existence of solutions for various Neumann boundary value problems associated to the Laplacian-type operators. The main results are obtained using the extension of Mawhin’s continuation theorem.
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Stabilization of 3D Navier–Stokes–Voigt equations Georgian Math. J. (IF 0.5) Pub Date : 2018-12-05 Cung The Anh; Nguyen Viet Tuan
We consider 3D Navier–Stokes–Voigt equations in smooth bounded domains with homogeneous Dirichlet boundary conditions. First, we study the existence and exponential stability of strong stationary solutions to the problem. Then we show that any unstable steady state can be exponentially stabilized by using either an internal feedback control with a support large enough or a multiplicative Itô noise
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