المؤلفون: Khan, Subuhi¹ (AUTHOR) subuhi2006@gmail.com, Haneef, Mehnaz¹ (AUTHOR) mehnaz272@gmail.com

المصدر: Forum Mathematicum. Jul2024, Vol. 36 Issue 4, p983-994. 12p.

مصطلحات موضوعية: *POLYNOMIALS, *INTEGRAL representations, *GENERATING functions

مستخلص: In this article, the post quantum analogue of Sheffer polynomial sequences is introduced using concepts of post quantum calculus. The series representation, recurrence relations, determinant expression and certain other properties of this class are established. Further, the 2D-post quantum-Sheffer polynomials are introduced via generating function and their properties are established. Certain identities and integral representations for the 2D-post quantum-Hermite polynomials, 2D-post quantum-Laguerre polynomials, and 2D-post quantum-Bessel polynomials are also considered. [ABSTRACT FROM AUTHOR]

المؤلفون: Belousov, N.^1,2 (AUTHOR), Derkachov, S.^1,2 (AUTHOR) derkach@pdmi.ras.ru, Kharchev, S.^3,4 (AUTHOR), Khoroshkin, S.^4,5 (AUTHOR)

المصدر: Annales Henri Poincaré. Jul2024, Vol. 25 Issue 7, p3259-3296. 38p.

مصطلحات موضوعية: *INTEGRAL representations, *YANG-Baxter equation, *WAVE functions, *PROBLEM solving

مستخلص: In the previous paper, we introduced a commuting family of Baxter Q-operators for the quantum Ruijsenaars hyperbolic system. In the present work, we show that the wave functions of the quantum system found by M. Hallnäs and S. Ruijsenaars also diagonalize Baxter operators. Using this property, we prove the conjectured duality relation for the wave function. As a corollary, we show that the wave function solves bispectral problems for pairs of dual Macdonald and Baxter operators. Besides, we prove the conjectured symmetry of the wave function with respect to spectral variables and obtain new integral representation for it. [ABSTRACT FROM AUTHOR]

المؤلفون: Eleuteri, Michela¹ (AUTHOR) michela.eleuteri@unimore.it, Prinari, Francesca² (AUTHOR) francesca.prinari@unipi.it, Zappale, Elvira³ (AUTHOR) elvira.zappale@uniroma1.it

المصدر: Mathematical Models & Methods in Applied Sciences. Jul2024, Vol. 34 Issue 8, p1401-1443. 43p.

مصطلحات موضوعية: *INTEGRAL representations, *THIN films, *ENERGY density

مستخلص: In this paper, 3D–2D-dimensional reduction for hyperelastic thin films modeled through energies with point-dependent growth, assuming that the sample is clamped on the lateral boundary, is performed in the framework of Γ -convergence. Integral representation results, with a more regular Lagrangian related to the original energy density, are provided for the lower dimensional limiting energy, in different contexts. [ABSTRACT FROM AUTHOR]

المؤلفون: Huang, Yun¹ (AUTHOR), Deng, Guan-Tie² (AUTHOR) denggt@bnu.edu.cn, Qian, Tao³ (AUTHOR)

المصدر: Complex Variables & Elliptic Equations. Jun2024, Vol. 69 Issue 6, p1021-1040. 20p.

مصطلحات موضوعية: *INTEGRAL representations, *HOLOMORPHIC functions, *BERGMAN spaces, *TUBES

مستخلص: Herein, the Laplace transform representations for functions of weighted holomorphic Bergman spaces on the tube domains are developed. Then a weighted version of the edge-of-the-wedge theorem is derived as a byproduct of the main results. [ABSTRACT FROM AUTHOR]

المؤلفون: Alqarni, Mohammed Z.¹ (AUTHOR) mzalzarni@kku.edu.sa

المصدر: Mathematics (2227-7390). Jun2024, Vol. 12 Issue 11, p1674. 15p.

مصطلحات موضوعية: *MATRIX functions, *INTEGRAL representations, *BETA functions, *PROBABILITY theory, *ARGUMENT

مستخلص: The beta-logarithmic function substantially generalizes the standard beta function, which is widely recognized for its significance in many applications. This article is devoted to the study of a generalization of the classical beta-logarithmic function in a matrix setting called the extended beta-logarithmic matrix function. The proofs of some essential properties of this extension, such as convergence, partial derivative formulas, functional relations, integral representations, inequalities, and finite and infinite sums, are established. Moreover, an application of the extended beta-logarithmic function in matrix arguments is proposed in probability theory. Further, numerical examples and graphical presentations of the new generalization are obtained. [ABSTRACT FROM AUTHOR]

المؤلفون: Askari, Hassan¹ (AUTHOR), Ansari, Alireza¹ (AUTHOR) ansari.alireza@sku.ac.ir

المصدر: Fractional Calculus & Applied Analysis. Jun2024, Vol. 27 Issue 3, p1162-1185. 24p.

مصطلحات موضوعية: *INTEGRAL representations, *EQUATIONS

مستخلص: In this paper, we apply the steepest descent method to the Schläfli-type integral representation of the three-parameter Mittag-Leffler function (well-known as the Prabhakar function). We find the asymptotic expansions of this function for its large parameters with respect to the real and complex saddle points. For each parameter, we separately establish a relation between the variable and parameter of function to determine the leading asymptotic term. We also introduce differentiations of the three-parameter Mittag-Leffler functions with respect to parameters and modify the associated asymptotic expansions for their large parameters. As an application, we derive the leading asymptotic term of fundamental solution of the time-fractional sub-diffusion equation including the Bessel operator with large order. [ABSTRACT FROM AUTHOR]

المؤلفون: Alatawi, Maryam Salem¹ (AUTHOR) msoalatawi@ut.edu.sa, Kumar, Manoj² (AUTHOR) mkumar5@myamu.ac.in, Raza, Nusrat³ (AUTHOR) nusrat.wc@amu.ac.in, Khan, Waseem Ahmad⁴ (AUTHOR) wkhan1@pmu.edu.sa

المصدر: Mathematics (2227-7390). May2024, Vol. 12 Issue 10, p1497. 17p.

مصطلحات موضوعية: *POLYNOMIALS, *INTEGRAL representations, *GENERATING functions, *DIFFERENTIAL equations, *HERMITE polynomials, *SYMBOLIC computation, *HYPERGEOMETRIC series

مستخلص: This article aims to introduce a set of hybrid matrix polynomials associated with λ -polynomials and explore their properties using a symbolic approach. The main outcomes of this study include the derivation of generating functions, series definitions, and differential equations for the newly introduced two-variable Hermite λ -matrix polynomials. Furthermore, we establish the quasi-monomiality property of these polynomials, derive summation formulae and integral representations, and examine the graphical representation and symmetric structure of their approximate zeros using computer-aided programs. Finally, this article concludes by introducing the idea of 1-variable Hermite λ matrix polynomials and their structure of zeros using a computer-aided program. [ABSTRACT FROM AUTHOR]

المؤلفون: Stepanova, I. E.¹ (AUTHOR) tet@ifz.ru, Kolotov, I. I.² (AUTHOR)

المصدر: Doklady Earth Sciences. May2024, Vol. 516 Issue 1, p835-843. 9p.

مصطلحات موضوعية: *INTEGRAL representations, *INVERSION (Geophysics), *GEOPHYSICS, *GRAVITY, *TOMOGRAPHY

مستخلص: A fundamentally new approach to solving inverse problems in geophysics based on the linear integral representation method and the theories of discrete gravity and the magnetic potential is proposed. This approach makes it possible to reconstruct the continuously distributed masses with a relatively high accuracy from the heterogeneous data at some grid points. [ABSTRACT FROM AUTHOR]

المؤلفون: Knoerr, Jonas¹ (AUTHOR) jonas.knoerr@tuwien.ac.at

المصدر: Calculus of Variations & Partial Differential Equations. May2024, Vol. 63 Issue 4, p1-34. 34p.

مصطلحات موضوعية: *VALUATION, *INTEGRAL representations, *CONVEX functions, *RADON

مستخلص: Two classes of measure-valued valuations on convex functions related to Monge–Ampère operators are investigated and classified. It is shown that the space of all valuations with values in the space of complex Radon measures on R n that are locally determined, continuous, dually epi-translation invariant as well as translation equivariant, is finite dimensional. Integral representations of these valuations and a description in terms of mixed Monge–Ampère operators are established, as well as a characterization of SO (n) -equivariant valuations in terms of Hessian measures. [ABSTRACT FROM AUTHOR]

المؤلفون: Karachik, V. V.¹ (AUTHOR) karachik@susu.ru

المصدر: Computational Mathematics & Mathematical Physics. May2024, Vol. 64 Issue 5, p1015-1028. 14p.

مصطلحات موضوعية: *UNIT ball (Mathematics), *INTEGRAL representations, *EQUATIONS

مستخلص: The Green's function of the Riquier–Neumann problem for the polyharmonic equation in the unit ball is constructed, and an integral representation of solutions to the Riquier–Neumann problem is presented. Two examples are given. [ABSTRACT FROM AUTHOR]