Article
Mathematics
Maha A. Omair, Yusra A. Tashkandy, Sameh Askar, Abdulhamid A. Alzaid
Summary: In this paper, we present a general family of distributions based on the Whittaker function. The properties of the obtained distributions, including moments, ordering, percentiles, and unimodality, are studied. The parameters of the distributions are estimated using the methods of moments and maximum likelihood. Additionally, a generalized Whittaker distribution that includes a wider class of distributions is developed. The obtained results are validated using real-life data consisting of four data sets.
Article
Mathematics
Al-Nashri Al-Hossain Ahmad, Sami H. Altoum
Summary: In this article, we introduce the q-time deformed wave equation and the free-time wave equation, and provide their solutions and the limit case when q tends to 0.
JOURNAL OF MATHEMATICS
(2022)
Article
Mathematics
Eric Stade, Tien Trinh
Summary: In this paper, an explicit recurrence relation is developed for the Mellin transform T-n,T-a(s) of a spherical, principal series GL(n, R) Whittaker function using a recursive formula, involving strictly positive shifts. The focus is placed on the case n = 4, where further relations are derived involving strictly positive shifts in the coordinates of s. A recurrence relation for T-4,T-a(s) involving shifts in all three s(k)'s simultaneously is then deduced, providing insight into certain poles and residues. This residue information is connected to recent results on orthogonality of Fourier coefficients of SL(4, Z) Maass forms and the GL(4) Kuznetsov formula.
JOURNAL OF FUNCTIONAL ANALYSIS
(2021)
Article
Mathematics
Ryo Fujita, Kota Murakami
Summary: We provide an interpretation of the (q, t)-deformed Cartan matrices of finite type and their inverses using bigraded modules over the generalized preprojective algebras of Langlands dual type. As an application, we calculate the first extension groups between the generic kernels introduced by Hernandez-Leclerc and propose a conjecture that their dimensions coincide with the pole orders of the normalized R-matrices between the corresponding Kirillov-Reshetikhin modules.
INTERNATIONAL MATHEMATICS RESEARCH NOTICES
(2023)
Article
Mathematics
Sam Raskin
Summary: This paper initiates a study of D-modules on the FeiginFrenkel semi-infinite flag variety using the Beilinson-Drinfeld factorization theory. By calculating Whittaker-twisted cohomology groups of Zastava spaces, certain finite-dimensional subvarieties of the affine Grassmannian, it is shown that these cohomology groups realize the nilradical of a Borel subalgebra for the Langlands dual group in a precise sense. This geometric realization of the Langlands dual group is compared to the standard one provided by (factorizable) geometric Satake.
ADVANCES IN MATHEMATICS
(2021)
Article
Mathematics, Applied
Semyon Yakubovich
Summary: This research introduces and investigates discrete analogs of the index Whittaker transform, involving series and integrals with respect to parameters of the Whittaker function. Inversion formulas for suitable functions and sequences are established based on these series and integrals.
RESULTS IN MATHEMATICS
(2021)
Article
Mathematics
B. Feigin, M. Jimbo, E. Mukhin
Summary: This article considers sets of screening operators with fermionic screening currents. The sums of vertex operators that commute with the screening operators are studied, assuming that each vertex operator has rational contractions with all screening currents with only simple poles. The method of qq-characters, which are combinatorial objects described in terms of deformed Cartan matrix, is developed and used. It is shown that each qq-character gives rise to a sum of vertex operators commuting with screening operators, and ways to understand the sum in the case it is infinite are described. The combinatorics of the qq-characters and their relation to the q-characters of representations of quantum groups are discussed. Several explicit examples of qq-characters are provided, with an emphasis on the case of D(2, 1; alpha). A relationship of the examples to various integrals of motion is described.
ADVANCES IN MATHEMATICS
(2022)
Article
Computer Science, Information Systems
Maria Munoz-Guillermo
Summary: This paper presents an image encryption algorithm based on a deformed chaotic map, which increases the key space size and provides a parametric region for key selection to avoid non-chaotic regions, thereby enhancing the efficiency and robustness of the encryption algorithm in resisting attacks.
INFORMATION SCIENCES
(2021)
Article
Physics, Multidisciplinary
Andre A. Marinho, Francisco A. Brito
Summary: By considering different combinations of deformed algebras, we propose the concept of a hybrid deformed algebra and study new scenarios using the mean value of the deformed occupation number. The deformation parameters drive the changes in thermodynamic quantities, and there exists a special relationship between deformed and ordinary derivatives at high temperatures.
EUROPEAN PHYSICAL JOURNAL PLUS
(2022)
Article
Mathematics, Applied
Limeng Xia, Kaiming Zhao
Summary: In this paper, we introduce and study the twisted Whittaker modules over U-q(gl(n+1)) by choosing different generators. We classify all the simple twisted Whittaker modules with nonsingular Whittaker functions, which agrees with Kostant's results for the simple complex Lie algebras sl(n+1) as q approaches 1.
SCIENCE CHINA-MATHEMATICS
(2023)
Article
Mathematics, Applied
Jose S. Canovas
Summary: The paper discusses the non-zero fixed points of the composition map f(a) circle phi(q) of the logistic family fa and a family of homeomorphisms phi(q), as well as the dynamics of the q-deformed system with special emphasis on parameters values that exhibit Parrondo's paradox. The study explores the dynamics when multiple q-deformations are applied.
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B
(2022)
Article
Mathematics, Interdisciplinary Applications
Jose S. Canovas, Houssem Eddine Rezgui
Summary: In this paper, we investigate the q-deformed logistic map family and analyze the stability regions of its fixed points as well as the regions where the dynamics exhibit complexity using topological entropy and Lyapunov exponents. Our findings suggest that the dynamics of this deformed family are richer compared to the q-deformed family studied in Canovas (2022).
CHAOS SOLITONS & FRACTALS
(2023)
Article
Physics, Applied
Ge Yi, Wei Wang, Kelei Tian, Ying Xu
Summary: In this paper, the form of q-cmKP hierarchy generated by the gauge transformation operator Tn+k is given. A necessary and sufficient condition is shown to reduce the generalized q-Wronskian solutions from the q-mKP hierarchy to the generalized q-Wronskian solutions of M-component q-cmKP hierarchy.
MODERN PHYSICS LETTERS B
(2022)
Article
Mathematics
Juan Camilo Arias, Erik Backelin
Summary: The Whittaker functor in a regular block of the BGG-category O of a semisimple complex Lie algebra can be obtained by composing a translation to the wall functor with the equivalence between the category of Whittaker modules and a singular block of O proposed by Soergel and Milicic. It is shown that the Whittaker functor is a quotient functor that commutes with all projective functors and endomorphisms between them.
JOURNAL OF ALGEBRA
(2021)
Article
Mathematics, Applied
Waewta Luangboon, Kamsing Nonlaopon, Jessada Tariboon, Sortiris K. Ntouyas
Summary: In this paper, a new (p, q)-integral identity is established, which is then used to derive (p, q)-integral Simpson type inequalities involving generalized strongly preinvex functions. Furthermore, the results are applied to study special cases and examples are provided to illustrate the findings.
