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Axioms, Volume 13, Issue 6

June 2024 - 78 articles

Cover Story: The Selberg trace formula is a celebrated theorem relating spectral theory, geometry and number theory. In its original form, it relates the spectrum of the Laplacian on a hyperbolic surface to lengths of closed geodesics on the surface. It can be viewed as a non-Abelian generalization of the Poisson summation formula in Fourier analysis. In this paper, we prove an analogue of this result for general linear groups of 3 by 3 matrices over finite fields by defining an analogue of the Poincare upper half plane for general linear groups over finite fields. We give explicit formulas for orbital sums defined by hyperbolic, elliptic and parabolic elements in the group. View this paper
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Articles (78)

  • Article
  • Open Access
1,151 Views
16 Pages

16 June 2024

Since its inception, evolution theory has garnered much attention from the scientific community for a good reason: it theorizes how various living organisms came to be and what changes are to be expected in a certain environment. While many models of...

  • Article
  • Open Access
2 Citations
1,295 Views
25 Pages

16 June 2024

Both theoretical and applied mathematics depend heavily on integral inequalities with generalized convexity. Because of its many applications, the theory of integral inequalities is currently one of the areas of mathematics that is evolving at the fa...

  • Article
  • Open Access
4 Citations
1,433 Views
16 Pages

On the Generalized Stabilities of Functional Equations via Isometries

  • Muhammad Sarfraz,
  • Jiang Zhou,
  • Yongjin Li and
  • John Michael Rassias

14 June 2024

The main goal of this research article is to investigate the stability of generalized norm-additive functional equations. This study demonstrates that these equations are Hyers-Ulam stable for surjective functions from an arbitrary group G to a real...

  • Article
  • Open Access
3 Citations
1,115 Views
19 Pages

14 June 2024

Convolution plays a pivotal role in the domains of signal processing and optics. This paper primarily focuses on studying the weighted convolution for quaternion linear canonical cosine transform (QLCcT) and its application in multiplicative filter a...

  • Article
  • Open Access
5 Citations
2,562 Views
27 Pages

Enhanced Real-Life Data Modeling with the Modified Burr III Odds Ratio–G Distribution

  • Haochong Yang,
  • Mingfang Huang,
  • Xinyu Chen,
  • Ziyan He and
  • Shusen Pu

14 June 2024

In this study, we introduce the modified Burr III Odds Ratio–G distribution, a novel statistical model that integrates the odds ratio concept with the foundational Burr III distribution. The spotlight of our investigation is cast on a key subcl...

  • Article
  • Open Access
1,112 Views
21 Pages

14 June 2024

In this paper, a high-accuracy conservative implicit algorithm for computing the space fractional coupled Schrödinger–Boussinesq system is constructed. Meanwhile, the conservative nature, a priori boundedness, and solvability of the numeri...

  • Feature Paper
  • Article
  • Open Access
1 Citations
1,559 Views
36 Pages

14 June 2024

A hypersurface M in Rn or Sn is said to be Dupin if along each curvature surface, the corresponding principal curvature is constant. A Dupin hypersurface is said to be proper Dupin if each principal curvature has constant multiplicity on M, i.e., the...

  • Article
  • Open Access
1 Citations
1,512 Views
13 Pages

14 June 2024

In this study, we employed the homotopy analysis transform method (HATM) to derive an iterative scheme to numerically solve a singular second-order hyperbolic pseudo-differential equation. We evaluated the effectiveness of the derived scheme in solvi...

  • Article
  • Open Access
4 Citations
1,881 Views
21 Pages

Statistical Advancement of a Flexible Unitary Distribution and Its Applications

  • Hugo S. Salinas,
  • Hassan S. Bakouch,
  • Fatimah E. Almuhayfith,
  • Wilson E. Caimanque,
  • Leonardo Barrios-Blanco and
  • Olayan Albalawi

14 June 2024

A flexible distribution has been introduced to handle random variables in the unit interval. This distribution is based on an exponential transformation of the truncated positive normal distribution with two parameters and can effectively fit data wi...

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Axioms - ISSN 2075-1680