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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
2 Citations
1,971 Views
15 Pages

Packing Spheres into a Minimum-Height Parabolic Container

  • Yuriy Stoyan,
  • Georgiy Yaskov,
  • Tetyana Romanova,
  • Igor Litvinchev,
  • José Manuel Velarde Cantú and
  • Mauricio López Acosta

13 June 2024

Sphere packing consists of placing several spheres in a container without mutual overlapping. While packing into regular-shape containers is well explored, less attention is focused on containers with nonlinear boundaries, such as ellipsoids or parab...

  • Article
  • Open Access
1 Citations
1,090 Views
15 Pages

Recent Advances in Proximity Point Theory Applied to Fractional Differential Equations

  • Nabil Mlaiki,
  • Dur-e-Shehwar Sagheer,
  • Sana Noreen,
  • Samina Batul and
  • Ahmad Aloqaily

13 June 2024

This article introduces the concept of generalized (ffF,b,ϕ˘) contraction in the context of b-metric spaces by utilizing the idea of F contraction introduced by Dariusz Wardowski. The main findings of the research focus on the existen...

  • Article
  • Open Access
3 Citations
1,340 Views
18 Pages

12 June 2024

This paper explores the inference for a constant-stress accelerated life test under a ranked set sampling scenario. When the lifetime of products follows the Fréchet distribution, and the failure times are collected under a maximum ranked set...

  • Article
  • Open Access
1 Citations
1,644 Views
17 Pages

12 June 2024

Monitoring the ratio of two correlated normal random variables is often used in many industrial manufacturing processes. At the same time, measurement errors inevitably exist in most processes, which have different effects on the performance of vario...

  • Article
  • Open Access
1 Citations
1,292 Views
16 Pages

12 June 2024

Monitoring the parameter of discrete distributions is common in industrial production. Also, it is often crucial to monitor the parameter of geometric distribution, which is often regarded as the nonconforming item rate. To enhance the detection of n...

  • Article
  • Open Access
2 Citations
1,125 Views
22 Pages

11 June 2024

In this paper, the stochastic Takagi–Sugeno fuzzy recurrent neural networks (STSFRNNS) with distributed delay is established based on the Takagi–Sugeno (TS) model and the fixed time synchronization problem is investigated. In order to syn...

  • Article
  • Open Access
1 Citations
1,303 Views
15 Pages

Bicubic Splines for Fast-Contracting Control Nets

  • Kȩstutis Karčiauskas,
  • Kyle Shih-Huang Lo,
  • Erkan Gunpinar and
  • Jörg Peters

9 June 2024

Merging parallel quad strips facilitates narrowing surface passages, and allows a design to transition to a simpler shape. While a number of spline surface constructions exist for the isotropic case where n pieces join, few existing spline constructi...

  • Article
  • Open Access
3 Citations
1,644 Views
17 Pages

8 June 2024

This paper proposes a precise motion control strategy for a three-wheeled mobile robot with two driven rear wheels and one steered front wheel so that an obstacle avoidance motion task is able to be well implemented. Initially, the motion laws under...

  • Article
  • Open Access
2,144 Views
18 Pages

AHD-SLE: Anomalous Hyperedge Detection on Hypergraph Symmetric Line Expansion

  • Yingle Li,
  • Hongtao Yu,
  • Haitao Li,
  • Fei Pan and
  • Shuxin Liu

7 June 2024

Graph anomaly detection aims to identify unusual patterns or structures in graph-structured data. Most existing research focuses on anomalous nodes in ordinary graphs with pairwise relationships. However, complex real-world systems often involve rela...

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Axioms - ISSN 2075-1680