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Mathematics, Volume 12, Issue 22

November-2 2024 - 187 articles

Cover Story: The article derives novel degree sequence-based bounds on matching numbers, valid for any simple graph. The figure shows an application in number theory: the first 200 prime gaps are represented as node degrees in a simple graph and are generated via the degree-preserving growth (DPG) mechanism. The DPG builds an ever-growing graph sequence by joining a newly incoming node of a given degree (the next prime gap value) to the nodes of a randomly selected matching of proper size, then discarding the edges of the matching. The incoming nodes’ degrees constrain the size of the matching that can be selected, which, in turn, constrains the sizes of the future incoming degrees. It has previously been proven, however, that, for the prime gap sequence, this process can be continued indefinitely, if the Riemann hypothesis holds. View this paper
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Articles (187)

  • Article
  • Open Access
4 Citations
1,605 Views
22 Pages

20 November 2024

This paper introduces a novel methodology for measuring and decomposing multidimensional inequality, allowing for the breakdown of overall inequality into contributions from distinct dimensions. This approach offers valuable insights for sustainable...

  • Feature Paper
  • Article
  • Open Access
12 Citations
1,835 Views
15 Pages

20 November 2024

The theory of multi-source information fusion plays a pivotal role in decision-making, especially when handling uncertain or imprecise information. Among the existing frameworks, evidence theory has proven effective for integrating diverse informatio...

  • Article
  • Open Access
3 Citations
1,450 Views
31 Pages

Mean-Median Compromise Method: A Novel Deepest Voting Function Balancing Range Voting and Majority Judgment

  • Ruffin-Benoît M. Ngoie,
  • Selain K. Kasereka,
  • Jean-Aimé B. Sakulu and
  • Kyandoghere Kyamakya

20 November 2024

A logical presentation of the Mean-Median Compromise Method (MMCM) is provided in this paper. The objective is to show that the method is a generalization of majority judgment, where each tie-break step is Lp deepest voting. Therefore, in its tie-bre...

  • Article
  • Open Access
1,624 Views
23 Pages

20 November 2024

The personalized federated averaging algorithm integrates a federated averaging approach with a model-agnostic meta-learning technique. In real-world heterogeneous scenarios, it is essential to implement additional privacy protection techniques for p...

  • Article
  • Open Access
1 Citations
831 Views
12 Pages

20 November 2024

The paper studies a nonlinear equation including both fractional and ordinary derivatives. The singular Cauchy problem is considered. The theorem of the existence of uniqueness of a solution in the neighborhood of a fixed singular point of algebraic...

  • Feature Paper
  • Article
  • Open Access
1 Citations
1,355 Views
22 Pages

20 November 2024

In this manuscript, we investigate the (2+1)-dimensional variable-coefficient Korteweg–de Vries (KdV) system with cubic–quintic nonlinearity. Based on different methods, we also obtain different solutions. Under the help of the wave ansatz method, we...

  • Article
  • Open Access
2,227 Views
23 Pages

Mask-Space Optimized Transformer for Semantic Segmentation of Lithium Battery Surface Defect Images

  • Daozong Sun,
  • Jiasi Chen,
  • Peiwen Wu,
  • Yucheng Pan,
  • Hongsheng Zhong,
  • Zihao Deng and
  • Xiuyun Xue

20 November 2024

The segmentation of surface defects in lithium batteries is crucial for enhancing the overall quality of the production process. However, the severe foreground–background imbalance in surface images of lithium batteries, along with the irregula...

  • Article
  • Open Access
1 Citations
1,732 Views
21 Pages

Brauer Configuration Algebras Induced by Integer Partitions and Their Applications in the Theory of Branched Coverings

  • Agustín Moreno Cañadas,
  • José Gregorio Rodríguez-Nieto and
  • Olga Patricia Salazar Díaz

20 November 2024

Brauer configuration algebras are path algebras induced by appropriated multiset systems. Since their structures underlie combinatorial data, the general description of some of their algebraic invariants (e.g., their dimensions or the dimensions of t...

  • Article
  • Open Access
1,137 Views
9 Pages

20 November 2024

In this paper, we investigate the inverse of the set of unknown functions (v,g) of the Burgers equation in the framework of optimal theory. Firstly, we prove the existence of functional minimizers in the optimal control problem and derive the necessa...

  • Article
  • Open Access
1,126 Views
14 Pages

20 November 2024

A class of semilinear elliptic differential equations was investigated in this study. By constructing the inverse function, using the method of upper and lower solutions and the principle of comparison, the existence of the maximum positive solution...

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Mathematics - ISSN 2227-7390