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Mathematics, Volume 13, Issue 21

November-1 2025 - 214 articles

Cover Story: We introduce the Spatial Regime Conversion Method (SRCM), a novel hybrid framework for simulating reaction–diffusion systems that adaptively switches between stochastic and deterministic representations based on local concentrations. By combining discrete reaction-diffusion master equation dynamics with continuum partial differential equations, the SRCM avoids fixed spatial interfaces and captures essential stochastic features where needed, while maintaining computational efficiency. Validated across multiple test cases—including diffusion, morphogen gradient formation, and travelling waves—the SRCM offers a powerful and flexible tool for modelling spatially heterogeneous systems. View this paper
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Articles (214)

  • Article
  • Open Access
1 Citations
363 Views
39 Pages

3 November 2025

This paper studies a mixed PDE containing the second time derivative and a quadratic nonlinearity of the Monge–Ampère type in two spatial variables, which is encountered in geophysical fluid dynamics. The Lie group symmetry analysis of t...

  • Article
  • Open Access
293 Views
20 Pages

3 November 2025

Counting data play a critical role in various real-life applications across different scientific fields. This study handles the classical and Bayesian estimation of the one-parameter discrete linear exponential distribution under randomly right-censo...

  • Article
  • Open Access
359 Views
23 Pages

A Fast Integration Method of Analysis and Optimization for the Contact Performance Design of a Face Gear Split-Torque Transmission

  • Zhen Yu,
  • Zhongwei Tang,
  • Yuansheng Zhou,
  • Weichen Tang,
  • Jinyuan Tang,
  • Bingquan Lu,
  • Ziheng Wu and
  • Xiao Hong

3 November 2025

The optimization design of the face gear split-torque transmission (FGST) consumes a lot of modeling and calculation costs. Implementing closed-loop design for data generation optimization improves system design efficiency. However, there are two cha...

  • Article
  • Open Access
319 Views
21 Pages

Some New Boole-Type Inequalities via Modified Convex Functions with Their Applications and Computational Analysis

  • Talha Anwar,
  • Abdul Mateen,
  • Hela Elmannai,
  • Muhammad Aamir Ali and
  • Loredana Ciurdariu

3 November 2025

In numerical analysis, the Boole’s formula serves as a pivotal tool for approximating definite integrals. The approximation of the definite integrals has a big role in numerical methods for differential equations; in particular, in the finite v...

  • Article
  • Open Access
330 Views
25 Pages

3 November 2025

The strategic positioning of heating and cooling segments within complex non-rectangular geometries has emerged as a critical engineering challenge across multiple industries in thermal management systems for electronic components. This analysis pres...

  • Feature Paper
  • Article
  • Open Access
415 Views
20 Pages

2 November 2025

The article is devoted to the synthesis, implementation, simulation and experimental study of a real-time Lyapunov-based two-degree-of-freedom model reference adaptive controller (MRAC) for an axial-piston pump. The controller of the developed real-t...

  • Feature Paper
  • Article
  • Open Access
313 Views
24 Pages

2 November 2025

This paper investigates the mean square exponential stability (MSES) and H∞ performance analysis of discrete networked control systems (NCSs) based on the FlexRay protocol (FRP) when confronted with randomly occurring cyber attacks (ROCAs). In...

  • Article
  • Open Access
419 Views
9 Pages

2 November 2025

Peakedness is an important characteristic of probability distributions, and an effective method for quantifying peakedness is essential for statistical modeling and comparing different probability distributions in many practical applications. However...

  • Feature Paper
  • Review
  • Open Access
577 Views
23 Pages

2 November 2025

Nonlocal models offer a unified framework for describing long-range spatial interactions and temporal memory effects. The review briefly outlines several representative physical problems, including anomalous diffusion, material fracture, viscoelastic...

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Mathematics - ISSN 2227-7390