Mathematical Analysis: Theory, Methods and Applications

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "E: Applied Mathematics".

Deadline for manuscript submissions: 20 July 2025 | Viewed by 388

Special Issue Editors


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Guest Editor
Department of Mathematics, Kennesaw State University, Kennesaw, GA, USA
Interests: mathematical analysis

E-Mail Website
Guest Editor
Department of Mathematics, Kennesaw State University, Kennesaw, GA, USA
Interests: mathematical analysis

Special Issue Information

Dear Colleagues,

Mathematical analysis can be traced back to the Ancient Greeks but remains relevant today, in no small part due to its vast connections with other areas of mathematics such as partial differential equations, calculus of variations, and functional analysis. However, it has become clear that more sophisticated analytical methods may be needed to handle problems which are nonlinear or have a fractal geometry, where classic analytical tools (such as the Browder degree theory or standard Sobolev trace theory) may not work. Indeed, with recent advances in materials science and related areas such as liquid crystal optics, metasurface design, and quantum optics, there is renewed interest in applying analytical methods to solve meaningful problems in the physical sciences.

We welcome submissions showcasing original research on mathematical analysis and its applications are particularly welcome, especially those related to partial differential equations, alongside advances in analytical methods, in particular for the treatment of nonlinear problems (broadly defined).

Dr. Eric Stachura
Dr. Timothy E. Faver
Guest Editors

Manuscript Submission Information

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Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • analysis
  • partial differential equations
  • functional analysis
  • calculus of variations
  • applied mathematics

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Published Papers (1 paper)

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Research

39 pages, 488 KiB  
Article
The Local Times for Additive Brownian Sheets and the Intersection Local Times for Independent Brownian Sheets
by Mingjie Liang and Chenfang Lin
Mathematics 2025, 13(9), 1425; https://doi.org/10.3390/math13091425 - 26 Apr 2025
Viewed by 83
Abstract
A new class of Gaussian random fields is introduced in this article, described as additive Brownian sheets (ABSs), which can be regarded as a type of generalized Brownian sheet encompassing Brownian motions, Brownian sheets, and additive Brownian motions. The existence, joint continuity and [...] Read more.
A new class of Gaussian random fields is introduced in this article, described as additive Brownian sheets (ABSs), which can be regarded as a type of generalized Brownian sheet encompassing Brownian motions, Brownian sheets, and additive Brownian motions. The existence, joint continuity and the Hölder law of the local times for ABSs are derived under certain conditions, and some results of the intersection local times for two independent Brownian sheets are also given as special cases. Furthermore, the intersection local times for two independent Brownian sheets in a Hida distribution is proved through white noise analysis, and the Wiener chaos expansion of the intersection local times is expressed in terms of S-transform. Additionally, the large deviations for the intersection local time of two independent Brownian sheets are established. The multi-parameter Gaussian random fields have become a core tool for complex system analysis due to their flexible multidimensional modeling capabilities. With the improvement of computational efficiency and interdisciplinary integration, the ABS constructed in this article will unleash greater potential in fields such as metaverse simulation, financial mathematics, climate science, precision medicine, quantum physics, and string theory. Full article
(This article belongs to the Special Issue Mathematical Analysis: Theory, Methods and Applications)
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