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Mathematics
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New Advances in Mathematical Analysis and Applications
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New Advances in Mathematical Analysis and Applications

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "C: Mathematical Analysis".

Deadline for manuscript submissions: 30 November 2026 | Viewed by 2213

Editors

Dr. Pavlina Atanasova

E-Mail Website
Guest Editor
Faculty of Mathematics and Informatics, University of Plovdiv Paisii Hilendarski, 24 Tzar Asen, 4000 Plovdiv, Bulgaria
Interests: numerical modeling; applied mathematics engineering; applied and computational mathematics; mathematical modelling; modeling and simulation; algorithms; numerical analysis; numerical mathematics; mathematical analysis; nonlinear dynamics
Dr. Magdalena Veselinova

E-Mail Website
Guest Editor
Faculty of Mathematics and Informatics, University of Plovdiv Paisii Hilendarski, 24 Tzar Asen, 4000 Plovdiv, Bulgaria
Interests: data modeling; database; differential equations; partial differential equation

Special Issue Information

Dear Colleagues,

The Special Issue “New Advances in Mathematical Analysis and Applications” aims to present recent developments in theoretical and applied aspects of mathematical analysis and its applications in science and engineering.

The Special Issue will focus on modern analytical methods, numerical techniques, and mathematical models that address nonlinear phenomena, differential equations, dynamical systems, and computational challenges arising in real-world problems.

Topics of interest include, but are not limited to, the following: qualitative analysis of differential equations; numerical methods for ordinary and partial differential equations; stability and convergence analysis; nonlinear dynamics; mathematical modeling in physics, engineering, and applied sciences.

The Special Issue seeks contributions that combine rigorous mathematical analysis with practical applications, as well as works that introduce new computational approaches or extend classical analytical results to contemporary problems.

Dr. Pavlina Atanasova
Dr. Magdalena Veselinova
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 250 words) can be sent to the Editorial Office for assessment.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-anonymized peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Mathematics is an international peer-reviewed open access semimonthly journal published by MDPI.

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

  • numerical analysis
  • mathematical analysis
  • differential equations
  • nonlinear dynamics
  • mathematical modeling
  • computational mathematics numerical methods

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Published Papers (4 papers)

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Research

12 pages, 263 KB  
Article
Improved Integrability Estimates on the Region W1 for Type A Singular Orbital Measures on SU(2, q)0/S(U(2) × U(q))
by Sanjiv Kumar Gupta
Mathematics 2026, 14(15), 2724; https://doi.org/10.3390/math14152724 - 1 Aug 2026
Viewed by 179
Abstract
In earlier work, Gupta and Spronk established an L1–L2 dichotomy for Type A singular orbital measures on the flat symmetric spaces [...] Read more.
In earlier work, Gupta and Spronk established an L1–L2 dichotomy for Type A singular orbital measures on the flat symmetric spaces SU(2,q)0/S(U(2)×U(q)). Their analysis reduced the unresolved endpoint case q=2, k=2 to the study of an integral over a region W1 of the Weyl chamber. In this paper we revisit the contribution from the region W1. We decompose W1 into near-diagonal and off-diagonal subregions according to the size of λ1−λ2. Applying the Mean Value Theorem in the near-diagonal region and standard decay estimates in the off-diagonal region, we prove that the contribution from W1 is finite for every q≥2 and every integer k≥2. Combined with their earlier analysis of the complementary region W2, this yields the endpoint case q=2, k=2, thereby resolving the open problem stated in Remark 4.4 of Gupta and Spronk. Full article
(This article belongs to the Special Issue New Advances in Mathematical Analysis and Applications)
57 pages, 2201 KB  
Article
Banach Space-Valued Approximation by Multi-Composite Sigmoid Neural Network Operators with Numerical Validation
by George A. Anastassiou and Seda Karateke
Mathematics 2026, 14(13), 2259; https://doi.org/10.3390/math14132259 - 24 Jun 2026
Viewed by 254
Abstract
We introduce and study a class of multi-composite sigmoid neural network operators for Banach space-valued approximation. The proposed operators are generated by density-type kernels induced by finite compositions of seven standard sigmoid-type activation functions. The approximation is considered for continuous functions on compact [...] Read more.
We introduce and study a class of multi-composite sigmoid neural network operators for Banach space-valued approximation. The proposed operators are generated by density-type kernels induced by finite compositions of seven standard sigmoid-type activation functions. The approximation is considered for continuous functions on compact intervals of the real line and on the whole real line, with values in an arbitrary Banach space (X,∥·∥). We prove quantitative pointwise and uniform convergence results by means of Jackson-type inequalities expressed through the first modulus of continuity. Higher-order and fractional approximation results are also obtained in terms of Banach space-valued derivatives and Caputo–Bochner fractional derivatives. The associated feed-forward neural network representation has one hidden layer and uses the multi-composite sigmoid function as its activation. Numerical experiments are presented to validate the theoretical estimates and to illustrate the approximation behavior of the proposed operators. In particular, we compare classical tanh-based operators, normalized self-composed activation operators, and heterogeneous multi-composite activation operators. The results show that self-composition and heterogeneous composition may improve the uniform approximation error for certain activation families and parameter choices, while also indicating that the observed improvement is activation-dependent and influenced by the composition order, kernel localization, and the regularity of the target function. Full article
(This article belongs to the Special Issue New Advances in Mathematical Analysis and Applications)
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16 pages, 292 KB  
Article
Approximation Properties Variant of Baskakov–Schurer–Szász Operators Induced by Sheffer Polynomials
by Naim L. Braha and Toufik Mansour
Mathematics 2026, 14(11), 1872; https://doi.org/10.3390/math14111872 - 28 May 2026
Viewed by 318
Abstract
This paper introduces a new class of Baskakov–Schurer–Szász operators generated by Sheffer polynomials in a special case. We establish a Korovkin-type theorem for these operators and investigate their uniform convergence and error estimates using the Ditzian–Totik modulus of smoothness. We also derive weighted [...] Read more.
This paper introduces a new class of Baskakov–Schurer–Szász operators generated by Sheffer polynomials in a special case. We establish a Korovkin-type theorem for these operators and investigate their uniform convergence and error estimates using the Ditzian–Totik modulus of smoothness. We also derive weighted approximation and shape-preserving properties for this class of operators. These results extend the theory of positive linear operators and provide tools applicable in approximation and numerical analysis. Full article
(This article belongs to the Special Issue New Advances in Mathematical Analysis and Applications)
14 pages, 273 KB  
Article
Exponential Stability of Swelling Soils with Thermodiffusion Effects
by Arar Mutlag A. Alajmi and Tijani A. Apalara
Mathematics 2026, 14(7), 1184; https://doi.org/10.3390/math14071184 - 1 Apr 2026
Viewed by 1068
Abstract
In this work, we study a one-dimensional coupled hyperbolic–parabolic system modeling the dynamics of swelling soils under thermodiffusion effects. The model describes the interaction between the deformation of the solid skeleton, the pore fluid motion, the temperature variation, and a diffusive process formulated [...] Read more.
In this work, we study a one-dimensional coupled hyperbolic–parabolic system modeling the dynamics of swelling soils under thermodiffusion effects. The model describes the interaction between the deformation of the solid skeleton, the pore fluid motion, the temperature variation, and a diffusive process formulated through chemical potential. Under mixed boundary conditions and without introducing additional mechanical damping or imposing restrictive relations among the physical parameters, we prove exponential stability of the system. Our analysis is based on the energy method. In contrast to the standard energy functional commonly used in related thermodiffusion models, we introduce a modified positive energy functional better adapted to the coupled structure of the system. By combining this energy with suitable auxiliary functionals, we construct an appropriate Lyapunov functional and derive an exponential stability estimate. Our result shows that thermodiffusion alone yields sufficient dissipation for exponential stabilization, complementing earlier works where exponential stability requires extra damping mechanisms or equal wave-speed assumptions. Full article
(This article belongs to the Special Issue New Advances in Mathematical Analysis and Applications)
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