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A special issue of Mathematics (ISSN 2227-7390).

Deadline for manuscript submissions: 20 May 2026 | Viewed by 5605

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Prof. Dr. Cristina Flaut

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Faculty of Mathematics and Computer Science, Ovidius University, Bd. Mamaia 124, 900527 Constanța, Romania
Interests: algebra (non-associative algebra, algebra obtained by the Cayley–Dickson process, and algebra of logic); coding theory; cryptography
Special Issues, Collections and Topics in MDPI journals

Dr. Cristina Sburlan

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Guest Editor

Faculty of Mathematics and Informatics, Ovidius University of Constanta, 900470 Constanta, Romania
Interests: nonlinear analysis; Navier-Stokes equations; topological and numerical methods for partial differential equations; bifurcation theory; continuous mechanics; computability; differential geometry; relativity and cosmology

Dr. Dragos Sburlan

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Guest Editor

Faculty of Mathematics and Informatics, Ovidius University of Constanta, 900470 Constanta, Romania
Interests: artificial intelligence; evolutionary computation; time series; data mining
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Special Issue Information

Dear Colleagues,

This collection aims to honor his contributions to the global mathematical community and aims to bring together high-quality, original research articles that highlight the recent advances in the domains of pure and applied mathematics and computer science fields with strong mathematical foundations. This Special Issue explores the application of mathematical concepts in solving real-world analytical problems across technology and science, while also fostering creativity in theoretical and applied mathematics. Topics of interest include, but are not limited to, the following:

Algebra, Geometry, Topology;
Analysis and Functional Analysis;
Differential Equations and Dynamical Systems;
Mathematical Physics;
Number Theory and Combinatorics;
Optimization and Operational Research;
Probability and Statistics;
Mathematical Logic and Foundations;
Numerical Analysis and Scientific Computing;
Computational Mathematics;
Discrete Mathematics;
Machine Learning and Artificial Intelligence;
Theoretical Computer Science;
Cryptography and Information Theory;
Mathematical Modeling and Applications in Sciences and Engineering.

Prof. Dr. Cristina Flaut
Dr. Cristina Sburlan
Dr. Dragos Sburlan
Guest Editors

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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-blind 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.

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Keywords

algebra and geometry
dynamical systems
computational mathematics
discrete mathematics
differential equations
difference equations
financial mathematics
mathematical physics
mathematical biology
theoretical computer science
probability theory
statistical methods

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Published Papers (11 papers)

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Research

20 pages, 466 KB

Open AccessArticle

Weighted Approximation by Szász–Mirakyan-Type Operators Preserving Two Exponential Functions

by Gülsüm Ulusoy Ada and Ali Aral

Mathematics 2026, 14(8), 1371; https://doi.org/10.3390/math14081371 - 19 Apr 2026

Viewed by 109

Abstract

In this paper, we study the weighted approximation properties of a family of Szász–Mirakyan-type operators preserving two exponential functions on the unbounded interval

[0, \infty)

. The operators act on exponential weighted spaces and are analyzed within the framework of [...] Read more.

In this paper, we study the weighted approximation properties of a family of Szász–Mirakyan-type operators preserving two exponential functions on the unbounded interval

[0, \infty)

. The operators act on exponential weighted spaces and are analyzed within the framework of positive linear operator theory. We first establish their well-definedness and boundedness between suitable weighted spaces. By applying a weighted Korovkin-type theorem, we prove convergence in the corresponding weighted norm. Furthermore, we obtain quantitative estimates in terms of a weighted modulus of continuity and derive an order of convergence result. A Voronovskaya-type asymptotic formula is also established, describing the precise asymptotic behavior of the operators. Numerical examples are included to support the theoretical results. Full article

(This article belongs to the Special Issue Recent Developments in Theoretical and Applied Mathematics)

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20 pages, 483 KB

Open AccessArticle

Numerical Simulation of the Kudryashov–Sinelshchikov Equation for Modeling Pressure Waves in Liquids with Gas Bubbles

by Gayatri Das, Bibekananda Sitha, Rajesh Kumar Mohapatra, Predrag Stanimirović and Tzung-Pei Hong

Mathematics 2026, 14(4), 710; https://doi.org/10.3390/math14040710 - 17 Feb 2026

Viewed by 404

Abstract

The Kudryashov–Sinelshchikov equation (KSE) is crucial in modeling pressure waves in liquids containing gas bubbles, capturing both nonlinear wave phenomena and dispersion effects. This article applies the reproducing kernel Hilbert space method (RKHSM) to find a numerical solution for the time-fractional KSE. We develop a numerical solution to the KSE using the RKHSM, which offers an efficient and accurate approach for solving nonlinear partial differential equations due to its smoothness and orthogonality properties. The key components of this method include the reproducing kernel (RK) theory, important Hilbert spaces, normal basis, orthogonalization, and homogenization. We construct an appropriate RK and derive an iterative solution that converges rapidly to the exact solution. The effectiveness of this approach is demonstrated through numerical simulations in which we analyze the behavior of pressure waves and compare the results with existing analytical and numerical solutions. The RKHSM consistently demonstrates highly accurate, rapid convergence, and remarkable stability across a wide range of problems. Thus, the RKHSM is a promising tool for studying wave propagation in bubbly liquids. Full article

(This article belongs to the Special Issue Recent Developments in Theoretical and Applied Mathematics)

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11 pages, 236 KB

Open AccessArticle

A Super-Multiplicative Inequality for the Number of Finite Unlabeled and T₀ Topologies

by Ibtsam A. R. Alroily and Brahim Chaourar

Mathematics 2026, 14(4), 681; https://doi.org/10.3390/math14040681 - 14 Feb 2026

Viewed by 237

Abstract

Let n be a nonnegative integer, and let

f (n)

denote the number of unlabeled finite topologies on n points. We show that the inequality

f (n + m) \geq f (n) f (m)

holds [...] Read more.

Let n be a nonnegative integer, and let

f (n)

denote the number of unlabeled finite topologies on n points. We show that the inequality

f (n + m) \geq f (n) f (m)

holds both for both labeled and unlabeled finite topologies. In addition, we establish a similar inequality for labeled and unlabeled

T_{0}

topologies. Full article

(This article belongs to the Special Issue Recent Developments in Theoretical and Applied Mathematics)

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35 pages, 492 KB

Open AccessArticle

Analysis of Implicit Neutral-Tempered Caputo Fractional Volterra–Fredholm Integro-Differential Equations Involving Retarded and Advanced Arguments

by Abdulrahman A. Sharif and Muath Awadalla

Mathematics 2026, 14(3), 470; https://doi.org/10.3390/math14030470 - 29 Jan 2026

Viewed by 407

Abstract

This paper investigates a class of implicit neutral fractional integro-differential equations of Volterra–Fredholm type. The equations incorporate a tempered fractional derivative in the Caputo sense, along with both retarded (delay) and advanced arguments. The problem is formulated on a time domain segmented into past, present, and future intervals and includes nonlinear mixed integral operators. Using Banach’s contraction mapping principle and Schauder’s fixed point theorem, we establish sufficient conditions for the existence and uniqueness of solutions within the space of continuous functions. The study is then extended to general Banach spaces by employing Darbo’s fixed point theorem combined with the Kuratowski measure of noncompactness. Ulam–Hyers–Rassias stability is also analyzed under appropriate conditions. To demonstrate the practical applicability of the theoretical framework, explicit examples with specific nonlinear functions and integral kernels are provided. Furthermore, detailed numerical simulations are conducted using MATLAB-based specialized algorithms, illustrating solution convergence and behavior in both finite-dimensional and Banach space contexts. Full article

(This article belongs to the Special Issue Recent Developments in Theoretical and Applied Mathematics)

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22 pages, 394 KB

Open AccessArticle

A Fractional Calculus Approach to Energy Balance Modeling: Incorporating Memory for Responsible Forecasting

by Muath Awadalla and Abulrahman A. Sharif

Mathematics 2026, 14(2), 223; https://doi.org/10.3390/math14020223 - 7 Jan 2026

Cited by 3 | Viewed by 567

Abstract

Global climate change demands modeling approaches that are both computationally efficient and physically faithful to the system’s long-term dynamics. Classical Energy Balance Models (EBMs), while valuable, are fundamentally limited by their memoryless exponential response, which fails to represent the prolonged thermal inertia of the climate system—particularly that associated with deep-ocean heat uptake. In this study, we introduce a fractional Energy Balance Model (fEBM) by replacing the classical integer-order time derivative with a Caputo fractional derivative of order

α (0 < α \leq 1)

, thereby embedding long-range memory directly into the model structure. We establish a rigorous mathematical foundation for the fEBM, including proofs of existence, uniqueness, and asymptotic stability, ensuring theoretical well-posedness and numerical reliability. The model is calibrated and validated against historical global mean surface temperature data from NASA GISTEMP and radiative forcing estimates from IPCC AR6. Relative to the classical EBM, the fEBM achieves a substantially improved representation of observed temperatures, reducing the root mean square error by approximately 29% during calibration (1880–2010) and by 47% in out-of-sample forecasting (2011–2023). The optimized fractional order

α = 0.75 \pm 0.03

emerges as a physically interpretable measure of aggregate climate memory, consistent with multi-decadal ocean heat uptake and observed persistence in temperature anomalies. Residual diagnostics and robustness analyses further demonstrate that the fractional formulation captures dominant temporal dependencies without overfitting. By integrating mathematical rigor, uncertainty quantification, and physical interpretability, this work positions fractional calculus as a powerful and responsible framework for reduced-order climate modeling and long-term projection analysis. Full article

(This article belongs to the Special Issue Recent Developments in Theoretical and Applied Mathematics)

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13 pages, 1261 KB

Open AccessArticle

The Self-Adjoint Fractional Heun Operator and Its Spectral Properties

by Muath Awadalla

Mathematics 2026, 14(2), 204; https://doi.org/10.3390/math14020204 - 6 Jan 2026

Viewed by 435

Abstract

This paper introduces a rigorously defined fractional Heun operator constructed through a symmetric composition of left and right Riemann–Liouville fractional derivatives. By deriving a compatible fractional Pearson-type equation, a new weight function and Hilbert space setting are established, ensuring the operator’s self-adjointness under natural fractional boundary conditions. Within this framework, we prove the existence of a real, discrete spectrum and demonstrate that the corresponding eigenfunctions form a complete orthogonal system in

L_{ω_{α}}^{2} (a, b)

. The central theoretical result shows that the fractional eigenpairs

(λ_{n}^{(α)}, u_{n}^{(α)})

converge continuously to their classical Heun counterparts

(λ_{n}^{(1)}, u_{n}^{(1)})

α \to 1^{-}

. This provides a rigorous analytic bridge between fractional and classical spectral theories. A numerical study based on the fractional Legendre case confirms the predicted self-adjointness and spectral convergence, illustrating the smooth deformation of the classical eigenfunctions into their fractional counterparts. The results establish the fractional Heun operator as a mathematically consistent generalization capable of generating new families of orthogonal fractional functions. Full article

(This article belongs to the Special Issue Recent Developments in Theoretical and Applied Mathematics)

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10 pages, 349 KB

Open AccessFeature PaperArticle

Revisiting Wilf’s Question for Numerical Semigroups S₃ and Inequalities for Rescaled Genera

by Leonid G. Fel

Mathematics 2025, 13(23), 3771; https://doi.org/10.3390/math13233771 - 24 Nov 2025

Viewed by 389

Abstract

We consider numerical semigroups

S_{3} = ⟨ d_{1}, d_{2}, d_{3} ⟩

, which are minimally generated by three positive integers. We revisit the Wilf question for

S_{3}

and, making use of identities for degrees of syzygies [...] Read more.

We consider numerical semigroups

S_{3} = ⟨ d_{1}, d_{2}, d_{3} ⟩

, which are minimally generated by three positive integers. We revisit the Wilf question for

S_{3}

and, making use of identities for degrees of syzygies of such semigroups, we provide a short proof of existence of an affirmative answer. Finally, we find the upper and lower bounds for the rescaled genera of numerical semigroups

S_{3}

. Full article

(This article belongs to the Special Issue Recent Developments in Theoretical and Applied Mathematics)

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19 pages, 319 KB

Open AccessFeature PaperArticle

Optimal Consumption and Investment Problem with Consumption Ratcheting in Luxury Goods

by Geonwoo Kim and Junkee Jeon

Mathematics 2025, 13(22), 3732; https://doi.org/10.3390/math13223732 - 20 Nov 2025

Viewed by 483

Abstract

This paper investigates an infinite-horizon optimal consumption and investment problem for an agent who consumes two types of goods: necessities and luxuries. The agent derives utility from both goods but faces a ratcheting constraint on luxury consumption, which prohibits any decline in its level over time. This constraint captures the irreversible nature of high living standards or luxury habits often observed in real economies. We formulate the problem in a complete financial market with a risk-free asset and a risky stock and solve it analytically using the dual–martingale method. The dual problem is shown to reduce to a family of optimal stopping problems, from which we derive explicit closed-form solutions for the value function and optimal policies. Our results reveal that the ratcheting constraint generates asymmetric consumption dynamics: necessities adjust freely, whereas luxuries exhibit downward rigidity. As a consequence, the marginal propensity to consume necessities declines with wealth, while luxury consumption and portfolio risk exposure increase more sharply compared to the benchmark case without ratcheting. The model provides a continuous-time microfoundation for persistent high consumption levels and greater risk-taking among wealthy individuals. Full article

(This article belongs to the Special Issue Recent Developments in Theoretical and Applied Mathematics)

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27 pages, 474 KB

Open AccessArticle

On Approximate Solutions for Nonsmooth Interval-Valued Multiobjective Optimization Problems with Vanishing Constraints

by Akriti Dwivedi, Vivek Laha, Miruna-Mihaela Beldiman and Andrei-Dan Halanay

Mathematics 2025, 13(22), 3699; https://doi.org/10.3390/math13223699 - 18 Nov 2025

Viewed by 400

Abstract

The purpose of this research is to develop approximate weak and strong stationary conditions for interval-valued multiobjective optimization problems with vanishing constraints (IVMOPVC) involving nonsmooth functions. In many real-world situations, the exact values of objectives are uncertain or imprecise; hence, interval-valued formulations are used to model such uncertainty more effectively. The proposed approximate weak and strong stationarity conditions provide a robust framework for deriving meaningful optimality results even when the usual constraint and data qualifications fail. We first introduce approximate variants of these qualifications and establish their relationships. Secondly, we establish some approximate KKT type necessary optimality conditions in terms of approximate weak strongly stationary points and approximate strong strongly stationary points to identify type-2

E

-quasi weakly Pareto and type-1

E

-quasi Pareto solutions of the IVMOPVC. Lastly, we show that the approximate weak and strong strongly stationary conditions are sufficient for optimality under some approximate convexity assumptions. All the outcomes are well illustrated by examples. Full article

(This article belongs to the Special Issue Recent Developments in Theoretical and Applied Mathematics)

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20 pages, 378 KB

Open AccessArticle

Optimal GQPC Codes over the Finite Field F_q

by Kundan Suxena, Om Prakash, Indibar Debnath and Patrick Solé

Mathematics 2025, 13(22), 3655; https://doi.org/10.3390/math13223655 - 14 Nov 2025

Cited by 1 | Viewed by 568

Abstract

This paper presents the algebraic structure of generalized quasi-polycyclic (GQPC) codes, which is a generalization of the right quasi-polycyclic (QPC) and generalized quasi-cyclic (GQC) codes over a finite field

F_{q}

. Here, we mainly study the multi-generator polynomial of the right GQPC [...] Read more.

F_{q}

. Here, we mainly study the multi-generator polynomial of the right GQPC codes of index l. In this regard, we use the Chinese Remainder Theorem to decompose the right GQPC codes into their constituent codes. Further, we determine the dimension of a right GQPC code and provide a method for finding a normalized generating set for a multi-generator right GQPC code. As a by-product, we provide some examples of GQPC codes and obtain several optimal and near-optimal 2-generator right GQPC codes of index 2 over

F_{2}

. Full article

(This article belongs to the Special Issue Recent Developments in Theoretical and Applied Mathematics)

25 pages, 415 KB

Open AccessArticle

Compactness of the Complex Green Operator on C¹ Pseudoconvex Boundaries in Stein Manifolds

by Abdullah Alahmari, Emad Solouma, Marin Marin, A. F. Aljohani and Sayed Saber

Mathematics 2025, 13(21), 3567; https://doi.org/10.3390/math13213567 - 6 Nov 2025

Cited by 1 | Viewed by 626

Abstract

We study compactness for the complex Green operator

G_{q}

associated with the Kohn Laplacian

□_{b}

on boundaries of pseudoconvex domains in Stein manifolds. Let

Ω ⋐ X

be a bounded pseudoconvex domain in a Stein manifold X of complex dimension n [...] Read more.

We study compactness for the complex Green operator

G_{q}

associated with the Kohn Laplacian

□_{b}

on boundaries of pseudoconvex domains in Stein manifolds. Let

Ω ⋐ X

be a bounded pseudoconvex domain in a Stein manifold X of complex dimension n with

C^{1}

boundary. For

1 \leq q \leq n - 2

, we first prove a compactness theorem under weak potential-theoretic hypotheses: if

b Ω

satisfies weak

(P_{q})

and weak

(P_{n - 1 - q})

, then

G_{q}

and

G_{n - 1 - q}

are compact on

L_{p, q}^{2} (b Ω)

. This extends known

C^{\infty}

results in

C^{n}

to the minimal regularity

C^{1}

and to the Stein setting. On locally convexifiable

C^{1}

boundaries, we obtain a full characterization: compactness of

G_{q}

is equivalent to simultaneous compactness of

G_{q}

and

G_{n - 1 - q}

, to compactness of the

\bar{\partial}

-Neumann operators

N_{q}

and

N_{n - 1 - q}

in the interior, to weak

(P_{q})

and

(P_{n - 1 - q})

, and to the absence of (germs of) complex varieties of dimensions q and

n - 1 - q

b Ω

. A key ingredient is an annulus compactness transfer on

Ω_{+} = Ω_{2} ∖ \bar{Ω_{1}}

, which yields compactness of

N_{q}^{Ω_{+}}

from weak

(P)

near each boundary component and allows us to build compact

{\bar{\partial}}_{b}

-solution operators via jump formulas. Consequences include the following: compact canonical solution operators for

{\bar{\partial}}_{b}

, compact resolvent for

□_{b}

on the orthogonal complement of its harmonic space (hence discrete spectrum and finite-dimensional harmonic forms), equivalence between compactness and standard compactness estimates, closed range and

L^{2}

Hodge decompositions, trace-class heat flow, stability under

C^{1}

boundary perturbations, vanishing essential norms, Sobolev mapping (and gains under subellipticity), and compactness of Bergman-type commutators when

q = 1

. Full article

(This article belongs to the Special Issue Recent Developments in Theoretical and Applied Mathematics)

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