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A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "C1: Difference and Differential Equations".

Deadline for manuscript submissions: 28 February 2026 | Viewed by 10728

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Dr. Arsen Palestini

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MEMOTEF, Sapienza University of Rome, Piazzale Aldo Moro 5, 00185 Rome, Italy
Interests: game theory; ordinary differential equations; mathematical economics; voting games
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Special Issue Information

Dear Colleagues,

It is with great pleasure that I introduce a new and exciting project, specifically devoted to exploring the rich and dynamic fields of equations, algebra, and discrete mathematics. Algebra, as one of the foundational pillars of mathematical sciences, continues to captivate and challenge us with its deep complexities and structures. Equations, both differential and difference, are crucial in understanding dynamic systems and modeling various phenomena, while discrete mathematics opens up pathways to computational innovations and theoretical advancements.

This Special Issue aims to be as inclusive as possible. I am particularly interested in novel contributions in these areas, including but not limited to studies on number theory, algebraic topology, computational algebra, algebraic curves and surfaces, algebraic combinatorics, complex equations, and discrete mathematics.

I encourage researchers and scholars from all over the world to submit their high-quality papers to this Special Issue. I am sure that a lot of new and interesting results will be published and appreciated by the mathematical community worldwide.

Dr. Arsen Palestini
Guest Editor

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-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.

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

primes
conjecture
analytic number theory
discrete mathematics
Diophantine equations
finite fields
approximation of constants
continued fractions
Ramanujan theories
algebraic equations
additive number theory
algebraic combinatorics
algebraic topology

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Published Papers (6 papers)

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Research

11 pages, 290 KB

Open AccessFeature PaperArticle

Optimal One-Coincidence Sequence Sets with a Large Alphabet and Prime Length

by Jin-Ho Chung, Duehee Lee and Dongsup Jin

Mathematics 2026, 14(2), 214; https://doi.org/10.3390/math14020214 - 6 Jan 2026

Viewed by 100

Abstract

The performance of a frequency-hopping spread-spectrum system is mainly dependent on the mathematical properties of its hopping sequences, which are designed to minimize interference between different users. The one-coincidence sequence frequency-hopping sequence (OC-FHS) set is one of the primary types, because it achieves [...] Read more.

p q

for two primes p and q using a block structure modulo

p q

. In particular, when

p = q

, our construction provides a significantly larger set size compared with a previously known OC-FHS set with the same length and the same alphabet size. Moreover, the set size is optimal with respect to the bound established by Cao, Ge, and Miao. This extended set size can be applied to FHMA systems that need to accommodate a large number of users. Full article

(This article belongs to the Special Issue Advances in Mathematics: Equations, Algebra, and Discrete Mathematics)

13 pages, 278 KB

Open AccessArticle

The Structure of D-Derivations and Their Decomposition in Lie Algebras

by Keli Zheng, Jiale Chen, Wei Shan and Ying Guo

Mathematics 2026, 14(1), 129; https://doi.org/10.3390/math14010129 - 29 Dec 2025

Viewed by 184

Abstract

A D-derivation of a Lie algebra L is a linear map

φ

for which there exists a derivation D such that [...] Read more.

A D-derivation of a Lie algebra L is a linear map

φ

for which there exists a derivation D such that

φ ([x, y]) = [φ (x), y] + [x, D (y)]

for all

x, y \in L

. This paper presents explicit structural results concerning D-derivations in Lie algebras over arbitrary fields. It is established that the set of D-derivations forms a Lie algebra, which decomposes as the sum of derivations and centroids, intersecting precisely at the space of central derivations. For centerless Lie algebras, the inclusion chain for D-derivations within existing derivation classes is completed, resulting in a refined hierarchy. It is proven that for both perfect and centerless Lie algebras, D-derivations decompose as a direct sum of derivations and centroids. In particular, for semisimple Lie algebras, it is shown that

{Der}_{D} (L) = ad (L) \oplus C (L)

, and for simple Lie algebras over an algebraically closed field of characteristic zero,

{Der}_{D} (L) = ad (L) \oplus F {id}_{L}

. Furthermore, for any centerless Lie algebra, the Lie algebra of D-derivations is shown to be isomorphic to the semidirect product of the derivation and centroid algebras, with explicit descriptions provided for semisimple and solvable cases. Examples involving

so (3)

so (1, 3)

aff (1)

, and

h_{3}

confirm these decompositions and offer matrix realizations of their D-derivations, thereby supporting and illustrating the main theorems. Full article

(This article belongs to the Special Issue Advances in Mathematics: Equations, Algebra, and Discrete Mathematics)

15 pages, 444 KB

Open AccessFeature PaperArticle

Exploring the Crossing Numbers of Three Join Products of 6-Vertex Graphs with Discrete Graphs

by Michal Staš and Mária Švecová

Mathematics 2025, 13(10), 1694; https://doi.org/10.3390/math13101694 - 21 May 2025

Viewed by 1336

Abstract

The significance of searching for edge crossings in graph theory lies inter alia in enhancing the clarity and readability of graph representations, which is essential for various applications such as network visualization, circuit design, and data representation. This paper focuses on exploring the [...] Read more.

G^{*} + D_{n}

, where

G^{*}

is a graph isomorphic to the path on four vertices

P_{4}

with an additional two vertices adjacent to two inner vertices of

P_{4}

, and

D_{n}

is a discrete graph composed of n isolated vertices. The proof is based on exact crossing-number values for join products involving particular subgraphs

H_{k}

G^{*}

with discrete graphs

D_{n}

combined with the symmetrical properties of graphs. This approach could also be adapted to determine the unknown crossing numbers of two other 6-vertices graphs obtained by adding one or two additional edges to the graph

G^{*}

. Full article

(This article belongs to the Special Issue Advances in Mathematics: Equations, Algebra, and Discrete Mathematics)

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Figure 1

20 pages, 311 KB

Open AccessArticle

On Ulam–Hyers–Mittag-Leffler Stability of Fractional Integral Equations Containing Multiple Variable Delays

by Osman Tunç and Cemil Tunç

Mathematics 2025, 13(4), 606; https://doi.org/10.3390/math13040606 - 12 Feb 2025

Cited by 3 | Viewed by 1659

Abstract

In recent decades, many researchers have pointed out that derivatives and integrals of the non-integer order are well suited for describing various real-world materials, for example, polymers. It has also been shown that fractional-order mathematical models are more effective than integer-order mathematical models. Thereby, given these considerations, the investigation of qualitative properties, in particular, Ulam-type stabilities of fractional differential equations, fractional integral equations, etc., has now become a highly attractive subject for mathematicians, as this represents an important field of study due to their extensive applications in various branches of aerodynamics, biology, chemistry, the electrodynamics of complex media, polymer science, physics, rheology, and so on. Meanwhile, the qualitative concepts called Ulam–Hyers–Mittag-Leffler (U-H-M-L) stability and Ulam–Hyers–Mittag-Leffler–Rassias (U-H-M-L-R) stability are well-suited for describing the characteristics of fractional Ulam-type stabilities. The Banach contraction principle is a fundamental tool in nonlinear analysis, with numerous applications in operational equations, fractal theory, optimization theory, and various other fields. In this study, we consider a nonlinear fractional Volterra integral equation (FrVIE). The nonlinear terms in the FrVIE contain multiple variable delays. We prove the U-H-M-L stability and U-H-M-L-R stability of the FrVIE on a finite interval. Throughout this article, new sufficient conditions are obtained via six new results with regard to the U-H-M-L stability or the U-H-M-L-R stability of the FrVIE. The proofs depend on Banach’s fixed-point theorem, as well as the Chebyshev and Bielecki norms. In the particular case of the FrVIE, an example is delivered to illustrate U-H-M-L stability. Full article

(This article belongs to the Special Issue Advances in Mathematics: Equations, Algebra, and Discrete Mathematics)

20 pages, 356 KB

Open AccessArticle

Pre-Compactness of Sets and Compactness of Commutators for Riesz Potential in Global Morrey-Type Spaces

by Nurzhan Bokayev, Victor Burenkov, Dauren Matin and Aidos Adilkhanov

Mathematics 2024, 12(22), 3533; https://doi.org/10.3390/math12223533 - 12 Nov 2024

Cited by 2 | Viewed by 2268

Abstract

In this paper, we establish sufficient conditions for the pre-compactness of sets in the global Morrey-type spaces

G M_{p θ}^{w (\cdot)}

. Our main result is the compactness of the commutators of the Riesz potential

[b, I_{α}]

[...] Read more.

In this paper, we establish sufficient conditions for the pre-compactness of sets in the global Morrey-type spaces

G M_{p θ}^{w (\cdot)}

. Our main result is the compactness of the commutators of the Riesz potential

[b, I_{α}]

in global Morrey-type spaces from

G M_{p_{1} θ_{1}}^{w_{1} (\cdot)}

G M_{p_{2} θ_{2}}^{w_{2} (\cdot)}

. We also present new sufficient conditions for the commutator

[b, I_{α}]

to be bounded from

G M_{p_{1} θ_{1}}^{w_{1} (\cdot)}

G M_{p_{2} θ_{2}}^{w_{2} (\cdot)}

. In the proof of the theorem regarding the compactness of the commutator for the Riesz potential, we primarily utilize the boundedness condition for the commutator for the Riesz potential

[b, I_{α}]

in global Morrey-type spaces

G M_{p θ}^{w (\cdot)}

, and the sufficient conditions derived from the theorem on pre-compactness of sets in global Morrey-type spaces

G M_{p θ}^{w (\cdot)}

. Full article

(This article belongs to the Special Issue Advances in Mathematics: Equations, Algebra, and Discrete Mathematics)

15 pages, 278 KB

Open AccessArticle

Unique Solutions for Caputo Fractional Differential Equations with Several Delays Using Progressive Contractions

by Cemil Tunç and Fahir Talay Akyildiz

Mathematics 2024, 12(18), 2799; https://doi.org/10.3390/math12182799 - 10 Sep 2024

Cited by 5 | Viewed by 2518

Abstract

We take into account a nonlinear Caputo fractional-order differential equation including several variable delays. We examine whether the solutions to the Caputo fractional-order differential equation taken under consideration, which has numerous variable delays, are unique. In the present study, first, we will apply the method of progressive contractions, which belongs to T.A. Burton, to Caputo fractional-order differential equation, including multiple variable delays, which has not yet appeared in the relevant literature by this time. The significant point of the method of progressive contractions consists of a very flexible idea to discuss the uniqueness of solutions for various mathematical models. Lastly, we provide two examples to demonstrate how this paper’s primary outcome can be applied. Full article

(This article belongs to the Special Issue Advances in Mathematics: Equations, Algebra, and Discrete Mathematics)

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