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Mathematics
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Mathematics and Applications
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Mathematics and Applications

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

Deadline for manuscript submissions: 20 May 2025 | Viewed by 4037

Special Issue Editors

Prof. Dr. Francisco Chiclana

grade E-Mail Website
Guest Editor
School of Computer Science and Informatics, De Montfort University, The Gateway, Leicester LE1 9BH, UK
Interests: fuzzy decision making; fuzzy preference modeling; decision support systems; consensus; recommender systems; social networks; rationality/consistency; aggregation; type-2 fuzzy logic; opinion dynamics; trust propagation
Special Issues, Collections and Topics in MDPI journals
Prof. Dr. Paolo Mercorelli

E-Mail Website
Guest Editor
Institute of Product and Process Innovation, Leuphana, University of Lueneburg, 21335 Lueneburg, Germany
Interests: control systems; mechatronics; actuators; engines control; signal processing; wavelets; Kalman filter; optimal energy control
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

The Special Issue not only reflects on the title itself, as it also celebrates the 1st International Electronic Conference on Mathematics and Applications held by the journal from 1 to 15 May 2023. Mathematics highlights studies devoted to the mathematical treatment of questions arising in physics, chemistry, biology, statistics, finance, computer science, engineering and sociology, particularly those that engage with analytical/ algebraic aspects and novel problems and their solution.

The following topics in different sections are all of great interest to the Special Issue:

  • Engineering Mathematics: Submissions reporting novel mathematical methods and computational techniques for engineering and industry problems are welcome.
  • Mathematics and Computer Science: Research paradigms combining mathematical reasoning and computing will be welcome.
  • Dynamical Systems: Open to research in the following areas (in which mathematics play a key role): complex dynamical systems; nonlinear systems; arithmetic dynamics; chaos theory; control theory; ergodic theory; functional analysis; graph dynamical systems; symbolic dynamics; system dynamics; topological dynamics.
  • Financial Mathematics: Applications of mathematical methods/modeling to financial problems, such as derivatives pricing, risk and portfolio management, etc.
  • Mathematical Physics: Contributions that discuss modern methods of functional analysis, probability theory, differential geometry, ordinary and partial differential equations, algebraic topology, algebra and mathematical logic to any area of physics are of particular interest.
  • Algebra and Geometry with Applications to Related Fields: Includes algebra, differential geometry, global analysis, complex geometry, computational aspects, arithmetic, cryptography, and topology.
  • Probability and Statistics: Research on the theory and applications of probability and statistical techniques in regard to random phenomena and diverse areas are welcome.
  • Mathematical Biology: Focusing on research reporting new concepts or an understanding of biological systems using mathematical models/approaches.
  • Network Science: Research at the interface of mathematics, physics, biology, sociology, data science, and network science is the focus.
  • Fuzzy Set Theory: Aiming to disseminate and communicate fuzzy-set-theory-driven scientific knowledge and impactful discoveries for academia, the industry, and the public worldwide.
  • Difference and Differential Equations: Both qualitative and qualitative theories of difference and differential equations along with their cross-disciplinary applications will be of interest.
  • Computational Mathematics: Covering all areas of modern computational mathematics and analysis, such as functional analysis, numerical linear algebra, numerical optimization, numerical approximation, computational geometry, numerical ODEs and PDEs, inverse problems, etc.

The Special Issue is open to submissions from all the authors who are interested in the topic even if they did not participate in the event. All papers accepted in this Special Issue will meet the usual standards for publication held by Mathematics.

Prof. Dr. Francisco Chiclana
Prof. Dr. Paolo Mercorelli
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 100 words) can be sent to the Editorial Office for announcement on this website.

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

  • engineering mathematics
  • mathematical biology
  • mathematics and computer science
  • network science
  • dynamical systems
  • computational and applied mathematics
  • fuzzy sets, systems and decision making
  • difference and differential equations
  • financial mathematics
  • mathematical physics
  • algebra and geometry
  • probability and statistics
  • functional interpolation

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  • Ease of navigation: Grouping papers by topic helps scholars navigate broad scope journals more efficiently.
  • Greater discoverability: Special Issues support the reach and impact of scientific research. Articles in Special Issues are more discoverable and cited more frequently.
  • Expansion of research network: Special Issues facilitate connections among authors, fostering scientific collaborations.
  • External promotion: Articles in Special Issues are often promoted through the journal's social media, increasing their visibility.
  • e-Book format: Special Issues with more than 10 articles can be published as dedicated e-books, ensuring wide and rapid dissemination.

Further information on MDPI's Special Issue policies can be found here.

Published Papers (6 papers)

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6 pages, 212 KiB  
Article
Revisiting the Group Classification of the General Nonlinear Heat Equation ut = (K(u)ux)x
by Winter Sinkala
Mathematics 2025, 13(6), 911; https://doi.org/10.3390/math13060911 - 9 Mar 2025
Viewed by 155
Abstract
Group classification is a powerful tool for identifying and selecting the free elements—functions or parameters—in partial differential equations (PDEs) that maximize the symmetry properties of the model. In this paper, we revisit the group classification of the general nonlinear heat (or diffusion) equation [...] Read more.
Group classification is a powerful tool for identifying and selecting the free elements—functions or parameters—in partial differential equations (PDEs) that maximize the symmetry properties of the model. In this paper, we revisit the group classification of the general nonlinear heat (or diffusion) equation ut=K(u)uxx, where K(u) is a non-constant function of the dependent variable. We present the group classification framework, derive the determining equations for the coefficients of the infinitesimal generators of the admitted symmetry groups, and systematically solve for admissible forms of K(u). Our analysis recovers the classical results of Ovsyannikov and Bluman and provides additional clarity and detailed derivations. The classification yields multiple cases, each corresponding to a specific form of K(u), and reveals the dimension of the associated Lie symmetry algebra. Full article
(This article belongs to the Special Issue Mathematics and Applications)
10 pages, 252 KiB  
Article
Generalized Local Charge Conservation in Many-Body Quantum Mechanics
by F. Minotti and G. Modanese
Mathematics 2025, 13(5), 892; https://doi.org/10.3390/math13050892 - 6 Mar 2025
Viewed by 89
Abstract
In the framework of the quantum theory of many-particle systems, we study the compatibility of approximated non-equilibrium Green’s functions (NEGFs) and of approximated solutions of the Dyson equation with a modified continuity equation of the form [...] Read more.
In the framework of the quantum theory of many-particle systems, we study the compatibility of approximated non-equilibrium Green’s functions (NEGFs) and of approximated solutions of the Dyson equation with a modified continuity equation of the form ∂t⟨ρ⟩+(1−γ)∇·⟨J⟩=0. A continuity equation of this kind allows the e.m. coupling of the system in the extended Aharonov–Bohm electrodynamics, but not in Maxwell electrodynamics. Focusing on the case of molecular junctions simulated numerically with the Density Functional Theory (DFT), we further discuss the re-definition of local current density proposed by Wang et al., which also turns out to be compatible with the extended Aharonov–Bohm electrodynamics. Full article
(This article belongs to the Special Issue Mathematics and Applications)
26 pages, 2209 KiB  
Article
A Non-Self-Referential Characterization of the Gram–Schmidt Process via Computational Induction
by Ray-Ming Chen
Mathematics 2025, 13(5), 768; https://doi.org/10.3390/math13050768 - 26 Feb 2025
Viewed by 111
Abstract
The Gram–Schmidt process (GSP) plays an important role in algebra. It provides a theoretical and practical approach for generating an orthonormal basis, QR decomposition, unitary matrices, etc. It also facilitates some applications in the fields of communication, machine learning, feature extraction, etc. The [...] Read more.
The Gram–Schmidt process (GSP) plays an important role in algebra. It provides a theoretical and practical approach for generating an orthonormal basis, QR decomposition, unitary matrices, etc. It also facilitates some applications in the fields of communication, machine learning, feature extraction, etc. The typical GSP is self-referential, while the non-self-referential GSP is based on the Gram determinant, which has exponential complexity. The motivation for this article is to find a way that could convert a set of linearly independent vectors {u→i}j=1n into a set of orthogonal vectors {v→}j=1n via a non-self-referential GSP (NsrGSP). The approach we use is to derive a method that utilizes the recursive property of the standard GSP to retrieve a NsrGSP. The individual orthogonal vector form we obtain is v→k=∑j=1kβ[k→j]u→j, and the collective orthogonal vectors, in a matrix form, are Vk=Uk(BΔk+). This approach could reduce the exponential computational complexity to a polynomial one. It also has a neat representation. To this end, we also apply our approach on a classification problem based on real data. Our method shows the experimental results are much more persuasive than other familiar methods. Full article
(This article belongs to the Special Issue Mathematics and Applications)
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11 pages, 284 KiB  
Article
An Entropic Approach to Constrained Linear Regression
by Argimiro Arratia and Henryk Gzyl
Mathematics 2025, 13(3), 456; https://doi.org/10.3390/math13030456 - 29 Jan 2025
Viewed by 343
Abstract
We introduce a novel entropy minimization approach for the solution of constrained linear regression problems. Rather than minimizing the quadratic error, our method minimizes the Fermi–Dirac entropy, with the problem data incorporated as constraints. In addition to providing a solution to the linear [...] Read more.
We introduce a novel entropy minimization approach for the solution of constrained linear regression problems. Rather than minimizing the quadratic error, our method minimizes the Fermi–Dirac entropy, with the problem data incorporated as constraints. In addition to providing a solution to the linear regression problem, this approach also estimates the measurement error. The only prior assumption made about the errors is analogous to the assumption made about the unknown regression coefficients: specifically, the size of the interval within which they are expected to lie. We compare the results of our approach with those obtained using the disciplined convex optimization methodology. Furthermore, we address consistency issues and present examples to illustrate the effectiveness of our method. Full article
(This article belongs to the Special Issue Mathematics and Applications)
18 pages, 315 KiB  
Article
Generalizations and Properties of Normalized Similarity Measures for Boolean Models
by Amelia Bădică, Costin Bădică, Doina Logofătu and Ionuţ-Dragoş Neremzoiu
Mathematics 2025, 13(3), 384; https://doi.org/10.3390/math13030384 - 24 Jan 2025
Viewed by 448
Abstract
In this paper, we provide a closer look at some of the most popular normalized similarity/distance measures for Boolean models. This work includes the generalization of three classes of measures described as generalized Kulczynski, generalized Jaccard, and generalized Consonni and Todeschini measures, theoretical [...] Read more.
In this paper, we provide a closer look at some of the most popular normalized similarity/distance measures for Boolean models. This work includes the generalization of three classes of measures described as generalized Kulczynski, generalized Jaccard, and generalized Consonni and Todeschini measures, theoretical ordering of the similarity measures inside each class, as well as between classes, and positive and negative results regarding the metric properties of measures related to satisfying or not satisfying the triangle inequality axiom. Full article
(This article belongs to the Special Issue Mathematics and Applications)
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14 pages, 457 KiB  
Article
Counting Rules for Computing the Number of Independent Sets of a Grid Graph
by Guillermo De Ita Luna, Pedro Bello López and Raymundo Marcial-Romero
Mathematics 2024, 12(6), 922; https://doi.org/10.3390/math12060922 - 21 Mar 2024
Cited by 3 | Viewed by 1536
Abstract
The issue of counting independent sets of a graph, G, represented as i(G), is a significant challenge within combinatorial mathematics. This problem finds practical applications across various fields, including mathematics, computer science, physics, and chemistry. In chemistry, [...] Read more.
The issue of counting independent sets of a graph, G, represented as i(G), is a significant challenge within combinatorial mathematics. This problem finds practical applications across various fields, including mathematics, computer science, physics, and chemistry. In chemistry, i(G) is recognized as the Merrifield–Simmons (M-S) index for molecular graphs, which is one of the most relevant topological indices related to the boiling point in chemical compounds. This article introduces an innovative algorithm designed for tallying independent sets within grid-like structures. The proposed algorithm is based on the ‘branch-and-bound’ technique and is applied to compute i(Gm,n) for a square grid formed by m rows and n columns. The proposed approach incorporates the widely recognized vertex reduction rule as the basis for splitting the current subgraph. The methodology involves breaking down the initial grid iteratively until outerplanar graphs are achieved, serving as the ’basic cases’ linked to the leaf nodes of the computation tree or when no neighborhood is incident to a minimum of five rectangular internal faces. The time complexity of the branch-and-bound algorithm speeds up the computation of i(Gm,n) compared to traditional methods, like the transfer matrix method. Furthermore, the scope of the proposed algorithm is more general than the algorithms focused on grids since it could be applied to process general mesh graphs. Full article
(This article belongs to the Special Issue Mathematics and Applications)
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