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Axioms
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Advances in Classical and Applied Mathematics
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Advances in Classical and Applied Mathematics

A special issue of Axioms (ISSN 2075-1680).

Deadline for manuscript submissions: 28 February 2025 | Viewed by 7071

Special Issue Editors

Prof. Dr. Cristina Flaut

E-Mail Website
Guest Editor
Faculty of Mathematics and Computer Science, Ovidius University, Bd. Mamaia 124, 900527 Constanta, Romania
Interests: algebra (non-associative algebra, algebra obtained by the Cayley–Dickson process, and algebra of logic); coding theory; cryptography
Dr. Dana Piciu

E-Mail Website
Guest Editor
Faculty of Science, University of Craiova, 200585 Craiova, Romania
Interests: lattice theory; set theory; algebraic topology; category theory; algebra
Prof. Dr. Murat Tosun

E-Mail Website
Guest Editor
Department of Mathematics, Faculty of Science, Sakarya University, 54187 Sakarya, Turkey
Interests: differential geometry; curve theory; surface theory; number theory; quaternions; special numbers

Special Issue Information

Dear Colleagues,

This Special Issue will be devoted to publishing papers with significant results in classical and applied mathematics. The theme of this Special Issue is expansive and can be approached from any mathematical point of view. Progress within mathematics is based on innovative ideas comprising a kind of cycle which starts from an identified need to develop a solution. First of all, that need is transformed in a problem which must be clearly defined in order to find a solution.

In classical mathematics, a lot of computations are involved and domains are used (including in algebra, geometry, classical logic, set theory, mathematical analyses, statistic, etc.). Applied mathematics focuses on mathematical principles and involves the application of mathematics to problems which arise in various areas, such as engineering or other domains of science or life. All these inform the development of new or improved methods which allow us to obtain solutions for new problems.

To emphasize the ideas above, this Special Issue will present some aspects regarding, but not limited to, the following:

- computer science (new theoretical and practical applications);

- mathematics (classical and applied mathematics results presented with new approaches and applications, mathematical models, all mathematical results containing new ideas starting from old subjects which can improve another known results, some new aspects regarding history of mathematics, etc.).

Prof. Dr. Cristina Flaut
Dr. Dana Piciu
Prof. Dr. Murat Tosun
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. Axioms is an international peer-reviewed open access monthly 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 2400 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

  • classical mathematics
  • applied mathematics
  • mathematical models
  • mathematical principles
  • computer science

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Published Papers (9 papers)

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Research

14 pages, 709 KiB  
Article
Characterizations of Spatial Quaternionic Partner-Ruled Surfaces
by Soley Ersoy, Kemal Eren and Abdussamet Çalışkan
Axioms 2024, 13(9), 612; https://doi.org/10.3390/axioms13090612 - 9 Sep 2024
Viewed by 231
Abstract
In this paper, we investigate the spatial quaternionic expressions of partner-ruled surfaces. Moreover, we formulate the striction curves and dralls of these surfaces by use of the quaternionic product. Furthermore, the pitches and angles of pitches are interpreted for the spatial quaternionic ruled [...] Read more.
In this paper, we investigate the spatial quaternionic expressions of partner-ruled surfaces. Moreover, we formulate the striction curves and dralls of these surfaces by use of the quaternionic product. Furthermore, the pitches and angles of pitches are interpreted for the spatial quaternionic ruled surfaces that are closed. Additionally, we calculate the integral invariants of these surfaces using quaternionic formulas. Finally, the partner-ruled surfaces of a given spatial quaternionic ruled surface are demonstrated as an example, and their graphics are drawn. Full article
(This article belongs to the Special Issue Advances in Classical and Applied Mathematics)
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22 pages, 18029 KiB  
Article
Numerical Analysis of the Cylindrical Shell Pipe with Preformed Holes Subjected to a Compressive Load Using Non-Uniform Rational B-Splines and T-Splines for an Isogeometric Analysis Approach
by Said EL Fakkoussi, Ouadie Koubaiti, Ahmed Elkhalfi, Sorin Vlase and Marin Marin
Axioms 2024, 13(8), 529; https://doi.org/10.3390/axioms13080529 - 3 Aug 2024
Viewed by 1005
Abstract
In this paper, we implement the finite detail technique primarily based on T-Splines for approximating solutions to the linear elasticity equations in the connected and bounded Lipschitz domain. Both theoretical and numerical analyses of the Dirichlet and Neumann boundary problems are presented. The [...] Read more.
In this paper, we implement the finite detail technique primarily based on T-Splines for approximating solutions to the linear elasticity equations in the connected and bounded Lipschitz domain. Both theoretical and numerical analyses of the Dirichlet and Neumann boundary problems are presented. The Reissner–Mindlin (RM) hypothesis is considered for the investigation of the mechanical performance of a 3D cylindrical shell pipe without and with preformed hole problems under concentrated and compression loading in the linear elastic behavior for trimmed and untrimmed surfaces in structural engineering problems. Bézier extraction from T-Splines is integrated for an isogeometric analysis (IGA) approach. The numerical results obtained, particularly for the displacement and von Mises stress, are compared with and validated against the literature results, particularly with those for Non-Uniform Rational B-Spline (NURBS) IGA and the finite element method (FEM) Abaqus methods. The obtained results show that the computation time of the IGA based on the T-Spline method is shorter than that of the IGA NURBS and FEM Abaqus/CAE (computer-aided engineering) methods. Furthermore, the highlighted results confirm that the IGA approach based on the T-Spline method shows more success than numerical reference methods. We observed that the NURBS IGA method is very limited for studying trimmed surfaces. The T-Spline method shows its power and capability in computing trimmed and untrimmed surfaces. Full article
(This article belongs to the Special Issue Advances in Classical and Applied Mathematics)
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24 pages, 2445 KiB  
Article
On Some Distance Spectral Characteristics of Trees
by Sakander Hayat, Asad Khan and Mohammed J. F. Alenazi
Axioms 2024, 13(8), 494; https://doi.org/10.3390/axioms13080494 - 23 Jul 2024
Viewed by 486
Abstract
Graham and Pollack in 1971 presented applications of eigenvalues of the distance matrix in addressing problems in data communication systems. Spectral graph theory employs tools from linear algebra to retrieve the properties of a graph from the spectrum of graph-theoretic matrices. The study [...] Read more.
Graham and Pollack in 1971 presented applications of eigenvalues of the distance matrix in addressing problems in data communication systems. Spectral graph theory employs tools from linear algebra to retrieve the properties of a graph from the spectrum of graph-theoretic matrices. The study of graphs with “few eigenvalues” is a contemporary problem in spectral graph theory. This paper studies graphs with few distinct distance eigenvalues. After mentioning the classification of graphs with one and two distinct distance eigenvalues, we mainly focus on graphs with three distinct distance eigenvalues. Characterizing graphs with three distinct distance eigenvalues is “highly” non-trivial. In this paper, we classify all trees whose distance matrix has precisely three distinct eigenvalues. Our proof is different from earlier existing proof of the result as our proof is extendable to other similar families such as unicyclic and bicyclic graphs. The main tools which we employ include interlacing and equitable partitions. We also list all the connected graphs on ν ≤ 6 vertices and compute their distance spectra. Importantly, all these graphs on ν ≤ 6 vertices are determined from their distance spectra. We deliver a distance cospectral pair of order 7, thus making it a distance cospectral pair of the smallest order. This paper is concluded with some future directions. Full article
(This article belongs to the Special Issue Advances in Classical and Applied Mathematics)
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15 pages, 617 KiB  
Article
On Some Properties of the Equilateral Triangles with Vertices Located on the Support Sides of a Triangle
by Dorin Andrica and Ovidiu Bagdasar
Axioms 2024, 13(7), 478; https://doi.org/10.3390/axioms13070478 - 17 Jul 2024
Viewed by 452
Abstract
The possible positions of an equilateral triangle whose vertices are located on the support sides of a generic triangle are studied. Using complex coordinates, we show that there are infinitely many such configurations, then we prove that the centroids of these equilateral triangles [...] Read more.
The possible positions of an equilateral triangle whose vertices are located on the support sides of a generic triangle are studied. Using complex coordinates, we show that there are infinitely many such configurations, then we prove that the centroids of these equilateral triangles are collinear, defining two lines perpendicular to the Euler’s line of the original triangle. Finally, we obtain the complex coordinates of the intersection points and study some particular cases. Full article
(This article belongs to the Special Issue Advances in Classical and Applied Mathematics)
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10 pages, 254 KiB  
Article
Some Remarks Regarding Special Elements in Algebras Obtained by the Cayley–Dickson Process over Zp
by Cristina Flaut and Andreea Baias
Axioms 2024, 13(6), 351; https://doi.org/10.3390/axioms13060351 - 24 May 2024
Viewed by 602
Abstract
In this paper, we provide some properties of k-potent elements in algebras obtained by the Cayley–Dickson process over Zp. Moreover, we find a structure of nonunitary ring over Fibonacci quaternions over Z3 and we present a method to encrypt [...] Read more.
In this paper, we provide some properties of k-potent elements in algebras obtained by the Cayley–Dickson process over Zp. Moreover, we find a structure of nonunitary ring over Fibonacci quaternions over Z3 and we present a method to encrypt plain texts, by using invertible elements in some of these algebras. Full article
(This article belongs to the Special Issue Advances in Classical and Applied Mathematics)
18 pages, 617 KiB  
Article
A Progressive Outlook on Possibility Multi-Fuzzy Soft Ordered Semigroups: Theory and Analysis
by Sana Habib, Faiz Muhammad Khan and Violeta Leoreanu-Fotea
Axioms 2024, 13(6), 340; https://doi.org/10.3390/axioms13060340 - 21 May 2024
Viewed by 563
Abstract
The concept of possibility fuzzy soft sets is a step in a new direction towards a soft set approach that can be used to solve decision-making issues. In this piece of research, an innovative and comprehensive conceptual framework for possibility multi-fuzzy soft ordered [...] Read more.
The concept of possibility fuzzy soft sets is a step in a new direction towards a soft set approach that can be used to solve decision-making issues. In this piece of research, an innovative and comprehensive conceptual framework for possibility multi-fuzzy soft ordered semigroups by making use of the notions that are associated with possibility multi-fuzzy soft sets as well as ordered semigroups is introduced. Possibility multi-fuzzy soft ordered semigroups mark a newly developed theoretical avenue, and the central aim of this paper is to investigate it. The focus lies on investigating this newly developed theoretical direction, with practical examples drawn from decision-making and diagnosis practices to enhance understanding and appeal to researchers’ interests. We strictly build the notions of possibility multi-fuzzy soft left (right) ideals, as well as l-idealistic and r-idealistic possibility multi-fuzzy soft ordered semigroups. Furthermore, various algebraic operations, such as union, intersection, as well as AND and OR operations are derived, while also providing a comprehensive discussion of their properties. To clarify these innovative ideas, the theoretical constructs are further reinforced with a set of demonstrative examples in order to guarantee deep and improved comprehension of the proposed framework. Full article
(This article belongs to the Special Issue Advances in Classical and Applied Mathematics)
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18 pages, 317 KiB  
Article
A Generalization of the First Tits Construction
by Thomas Moran and Susanne Pumpluen
Axioms 2024, 13(5), 299; https://doi.org/10.3390/axioms13050299 - 29 Apr 2024
Viewed by 1318
Abstract
Let F be a field of characteristic, not 2 or 3. The first Tits construction is a well-known tripling process to construct separable cubic Jordan algebras, especially Albert algebras. We generalize the first Tits construction by choosing the scalar employed in the tripling [...] Read more.
Let F be a field of characteristic, not 2 or 3. The first Tits construction is a well-known tripling process to construct separable cubic Jordan algebras, especially Albert algebras. We generalize the first Tits construction by choosing the scalar employed in the tripling process outside of the base field. This yields a new family of non-associative unital algebras which carry a cubic map, and maps that can be viewed as generalized adjoint and generalized trace maps. These maps display properties often similar to the ones in the classical setup. In particular, the cubic norm map permits some kind of weak Jordan composition law. Full article
(This article belongs to the Special Issue Advances in Classical and Applied Mathematics)
20 pages, 383 KiB  
Article
Ideals and Filters on Neutrosophic Topologies Generated by Neutrosophic Relations
by Ravi P. Agarwal, Soheyb Milles, Brahim Ziane, Abdelaziz Mennouni and Lemnaouar Zedam
Axioms 2024, 13(5), 292; https://doi.org/10.3390/axioms13050292 - 25 Apr 2024
Cited by 1 | Viewed by 815
Abstract
Recently, Milles and Hammami presented and studied the concept of a neutrosophic topology generated by a neutrosophic relation. As a continuation in the same direction, this paper studies the concepts of neutrosophic ideals and neutrosophic filters on that topology. More precisely, we offer [...] Read more.
Recently, Milles and Hammami presented and studied the concept of a neutrosophic topology generated by a neutrosophic relation. As a continuation in the same direction, this paper studies the concepts of neutrosophic ideals and neutrosophic filters on that topology. More precisely, we offer the lattice structure of neutrosophic open sets of a neutrosophic topology generated via a neutrosophic relation and examine its different characteristics. Furthermore, we enlarge to this lattice structure the notions of ideals (respectively, filters) and characterize them with regard to the lattice operations. We end this work by studying the prime neutrosophic ideal and prime neutrosophic filter as interesting types of neutrosophic ideals and neutrosophic filters. Full article
(This article belongs to the Special Issue Advances in Classical and Applied Mathematics)
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12 pages, 267 KiB  
Article
Monotonic Random Variables According to a Direction
by José Juan Quesada-Molina and Manuel Úbeda-Flores
Axioms 2024, 13(4), 275; https://doi.org/10.3390/axioms13040275 - 20 Apr 2024
Viewed by 749
Abstract
In this paper, we introduce the concept of monotonicity according to a direction for a set of random variables. This concept extends well-known multivariate dependence notions, such as corner set monotonicity, and can be used to detect dependence in multivariate distributions not detected [...] Read more.
In this paper, we introduce the concept of monotonicity according to a direction for a set of random variables. This concept extends well-known multivariate dependence notions, such as corner set monotonicity, and can be used to detect dependence in multivariate distributions not detected by other known concepts of dependence. Additionally, we establish relationships with other known multivariate dependence concepts, outline some of their salient properties, and provide several examples. Full article
(This article belongs to the Special Issue Advances in Classical and Applied Mathematics)
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