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Mathematics
Special Issues
Mathematical Structures and Their Applications
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Mathematical Structures and Their Applications

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "Algebra, Geometry and Topology".

Deadline for manuscript submissions: 31 July 2024 | Viewed by 5522

Special Issue Editor

Prof. Dr. Nelson Martins Ferreira

E-Mail Website
Guest Editor
Department of Mathematics, Polytechnic Institute of Leiria, Leiria, Portugal
Interests: homological and categorical algebra; category theory; topological geometry; computer science; development of algorithms and structured data sets

Special Issue Information

Dear Colleagues,

Classically, a mathematical structure is a set endowed with some additional features such as an operation, a relation, a metric, or a topology. The additional features are often attached to the set to provide it with some additional meaning or significance.

In this issue, we will be looking for the categorical version of a mathematical structure. By that, we mean a diagram in a category, consisting of objects, morphisms, 2-cells, etc., which are required to satisfy some limiting or colimiting conditions as well as identities or pseudo-identities. Examples include directed graphs, spans, cospans, reflexive graphs, internal categories, groupoids, crossed-modules, bicategories, triangulations, chain-complexes, graded algebras, n-dimensional categories, homotopy types, etc.

Each such structure can be interpreted in any category (perhaps with some additional features) and may give rise to different applications both in mathematics and other areas of study. Such areas may include physics, biology, chemistry, computer science, and several others on the verge of technology and engineering.

Papers that introduce new structures and study their properties, as well as papers that consider new applications or interpretations of known ones are welcome to this topic.

Prof. Dr. Nelson Martins Ferreira
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 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

  • category
  • structure
  • diagram
  • mathematical structure
  • directed graph
  • span
  • cospan
  • reflexive graph
  • internal categories
  • groupoid
  • crossed module
  • bicategory
  • triangulation
  • chain complex

Published Papers (3 papers)

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Research

34 pages, 403 KiB  
Article
Internal Categorical Structures and Their Applications
by Nelson Martins-Ferreira
Mathematics 2023, 11(3), 660; https://doi.org/10.3390/math11030660 - 28 Jan 2023
Cited by 1 | Viewed by 930
Abstract
While surveying some internal categorical structures and their applications, it is shown that triangulations and internal groupoids can be unified as two different instances of the same common structure, namely a multi-link. A brief survey includes the categories of directed graphs, reflexive graphs, [...] Read more.
While surveying some internal categorical structures and their applications, it is shown that triangulations and internal groupoids can be unified as two different instances of the same common structure, namely a multi-link. A brief survey includes the categories of directed graphs, reflexive graphs, links, multi-links, triangulations, trigraphs, multiplicative graphs, groupoids, pregroupoids, internal categories, kites, directed kites and multiplicative kites. Most concepts are well-known, and all of them have appeared in print at least once. For example, a multiplicative directed kite has been used as a common generalization for an internal category and a pregroupoid. The scope of the notion of centralization for equivalence relations is widened into the context of digraphs while providing a new characterization of internal groupoids. Full article
(This article belongs to the Special Issue Mathematical Structures and Their Applications)
13 pages, 3392 KiB  
Article
Three-Dimensional Force Decouping-Sensing Soft Sensor with Topological Elastomer
by Dachang Zhu, Longfei Wu and Yonglong He
Mathematics 2023, 11(2), 396; https://doi.org/10.3390/math11020396 - 12 Jan 2023
Cited by 1 | Viewed by 1379
Abstract
Sensing the deformation of soft sensor elastomer can realize the flexible operation of soft robot and enhance the perception of human-computer interaction. The structural configuration of elastomer and its elastic deformation force transfer path are crucial for decoupling sensing and studying the sensing [...] Read more.
Sensing the deformation of soft sensor elastomer can realize the flexible operation of soft robot and enhance the perception of human-computer interaction. The structural configuration of elastomer and its elastic deformation force transfer path are crucial for decoupling sensing and studying the sensing performance of three-dimensional force soft sensor. In this article, we present a theoretical method for soft sensor with three-dimensional force decoupling-sensing. First, the constraint types of parallel manipulator with three translational motion characteristics are analyzed and used to set the constraint conditions for topology optimization. In addition, the differential kinematic modeling method is adopted to establish the differential kinematic equation of the three translations parallel manipulator, which is used as a pseudo-rigid body model for sensor information perception. Second, combining the kinematic Jacobi matrix with solid isotropic material with penalization the (SIMP), the topological model is built for designing of sensor elastomer. We optimized the composition of the material and evaluate the model’s sensing capabilities. The results validate a elastomer of soft sensor for unity between structural stiffness and perceived sensitivity. Full article
(This article belongs to the Special Issue Mathematical Structures and Their Applications)
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23 pages, 320 KiB  
Article
On S-Evolution Algebras and Their Enveloping Algebras
by Farrukh Mukhamedov and Izzat Qaralleh
Mathematics 2021, 9(11), 1195; https://doi.org/10.3390/math9111195 - 25 May 2021
Cited by 8 | Viewed by 1678
Abstract
In the present paper, we introduce S-evolution algebras and investigate their solvability, simplicity, and semisimplicity. The structure of enveloping algebras has been carried out through the attached graph of S-evolution algebras. Moreover, we introduce the concept of E-linear derivation of [...] Read more.
In the present paper, we introduce S-evolution algebras and investigate their solvability, simplicity, and semisimplicity. The structure of enveloping algebras has been carried out through the attached graph of S-evolution algebras. Moreover, we introduce the concept of E-linear derivation of S-evolution algebras, and prove such derivations can be extended to their enveloping algebras under certain conditions. Full article
(This article belongs to the Special Issue Mathematical Structures and Their Applications)
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