Special Issue " Group Theory and its Applications in Engineering, Computer Science, and Structural Biology"

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "Mathematics and Computer Science".

Deadline for manuscript submissions: 31 March 2020.

Special Issue Editor

Prof. Simone Fiori
E-Mail Website
Guest Editor
Department of Information Engineering, Marches Polytechnic University, Via Brecce Bianche, Ancona I-60131, Italy
Interests: nonlinear statistical modeling of monotonic as well as nonmonotonic relationship between two random variables on the basis of complete or incomplete data pairs; computing statistical descriptors of random distributions on curved spaces
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Special Issue Information

Dear Colleagues,

For the past century, group-theoretic methods have been a cornerstone of all aspects of physics. More recently, group theory has been applied widely outside of physics, in fields ranging from robotics and computer vision, to the study of biomolecular symmetry and conformation, to the study of how information is processed in deep learning and in the mammalian visual cortex.

This Special Issue focuses on group theory as it relates to these applications. Moreover, the development of new and efficient computational tools that use group theory with these applications in mind are welcome.

Prof. Simone Fiori
Guest Editor

Manuscript Submission Information

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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 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 1200 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

  • Group theory
  • Algorithms
  • Pattern recognition
  • Robotics
  • Computer vision
  • Visual cortex
  • Crystallography
  • Molecular symmetry

Published Papers (2 papers)

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Research

Open AccessArticle
Model Formulation Over Lie Groups and Numerical Methods to Simulate the Motion of Gyrostats and Quadrotors
Mathematics 2019, 7(10), 935; https://doi.org/10.3390/math7100935 - 10 Oct 2019
Abstract
The present paper recalls a formulation of non-conservative system dynamics through the Lagrange–d’Alembert principle expressed through a generalized Euler–Poincaré form of the system equation on a Lie group. The paper illustrates applications of the generalized Euler–Poincaré equations on the rotation groups to a [...] Read more.
The present paper recalls a formulation of non-conservative system dynamics through the Lagrange–d’Alembert principle expressed through a generalized Euler–Poincaré form of the system equation on a Lie group. The paper illustrates applications of the generalized Euler–Poincaré equations on the rotation groups to a gyrostat satellite and a quadcopter drone. The numerical solution of the dynamical equations on the rotation groups is tackled via a generalized forward Euler method and an explicit Runge–Kutta integration method tailored to Lie groups. Full article
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Open AccessArticle
Some New Applications of Weakly ℋ-Embedded Subgroups of Finite Groups
Mathematics 2019, 7(2), 158; https://doi.org/10.3390/math7020158 - 10 Feb 2019
Abstract
A subgroup H of a finite group G is said to be weakly H -embedded in G if there exists a normal subgroup T of G such that H G = H T and H T H ( G ) , [...] Read more.
A subgroup H of a finite group G is said to be weakly H -embedded in G if there exists a normal subgroup T of G such that H G = H T and H T H ( G ) , where H G is the normal closure of H in G, and H ( G ) is the set of all H -subgroups of G. In the recent research, Asaad, Ramadan and Heliel gave new characterization of p-nilpotent: Let p be the smallest prime dividing | G | , and P a non-cyclic Sylow p-subgroup of G. Then G is p-nilpotent if and only if there exists a p-power d with 1 < d < | P | such that all subgroups of P of order d and p d are weakly H -embedded in G. As new applications of weakly H -embedded subgroups, in this paper, (1) we generalize this result for general prime p and get a new criterion for p-supersolubility; (2) adding the condition “ N G ( P ) is p-nilpotent”, here N G ( P ) = { g G | P g = P } is the normalizer of P in G, we obtain p-nilpotence for general prime p. Moreover, our tool is the weakly H -embedded subgroup. However, instead of the normality of H G = H T , we just need H T is S-quasinormal in G, which means that H T permutes with every Sylow subgroup of G. Full article
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