Mathematics

Journal Browser

► Journal Browser

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

Share This Special Issue

Special Issue Editor

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

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.

Benefits of Publishing in a Special Issue

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 polices can be found here.

Published Papers (3 papers)

Download All Papers

Order results

Result details

Show export options Show export options

Select all

Export citation of selected articles as:

Research

13 pages, 309 KiB

Open AccessArticle

Theoretical Bounds on Performance in Threshold Group Testing Schemes

by Jin-Taek Seong

Mathematics 2020, 8(4), 637; https://doi.org/10.3390/math8040637 - 21 Apr 2020

Cited by 4 | Viewed by 2536

Abstract

A threshold group testing (TGT) scheme with lower and upper thresholds is a general model of group testing (GT) which identifies a small set of defective samples. In this paper, we consider the TGT scheme that require the minimum number of tests. We aim to find lower and upper bounds for finding a set of defective samples in a large population. The decoding for the TGT scheme is exploited by minimization of the Hamming weight in channel coding theory and the probability of error is also defined. Then, we derive a new upper bound on the probability of error and extend a lower bound from conventional one to the TGT scheme. We show that the upper and lower bounds well match with each other at the optimal density ratio of the group matrix. In addition, we conclude that when the gaps between the two thresholds in the TGT framework increase, the group matrix with a high density should be used to achieve optimal performance. Full article

(This article belongs to the Special Issue Group Theory and its Applications in Engineering, Computer Science, and Structural Biology)

► Show Figures

Figure 1

35 pages, 2414 KiB

Open AccessArticle

Model Formulation Over Lie Groups and Numerical Methods to Simulate the Motion of Gyrostats and Quadrotors

by Simone Fiori

Mathematics 2019, 7(10), 935; https://doi.org/10.3390/math7100935 - 10 Oct 2019

Cited by 14 | Viewed by 3617

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 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

(This article belongs to the Special Issue Group Theory and its Applications in Engineering, Computer Science, and Structural Biology)

► Show Figures

Figure 1

10 pages, 305 KiB

Open AccessArticle

Some New Applications of Weakly ℋ-Embedded Subgroups of Finite Groups

by Li Zhang, Li-Jun Huo and Jia-Bao Liu

Mathematics 2019, 7(2), 158; https://doi.org/10.3390/math7020158 - 10 Feb 2019

Viewed by 2501

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 \cap T \in 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 \cap T \in 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 \in 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

(This article belongs to the Special Issue Group Theory and its Applications in Engineering, Computer Science, and Structural Biology)

Show export options Show export options

Select all

Export citation of selected articles as:

Displaying articles 1-3

Journal Menu

Journal Browser

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

Share This Special Issue

Special Issue Editor

Special Issue Information

Keywords

Benefits of Publishing in a Special Issue

Published Papers (3 papers)

Research

Further Information

Guidelines

MDPI Initiatives

Follow MDPI