Applications of Geometric Algebra

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

Deadline for manuscript submissions: 31 May 2024 | Viewed by 1420

Special Issue Editors


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Guest Editor

Special Issue Information

Dear Colleagues,

Geometric Algebra has emerged as a new fascinating mathematical framework for a variety of disciplines in science and engineering. At present, its application is somewhat limited, but it is increasingly being used by multiple authors in fields such as robotics, electrical engineering, image and signal processing, or deep learning to mention a few. By promoting the use of GA and its application, as well as its associated benefits, the aim is to increase its dissemination and visibility to the international scientific community for its progressive adoption as a comprehensive and universal tool.

This Special Issue invites researchers to submit original research papers and review articles related to any engineering o scientific discipline in which practical applications of Geometric Algebra are considered. The topics of interest include (but are not limited to):

  • GA in Engineering Applications: Robotics, Control, Electrical Engineering, Telecommunications, Path Planning, Optics, Material Science, Computer Graphics and Modelling,
  • GA in Applied Geometry: Spinors and Symmetry, Computation in Geometry, Molecular Geometry Furthermore, 3D Protein Structures, Computer Algebra, Curves and Surfaces,
  • GA in Information Processing: Neural Networks, Artificial Intelligence, Geographic Information Systems, Encryption and Cryptography.
  • GA in Applied Physics: Relativity, Gravity and Cosmology, Classical Physics, Electromagnetism and Optics, Quantum Physics.
  • GA in Signal, Image and Video Processing: Medical Imaging, Motion Processing, Estimation and Filtering, Features and Detection, Kernel Transformations (Fourier, Etc).
  • GA in Software: Software Libraries, Software Implementations, Software Frameworks.
  • GA in Education: Teaching GA, New Methodologies.

Prof. Dr. Francisco G. Montoya
Prof. Dr. Alfredo Alcayde
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.

Published Papers (1 paper)

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Research

18 pages, 361 KiB  
Article
Development of the Method of Averaging in Clifford Geometric Algebras
by Dmitry Shirokov
Mathematics 2023, 11(16), 3607; https://doi.org/10.3390/math11163607 - 21 Aug 2023
Viewed by 566
Abstract
We develop the method of averaging in Clifford (geometric) algebras suggested by the author in previous papers. We consider operators constructed using two different sets of anticommuting elements of real or complexified Clifford algebras. These operators generalize Reynolds operators from the representation theory [...] Read more.
We develop the method of averaging in Clifford (geometric) algebras suggested by the author in previous papers. We consider operators constructed using two different sets of anticommuting elements of real or complexified Clifford algebras. These operators generalize Reynolds operators from the representation theory of finite groups. We prove a number of new properties of these operators. Using the generalized Reynolds operators, we give a complete proof of the generalization of Pauli’s theorem to the case of Clifford algebras of arbitrary dimension. The results can be used in geometry, physics, engineering, computer science, and other applications. Full article
(This article belongs to the Special Issue Applications of Geometric Algebra)

Planned Papers

The below list represents only planned manuscripts. Some of these manuscripts have not been received by the Editorial Office yet. Papers submitted to MDPI journals are subject to peer-review.

Title: Generalization of the Conformal Model and Groupoïd of the Image Viewpoint Changes
Authors: Ghina EL MIR
Affiliation: Lebanese University
Abstract: n/a

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