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Symmetry
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Recent Advance in Pure and Applied Mathematics
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Recent Advance in Pure and Applied Mathematics

A special issue of Symmetry (ISSN 2073-8994). This special issue belongs to the section "Mathematics".

Deadline for manuscript submissions: closed (15 October 2021) | Viewed by 10629

Special Issue Editor

Prof. Dr. Mina Teicher

E-Mail Website
Guest Editor
Department of Mathematics and Gonda Brain Research Center, Bar-Ilan University, Ramat-Gan 52900, Israel
Interests: math; neural computation

Special Issue Information

Dear Colleagues,

Symmetry is a notion that drives nature from creation and is used in all theories describing the universe from relativity to quantum. Naturally, symmetry plays a central role in the mathematical theories supporting physics and chemistry. In particular, mirror symmetry became a bridge between mathematics and theoretical physics. Symmetry has spread to many other fields of mathematical research and phenomena of symmetry are found and considered significant in geometry, combinatorics, complex analysis, algebra, mathematical physics, biomathematics, neural computation and complex systems, and more. In this volume, we shall present a variety of new studies related to symmetry in mathematics.

Prof. Mina Teicher
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. Symmetry 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

  • symmetry
  • mirror symmetry
  • mathematical physics
  • braids
  • Neural Computation

Published Papers (5 papers)

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Research

17 pages, 1055 KiB  
Article
Neurocartographer: CC-WGAN Based SSVEP Data Generation to Produce a Model toward Symmetrical Behaviour to the Human Brain
by Sefa E. Karabulut, Mohammad Mehdi Khorasani and Adam Pantanowitz
Symmetry 2022, 14(8), 1600; https://doi.org/10.3390/sym14081600 - 4 Aug 2022
Viewed by 1812
Abstract
Brain–computer interfaces are an emerging field of medical technology that enable users to control external digital devices via brain activity. Steady-state evoked potential is a type of electroencephalogram signal that is widely used for brain–computer interface applications. Collecting electroencephalogram data is an effort-intensive [...] Read more.
Brain–computer interfaces are an emerging field of medical technology that enable users to control external digital devices via brain activity. Steady-state evoked potential is a type of electroencephalogram signal that is widely used for brain–computer interface applications. Collecting electroencephalogram data is an effort-intensive task that requires technical expertise, specialised equipment, and ethical considerations. This work proposes a class-conditioned Wasserstein generative adversarial network with a gradient penalty loss for electroencephalogram data generation. Electroencephalogram data were recorded via a g.tec HiAmp using 5, 6, 7.5, and 10 Hz flashing video stimuli. The resulting model replicates the key steady-state-evoked potential features after training for 100 epochs with 25 batches of 4 s steady-state-evoked potential data. This creates a model that mimics brain activity, producing a type of symmetry between the brain’s visual reaction to frequency-based stimuli as measured by electroencephalogram and the model output. Full article
(This article belongs to the Special Issue Recent Advance in Pure and Applied Mathematics)
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8 pages, 254 KiB  
Article
Characterization of Almost Yamabe Solitons and Gradient Almost Yamabe Solitons with Conformal Vector Fields
by Ali H. Alkhaldi, Pişcoran Laurian-Ioan, Abimbola Abolarinwa and Akram Ali
Symmetry 2021, 13(12), 2362; https://doi.org/10.3390/sym13122362 - 8 Dec 2021
Cited by 2 | Viewed by 1792
Abstract
In this paper, some sufficient conditions of almost Yamabe solitons are established, such that the solitons are Yamabe metrics, by which we mean metrics of constant scalar curvature. This is achieved by imposing fewer topological constraints. The properties of the conformal vector fields [...] Read more.
In this paper, some sufficient conditions of almost Yamabe solitons are established, such that the solitons are Yamabe metrics, by which we mean metrics of constant scalar curvature. This is achieved by imposing fewer topological constraints. The properties of the conformal vector fields are exploited for the purpose of establishing various necessary criteria on the soliton vector fields of gradient almost Yamabe solitons so as to obtain Yamabe metrics. Full article
(This article belongs to the Special Issue Recent Advance in Pure and Applied Mathematics)
16 pages, 874 KiB  
Article
Impact of Bioconvection and Chemical Reaction on MHD Nanofluid Flow Due to Exponential Stretching Sheet
by Muhammad Imran Asjad, Noman Sarwar, Bagh Ali, Sajjad Hussain, Thanin Sitthiwirattham and Jiraporn Reunsumrit
Symmetry 2021, 13(12), 2334; https://doi.org/10.3390/sym13122334 - 5 Dec 2021
Cited by 27 | Viewed by 2396
Abstract
Thermal management is a crucial task in the present era of miniatures and other gadgets of compact heat density. This communication presents the momentum and thermal transportation of nanofluid flow over a sheet that stretches exponentially. The fluid moves through a porous matrix [...] Read more.
Thermal management is a crucial task in the present era of miniatures and other gadgets of compact heat density. This communication presents the momentum and thermal transportation of nanofluid flow over a sheet that stretches exponentially. The fluid moves through a porous matrix in the presence of a magnetic field that is perpendicular to the flow direction. To achieve the main objective of efficient thermal transportation with increased thermal conductivity, the possible settling of nano entities is avoided with the bioconvection of microorganisms. Furthermore, thermal radiation, heat source dissipation, and activation energy are also considered. The formulation in the form of a partial differential equation is transmuted into an ordinary differential form with the implementation of appropriate similarity variables. Numerical treatment involving Runge–Kutta along with the shooting technique method was chosen to resolve the boundary values problem. To elucidate the physical insights of the problem, computational code was run for suitable ranges of the involved parameters. The fluid temperature directly rose with the buoyancy ratio parameter, Rayleigh number, Brownian motion parameter, and thermophoresis parameter. Thus, thermal transportation enhances with the inclusion of nano entities and the bioconvection of microorganisms. The findings are useful for heat exchangers working in various technological processors. The validation of the obtained results is also assured through comparison with the existing result. The satisfactory concurrence was also observed while comparing the present symmetrical results with the existing literature. Full article
(This article belongs to the Special Issue Recent Advance in Pure and Applied Mathematics)
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17 pages, 343 KiB  
Article
Stone Duality for Kolmogorov Locally Small Spaces
by Artur Piękosz
Symmetry 2021, 13(10), 1791; https://doi.org/10.3390/sym13101791 - 26 Sep 2021
Cited by 3 | Viewed by 1349
Abstract
In this paper, we prove new versions of Stone Duality. The main version is the following: the category of Kolmogorov locally small spaces and bounded continuous mappings is equivalent to the category of spectral spaces with decent lumps and with bornologies in the [...] Read more.
In this paper, we prove new versions of Stone Duality. The main version is the following: the category of Kolmogorov locally small spaces and bounded continuous mappings is equivalent to the category of spectral spaces with decent lumps and with bornologies in the lattices of (quasi-) compact open sets as objects and spectral mappings respecting those decent lumps and satisfying a boundedness condition as morphisms. Furthermore, it is dually equivalent to the category of bounded distributive lattices with bornologies and with decent lumps of prime filters as objects and homomorphisms of bounded lattices respecting those decent lumps and satisfying a domination condition as morphisms. This helps to understand Kolmogorov locally small spaces and morphisms between them. We comment also on spectralifications of topological spaces. Full article
(This article belongs to the Special Issue Recent Advance in Pure and Applied Mathematics)
11 pages, 251 KiB  
Article
Homeomorphic Arrangements of Smooth Manifolds
by Eran Liberman and Mina Teicher
Symmetry 2021, 13(6), 981; https://doi.org/10.3390/sym13060981 - 1 Jun 2021
Cited by 1 | Viewed by 1821
Abstract
Symmetry between mathematical constructions is a very desired phenomena in mathematics in general, and in algebraic geometry in particular. For line arrangements, symmetry between topological characterizations and the combinatorics of the arrangement has often been studied, and the first counterexample where symmetry breaks [...] Read more.
Symmetry between mathematical constructions is a very desired phenomena in mathematics in general, and in algebraic geometry in particular. For line arrangements, symmetry between topological characterizations and the combinatorics of the arrangement has often been studied, and the first counterexample where symmetry breaks is in dimension 13. In the first part of this paper, we shall prove that two arrangements of smooth compact manifolds of any dimension that are connected through smooth functions are homeomorphic. In the second part, we prove this in the affine case in dimension 4. Full article
(This article belongs to the Special Issue Recent Advance in Pure and Applied Mathematics)
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