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Symmetry
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Symmetry/Asymmetry: Feature Review Papers
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Symmetry/Asymmetry: Feature Review Papers

A special issue of Symmetry (ISSN 2073-8994).

Deadline for manuscript submissions: closed (31 December 2023) | Viewed by 18038

Special Issue Editors

Prof. Dr. Sergei D. Odintsov

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Guest Editor
ICREA, P. Lluis Companyas 23, 08010 Barcelona and Institute of Space Sciences (IEEC-CSIC), C. Can Magrans s/n, 08193 Barcelona, Spain
Interests: cosmology; dark energy and inflation; quantum gravity; modified gravity and beyond general relativity; quantum fields at external fields
Special Issues, Collections and Topics in MDPI journals
Prof. Dr. Juan Luis García Guirao

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Guest Editor
Department of Applied Mathematics and Statistics, Technical University of Cartagena, 30203 Cartagena, Spain
Interests: dynamical systems; celestial mechanics; Hamiltonian systems; low-dimensional dynamics; differential equations
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Prof. Dr. Vasilis K. Oikonomou

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Physics Department, Aristotle University of Thessaloniki, 541 24 Thessaloniki, Greece
Interests: cosmology; inflationary cosmology; modified theories of gravity; physics of the early universe; dark energy; dark matter; supersymmetry; mathematical physics; high energy physics; theoretical physics; epistemic game theory; game theory
Special Issues, Collections and Topics in MDPI journals
Prof. Dr. John H. Graham

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Department of Biology, Berry College, Mount Berry, GA 30149, USA
Interests: fluctuating asymmetry; developmental instability; evolutionary genetics; hybrid zones; community ecology
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Prof. Dr. György Keglevich

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Department of Organic Chemistry and Technology, Budapest University of Technology and Economics, 1521 Budapest, Hungary
Interests: organophosphorus chemistry; green chemistry; microwave chemistry; catalysts; ionic liquids
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

This Special Issue aims to publish high-quality long and complete review papers in Symmetry. The Issue will highlight a diverse set of topics related to symmetry/asymmetry phenomena wherever they occur in all aspects of natural sciences (e.g., physics, chemistry, biology, mathematics, materials, engineering science and computer science).

We are particularly interested in receiving manuscripts that review experimental and theoretical/computational studies as well as contributions from all disciplines.

All submissions should be explicitly related to symmetry studies and the related areas of symmetry already discussed in the journal Symmetry.

Prof. Dr. Sergei D. Odintsov
Prof. Dr. Juan Luis García Guirao
Prof. Dr. Vasilis Oikonomou
Prof. Dr. John H. Graham
Prof. Dr. György Keglevich
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. 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

  • physics
  • chemistry
  • biology
  • mathematics
  • materials
  • engineering science
  • computer science

Related Special Issue

Published Papers (10 papers)

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Review

40 pages, 953 KiB  
Review
Recent Advances in Cosmological Singularities
by Oem Trivedi
Symmetry 2024, 16(3), 298; https://doi.org/10.3390/sym16030298 - 03 Mar 2024
Cited by 4 | Viewed by 1110
Abstract
The discovery of the Universe’s late-time acceleration and dark energy has led to a great deal of research into cosmological singularities, and in this brief review, we discuss all the prominent developments in this field for the best part of the last two [...] Read more.
The discovery of the Universe’s late-time acceleration and dark energy has led to a great deal of research into cosmological singularities, and in this brief review, we discuss all the prominent developments in this field for the best part of the last two decades. We discuss the fundamentals of spacetime singularities, after which we discuss in detail all the different forms of cosmological singularities that have been discovered in recent times. We then address methods and techniques to avoid or moderate these singularities in various theories and discuss how these singularities can also occur in non-conventional cosmologies. We then discuss a useful dynamical systems approach to deal with these singularities and finish up with some outlooks for the field. We hope that this work serves as a good resource to anyone who wants to update themselves with the developments in this very exciting area. Full article
(This article belongs to the Special Issue Symmetry/Asymmetry: Feature Review Papers)
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19 pages, 643 KiB  
Review
The Problem of Moments: A Bunch of Classical Results with Some Novelties
by Pier Luigi Novi Inverardi, Aldo Tagliani and Jordan M. Stoyanov
Symmetry 2023, 15(9), 1743; https://doi.org/10.3390/sym15091743 - 11 Sep 2023
Cited by 1 | Viewed by 545
Abstract
We summarize significant classical results on (in)determinacy of measures in terms of their finite positive integer order moments. Well known is the role of the smallest eigenvalues of Hankel matrices, starting from Hamburger’s results a century ago and ending with the great progress [...] Read more.
We summarize significant classical results on (in)determinacy of measures in terms of their finite positive integer order moments. Well known is the role of the smallest eigenvalues of Hankel matrices, starting from Hamburger’s results a century ago and ending with the great progress made only in recent times by C. Berg and collaborators. We describe here known results containing necessary and sufficient conditions for moment (in)determinacy in both Hamburger and Stieltjes moment problems. In our exposition, we follow an approach different from that commonly used. There are novelties well complementing the existing theory. Among them are: (a) to emphasize on the geometric interpretation of the indeterminacy conditions; (b) to exploit fine properties of the eigenvalues of perturbed symmetric matrices allowing to derive new lower bounds for the smallest eigenvalues of Hankel matrices (these bounds are used for concluding indeterminacy); (c) to provide new arguments to confirm classical results; (d) to give new numerical illustrations involving commonly used probability distributions. Full article
(This article belongs to the Special Issue Symmetry/Asymmetry: Feature Review Papers)
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27 pages, 12047 KiB  
Review
Symmetric Strange Attractors: A Review of Symmetry and Conditional Symmetry
by Chunbiao Li, Zhinan Li, Yicheng Jiang, Tengfei Lei and Xiong Wang
Symmetry 2023, 15(8), 1564; https://doi.org/10.3390/sym15081564 - 10 Aug 2023
Cited by 6 | Viewed by 1992
Abstract
A comprehensive review of symmetry and conditional symmetry is made from the core conception of symmetry and conditional symmetry. For a dynamical system, the structure of symmetry means its robustness against the polarity change of some of the system variables. Symmetric systems typically [...] Read more.
A comprehensive review of symmetry and conditional symmetry is made from the core conception of symmetry and conditional symmetry. For a dynamical system, the structure of symmetry means its robustness against the polarity change of some of the system variables. Symmetric systems typically show symmetrical dynamics, and even when the symmetry is broken, symmetric pairs of coexisting attractors are born, annotating the symmetry in another way. The polarity balance can be recovered through combinations of the polarity reversal of system variables, and furthermore, it can also be restored by the offset boosting of some of the system variables if the variables lead to the polarity reversal of their functions. In this case, conditional symmetry is constructed, giving a chance for a dynamical system outputting coexisting attractors. Symmetric strange attractors typically represent the flexible polarity reversal of some of the system variables, which brings more alternatives of chaotic signals and more convenience for chaos application. Symmetric and conditionally symmetric coexisting attractors can also be found in memristive systems and circuits. Therefore, symmetric chaotic systems and systems with conditional symmetry provide sufficient system options for chaos-based applications. Full article
(This article belongs to the Special Issue Symmetry/Asymmetry: Feature Review Papers)
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26 pages, 5945 KiB  
Review
Chiral Organophosphorus Pharmaceuticals: Properties and Application
by Anastasy O. Kolodiazhna and Oleg I. Kolodiazhnyi
Symmetry 2023, 15(8), 1550; https://doi.org/10.3390/sym15081550 - 07 Aug 2023
Cited by 6 | Viewed by 1230
Abstract
This review considers the chiral phosphorus-containing drugs used to treat patients in the clinic, as well as the promising and experimental drugs that are in the process of being researched. Natural and synthetic representatives of phosphorus-containing drugs, such as tenofovir (hepatitis B and [...] Read more.
This review considers the chiral phosphorus-containing drugs used to treat patients in the clinic, as well as the promising and experimental drugs that are in the process of being researched. Natural and synthetic representatives of phosphorus-containing drugs, such as tenofovir (hepatitis B and HIV treatment), fosfomycin (antibiotic), valinofos (antibiotic), phosphazinomycin A (antibiotic), (R)-phospholeucine, various antibacterial and antifungal agents, renin inhibitors, etc., have found practical applications as medicines and bioregulators and other medicines. The influence of the chirality of both carbon atoms and phosphorus atoms on the pharmacodynamics, pharmacokinetics, and toxicological properties of phosphorus drugs has been demonstrated. Therefore, the choice of enantiomers is critical since the wrong choice of a chiral drug can lead to undesirable consequences, carcinogenicity, and teratogenicity. New chiral technologies affecting drug development are discussed, such as the “chiral switch” of racemates already on the market, as well as phosphorus-containing prodrugs with a higher biological selectivity and low adverse effects. Full article
(This article belongs to the Special Issue Symmetry/Asymmetry: Feature Review Papers)
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38 pages, 11844 KiB  
Review
Azulene, Reactivity, and Scientific Interest Inversely Proportional to Ring Size; Part 2: The Seven-Membered Ring
by Alexandru C. Razus
Symmetry 2023, 15(7), 1391; https://doi.org/10.3390/sym15071391 - 10 Jul 2023
Cited by 1 | Viewed by 4071
Abstract
The second part of the article Azulene, Reactivity, and Scientific Interest Inversely Proportional to Ring Size deals with the chemical behavior of the seven-atom azulenic ring. As the title states, the ability of this system to react is lesser compared to [...] Read more.
The second part of the article Azulene, Reactivity, and Scientific Interest Inversely Proportional to Ring Size deals with the chemical behavior of the seven-atom azulenic ring. As the title states, the ability of this system to react is lesser compared to that of the five-atom ring; despite this, a large number of syntheses contain it as a participant in the molecules of starting compounds. This review is focused on certain more frequent syntheses such as nucleophilic substitution of the seven-atom ring or its substituents, vicarious nucleophilic substitutions, substitutions of azulene metallic compounds, or reactions catalyzed by complexes of certain transition metals. The syntheses of tricyclic compounds, porphyrinogenic systems, or azulenocyanines containing an azulenyl moiety are also presented. The adopted presentation is mainly based on reaction schemes that include the reaction conditions, as well as the yields of the products formed. Full article
(This article belongs to the Special Issue Symmetry/Asymmetry: Feature Review Papers)
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31 pages, 5754 KiB  
Review
Symmetry Perception and Psychedelic Experience
by Alexis D. J. Makin, Marco Roccato, Elena Karakashevska, John Tyson-Carr and Marco Bertamini
Symmetry 2023, 15(7), 1340; https://doi.org/10.3390/sym15071340 - 30 Jun 2023
Cited by 2 | Viewed by 3581
Abstract
This review of symmetry perception has six parts. Psychophysical studies have investigated symmetry perception for over 100 years (part 1). Neuroscientific studies on symmetry perception have accumulated in the last 20 years. Functional MRI and EEG experiments have conclusively shown that regular visual [...] Read more.
This review of symmetry perception has six parts. Psychophysical studies have investigated symmetry perception for over 100 years (part 1). Neuroscientific studies on symmetry perception have accumulated in the last 20 years. Functional MRI and EEG experiments have conclusively shown that regular visual arrangements, such as reflectional symmetry, Glass patterns, and the 17 wallpaper groups all activate the extrastriate visual cortex. This activation generates an event-related potential (ERP) called sustained posterior negativity (SPN). SPN amplitude scales with the degree of regularity in the display, and the SPN is generated whether participants attend to symmetry or not (part 2). It is likely that some forms of symmetry are detected automatically, unconsciously, and pre-attentively (part 3). It might be that the brain is hardwired to detect reflectional symmetry (part 4), and this could contribute to its aesthetic appeal (part 5). Visual symmetry and fractal geometry are prominent in hallucinations induced by the psychedelic drug N,N-dimethyltryptamine (DMT), and visual flicker (part 6). Integrating what we know about symmetry processing with features of induced hallucinations is a new frontier in neuroscience. We propose that the extrastriate cortex can generate aesthetically fascinating symmetrical representations spontaneously, in the absence of external symmetrical stimuli. Full article
(This article belongs to the Special Issue Symmetry/Asymmetry: Feature Review Papers)
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41 pages, 496 KiB  
Review
Fluxbrane Polynomials and Melvin-like Solutions for Simple Lie Algebras
by Sergey V. Bolokhov and Vladimir D. Ivashchuk
Symmetry 2023, 15(6), 1199; https://doi.org/10.3390/sym15061199 - 03 Jun 2023
Cited by 1 | Viewed by 680
Abstract
This review dealt with generalized Melvin solutions for simple finite-dimensional Lie algebras. Each solution appears in a model which includes a metric and n scalar fields coupled to n Abelian 2-forms with dilatonic coupling vectors determined by simple Lie algebra of rank n [...] Read more.
This review dealt with generalized Melvin solutions for simple finite-dimensional Lie algebras. Each solution appears in a model which includes a metric and n scalar fields coupled to n Abelian 2-forms with dilatonic coupling vectors determined by simple Lie algebra of rank n. The set of n moduli functions Hs(z) comply with n non-linear (ordinary) differential equations (of second order) with certain boundary conditions set. Earlier, it was hypothesized that these moduli functions should be polynomials in z (so-called “fluxbrane” polynomials) depending upon certain parameters ps>0, s=1,…,n. Here, we presented explicit relations for the polynomials corresponding to Lie algebras of ranks n=1,2,3,4,5 and exceptional algebra E6. Certain relations for the polynomials (e.g., symmetry and duality ones) were outlined. In a general case where polynomial conjecture holds, 2-form flux integrals are finite. The use of fluxbrane polynomials to dilatonic black hole solutions was also explored. Full article
(This article belongs to the Special Issue Symmetry/Asymmetry: Feature Review Papers)
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40 pages, 12642 KiB  
Review
Azulene, Reactivity, and Scientific Interest Inversely Proportional to Ring Size; Part 1: The Five-Membered Ring
by Alexandru C. Razus
Symmetry 2023, 15(2), 310; https://doi.org/10.3390/sym15020310 - 22 Jan 2023
Cited by 3 | Viewed by 1653
Abstract
The lack of azulene symmetry with respect to the axis perpendicular to a molecule creates an asymmetry of the electronic system, increasing the charge density of the five-atom ring and favoring its electrophilic substitutions. The increased reactivity of this ring has contributed to [...] Read more.
The lack of azulene symmetry with respect to the axis perpendicular to a molecule creates an asymmetry of the electronic system, increasing the charge density of the five-atom ring and favoring its electrophilic substitutions. The increased reactivity of this ring has contributed to ongoing interest about the syntheses in which it is involved. The aim of this review is to present briefly and mainly in the form of reaction schemes the behavior of this system. After a short chapter that includes the research until 1984, subsequent research is presented as generally accepted chapters and subchapters to describe the behavior of the azulene system: metal free catalyst reactions; reactions catalyzed by metals; various azulene five-ring substitutions. The author insists on reaction yields, and in some cases considers it useful to present the proposed reaction mechanisms. Full article
(This article belongs to the Special Issue Symmetry/Asymmetry: Feature Review Papers)
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19 pages, 1050 KiB  
Review
Orbits of Particles and Photons around Regular Rotating Black Holes and Solitons
by Irina Dymnikova and Anna Dobosz
Symmetry 2023, 15(2), 273; https://doi.org/10.3390/sym15020273 - 18 Jan 2023
Cited by 2 | Viewed by 1338
Abstract
We briefly overview the basic properties and generic behavior of circular equatorial particle orbits and light rings around regular rotating compact objects with dark energy interiors, which are described by regular metrics of the Kerr–Schild class and include rotating black holes and self-gravitating [...] Read more.
We briefly overview the basic properties and generic behavior of circular equatorial particle orbits and light rings around regular rotating compact objects with dark energy interiors, which are described by regular metrics of the Kerr–Schild class and include rotating black holes and self-gravitating spinning solitons replacing naked singularities. These objects have an internal de Sitter vacuum disk and can have two types of dark interiors, depending on the energy conditions. The first type reduces to the de Sitter disk, the second contains a closed de Sitter surface and an S surface with the de Sitter disk as the bridge and an anisotropic phantom fluid in the regions between the S surface and the disk. In regular geometry, the potentials decrease from V(r)→∞ to their minima, which ensures the existence of the innermost stable photon and particle orbits that are essential for processes of energy extraction occurring within the ergoregions, which for the second type of interiors contain the phantom energy. The innermost orbits provide a diagnostic tool for investigation of dark interiors of de Sitter–Kerr objects. They include light rings which confine these objects and ensure the most informative observational signature for rotating black holes presented by their shadows. Full article
(This article belongs to the Special Issue Symmetry/Asymmetry: Feature Review Papers)
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19 pages, 359 KiB  
Review
Some Applications of Affine in Velocities Lagrangians in Two-Dimensional Systems
by José F. Cariñena and José Fernández-Núñez
Symmetry 2022, 14(12), 2520; https://doi.org/10.3390/sym14122520 - 29 Nov 2022
Cited by 2 | Viewed by 788
Abstract
The two-dimensional inverse problem for first-order systems is analysed and a method to construct an affine Lagrangian for such systems is developed. The determination of such Lagrangians is based on the theory of the Jacobi multiplier for the system of differential equations. We [...] Read more.
The two-dimensional inverse problem for first-order systems is analysed and a method to construct an affine Lagrangian for such systems is developed. The determination of such Lagrangians is based on the theory of the Jacobi multiplier for the system of differential equations. We illustrate our analysis with several examples of families of forces that are relevant in mechanics, on one side, and of some relevant biological systems, on the other. Full article
(This article belongs to the Special Issue Symmetry/Asymmetry: Feature Review Papers)
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