Symmetry: Feature Papers 2017

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

Deadline for manuscript submissions: closed (31 December 2017) | Viewed by 13777

Special Issue Editor

Special Issue Information

Dear Colleagues,

As Editor-in-Chief of the journal Symmetry, after the success of the Special Issue “Symmetry: Feature Papers 2016” (https://www.mdpi.com/journal/symmetry/special_issues/symmetry_feature_papers_2016), I am glad to announce the Special Issue “Symmetry: Feature Papers 2017” online. In 2016, we cooperated with some excellent scholars/scientific groups and published several very important high-level works which have already been cited according to the data of Web of Science. We aim to introduce a new insight into science development or cutting edge technology related to the symmetry field, which will make a great contribution to the community. Thus, we will continue the Special Issue “Symmetry: Feature Papers” series in 2017. We will strictly select 5–10 papers from excellent scholars around the world to publish for free in order to benefit both authors and readers.

You are welcome to send short proposals for submissions of Feature Papers to our Editorial Office (symmetry@mdpi.com). They will be evaluated by Editors first. Please note that selected full papers will still be subject to a thorough and rigorous peer review.

Prof. Dr. Sergei D. Odintsov
Editor-in-Chief and Guest Editor

Published Papers (5 papers)

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Research

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251 KiB  
Article
Boundary Value Problems for Some Important Classes of Recurrent Relations with Two Independent Variables
Symmetry 2017, 9(12), 323; https://doi.org/10.3390/sym9120323 - 20 Dec 2017
Cited by 3 | Viewed by 2718
Abstract
It is shown that complex-valued boundary value problems for several classes of recurrent relations with two independent variables, of some considerable interest, are solvable on the following domain: [...] Read more.
It is shown that complex-valued boundary value problems for several classes of recurrent relations with two independent variables, of some considerable interest, are solvable on the following domain: C = { ( n , k ) : 0 k n , k N 0 , n N } , the so called combinatorial domain. The recurrent relations include some of the most important combinatorial ones, which, among other things, serve as a motivation for the investigation. The methods for solving the boundary value problems are presented and explained in detail. Full article
(This article belongs to the Special Issue Symmetry: Feature Papers 2017)
414 KiB  
Article
Evaporation and Antievaporation Instabilities
Symmetry 2017, 9(11), 249; https://doi.org/10.3390/sym9110249 - 26 Oct 2017
Cited by 6 | Viewed by 2824
Abstract
We review (anti)evaporation phenomena within the context of quantum gravity and extended theories of gravity. The (anti)evaporation effect is an instability of the black hole horizon discovered in many different scenarios: quantum dilaton-gravity, f ( R ) -gravity, f ( T ) -gravity, [...] Read more.
We review (anti)evaporation phenomena within the context of quantum gravity and extended theories of gravity. The (anti)evaporation effect is an instability of the black hole horizon discovered in many different scenarios: quantum dilaton-gravity, f ( R ) -gravity, f ( T ) -gravity, string-inspired black holes, and brane-world cosmology. Evaporating and antievaporating black holes seem to have completely different thermodynamical features compared to standard semiclassical black holes. The purpose of this review is to provide an introduction to conceptual and technical aspects of (anti)evaporation effects, while discussing problems that are still open. Full article
(This article belongs to the Special Issue Symmetry: Feature Papers 2017)
341 KiB  
Article
Solvability of the Class of Two-Dimensional Product-Type Systems of Difference Equations of Delay-Type (1, 3, 1, 1)
Symmetry 2017, 9(10), 200; https://doi.org/10.3390/sym9100200 - 25 Sep 2017
Cited by 2 | Viewed by 2142
Abstract
This paper essentially presents the last and important steps in the study of (practical) solvability of two-dimensional product-type systems of difference equations of the following form z n = α z n - k a w n - l b , [...] Read more.
This paper essentially presents the last and important steps in the study of (practical) solvability of two-dimensional product-type systems of difference equations of the following form z n = α z n - k a w n - l b , w n = β w n - m c z n - s d , n N 0 , where k , l , m , s N , a , b , c , d Z , and where α , β and the initial values are complex numbers. It is devoted to the most complex case which has not been considered so far (the case k = l = s = 1 and m = 3 ). Closed form formulas for solutions to the system are found in all possible cases. The structure of the solutions to the system is considered in detail. The following five cases: (1) b = 0 ; (2) c = 0 ; (3) d = 0 ; (4) a c 0 ; (5) a = 0 , b c d 0 , are considered separately. Some of the situations appear for the first time in the literature. Full article
(This article belongs to the Special Issue Symmetry: Feature Papers 2017)

Review

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320 KiB  
Review
Supersymmetric Higher Spin Models in Three Dimensional Spaces
Symmetry 2018, 10(1), 9; https://doi.org/10.3390/sym10010009 - 28 Dec 2017
Cited by 14 | Viewed by 2395
Abstract
We review the component Lagrangian construction of the supersymmetric higher spin models in three-dimensional (3D) Minkowski and anti de Sitter ( A d S ) spaces. The approach is based on the frame-like gauge-invariant formulation, where massive higher spin fields are realized through [...] Read more.
We review the component Lagrangian construction of the supersymmetric higher spin models in three-dimensional (3D) Minkowski and anti de Sitter ( A d S ) spaces. The approach is based on the frame-like gauge-invariant formulation, where massive higher spin fields are realized through a system of massless ones. We develop a supersymmetric generalization of this formulation to the Lagrangian construction of the on-shell N = 1 , 3D higher spin supermultiplets. In 3D Minkowski space, we show that the massive supermultiplets can be constructed from one extended massless supermultiplet by adding the mass terms to the Lagrangian and the corresponding corrections to the supertransformations of the fermionic fields. In 3D A d S space, we construct massive supermultiplets using a formulation of the massive fields in terms of the set of gauge-invariant objects (curvatures) in the process of their consistent supersymmetric deformation. Full article
(This article belongs to the Special Issue Symmetry: Feature Papers 2017)
709 KiB  
Review
On Brane Solutions with Intersection Rules Related to Lie Algebras
Symmetry 2017, 9(8), 155; https://doi.org/10.3390/sym9080155 - 13 Aug 2017
Cited by 10 | Viewed by 2997
Abstract
The review is devoted to exact solutions with hidden symmetries arising in a multidimensional gravitational model containing scalar fields and antisymmetric forms. These solutions are defined on a manifold of the form M = M0 x M1 x . . . [...] Read more.
The review is devoted to exact solutions with hidden symmetries arising in a multidimensional gravitational model containing scalar fields and antisymmetric forms. These solutions are defined on a manifold of the form M = M0 x M1 x . . . x Mn , where all Mi with i >= 1 are fixed Einstein (e.g., Ricci-flat) spaces. We consider a warped product metric on M. Here, M0 is a base manifold, and all scale factors (of the warped product), scalar fields and potentials for monomial forms are functions on M0 . The monomial forms (of the electric or magnetic type) appear in the so-called composite brane ansatz for fields of forms. Under certain restrictions on branes, the sigma-model approach for the solutions to field equations was derived in earlier publications with V.N.Melnikov. The sigma model is defined on the manifold M0 of dimension d0 ≠ 2 . By using the sigma-model approach, several classes of exact solutions, e.g., solutions with harmonic functions, S-brane, black brane and fluxbrane solutions, are obtained. For d0 = 1 , the solutions are governed by moduli functions that obey Toda-like equations. For certain brane intersections related to Lie algebras of finite rank—non-singular Kac–Moody (KM) algebras—the moduli functions are governed by Toda equations corresponding to these algebras. For finite-dimensional semi-simple Lie algebras, the Toda equations are integrable, and for black brane and fluxbrane configurations, they give rise to polynomial moduli functions. Some examples of solutions, e.g., corresponding to finite dimensional semi-simple Lie algebras, hyperbolic KM algebras: H2(q, q) , AE3, HA(1)2, E10 and Lorentzian KM algebra P10 , are presented. Full article
(This article belongs to the Special Issue Symmetry: Feature Papers 2017)
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