Symmetry

19 pages, 507 KiB

Open AccessArticle

Lagrangian Reconstruction of Barrow Holographic Dark Energy in Interacting Tachyon Model

by Giuseppe Gaetano Luciano and Yang Liu

Symmetry 2023, 15(5), 1129; https://doi.org/10.3390/sym15051129 - 22 May 2023

Cited by 12 | Viewed by 1316

We consider a correspondence between the tachyon dark energy model and Barrow holographic dark energy (BHDE). The latter is a modified scenario based on the application of the holographic principle with Barrow entropy instead of the usual Bekenstein–Hawking one. We reconstruct the dynamics [...] Read more.

We consider a correspondence between the tachyon dark energy model and Barrow holographic dark energy (BHDE). The latter is a modified scenario based on the application of the holographic principle with Barrow entropy instead of the usual Bekenstein–Hawking one. We reconstruct the dynamics of the tachyon scalar field T in a curved Friedmann–Robertson–Walker universe both in the presence and absence of interactions between dark energy and matter. As a result, we show that the tachyon field exhibits non-trivial dynamics. In a flat universe,

{\dot{T}}^{2}

must always be vanishing, independently of the existence of interaction. This implies

ω_{D} = - 1

for the equation-of-state parameter, which in turn can be used for modeling the cosmological constant behavior. On the other hand, for a non-flat universe and various values of the Barrow parameter, we find that

{\dot{T}}^{2}

decreases monotonically for increasing

cos (R_{h} / a)

and

cosh (R_{h} / a)

, where

R_{h}

and a are the future event horizon and the scale factor, respectively. Specifically,

{\dot{T}}^{2} \geq 0

for a closed universe, while

{\dot{T}}^{2} < 0

for an open one, which is physically not allowed. We finally comment on the inflation mechanism and trans-Planckian censorship conjecture in BHDE and discuss observational consistency of our model. Full article

(This article belongs to the Special Issue Noether Symmetries in Gravitation and Cosmology)

► Show Figures

Figure 1

25 pages, 367 KiB

Open AccessArticle

Improved Oscillation Theorems for Even-Order Quasi-Linear Neutral Differential Equations

by Yousef Alnafisah, Fahd Masood, Ali Muhib and Osama Moaaz

Symmetry 2023, 15(5), 1128; https://doi.org/10.3390/sym15051128 - 22 May 2023

Cited by 5 | Viewed by 1355

Abstract

In this study, our goal was to establish improved inequalities that enhance the asymptotic and oscillatory behaviors of solutions to even-order neutral differential equations. In the oscillation theory of neutral differential equations, the connection between the solution and its corresponding function plays a [...] Read more.

In this study, our goal was to establish improved inequalities that enhance the asymptotic and oscillatory behaviors of solutions to even-order neutral differential equations. In the oscillation theory of neutral differential equations, the connection between the solution and its corresponding function plays a critical role. We refined these relationships by leveraging the modified monotonic properties of positive solutions and introduced new conditions that ensure the absence of positive solutions, confirming the oscillation of all solutions to the studied equation. Based on the concept of symmetry between the positive and negative solutions of the studied equation, we obtained criteria that guarantee the oscillation of all solutions by excluding positive solutions only. In order to demonstrate the significance of our findings, we examined certain instances of the studied equation and compared them with previous results in the literature. Full article

(This article belongs to the Section Mathematics)

13 pages, 314 KiB

Open AccessArticle

Time Optimal Feedback Control for 3D Navier–Stokes-Voigt Equations

by Yunxiang Li, Maojun Bin and Cuiyun Shi

Symmetry 2023, 15(5), 1127; https://doi.org/10.3390/sym15051127 - 22 May 2023

Viewed by 1282

Abstract

In this article, we discuss a time optimal feedback control for asymmetrical 3D Navier–Stokes–Voigt equations. Firstly, we consider the existence of the admissible trajectories for the asymmetrical 3D Navier–Stokes–Voigt equations by using the well-known Cesari property and the Fillippove’s theorem. Secondly, we study [...] Read more.

In this article, we discuss a time optimal feedback control for asymmetrical 3D Navier–Stokes–Voigt equations. Firstly, we consider the existence of the admissible trajectories for the asymmetrical 3D Navier–Stokes–Voigt equations by using the well-known Cesari property and the Fillippove’s theorem. Secondly, we study the existence result of a time optimal control for the feedback control systems. Lastly, asymmetrical Clarke’s subdifferential inclusions and asymmetrical 3D Navier–Stokes–Voigt differential variational inequalities are given to explain our main results. Full article

(This article belongs to the Special Issue Theories and Applications for Dynamical Systems, Symmetry Problems and Differential Equations)

11 pages, 370 KiB

Open AccessArticle

New Comparison Theorems to Investigate the Asymptotic Behavior of Even-Order Neutral Differential Equations

by Barakah Almarri, Osama Moaaz, Ahmed E. Abouelregal and Amira Essam

Symmetry 2023, 15(5), 1126; https://doi.org/10.3390/sym15051126 - 22 May 2023

Cited by 1 | Viewed by 1110

Abstract

Based on a comparison with first-order equations, we obtain new criteria for investigating the asymptotic behavior of a class of differential equations with neutral arguments. In this work, we consider the non-canonical case for an even-order equation. We concentrate on the requirements for [...] Read more.

Based on a comparison with first-order equations, we obtain new criteria for investigating the asymptotic behavior of a class of differential equations with neutral arguments. In this work, we consider the non-canonical case for an even-order equation. We concentrate on the requirements for excluding positive solutions, as the method used considers the symmetry between the positive and negative solutions of the studied equation. The results obtained do not require some restrictions that were necessary to apply previous relevant results in the literature. Full article

(This article belongs to the Section Mathematics)

► Show Figures

Figure 1

11 pages, 1031 KiB

Open AccessArticle

Postural Stability Romberg’s Test in 3D Using an Inertial Sensor in Healthy Adults

by Dmitry Skvortsov and Nikita Painev

Symmetry 2023, 15(5), 1125; https://doi.org/10.3390/sym15051125 - 21 May 2023

Viewed by 1455

Abstract

Currently, inertial sensors are often used to study balance in an upright stance. There are various options for recording balance data with different locations and numbers of sensors used. Methods of data processing and presentation also differ significantly in published studies. We propose [...] Read more.

Currently, inertial sensors are often used to study balance in an upright stance. There are various options for recording balance data with different locations and numbers of sensors used. Methods of data processing and presentation also differ significantly in published studies. We propose a certain technical implementation of the method and a previously tested method for processing primary data. In addition, the data were processed along three mutually perpendicular planes. The study was conducted on 109 healthy adults. A specially developed inertial sensor, commercially available for medical purposes, was used. Thus, this work can outline the limits of normative values for the calculated stabilometric measures. Normative data were obtained for three oscillation planes with the sensor located on the sacrum. The obtained parameters for the vertical component of the oscillations are of the same order as for the frontal and sagittal components. Normative parameters are required in any clinical study, as the basis from which we start in the evaluation of clinical data. In this study, such normative parameters are given for one of the most commonly used Romberg’s tests. The obtained normative data can be used for scientific and clinical research. Full article

(This article belongs to the Special Issue Gait and Balance Features in Patients with Movement Disorders and Healthy Subjects)

► Show Figures

Figure 1

12 pages, 299 KiB

Open AccessArticle

Radius Results for Certain Strongly Starlike Functions

by Afis Saliu, Kanwal Jabeen, Qin Xin, Fairouz Tchier and Sarfraz Nawaz Malik

Symmetry 2023, 15(5), 1124; https://doi.org/10.3390/sym15051124 - 21 May 2023

Viewed by 1298

Abstract

This article comprises the study of strongly starlike functions which are defined by using the concept of subordination. The function

φ

defined by

φ (ζ) = {(1 + ζ)}^{λ}

,

0 < λ < 1

maps the open [...] Read more.

This article comprises the study of strongly starlike functions which are defined by using the concept of subordination. The function

φ

defined by

φ (ζ) = {(1 + ζ)}^{λ}

,

0 < λ < 1

maps the open unit disk in the complex plane to a domain symmetric with respect to the real axis in the right-half plane. Using this mapping, we obtain some radius results for a family of starlike functions. It is worth noting that all the presented results are sharp. Full article

(This article belongs to the Special Issue Selected Papers from International Symposium on Geometric Function Theory and Applications (GFTA))

26 pages, 16642 KiB

Open AccessFeature PaperEditor’s ChoiceArticle

A Deep Learning Approach to Extracting Nuclear Matter Properties from Neutron Star Observations

by Plamen G. Krastev

Symmetry 2023, 15(5), 1123; https://doi.org/10.3390/sym15051123 - 20 May 2023

Cited by 14 | Viewed by 2078

Abstract

Understanding the equation of state of dense neutron-rich matter remains a major challenge in modern physics and astrophysics. Neutron star observations from electromagnetic and gravitational wave spectra provide critical insights into the behavior of dense neutron-rich matter. The next generation of telescopes and [...] Read more.

Understanding the equation of state of dense neutron-rich matter remains a major challenge in modern physics and astrophysics. Neutron star observations from electromagnetic and gravitational wave spectra provide critical insights into the behavior of dense neutron-rich matter. The next generation of telescopes and gravitational wave detectors will offer even more detailed neutron-star observations. Employing deep learning techniques to map neutron star mass and radius observations to the equation of state allows for its accurate and reliable determination. This work demonstrates the feasibility of using deep learning to extract the equation of state directly from observations of neutron stars, and to also obtain related nuclear matter properties such as the slope, curvature, and skewness of nuclear symmetry energy at saturation density. Most importantly, it shows that this deep learning approach is able to reconstruct realistic equations of state and deduce realistic nuclear matter properties. This highlights the potential of artificial neural networks in providing a reliable and efficient means to extract crucial information about the equation of state and related properties of dense neutron-rich matter in the era of multi-messenger astrophysics. Full article

(This article belongs to the Special Issue Symmetries and Ultra Dense Matter of Compact Stars)

► Show Figures

Figure 1

13 pages, 343 KiB

Open AccessArticle

Kirchhoff Index and Degree Kirchhoff Index of Tetrahedrane-Derived Compounds

by Duoduo Zhao, Yuanyuan Zhao, Zhen Wang, Xiaoxin Li and Kai Zhou

Symmetry 2023, 15(5), 1122; https://doi.org/10.3390/sym15051122 - 20 May 2023

Cited by 2 | Viewed by 1434

Abstract

Tetrahedrane-derived compounds consist of n crossed quadrilaterals and possess complex three-dimensional structures with high symmetry and dense spatial arrangements. As a result, these compounds hold great potential for applications in materials science, catalytic chemistry, and other related fields. The Kirchhoff index of a [...] Read more.

Tetrahedrane-derived compounds consist of n crossed quadrilaterals and possess complex three-dimensional structures with high symmetry and dense spatial arrangements. As a result, these compounds hold great potential for applications in materials science, catalytic chemistry, and other related fields. The Kirchhoff index of a graph G is defined as the sum of resistive distances between any two vertices in G. This article focuses on studying a type of tetrafunctional compound with a linear crossed square chain shape. The Kirchhoff index and degree Kirchhoff index of this compound are calculated, and a detailed analysis and discussion is conducted. The calculation formula for the Kirchhoff index is obtained based on the relationship between the Kirchhoff index and Laplace eigenvalue, and the number of spanning trees is derived for linear crossed quadrangular chains. The obtained formula is validated using Ohm’s law and Cayley’s theorem. Asymptotically, the ratio of Kirchhoff index to Wiener index approaches one-fourth. Additionally, the expression for the degree Kirchhoff index of the linear crossed quadrangular chain is obtained through the relationship between the degree Kirchhoff index and the regular Laplace eigenvalue and matrix decomposition theorem. Full article

► Show Figures

Figure 1

24 pages, 1290 KiB

Open AccessArticle

An Efficient Stress–Strength Reliability Estimate of the Unit Gompertz Distribution Using Ranked Set Sampling

by Najwan Alsadat, Amal S. Hassan, Mohammed Elgarhy, Christophe Chesneau and Rokaya Elmorsy Mohamed

Symmetry 2023, 15(5), 1121; https://doi.org/10.3390/sym15051121 - 20 May 2023

Cited by 12 | Viewed by 1520

Abstract

In this paper, the estimation of the stress–strength reliability is taken into account when the stress and strength variables have unit Gompertz distributions with a similar scale parameter. The consideration of the unit Gompertz distribution in this context is because of its intriguing [...] Read more.

In this paper, the estimation of the stress–strength reliability is taken into account when the stress and strength variables have unit Gompertz distributions with a similar scale parameter. The consideration of the unit Gompertz distribution in this context is because of its intriguing symmetric and asymmetric properties that can accommodate various histogram proportional-type data shapes. As the main contribution, the reliability estimate is determined via seven frequentist techniques using the ranked set sampling (RSS) and simple random sampling (SRS). The proposed methods are the maximum likelihood, least squares, weighted least squares, maximum product spacing, Cramér–von Mises, Anderson–Darling, and right tail Anderson–Darling methods. We perform a simulation work to evaluate the effectiveness of the recommended RSS-based estimates by using accuracy metrics. We draw the conclusion that the reliability estimates in the maximum product spacing approach have the lowest value compared to other approaches. In addition, we note that the RSS-based estimates are superior to those obtained by a comparable SRS approach. Additional results are obtained using two genuine data sets that reflect the survival periods of head and neck cancer patients. Full article

(This article belongs to the Special Issue Symmetry in Statistics and Data Science, Volume 2)

► Show Figures

Figure 1

19 pages, 2626 KiB

Open AccessArticle

Differential Evolution and Agglomerative-Clustering-Based Mutation Strategy for Complex Numerical Optimization Problems

by Tassawar Ali, Hikmat Ullah Khan, Tasswar Iqbal, Fawaz Khaled Alarfaj, Abdullah Mohammad Alomair and Naif Almusallam

Symmetry 2023, 15(5), 1120; https://doi.org/10.3390/sym15051120 - 20 May 2023

Viewed by 1260

Abstract

Differential evolution is an evolutionary algorithm that is used to solve complex numerical optimization problems. Differential evolution balances exploration and exploitation to find the best genes for the objective function. However, finding this balance is a challenging task. To overcome this challenge, we [...] Read more.

Differential evolution is an evolutionary algorithm that is used to solve complex numerical optimization problems. Differential evolution balances exploration and exploitation to find the best genes for the objective function. However, finding this balance is a challenging task. To overcome this challenge, we propose a clustering-based mutation strategy called Agglomerative Best Cluster Differential Evolution (ABCDE). The proposed model converges in an efficient manner without being trapped in local optima. It works by clustering the population to identify similar genes and avoids local optima. The adaptive crossover rate ensures that poor-quality genes are not reintroduced into the population. The proposed ABCDE is capable of generating a population efficiently where the difference between the values of the trial vector and objective vector is even less than 1% for some benchmark functions, and hence it outperforms both classical mutation strategies and the random neighborhood mutation strategy. The optimal and fast convergence of differential evolution has potential applications in the weight optimization of artificial neural networks and in stochastic and time-constrained environments such as cloud computing. Full article

(This article belongs to the Section Mathematics)

► Show Figures

Figure 1

15 pages, 295 KiB

Open AccessArticle

Aharonov–Bohm Electrodynamics in Material Media: A Scalar e.m. Field Cannot Cause Dissipation in a Medium

by Fernando Minotti and Giovanni Modanese

Symmetry 2023, 15(5), 1119; https://doi.org/10.3390/sym15051119 - 19 May 2023

Cited by 2 | Viewed by 1325

Abstract

In the extension of Maxwell equations based on the Aharonov–Bohm Lagrangian, the e.m. field has an additional degree of freedom, namely, a scalar field generated by charge and currents that are not locally conserved. We analyze the propagation of this scalar field through [...] Read more.

In the extension of Maxwell equations based on the Aharonov–Bohm Lagrangian, the e.m. field has an additional degree of freedom, namely, a scalar field generated by charge and currents that are not locally conserved. We analyze the propagation of this scalar field through two different media (a pure dielectric and an ohmic conductor) and study its property over a frequency range where the properties of the media are frequency-independent. We find that an electromagnetic (e.m.) scalar wave cannot propagate in a material medium. If a scalar wave in vacuum impinges on a material medium it is reflected, at most exciting in the medium a pure “potential” wave (which we also call a “gauge” wave) propagating at c, the speed of light in vacuum, with a vector potential whose Fourier amplitude is related to that of the scalar potential by

ω A_{0} = k ϕ_{0}

, where

ω^{2} = c^{2} {|k|}^{2}

. Full article

(This article belongs to the Special Issue Symmetry, Extended Maxwell Equations and Non-local Wavefunctions)

► Show Figures

Figure 1

21 pages, 5300 KiB

Open AccessArticle

Topology Optimization of Continuum Structures Based on Binary Hunter-Prey Optimization Algorithm

by Zhuanzhe Zhao, Yujian Rui, Yongming Liu, Zhibo Liu and Zhijian Tu

Symmetry 2023, 15(5), 1118; https://doi.org/10.3390/sym15051118 - 19 May 2023

Cited by 3 | Viewed by 1589

Abstract

According to BESO’s principle of binarizing continuous design variables and the excellent performance of the standard HPO algorithm in terms of solving continuous optimization problems, a discrete binary Hunter-prey optimization algorithm is introduced to construct an efficient topology optimization model. It was used [...] Read more.

According to BESO’s principle of binarizing continuous design variables and the excellent performance of the standard HPO algorithm in terms of solving continuous optimization problems, a discrete binary Hunter-prey optimization algorithm is introduced to construct an efficient topology optimization model. It was used to solve the problems that the BESO method of topology optimization has, such as easily falling into the local optimal value and being unable to obtain the optimal topology configuration; the metaheuristic algorithm was able to solve the topology optimization model’s low computational efficiency and could easily produce intermediate elements and unclear boundaries. Firstly, the BHPO algorithm was constructed by discrete binary processing using the s-shape transformation function. Secondly, BHPO-BESO topology optimization theory was established by combining the BHPO algorithm with BESO topology optimization. Using the sensitivity information of the objective function and the updated principle of the meta-heuristic of the BHPO algorithm, a semi-random search for the optimal topology configuration was carried out. Finally, numerical simulation experiments were conducted by using the three typical examples of the cantilever beam, simply supported beam, and clamping beam as optimization objects and the results were compared with the solution results of BESO topology optimization. The experimental results showed that compared with BESO, BHPO-BESO could find the optimal topology configuration with lower compliance and maximum stiffness, and it has higher computational efficiency, which can solve the above problems. Full article

(This article belongs to the Special Issue Meta-Heuristics for Manufacturing Systems Optimization Ⅱ)

► Show Figures

Figure 1

16 pages, 305 KiB

Open AccessArticle

Quantization of Constrained Systems as Dirac First Class versus Second Class: A Toy Model and Its Implications

by Eyo Eyo Ita III, Chopin Soo and Abraham Tan

Symmetry 2023, 15(5), 1117; https://doi.org/10.3390/sym15051117 - 19 May 2023

Viewed by 1328

Abstract

A toy model (suggested by Klauder) was analyzed from the perspective of first-class and second-class Dirac constrained systems. First-class constraints are often associated with the existence of important gauge symmetries in a system. A comparison was made by turning a first-class system into [...] Read more.

A toy model (suggested by Klauder) was analyzed from the perspective of first-class and second-class Dirac constrained systems. First-class constraints are often associated with the existence of important gauge symmetries in a system. A comparison was made by turning a first-class system into a second-class system with the introduction of suitable auxiliary conditions. The links between Dirac’s system of constraints, the Faddeev–Popov canonical functional integral method and the Maskawa–Nakajima procedure for reducing the phase space are explicitly illustrated. The model reveals stark contrasts and physically distinguishable results between first and second-class routes. Physically relevant systems such as the relativistic point particle and electrodynamics are briefly recapped. Besides its pedagogical value, the article also advocates the route of rendering first-class systems into second-class systems prior to quantization. Second-class systems lead to a well-defined reduced phase space and physical observables; an absence of inconsistencies in the closure of quantum constraint algebra; and the consistent promotion of fundamental Dirac brackets to quantum commutators. As first-class systems can be turned into well-defined second-class ones, this has implications for the soundness of the “Dirac quantization” of first-class constrained systems by the simple promotion of Poisson brackets, rather than Dirac brackets, to commutators without proceeding through second-class procedures. Full article

(This article belongs to the Special Issue Advances in Theoretical Physics, Quantum Gravity and Spacetime Symmetries)

23 pages, 2165 KiB

Open AccessArticle

Extension of King’s Iterative Scheme by Means of Memory for Nonlinear Equations

by Saima Akram, Maira Khalid, Moin-ud-Din Junjua, Shazia Altaf and Sunil Kumar

Symmetry 2023, 15(5), 1116; https://doi.org/10.3390/sym15051116 - 19 May 2023

Cited by 4 | Viewed by 1800

Abstract

We developed a new family of optimal eighth-order derivative-free iterative methods for finding simple roots of nonlinear equations based on King’s scheme and Lagrange interpolation. By incorporating four self-accelerating parameters and a weight function in a single variable, we extend the proposed family [...] Read more.

We developed a new family of optimal eighth-order derivative-free iterative methods for finding simple roots of nonlinear equations based on King’s scheme and Lagrange interpolation. By incorporating four self-accelerating parameters and a weight function in a single variable, we extend the proposed family to an efficient iterative scheme with memory. Without performing additional functional evaluations, the order of convergence is boosted from 8 to

15.51560

, and the efficiency index is raised from

1.6817

to

1.9847

. To compare the performance of the proposed and existing schemes, some real-world problems are selected, such as the eigenvalue problem, continuous stirred-tank reactor problem, and energy distribution for Planck’s radiation. The stability and regions of convergence of the proposed iterative schemes are investigated through graphical tools, such as 2D symmetric basins of attractions for the case of memory-based schemes and 3D stereographic projections in the case of schemes without memory. The stability analysis demonstrates that our newly developed schemes have wider symmetric regions of convergence than the existing schemes in their respective domains. Full article

(This article belongs to the Special Issue The Advances of Nonlinear Equations: Mathematical Models, Symmetry and Applications)

► Show Figures

Figure 1

19 pages, 250 KiB

Open AccessArticle

Study on Poisson Algebra and Automorphism of a Special Class of Solvable Lie Algebras

by Demin Yu, Chan Jiang and Jiejing Ma

Symmetry 2023, 15(5), 1115; https://doi.org/10.3390/sym15051115 - 19 May 2023

Cited by 2 | Viewed by 1208

Abstract

We define a four-dimensional Lie algebra g in this paper and then prove that this Lie algebra is solvable but not nilpotent. Due to the fact that g is a Lie algebra,

\forall x, y \in g

, [...] Read more.

We define a four-dimensional Lie algebra g in this paper and then prove that this Lie algebra is solvable but not nilpotent. Due to the fact that g is a Lie algebra,

\forall x, y \in g

,

[x, y] = - [y, x]

, that is, the operation

[,]

has anti symmetry. Symmetry is a very important law, and antisymmetry is also a very important law. We studied the structure of Poisson algebras on g using the matrix method. We studied the necessary and sufficient conditions for the automorphism of this class of Lie algebras, and give the decomposition of its automorphism group by

A u t (g) = G_{3} G_{1} G_{2} G_{3} G_{4} G_{7} G_{8} G_{5}

, or

A u t (g) = G_{3} G_{1} G_{2} G_{3} G_{4} G_{7} G_{8} G_{5} G_{6}

, or

A u t (g) = G_{3} G_{1} G_{2} G_{3} G_{4} G_{7} G_{8} G_{5} G_{3}

, where

G_{i}

is a commutative subgroup of

A u t (g)

. We give some subgroups of g’s automorphism group and systematically studied the properties of these subgroups. Full article

(This article belongs to the Special Issue Analytic/Numeric Solutions of Schrödinger-Type Equations: Applications of Lie Symmetry and Other Methods)

30 pages, 363 KiB

Open AccessFeature PaperArticle

Minimal Non-C-Perfect Hypergraphs with Circular Symmetry

by Péter Bence Czaun, Pál Pusztai, Levente Sebők and Zsolt Tuza

Symmetry 2023, 15(5), 1114; https://doi.org/10.3390/sym15051114 - 19 May 2023

Viewed by 4353

Abstract

In this research paper, we study 3-uniform hypergraphs

H = (X, E)

with circular symmetry. Two parameters are considered: the largest size

α (H)

of a set

S \subset X

not containing any edge

E \in E

, [...] Read more.

In this research paper, we study 3-uniform hypergraphs

H = (X, E)

with circular symmetry. Two parameters are considered: the largest size

α (H)

of a set

S \subset X

not containing any edge

E \in E

, and the maximum number

\bar{χ} (H)

of colors in a vertex coloring of

H

such that each

E \in E

contains two vertices of the same color. The problem considered here is to characterize those

H

in which the equality

\bar{χ} (H^{'}) = α (H^{'})

holds for every induced subhypergraph

H^{'} = (X^{'}, E^{'})

of

H

. A well-known objection against

\bar{χ} (H^{'}) = α (H^{'})

is where

|\cap_{E \in E^{'}} E| = 1

, termed “monostar”. Steps toward a solution to this approach is to investigate the properties of monostar-free structures. All such

H

are completely identified up to 16 vertices, with the aid of a computer. Most of them can be shown to satisfy

\bar{χ} (H) = α (H)

, and the few exceptions contain one or both of two specific induced subhypergraphs

H_{5}^{^{⥁}}

,

H_{6}^{^{⥁}}

on five and six vertices, respectively, both with

\bar{χ} = 2

and

α = 3

. Furthermore, a general conjecture is raised for hypergraphs of prime orders. Full article

(This article belongs to the Special Issue Labelings, Colorings and Distances in Graphs)

15 pages, 341 KiB

Open AccessArticle

The Existence of Odd Symmetric Periodic Solutions in the Generalized Elliptic Sitnikov

(N + 1)

-Body Problem

by Xuhua Cheng and Baoting Liu

Symmetry 2023, 15(5), 1113; https://doi.org/10.3390/sym15051113 - 19 May 2023

Viewed by 1086

Abstract

In this paper, we study the existence of the families of odd symmetric periodic solutions in the generalized elliptic Sitnikov

(N + 1)

-body problem for all values of the eccentricity

e \in [0, 1)

using the global [...] Read more.

In this paper, we study the existence of the families of odd symmetric periodic solutions in the generalized elliptic Sitnikov

(N + 1)

-body problem for all values of the eccentricity

e \in [0, 1)

using the global continuation method. First, we obtain the properties of the period of the solution of the corresponding autonomous equation (eccentricity

e = 0

) using elliptic functions. Then, according to these properties and the global continuation method of the zeros of a function depending on one parameter, we derive the existence of odd periodic solutions for all

e \in [0, 1)

. It is shown that the temporal frequencies of period solutions depend on the total mass

λ

(or the number N) of the primaries in a delicate way. Full article

(This article belongs to the Section Mathematics)

► Show Figures

Figure 1

15 pages, 314 KiB

Open AccessFeature PaperArticle

Statistical Formulation of Background Independence in Manifestly-Covariant Quantum Gravity Theory

by Claudio Cremaschini and Massimo Tessarotto

Symmetry 2023, 15(5), 1112; https://doi.org/10.3390/sym15051112 - 19 May 2023

Viewed by 1161

Abstract

The notion of background independence is a distinguished feature that should characterize the conceptual foundation of any physically-acceptable theory of quantum gravity. It states that the structure of the space-time continuum described by classical General Relativity should possess an emergent character, namely, that [...] Read more.

The notion of background independence is a distinguished feature that should characterize the conceptual foundation of any physically-acceptable theory of quantum gravity. It states that the structure of the space-time continuum described by classical General Relativity should possess an emergent character, namely, that it should arise from the quantum-dynamical gravitational field. In this paper, the above issue is addressed in the framework of manifestly-covariant quantum gravity theory. Accordingly, a statistical formulation of background independence is provided, consistent with the principle of manifest covariance. In particular, it is shown that the classical background metric tensor determining the geometric properties of space-time can be expressed consistently in terms of a suitable statistical average of the stochastic quantum gravitational field tensor. As an application, a particular realization of background independence is shown to hold for analytical Gaussian solutions of the quantum probability density function. Full article

13 pages, 315 KiB

Open AccessArticle

Killing Vector Fields of Static Cylindrically Symmetric Spacetime—A Rif Tree Approach

by Maryam Khalid Albuhayr, Ashfaque H. Bokhari and Tahir Hussain

Symmetry 2023, 15(5), 1111; https://doi.org/10.3390/sym15051111 - 19 May 2023

Viewed by 1405

Abstract

In this paper, we use an algebraic approach to classify cylindrically symmetric static spacetimes according to their killing vector fields. This approach is based on using a maple algorithm to re-cast the Killing’s equations into a reduced involutive form and integrating the Killing’s [...] Read more.

In this paper, we use an algebraic approach to classify cylindrically symmetric static spacetimes according to their killing vector fields. This approach is based on using a maple algorithm to re-cast the Killing’s equations into a reduced involutive form and integrating the Killing’s equations subject to the constraints given by the algorithm. It is shown that this approach provides some additional spacetime metrics, which were not provided previously by solving the Killing’s equations using a direct integration technique. To discuss some physical implications of the obtained spacetime metrics, we use them in the Einstein equations and discuss their significance. Full article

(This article belongs to the Special Issue Noether and Space-Time Symmetries in Physics)

► Show Figures

Figure 1

30 pages, 558 KiB

Open AccessArticle

On the Jacobi Stability of Two SIR Epidemic Patterns with Demography

by Florian Munteanu

Symmetry 2023, 15(5), 1110; https://doi.org/10.3390/sym15051110 - 18 May 2023

Cited by 3 | Viewed by 1958

Abstract

In the present work, two SIR patterns with demography will be considered: the classical pattern and a modified pattern with a linear coefficient of the infection transmission. By reformulating of each first-order differential systems as a system with two second-order differential equations, we [...] Read more.

In the present work, two SIR patterns with demography will be considered: the classical pattern and a modified pattern with a linear coefficient of the infection transmission. By reformulating of each first-order differential systems as a system with two second-order differential equations, we will examine the nonlinear dynamics of the system from the Jacobi stability perspective through the Kosambi–Cartan–Chern (KCC) geometric theory. The intrinsic geometric properties of the systems will be studied by determining the associated geometric objects, i.e., the zero-connection curvature tensor, the nonlinear connection, the Berwald connection, and the five KCC invariants: the external force

ε^{i}

—the first invariant; the deviation curvature tensor

P_{j}^{i}

—the second invariant; the torsion tensor

P_{j k}^{i}

—the third invariant; the Riemann–Christoffel curvature tensor

P_{j k l}^{i}

—the fourth invariant; the Douglas tensor

D_{j k l}^{i}

—the fifth invariant. In order to obtain necessary and sufficient conditions for the Jacobi stability near each equilibrium point, the deviation curvature tensor will be determined at each equilibrium point. Furthermore, we will compare the Jacobi stability with the classical linear stability, inclusive by diagrams related to the values of parameters of the system. Full article

(This article belongs to the Special Issue Geometric Algebra and Its Applications)

► Show Figures

Figure 1

14 pages, 314 KiB

Open AccessArticle

Investigating New Subclasses of Bi-Univalent Functions Associated with q-Pascal Distribution Series Using the Subordination Principle

by Abdullah Alsoboh, Ala Amourah, Maslina Darus and Carla Amoi Rudder

Symmetry 2023, 15(5), 1109; https://doi.org/10.3390/sym15051109 - 18 May 2023

Cited by 13 | Viewed by 1333

Abstract

In the real world, there are many applications that find the Pascal distribution to be a useful and relevant model. One of these is the normal distribution. In this work, we develop a new subclass of analytic bi-univalent functions by making use of [...] Read more.

In the real world, there are many applications that find the Pascal distribution to be a useful and relevant model. One of these is the normal distribution. In this work, we develop a new subclass of analytic bi-univalent functions by making use of the q-Pascal distribution series as a construction. These functions involve the q-Gegenbauer polynomials, and we use them to establish our new subclass. Moreover, we solve the Fekete–Szegö functional problem and analyze various different estimates of the Maclaurin coefficients for functions that belong to the new subclass. Full article

(This article belongs to the Special Issue Symmetry in Geometric Function Theory)

21 pages, 3071 KiB

Open AccessArticle

Enhanced Dispersion Monitoring Structures Based on Modified Successive Sampling: Application to Fertilizer Production Process

by Mehvish Hyder, Syed Muhammad Muslim Raza, Tahir Mahmood and Nasir Abbas

Symmetry 2023, 15(5), 1108; https://doi.org/10.3390/sym15051108 - 18 May 2023

Cited by 3 | Viewed by 1491

Abstract

In this era of Industry 4.0, efficient and affordable monitoring solutions are needed for the surveillance of manufacturing/service operations. In general, memory-type control charts outperform memoryless control charts when it comes to determining the changes in location and dispersion parameters of symmetrically distributed [...] Read more.

In this era of Industry 4.0, efficient and affordable monitoring solutions are needed for the surveillance of manufacturing/service operations. In general, memory-type control charts outperform memoryless control charts when it comes to determining the changes in location and dispersion parameters of symmetrically distributed processes. Before monitoring the process location, it is essential to monitor the process dispersion, since the latter presumes that the process variance remains stable. In practice, the modified successive sampling (MSS) mechanism is preferred over simple random sampling for its cost-effectiveness and efficiency. This study was designed in order to propose moving average and double moving average control charts based on the MSS mechanism for monitoring the dispersion parameter. The performance of the proposed charts is evaluated using run-length measures, and a comparison is made with an existing control chart based on MSS and repetitive sampling. Furthermore, the application of the designed moving and double moving average charts is demonstrated using a case study related to fertilizer production. It is observed that the proposed double moving average control chart performs better than the other control charts designed under the MSS and repetitive sampling schemes. Full article

(This article belongs to the Special Issue Mathematical Models and Methods in Various Sciences)

► Show Figures

Figure 1

15 pages, 8974 KiB

Open AccessArticle

A Single-Averaged Model for the Solar Radiation Pressure Applied to Space Debris Mitigation Using a Solar Sail

by J. P. S. Carvalho, J. Cardoso dos Santos, J. S. Lima, L. F. Brejão and A. F. B. A. Prado

Symmetry 2023, 15(5), 1107; https://doi.org/10.3390/sym15051107 - 18 May 2023

Cited by 2 | Viewed by 1707

Abstract

Several non-functional objects are orbiting around the Earth and they are called space debris. In this work, we investigate the process of space debris mitigation from the GEO region using a solar sail. The acceleration induced by the solar radiation pressure (SRP) is [...] Read more.

Several non-functional objects are orbiting around the Earth and they are called space debris. In this work, we investigate the process of space debris mitigation from the GEO region using a solar sail. The acceleration induced by the solar radiation pressure (SRP) is the most relevant perturbation for objects in orbit around the Earth with a high area-to-mass ratio (

A / m

). We consider the single-averaged SRP model with the Sun in an elliptical and inclined orbit. In addition to the SRP effect, the orbital evolution of space debris is analyzed considering the perturbations due to the Earth’s flattening and third-body perturbations in the dynamical system. The idea is to use the solar sail as a propulsion system using the Sun itself as a clean and abundant energy source so that it can remove space debris from the geostationary orbit and also contribute to the sustainability of space exploration. Using averaged dynamical maps as a tool, the numerical simulations show that the solar sail contributes strongly to exciting the eccentricity of the space debris, causing its reentry into Earth’s atmosphere. To perform the numerical simulations, we consider data from real space debris. We also show that the solar sail can be used to remove space debris for a graveyard orbit. In this way, the solar sail can work as a clean and sustainable space-debris-removal mechanism. Finally, we show that the convenient choice of the argument of perigee and the longitude of the ascending node might contribute to amplify the growth of eccentricity. It is also shown that solar radiation pressure destroys the symmetry of the orbits that can be observed in keplerian orbits, so all the orbits will be asymmetric when considering the presence of this force. Full article

► Show Figures

Figure 1

11 pages, 278 KiB

Open AccessArticle

Hyperstructure Theory Applied to BF-Algebras

by Ghulam Muhiuddin, Nabilah Abughazalah, Ahsan Mahboob and Abdullah G. Alotaibi

Symmetry 2023, 15(5), 1106; https://doi.org/10.3390/sym15051106 - 18 May 2023

Cited by 1 | Viewed by 1223

Abstract

This study applies the hyperstructure theory to BF-algebra, which is an algebraic structure. In fact, we define hyper-BF-algebras and hyper-BF ideals and investigate several of their related characteristics. BF-algebra and hyper-BF ideal characteristics are taken into account, and supported examples are built. Here, [...] Read more.

This study applies the hyperstructure theory to BF-algebra, which is an algebraic structure. In fact, we define hyper-BF-algebras and hyper-BF ideals and investigate several of their related characteristics. BF-algebra and hyper-BF ideal characteristics are taken into account, and supported examples are built. Here, we also develop new concepts known as hyper-B-algebra, hyper-BG-algebra, and hyper-BH algebra as generalizations of other classes of hyper-BCK-/BCI-algebras. Additionally, we demonstrate that each hyper-BF is a weak hyper-BF in hyper-BF-algebra, but the opposite is not true. It is further established that the intersection of the weak hyper-BF ideal family is weak. Full article

(This article belongs to the Special Issue Symmetry in Functional Analysis and Its Applications)

10 pages, 430 KiB

Open AccessArticle

Preassigned-Time Bipartite Flocking Consensus Problem in Multi-Agent Systems

by Xiejun Cheng, Jiashang Yu, Xiurong Chen, Jiaju Yu and Bing Cheng

Symmetry 2023, 15(5), 1105; https://doi.org/10.3390/sym15051105 - 18 May 2023

Cited by 2 | Viewed by 1167

Abstract

This article is concerned with the bipartite flocking problem in multi-agent systems. Our contributions can be summarized as follows. Firstly, a class of preassigned-time consensus protocols is proposed to solve the issue of multi-agent systems. Secondly, with the aid of the symmetric properties [...] Read more.

This article is concerned with the bipartite flocking problem in multi-agent systems. Our contributions can be summarized as follows. Firstly, a class of preassigned-time consensus protocols is proposed to solve the issue of multi-agent systems. Secondly, with the aid of the symmetric properties of the graph theory and the Lyapunov stability theorem, we prove that agents can be divided into two disjointed clusters in a finite time, and they move to opposite directions at the same magnitude and speed. The protocol is novel among existing fixed/finite-time protocols in that the associated settling time is a preassigned constant and a parameter of the protocol. Moreover, it is proven that the diameters of the clusters are bounded and independent of other the protocol parameters. These results are demonstrated through both theoretical analysis and simulation examples. Full article

(This article belongs to the Special Issue Symmetry in Optimization Theory, Algorithm and Applications)

► Show Figures

Figure 1

12 pages, 3091 KiB

Open AccessArticle

A Novel Image Similarity Measure Based on Greatest and Smallest Eigen Fuzzy Sets

by Ferdinando Di Martino and Salvatore Sessa

Symmetry 2023, 15(5), 1104; https://doi.org/10.3390/sym15051104 - 18 May 2023

Cited by 2 | Viewed by 1686

Abstract

A novel image similarity index based on the greatest and smallest fuzzy set solutions of the max–min and min–max compositions of fuzzy relations, respectively, is proposed. The greatest and smallest fuzzy sets are found symmetrically as the min–max and max–min solutions, respectively, to [...] Read more.

A novel image similarity index based on the greatest and smallest fuzzy set solutions of the max–min and min–max compositions of fuzzy relations, respectively, is proposed. The greatest and smallest fuzzy sets are found symmetrically as the min–max and max–min solutions, respectively, to a fuzzy relation equation. The original image is partitioned into squared blocks and the pixels in each block are normalized to [0, 1] in order to have a fuzzy relation. The greatest and smallest fuzzy sets, found for each block, are used to measure the similarity between the original image and the image reconstructed by joining the squared blocks. Comparison tests with other well-known image metrics are then carried out where source images are noised by applying Gaussian filters. The results show that the proposed image similarity measure is more effective and robust to noise than the PSNR and SSIM-based measures. Full article

(This article belongs to the Special Issue Symmetry in Fuzzy Relation Equations)

► Show Figures

Figure 1

3 pages, 161 KiB

Open AccessEditorial

Introduction to the Special Issue in Symmetry Titled “Symmetry in Statistics and Data Science”

by Christophe Chesneau

Symmetry 2023, 15(5), 1103; https://doi.org/10.3390/sym15051103 - 18 May 2023

Viewed by 1026

Abstract

In order to introduce this Special Issue, some motivational facts are given [...] Full article

(This article belongs to the Special Issue Symmetry in Statistics and Data Science)

19 pages, 6604 KiB

Open AccessArticle

An Analysis of Global and Adaptive Thresholding for Biometric Images Based on Neutrosophic Overset and Underset Approaches

by Vinoth Dhatchinamoorthy and Ezhilmaran Devarasan

Symmetry 2023, 15(5), 1102; https://doi.org/10.3390/sym15051102 - 18 May 2023

Cited by 3 | Viewed by 2121

Abstract

The study introduces a new threshold method based on a neutrosophic set. The proposal applies the neutrosophic overset and underset concepts for thresholding the image. The global threshold method and the adaptive threshold method were used as the two types of thresholding methods [...] Read more.

The study introduces a new threshold method based on a neutrosophic set. The proposal applies the neutrosophic overset and underset concepts for thresholding the image. The global threshold method and the adaptive threshold method were used as the two types of thresholding methods in this article. Images could be symmetrical or asymmetrical in professional disciplines; the government maintains facial image databases as symmetrical. General-purpose images do not need to be symmetrical. Therefore, it is essential to know how thresholding functions in both scenarios. Since the article focuses on biometric image data, face and fingerprint data were considered for the analysis. The proposal provides six techniques for the global threshold method based on neutrosophic membership, indicating neutrosophic

T F

overset (

{NO}_{T F}

), neutrosophic

T I

overset (

{NO}_{T I}

), neutrosophic

T I F

overset (

{NO}_{T I F}

), neutrosophic

T F

underset (

{NU}_{T F}

), neutrosophic

T I

underset (

{NU}_{T I}

), neutrosophic

T I F

underset (

{NU}_{T I F}

); similarly, in this study, the researchers generated six novel approaches for the adaptive method. These techniques involved an investigation using biometric data, such as fingerprints and facial images. The achievement was

98 %

accurate for facial image data and

100 %

accurate for fingerprint data. Full article

(This article belongs to the Section Computer)

► Show Figures

Figure 1

21 pages, 849 KiB

Open AccessArticle

A Comparative Study of the Fractional Partial Differential Equations via Novel Transform

by Abdul Hamid Ganie, Mashael M. AlBaidani and Adnan Khan

Symmetry 2023, 15(5), 1101; https://doi.org/10.3390/sym15051101 - 17 May 2023

Cited by 16 | Viewed by 2245

Abstract

In comparison to fractional-order differential equations, integer-order differential equations generally fail to properly explain a variety of phenomena in numerous branches of science and engineering. This article implements efficient analytical techniques within the Caputo operator to investigate the solutions of some fractional partial [...] Read more.

In comparison to fractional-order differential equations, integer-order differential equations generally fail to properly explain a variety of phenomena in numerous branches of science and engineering. This article implements efficient analytical techniques within the Caputo operator to investigate the solutions of some fractional partial differential equations. The Adomian decomposition method, homotopy perturbation method, and Elzaki transformation are used to calculate the results for the specified issues. In the current procedures, we first used the Elzaki transform to simplify the problems and then applied the decomposition and perturbation methods to obtain comprehensive results for the problems. For each targeted problem, the generalized schemes of the suggested methods are derived under the influence of each fractional derivative operator. The current approaches give a series-form solution with easily computable components and a higher rate of convergence to the precise solution of the targeted problems. It is observed that the derived solutions have a strong connection to the actual solutions of each problem as the number of terms in the series solution of the problems increases. Graphs in two and three dimensions are used to plot the solution of the proposed fractional models. The methods used currently are simple and efficient for dealing with fractional-order problems. The primary benefit of the suggested methods is less computational time. The results of the current study will be regarded as a helpful tool for dealing with the solution of fractional partial differential equations. Full article

(This article belongs to the Special Issue Symmetry and Partial Differential Equations: Theory and Application)

► Show Figures

Figure 1

11 pages, 269 KiB

Open AccessArticle

Controlled S-Metric-Type Spaces and Applications to Fractional Integrals

by Nilay Ekiz Yazici, Ozgur Ege, Nabil Mlaiki and Aiman Mukheimer

Symmetry 2023, 15(5), 1100; https://doi.org/10.3390/sym15051100 - 17 May 2023

Cited by 3 | Viewed by 1310

Abstract

In this paper, we introduce controlled S-metric-type spaces and give some of their properties and examples. Moreover, we prove the Banach fixed point theorem and a more general fixed point theorem in this new space. Finally, using the new results, we give two [...] Read more.

In this paper, we introduce controlled S-metric-type spaces and give some of their properties and examples. Moreover, we prove the Banach fixed point theorem and a more general fixed point theorem in this new space. Finally, using the new results, we give two applications on Riemann–Liouville fractional integrals and Atangana–Baleanu fractional integrals. Full article

(This article belongs to the Special Issue Symmetry Application in Fixed Point Theory)

Journal Menu

Journal Browser

Symmetry, Volume 15, Issue 5 (May 2023) – 172 articles

Further Information

Guidelines

MDPI Initiatives

Follow MDPI