Symmetry

19 pages, 6053 KiB

Open AccessArticle

Assorted Spatial Optical Dynamics of a Generalized Fractional Quadruple Nematic Liquid Crystal System in Non-Local Media

by Mohammad A. Al Zubi, Kallekh Afef and Emad A. Az-Zo’bi

Symmetry 2024, 16(6), 778; https://doi.org/10.3390/sym16060778 - 20 Jun 2024

Viewed by 685

Abstract

Nematicons upgrade the recognition of light localization in the reorientation of non-local media. the current research employs a powerful integral scheme using a different procedure, namely, the modified simple equation method (MSEM), to analyze nematicons in liquid crystals from the controlling model. The [...] Read more.

Nematicons upgrade the recognition of light localization in the reorientation of non-local media. the current research employs a powerful integral scheme using a different procedure, namely, the modified simple equation method (MSEM), to analyze nematicons in liquid crystals from the controlling model. The expanded MSEM is investigated to enlarge the applicability of the standard one. The suggested expansion depends on merging the MSEM and the ansatz method. The new generalized nonlinear n-times quadruple power law is included. With the aid of the symbolic computational package Mathematica, new explicit complex hyperbolic, periodic, and more exact spatial soliton solutions are derived. Moreover, the related existence constraints are obtained. To show the dynamical properties of some of the obtained nematicons, three-dimensional profiles with corresponding contours are depicted with the choice of appropriate values of arbitrary parameters. The fractional impacts in various applicable senses are analyzed to investigate the generality of the considered model. Full article

(This article belongs to the Special Issue Mathematical Theories, Models and Methods in Applied Sciences: Deterministic, Stochastic and Symmetry Perspectives)

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23 pages, 350 KiB

Open AccessArticle

Introducing Fixed-Point Theorems and Applications in Fuzzy Bipolar b-Metric Spaces with ψ_α- and ϝ_η-Contractive Maps

by Salam Alnabulsi, Wael Mahmoud Mohammad Salameh and Mohammad H. M. Rashid

Symmetry 2024, 16(6), 777; https://doi.org/10.3390/sym16060777 - 20 Jun 2024

Viewed by 1064

Abstract

In this study, we introduce novel concepts within the framework of fuzzy bipolar b-metric spaces, focusing on various mappings such as

ψ_{α}

-contractive and

ϝ_{η}

-contractive mappings, which are essential for quantifying distances between dissimilar elements. We establish fixed-point theorems [...] Read more.

In this study, we introduce novel concepts within the framework of fuzzy bipolar b-metric spaces, focusing on various mappings such as

ψ_{α}

-contractive and

ϝ_{η}

-contractive mappings, which are essential for quantifying distances between dissimilar elements. We establish fixed-point theorems for these mappings, demonstrating the existence of invariant points under certain conditions. To enhance the credibility and applicability of our findings, we provide illustrative examples that support these theorems and expand the existing knowledge in this field. Furthermore, we explore practical applications of our research, particularly in solving integral equations and fractional differential equations, showcasing the robustness and utility of our theoretical advancements. Symmetry, both in its traditional sense and within the fuzzy context, is fundamental to our study of fuzzy bipolar b-metric spaces. The introduced contractive mappings and fixed-point theorems expand the theoretical framework and offer robust tools for addressing practical problems where symmetry is significant. Full article

(This article belongs to the Topic Fuzzy Number, Fuzzy Difference, Fuzzy Differential: Theory and Applications)

13 pages, 265 KiB

Open AccessArticle

Measurement and Control of Risk Contagion in Portfolio Optimization Processes

by Risheng Qiao and Yongsheng Qiao

Symmetry 2024, 16(6), 776; https://doi.org/10.3390/sym16060776 - 20 Jun 2024

Viewed by 628

Abstract

The success of an investment portfolio is not only related to its yield, but is also influenced by market risks, especially the contagion risks that may exist between assets. Therefore, effective portfolio optimization requires first studying the risk contagion relationship between financial assets. [...] Read more.

The success of an investment portfolio is not only related to its yield, but is also influenced by market risks, especially the contagion risks that may exist between assets. Therefore, effective portfolio optimization requires first studying the risk contagion relationship between financial assets. We selected a total of six financial assets from different stock and exchange rate markets as the research objects, and explored the risk contagion relationships of various assets in the investment portfolio through Vine Copula. Research has shown that there is often a structural mutation in one or some assets of an investment portfolio, leading to significant fluctuations in investment returns. The Vine Copula model can effectively measure the risk contagion between assets caused by asset structural mutations. Full article

(This article belongs to the Section Mathematics)

18 pages, 2027 KiB

Open AccessArticle

Hopf-like Bifurcation Analysis of a Fractional-Order Tumor-Lymphatic Model Involving Two Time Delays

by Xueying Shi, Xiaoping Chen, Chengdai Huang, An Luo and Xin Yin

Symmetry 2024, 16(6), 775; https://doi.org/10.3390/sym16060775 - 20 Jun 2024

Viewed by 901

Abstract

This paper investigates the Hopf-like bifurcation of a fractional tumor-lymphatic model with two time delays. The two time delays are considered as branching parameters, and we analyze their influences on the dynamic properties of the model. Through an examination of the root distribution [...] Read more.

This paper investigates the Hopf-like bifurcation of a fractional tumor-lymphatic model with two time delays. The two time delays are considered as branching parameters, and we analyze their influences on the dynamic properties of the model. Through an examination of the root distribution of the characteristic equation, we derive the properties of the positive steady state and the conditions for the occurrence of Hopf-like bifurcation near the positive equilibrium point. Numerical simulations are demonstrated to support our theoretical results. Full article

(This article belongs to the Section Mathematics)

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13 pages, 7840 KiB

Open AccessArticle

Stability and Numerical Simulation of a Nonlinear Hadamard Fractional Coupling Laplacian System with Symmetric Periodic Boundary Conditions

by Xiaojun Lv, Kaihong Zhao and Haiping Xie

Symmetry 2024, 16(6), 774; https://doi.org/10.3390/sym16060774 - 20 Jun 2024

Cited by 2 | Viewed by 973

Abstract

The Hadamard fractional derivative and integral are important parts of fractional calculus which have been widely used in engineering, biology, neural networks, control theory, and so on. In addition, the periodic boundary conditions are an important class of symmetric two-point boundary conditions for [...] Read more.

The Hadamard fractional derivative and integral are important parts of fractional calculus which have been widely used in engineering, biology, neural networks, control theory, and so on. In addition, the periodic boundary conditions are an important class of symmetric two-point boundary conditions for differential equations and have wide applications. Therefore, this article considers a class of nonlinear Hadamard fractional coupling

(p_{1}, p_{2})

-Laplacian systems with periodic boundary value conditions. Based on nonlinear analysis methods and the contraction mapping principle, we obtain some new and easily verifiable sufficient criteria for the existence and uniqueness of solutions to this system. Moreover, we further discuss the generalized Ulam–Hyers (GUH) stability of this problem by using some inequality techniques. Finally, three examples and simulations explain the correctness and availability of our main results. Full article

(This article belongs to the Special Issue Asymmetric and Symmetric Study on Applied Mathematics in ODE, PDE and FDE Model)

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10 pages, 254 KiB

Open AccessArticle

On Quasi-Subordination for Bi-Univalency Involving Generalized Distribution Series

by Sunday Olufemi Olatunji, Matthew Olanrewaju Oluwayemi, Saurabh Porwal and Alina Alb Lupas

Symmetry 2024, 16(6), 773; https://doi.org/10.3390/sym16060773 - 20 Jun 2024

Viewed by 814

Abstract

Various researchers have considered different forms of bi-univalent functions in recent times, and this has continued to gain more attention in Geometric Function Theory (GFT), but not much study has been conducted in the area of application of the certain probability concept in [...] Read more.

Various researchers have considered different forms of bi-univalent functions in recent times, and this has continued to gain more attention in Geometric Function Theory (GFT), but not much study has been conducted in the area of application of the certain probability concept in geometric functions. In this manuscript, our motivation is the application of analytic and bi-univalent functions. In particular, the researchers examine bi-univalency of a generalized distribution series related to Bell numbers as a family of Caratheodory functions. Some coefficients of the class of the function are obtained. The results are new as far work on bi-univalency is concerned. Full article

(This article belongs to the Special Issue Symmetry in Geometric Theory of Analytic Functions)

32 pages, 2877 KiB

Open AccessArticle

Cloud Manufacturing Service Composition Optimization Based on Improved Chaos Sparrow Search Algorithm with Time-Varying Reliability and Credibility Evaluation

by Yongxiang Li, Xifan Yao, Shanxiang Wei, Wenrong Xiao and Zongming Yin

Symmetry 2024, 16(6), 772; https://doi.org/10.3390/sym16060772 - 19 Jun 2024

Viewed by 870

Abstract

The economic friction and political conflicts between some countries and regions have made multinational corporations increasingly focus on the reliability and credibility of manufacturing supply chains. In view of the impact of poor manufacturing entity reliability and service reputation on the new-era manufacturing [...] Read more.

The economic friction and political conflicts between some countries and regions have made multinational corporations increasingly focus on the reliability and credibility of manufacturing supply chains. In view of the impact of poor manufacturing entity reliability and service reputation on the new-era manufacturing industry, the time-varying reliability and time-varying credibility of cloud manufacturing (CMfg) services were studied from the perspective of combining nature and society. Taking time-varying reliability, time-varying credibility, composition complexity, composition synergy, execution time, and execution cost as objective functions, a new six-dimension comprehensive evaluation model of service quality was constructed. To solve the optimization problem, this study proposes an improved chaos sparrow search algorithm (ICSSA), where the Bernoulli chaotic mapping formula was introduced to improve the basic sparrow search algorithm (BSSA), and the position calculation formulas of the explorer sparrow and the scouter sparrow were enhanced. The Bernoulli chaotic operator changed the symmetry of the BSSA, increased the uncertainty and randomness of the explorer sparrow position in the new algorithm, and affected the position update and movement strategies of the follower and scouter sparrows. The asymmetric chaotic characteristic brought better global search ability and optimization performance to the ICSSA. The comprehensive performance of the service composition (SvcComp) scheme was evaluated by calculating weighted relative deviation based on six evaluation elements. The WFG and DTLZ series test functions were selected, and the inverse generation distance (IGD) index and hyper volume (HV) index were used to compare and evaluate the convergence and diversity of the ICSSA, BSSA, PSO, SGA, and NSGA-III algorithms through simulation analysis experiments. The test results indicated that the ICSSA outperforms the BSSA, PSO, SGA, and NSGA-III in the vast majority of testing issues. Finally, taking disinfection robot manufacturing tasks as an example, the effectiveness of the proposed CMfg SvcComp optimization model and the ICSSA were verified. The case study results showed that the proposed ICSSA had faster convergence speed and better comprehensive performance for the CMfg SvcComp optimization problem compared with the BSSA, PSO, SGA, and NSGA-III. Full article

(This article belongs to the Section Computer)

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15 pages, 265 KiB

Open AccessArticle

Statistical Warped Product Immersions into Statistical Manifolds of (Quasi-)Constant Curvature

by Aliya Naaz Siddiqui, Meraj Ali Khan and Sudhakar Kumar Chaubey

Symmetry 2024, 16(6), 771; https://doi.org/10.3390/sym16060771 - 19 Jun 2024

Viewed by 934

Abstract

Warped products provide an elegant and versatile framework for exploring and understanding a wide range of geometric structures. Their ability to combine two distinct manifolds through a warping function introduces a rich and diverse set of geometries, thus making them a powerful tool [...] Read more.

Warped products provide an elegant and versatile framework for exploring and understanding a wide range of geometric structures. Their ability to combine two distinct manifolds through a warping function introduces a rich and diverse set of geometries, thus making them a powerful tool in various mathematical, physical, and computational applications. This article addresses the central query related to warped product submanifolds in the context of statistics. It focuses on deriving two new and distinct inequalities for a statistical warped product submanifold in a statistical manifold of a constant (quasi-constant) curvature. This article then finishes with some concluding remarks. Full article

(This article belongs to the Special Issue Symmetry and Its Application in Differential Geometry and Topology, 3rd Edition)

12 pages, 281 KiB

Open AccessArticle

Finite Sets—What Kind of Finite?

by Andrei Alexandru and Gabriel Ciobanu

Symmetry 2024, 16(6), 770; https://doi.org/10.3390/sym16060770 - 19 Jun 2024

Viewed by 997

Abstract

In mathematics, philosophy, cosmology, and theology, the notion of infinity has generated ample debate. Much less discussion has been generated by the notion of finiteness. However, when we consider finitely supported sets, the notion of finiteness becomes more interesting and richer. We present [...] Read more.

In mathematics, philosophy, cosmology, and theology, the notion of infinity has generated ample debate. Much less discussion has been generated by the notion of finiteness. However, when we consider finitely supported sets, the notion of finiteness becomes more interesting and richer. We present several independent definitions of finite sets within the framework of finitely supported structures, emphasizing the differences between these definitions. Full article

(This article belongs to the Section Mathematics)

13 pages, 297 KiB

Open AccessArticle

On Centralizers of Idempotents with Restricted Range

by Dilawar J. Mir and Amal S. Alali

Symmetry 2024, 16(6), 769; https://doi.org/10.3390/sym16060769 - 19 Jun 2024

Viewed by 879

Abstract

This study delves into the structure and properties of left inverse zero divisor bands within semigroups, identifying their maximal forms and broadening the theoretical landscape of semigroup analysis. A significant focus is placed on the automorphisms of a semigroup S of centralizers of [...] Read more.

This study delves into the structure and properties of left inverse zero divisor bands within semigroups, identifying their maximal forms and broadening the theoretical landscape of semigroup analysis. A significant focus is placed on the automorphisms of a semigroup S of centralizers of idempotent transformations with restricted range, revealing that these automorphisms are inner ones and induced by the units of S. Additionally, we establish that the automorphism group

Aut (S)

is isomorphic to

U_{S}

, the group of units of S. These findings extend previous results on semigroups of transformations, enhancing their applicability and providing a more unified theory. The practical implications of this work span multiple fields, including automata theory, coding theory, cryptography, and graph theory, offering tools for more efficient algorithms and models. By simplifying complex concepts and providing a solid foundation for future research, this study makes significant contributions to both theoretical and applied mathematics. Full article

(This article belongs to the Special Issue Algebraic Systems, Models and Applications)

11 pages, 282 KiB

Open AccessArticle

Diagonals–Parameter Symmetry Model and Its Property for Square Contingency Tables with Ordinal Categories

by Kouji Tahata and Kohei Matsuda

Symmetry 2024, 16(6), 768; https://doi.org/10.3390/sym16060768 - 19 Jun 2024

Viewed by 924

Abstract

The diagonals–parameter symmetry (DPS) model is a proposed method for analyzing square contingency tables with ordinal categories. Previously, it was stated that the generalized DPS (DPS[f]) model was equivalent to the DPS model for any function f, but the proof [...] Read more.

The diagonals–parameter symmetry (DPS) model is a proposed method for analyzing square contingency tables with ordinal categories. Previously, it was stated that the generalized DPS (DPS[f]) model was equivalent to the DPS model for any function f, but the proof was not provided. This paper presents the derivation of the DPS[f] model and the proof of the relationship between the two models. The findings offer various interpretations of the DPS model. Additionally, a new model is considered, and it is shown that the proposed model and the DPS[f] model are separable. Full article

(This article belongs to the Special Issue Symmetry in Mathematical Models)

16 pages, 26033 KiB

Open AccessArticle

Four-Point Bending of Basic Rails: Theory and Experimental Verification

by Zhikui Dong, Chunjiang Liu, Long Ma, Jiahao Yang and Yunhong Jiang

Symmetry 2024, 16(6), 767; https://doi.org/10.3390/sym16060767 - 19 Jun 2024

Viewed by 740

Abstract

Mathematical models of prediction provide theoretical support for basic rail automation. The three-point bending method for basic rails is characterized by its simplicity and flexibility, and, as such, it is widely used in bending processes. However, due to the significant curvature changes that [...] Read more.

Mathematical models of prediction provide theoretical support for basic rail automation. The three-point bending method for basic rails is characterized by its simplicity and flexibility, and, as such, it is widely used in bending processes. However, due to the significant curvature changes that occur after bending, it is not suitable for scenarios requiring large arc bending, and its range of achievable deflections is limited. This study focuses on four-point bending, dividing the bending process into three stages and using a power-law material hardening model to establish different bending moment expressions for each stage. We derived the relationships between curvature, elastic zone ratio, load, and deflection, ultimately creating a load–deflection model. Based on the simple springback law, we developed the final bending prediction model. Finite element simulations were conducted to simulate the bending process under various conditions, using top punch distances ranging from 200 mm to 400 mm and die distances ranging from 600 mm to 1000 mm. These simulations validated the advantages and accuracy of the four-point bending prediction model in large arc bending. Additionally, a four-point bending experimental setup was established under specified conditions. The experimental results were compared with the theoretical model calculations, showing errors within 0.2 mm and thus verifying the accuracy of the four-point bending prediction model. The mathematical model developed in this study provides theoretical support for the automation of basic rail bending. Full article

(This article belongs to the Section Engineering and Materials)

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25 pages, 8496 KiB

Open AccessArticle

Enhancing Transportation Efficiency with Interval-Valued Fermatean Neutrosophic Numbers: A Multi-Item Optimization Approach

by Muhammad Kamran, Muhammad Nadeem, Justyna Żywiołek, Manal Elzain Mohamed Abdalla, Anns Uzair and Aiman Ishtiaq

Symmetry 2024, 16(6), 766; https://doi.org/10.3390/sym16060766 - 18 Jun 2024

Viewed by 748

Abstract

In this study, we derive a simple transportation scheme by post-optimizing the costs of a modified problem. The strategy attempts to make the original (mainly feasible) option more practicable by adjusting the building components’ costs. Next, we employ the previously mentioned cell or [...] Read more.

In this study, we derive a simple transportation scheme by post-optimizing the costs of a modified problem. The strategy attempts to make the original (mainly feasible) option more practicable by adjusting the building components’ costs. Next, we employ the previously mentioned cell or area cost operators to gradually restore the modified costs to their initial levels, while simultaneously implementing the necessary adjustments to the “optimal” solution. This work presents a multi-goal, multi-item substantial transportation problem with interval-valued fuzzy variables, such as transportation costs, supplies, and demands, as parameters to maintain the transportation cost. This research addresses two circumstances where task ambiguity may occur: the interval solids transportation problem and the fuzzy substantial transportation issue. In the first scenario, we express data problems as intervals instead of exact values using an interval-valued fermatean neutrosophic number; in the second case, the information is not entirely obvious. We address both models when uncertainty solely affects the constraint set. For the interval scenario, we define an additional problem to solve. Our existing efficient systems have dependable transportation, so they are also capable of handling this new problem. In the fuzzy case, a parametric technique generates a fuzzy solution to the preceding problem. Since transportation costs have a direct impact on market prices, lowering them is the primary goal. Using parametric analysis, we provide optimal parameterization solutions for complementary situations. We provide a recommended algorithm for determining the stability set. In conclusion, we offer a sensitivity analysis and a numerical example of the transportation problem involving both balanced and imbalanced loads. Full article

(This article belongs to the Special Issue Symmetry with Optimization in Real-World Applications)

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23 pages, 5984 KiB

Open AccessArticle

Integration of Manifold Learning and Density Estimation for Fine-Tuned Face Recognition

by Huilin Ge, Zhiyu Zhu, Jiali Ouyang, Muhammad Awais Ashraf, Zhiwen Qiu and Umar Muhammad Ibrahim

Symmetry 2024, 16(6), 765; https://doi.org/10.3390/sym16060765 - 18 Jun 2024

Cited by 1 | Viewed by 878

Abstract

With the rapid advancements in data analysis and the increasing complexity of high-dimensional datasets, traditional dimensionality reduction techniques like Local Linear Embedding (LLE) often face challenges in maintaining accuracy and efficiency. This research aims to overcome the limitations of LLE, specifically its reliance [...] Read more.

With the rapid advancements in data analysis and the increasing complexity of high-dimensional datasets, traditional dimensionality reduction techniques like Local Linear Embedding (LLE) often face challenges in maintaining accuracy and efficiency. This research aims to overcome the limitations of LLE, specifically its reliance on the nearest neighbor concept, its inability to distinguish differences among manifold points, and its underutilization of data discrimination information. To address these issues, we propose an advanced LLE algorithm that integrates decision tree-based neighbor recognition with Gaussian kernel density estimation. Decision trees accurately determine neighboring relationships, which are then optimized using Gaussian kernel density estimation to better reflect the distribution of sample points on the manifold. The algorithm also incorporates data discrimination information to enhance classification accuracy and efficiency. Evaluations in facial recognition tasks using SVM classifiers demonstrate significant improvements. Integrating decision trees (LLE-DT) yielded accuracy gains, with LFW at 98.75%, CFP 96.10%, and Olivetti 92.18%. Gaussian density estimation (LLE-GDE) achieved further enhancements, especially in LFW (99.13%), with CFP at 96.85%, and Olivetti at 91.82%. Combining both methods (LLE-DT-GDE) led to substantial improvements: LFW 99.61%, CFP 97.23%, and Olivetti 93.56%, highlighting the synergy between decision trees and Gaussian estimation. This advanced LLE algorithm effectively addresses the limitations of traditional approaches, showing promising results in complex data processing tasks such as facial recognition. These findings suggest its potential for broader applications in fields requiring robust data analysis and classification. Full article

(This article belongs to the Special Issue Unraveling the Black Box: Unleashing the Power of Explainable Deep Learning in Advanced Engineering Sciences)

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23 pages, 1001 KiB

Open AccessArticle

A Fast Method for the Off-Boundary Evaluation of Laplace Layer Potentials by Convolution Sums

by Wenchao Guan, Zhicheng Wang, Leqi Xue and Yueen Hou

Symmetry 2024, 16(6), 764; https://doi.org/10.3390/sym16060764 - 18 Jun 2024

Viewed by 969

Abstract

In off-boundary computations of layer potentials, the near-singularities in integrals near the boundary presents challenges for conventional quadrature methods in achieving high precision. Additionally, the significant complexity of

O (n^{2})

interactions between n targets and n sources reduces the efficiency [...] Read more.

In off-boundary computations of layer potentials, the near-singularities in integrals near the boundary presents challenges for conventional quadrature methods in achieving high precision. Additionally, the significant complexity of

O (n^{2})

interactions between n targets and n sources reduces the efficiency of these methods. A fast and accurate numerical algorithm is presented for computing the Laplace layer potentials on a circle with a boundary described by a polar curve. This method can maintain high precision even when evaluating targets located at a close distance from the boundary. The radial symmetry of the integral kernels simplifies their description. By exploiting the polar form of the boundary and applying a one-dimensional exponential sum approximation along the radial direction, an approximation of layer potentials by the convolution sum is obtained. The algorithm uses FFT convolution to accelerate computation and employs a local quadrature to maintain accuracy for nearly singular terms. Consequently, it achieves spectral accuracy in regions outside of a sufficiently small neighborhood of the boundary and requires

O (n log n)

arithmetic operations. With the help of this algorithm, layer potentials can be efficiently evaluated on a computational domain. Full article

(This article belongs to the Special Issue Computational Mathematics and Its Applications in Numerical Analysis)

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38 pages, 513 KiB

Open AccessFeature PaperReview

Thermodynamics and Decay of de Sitter Vacuum

by Grigory E. Volovik

Symmetry 2024, 16(6), 763; https://doi.org/10.3390/sym16060763 - 18 Jun 2024

Cited by 11 | Viewed by 1192

Abstract

We discuss the consequences of the unique symmetry of de Sitter spacetime. This symmetry leads to the specific thermodynamic properties of the de Sitter vacuum, which produces a thermal bath for matter. de Sitter spacetime is invariant under the modified translations, [...] Read more.

We discuss the consequences of the unique symmetry of de Sitter spacetime. This symmetry leads to the specific thermodynamic properties of the de Sitter vacuum, which produces a thermal bath for matter. de Sitter spacetime is invariant under the modified translations,

r \to r - e^{H t} a

, where H is the Hubble parameter. For

H \to 0

, this symmetry corresponds to the conventional invariance of Minkowski spacetime under translations

r \to r - a

. Due to this symmetry, all the comoving observers at any point of the de Sitter space perceive the de Sitter environment as the thermal bath with temperature

T = H / π

, which is twice as large as the Gibbons–Hawking temperature of the cosmological horizon. This temperature does not violate de Sitter symmetry and, thus, does not require the preferred reference frame, as distinct from the thermal state of matter, which violates de Sitter symmetry. This leads to the heat exchange between gravity and matter and to the instability of the de Sitter state towards the creation of matter, its further heating, and finally the decay of the de Sitter state. The temperature

T = H / π

determines different processes in the de Sitter environment that are not possible in the Minkowski vacuum, such as the process of ionization of an atom in the de Sitter environment. This temperature also determines the local entropy of the de Sitter vacuum state, and this allows us to calculate the total entropy of the volume inside the cosmological horizon. The result reproduces the Gibbons–Hawking area law, which is attributed to the cosmological horizon,

S_{hor} = 4 π K A

, where

K = 1 / (16 π G)

. This supports the holographic properties of the cosmological event horizon. We extend the consideration of the local thermodynamics of the de Sitter state using the

f (R)

gravity. In this thermodynamics, the Ricci scalar curvature

R

and the effective gravitational coupling K are thermodynamically conjugate variables. The holographic connection between the bulk entropy of the Hubble volume and the surface entropy of the cosmological horizon remains the same but with the gravitational coupling

K = d f / d R

. Such a connection takes place only in the

3 + 1

spacetime, where there is a special symmetry due to which the variables K and

R

have the same dimensionality. We also consider the lessons from de Sitter symmetry for the thermodynamics of black and white holes. Full article

(This article belongs to the Special Issue Symmetry/Asymmetry: Feature Review Papers 2024)

20 pages, 311 KiB

Open AccessArticle

Gauss–Bonnet Theorem Related to the Semi-Symmetric Metric Connection in the Heisenberg Group

by Haiming Liu and Song Peng

Symmetry 2024, 16(6), 762; https://doi.org/10.3390/sym16060762 - 18 Jun 2024

Viewed by 918

Abstract

In this paper, we introduce the notion of the semi-symmetric metric connection in the Heisenberg group. Moreover, by using the method of Riemannian approximations, we define the notions of intrinsic curvature for regular curves, the intrinsic geodesic curvature of regular curves on a [...] Read more.

In this paper, we introduce the notion of the semi-symmetric metric connection in the Heisenberg group. Moreover, by using the method of Riemannian approximations, we define the notions of intrinsic curvature for regular curves, the intrinsic geodesic curvature of regular curves on a surface, and the intrinsic Gaussian curvature of the surface away from characteristic points in the Heisenberg group with the semi-symmetric metric connection. Finally, we derive the expressions of those curvatures and prove the Gauss–Bonnet theorem related to the semi-symmetric metric connection in the Heisenberg group. Full article

(This article belongs to the Section Mathematics)

18 pages, 8245 KiB

Open AccessArticle

Effect of an Adiabatic Obstacle on the Symmetry of the Temperature, Flow, and Electric Charge Fields during Electrohydrodynamic Natural Convection

by Mohamed Issam Elkhazen, Dalila Akrour, Walid Hassen, Mohammed A. Almeshaal, Murugesan Palaniappan, Karim Choubani and Nidhal Hnaien

Symmetry 2024, 16(6), 761; https://doi.org/10.3390/sym16060761 - 18 Jun 2024

Viewed by 3464

Abstract

This study explores the impact of an adiabatic obstacle on the symmetry of temperature, flow, and electric charge fields during electrohydrodynamic (EHD) natural convection. The configuration studied involves a square, differentially heated cavity with an adiabatic obstacle subjected to a destabilizing thermal gradient [...] Read more.

This study explores the impact of an adiabatic obstacle on the symmetry of temperature, flow, and electric charge fields during electrohydrodynamic (EHD) natural convection. The configuration studied involves a square, differentially heated cavity with an adiabatic obstacle subjected to a destabilizing thermal gradient and a potential difference between horizontal walls. A numerical analysis was performed using the finite volume method combined with Patankar’s “blocked-off-regions” technique, employing an in-house FORTRAN code. The study covers a range of dimensionless electrical Rayleigh numbers (0 to 700) and thermal Rayleigh numbers (10² to 10⁵), with various obstacle positions. Key findings indicate that while the obstacle reduces heat transfer, this can be counterbalanced by electric field effects, achieving up to 165% local heat transfer improvement and 100% average enhancement. Depending on the obstacle’s position and size, convective transfer can increase by 27% or decrease by 21%. The study introduces five multiparametric mathematical correlations for rapid Nusselt number determination, applicable to numerous engineering scenarios. This work uniquely combines passive (adiabatic obstacle) and active (electric field) techniques to control heat transfer, providing new insights into the flow behaviour and charge distribution in electro-thermo-hydrodynamic systems. Full article

(This article belongs to the Special Issue Symmetry in Thermal Fluid Sciences and Energy Applications)

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10 pages, 329 KiB

Open AccessArticle

Invariant Subspaces of Short Pulse-Type Equations and Reductions

by Guo-Hua Wang, Jia-Fu Pang, Yong-Yang Jin and Bo Ren

Symmetry 2024, 16(6), 760; https://doi.org/10.3390/sym16060760 - 18 Jun 2024

Viewed by 849

Abstract

In this paper, we extend the invariant subspace method to a class of short pulse-type equations. Complete classification results with invariant subspaces from 2 to 5 dimensions are provided. The key step is to take subspaces of solutions of linear ordinary differential equations [...] Read more.

In this paper, we extend the invariant subspace method to a class of short pulse-type equations. Complete classification results with invariant subspaces from 2 to 5 dimensions are provided. The key step is to take subspaces of solutions of linear ordinary differential equations as invariant subspaces that nonlinear operators admit. Some concrete examples and corresponding reduced systems are presented to illustrate this method. Full article

(This article belongs to the Section Mathematics)

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1 pages, 129 KiB

Open AccessCorrection

Correction: Lin, G.; Huang, H. The Dynamical and Kinetic Equations of Four-Five-Six-Wave Resonance for Ocean Surface Gravity Waves in Water with a Finite Depth. Symmetry 2024, 16, 618

by Guobin Lin and Hu Huang

Symmetry 2024, 16(6), 759; https://doi.org/10.3390/sym16060759 - 18 Jun 2024

Viewed by 414

Abstract

Addition of an author and his email [...] Full article

39 pages, 8597 KiB

Open AccessArticle

Multilevel Algorithm for Large-Scale Gravity Inversion

by Shujin Cao, Peng Chen, Guangyin Lu, Yajing Mao, Dongxin Zhang, Yihuai Deng and Xinyue Chen

Symmetry 2024, 16(6), 758; https://doi.org/10.3390/sym16060758 - 17 Jun 2024

Viewed by 1250

Abstract

Surface gravity inversion attempts to recover the density contrast distribution in the 3D Earth model for geological interpretation. Since airborne gravity is characterized by large data volumes, large-scale 3D inversion exceeds the capacity of desktop computing resources, making it difficult to achieve the [...] Read more.

Surface gravity inversion attempts to recover the density contrast distribution in the 3D Earth model for geological interpretation. Since airborne gravity is characterized by large data volumes, large-scale 3D inversion exceeds the capacity of desktop computing resources, making it difficult to achieve the appropriate depth/lateral resolution for geological interpretation. In addition, gravity data are finite and noisy, and their inversion is ill posed. Especially in the absence of a priori geological information, regularization must be introduced to overcome the difficulty of the non-uniqueness of the solutions to recover the most geologically plausible ones. Because the use of Haar wavelet operators has an edge-preserving property and can preserve the sensitivity matrix structure at each level of the multilevel method to obtain faster solvers, we present a multilevel algorithm for large-scale gravity inversion solved by the re-weighted regularized conjugate gradient (RRCG) algorithm to reduce the inversion computational resources and improve the depth/lateral resolution of the inversion results. The RRCG-based multilevel inversion was then applied to synthetic cases and airborne gravity data from the Quest-South project in British Columbia, Canada. Results from synthetic models and field data show that the RRCG-based multilevel inversion is suitable for obtaining density contrast distributions with appropriate horizontal and vertical resolution, especially for large-scale gravity inversions compared to Occam’s inversion. Full article

(This article belongs to the Special Issue Asymmetric and Symmetric Study on Algorithms Optimization)

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14 pages, 316 KiB

Open AccessArticle

Moment Problems and Integral Equations

by Cristian Octav Olteanu

Symmetry 2024, 16(6), 757; https://doi.org/10.3390/sym16060757 - 17 Jun 2024

Cited by 1 | Viewed by 1180

Abstract

The first part of this work provides explicit solutions for two integral equations; both are solved by means of Fourier transform. In the second part of this paper, sufficient conditions for the existence and uniqueness of the solutions satisfying sandwich constraints for two [...] Read more.

The first part of this work provides explicit solutions for two integral equations; both are solved by means of Fourier transform. In the second part of this paper, sufficient conditions for the existence and uniqueness of the solutions satisfying sandwich constraints for two types of full moment problems are provided. The only given data are the moments of all positive integer orders of the solution and two other linear, not necessarily positive, constraints on it. Under natural assumptions, all the linear solutions are continuous. With their value in the subspace of polynomials being given by the moment conditions, the uniqueness follows. When the involved linear solutions and constraints are positive, the sufficient conditions mentioned above are also necessary. This is achieved in the third part of the paper. All these conditions are written in terms of quadratic expressions. Full article

(This article belongs to the Special Issue Symmetry in Mathematical Analysis and Functional Analysis: 3rd Edition)

18 pages, 432 KiB

Open AccessArticle

Fixed Point Method for Nonlinear Fractional Differential Equations with Integral Boundary Conditions on Tetramethyl-Butane Graph

by Juan J. Nieto, Ashish Yadav, Trilok Mathur and Shivi Agarwal

Symmetry 2024, 16(6), 756; https://doi.org/10.3390/sym16060756 - 17 Jun 2024

Cited by 2 | Viewed by 948

Abstract

Until now, little investigation has been done to examine the existence and uniqueness of solutions for fractional differential equations on star graphs. In the published articles on the subject, the authors used a star graph with one junction node that has edges with [...] Read more.

Until now, little investigation has been done to examine the existence and uniqueness of solutions for fractional differential equations on star graphs. In the published articles on the subject, the authors used a star graph with one junction node that has edges with the other nodes, although there are no edges between them. These graph structures do not cover more generic non-star graph structures; they are specific examples. The purpose of this study is to prove the existence and uniqueness of solutions to a new family of fractional boundary value problems on the tetramethylbutane graph that have more than one junction node after presenting a labeling mechanism for graph vertices. The chemical compound tetramethylbutane has a highly symmetrical structure, due to which it has a very high melting point and a short liquid range; in fact, it is the smallest saturated acyclic hydrocarbon that appears as a solid at a room temperature of 25 °C. With vertices designated by 0 or 1, we propose a fractional-order differential equation on each edge of tetramethylbutane graph. Employing the fixed-point theorems of Schaefer and Banach, we demonstrate the existence and uniqueness of solutions for the suggested fractional differential equation satisfying the integral boundary conditions. In addition, we examine the stability of the system. Lastly, we present examples that illustrate our findings. Full article

(This article belongs to the Special Issue Fixed Point Theory and Its Applications Dedicated to the Memory of Professor William Arthur Kirk)

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21 pages, 2209 KiB

Open AccessArticle

New Parametric 2D Curves for Modeling Prostate Shape in Magnetic Resonance Images

by Rosario Corso, Albert Comelli, Giuseppe Salvaggio and Domenico Tegolo

Symmetry 2024, 16(6), 755; https://doi.org/10.3390/sym16060755 - 17 Jun 2024

Viewed by 1588

Abstract

Geometric shape models often help to extract specific contours in digital images (the segmentation process) with major precision. Motivated by this idea, we introduce two models for the representation of prostate shape in the axial plane of magnetic resonance images. In more detail, [...] Read more.

Geometric shape models often help to extract specific contours in digital images (the segmentation process) with major precision. Motivated by this idea, we introduce two models for the representation of prostate shape in the axial plane of magnetic resonance images. In more detail, the models are two parametric closed curves of the plane. The analytic study of the models includes the geometric role of the parameters describing the curves, symmetries, invariants, special cases, elliptic Fourier descriptors, conditions for simple curves and area of the enclosed surfaces. The models were validated for prostate shapes by fitting the curves to prostate contours delineated by a radiologist and measuring the errors with the mean distance, the Hausdorff distance and the Dice similarity coefficient. Validation was also conducted by comparing our models with the deformed superellipse model used in literature. Our models are equivalent in fitting metrics to the deformed superellipse model; however, they have the advantage of a more straightforward formulation and they depend on fewer parameters, implying a reduced computational time for the fitting process. Due to the validation, our models may be applied for developing innovative and performing segmentation methods or improving existing ones. Full article

(This article belongs to the Special Issue Feature Papers in Mathematics Section)

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17 pages, 10981 KiB

Open AccessArticle

Community-Detection Method of Complex Network Based on Node Influence Analysis

by Jiaqi Yao and Bin Liu

Symmetry 2024, 16(6), 754; https://doi.org/10.3390/sym16060754 - 17 Jun 2024

Viewed by 1216

Abstract

Community detection can help analyze the structural features and functions of complex networks, and plays important roles in many aspects such as project recommendation and network evolution analysis. Therefore, community detection has always been a hot topic in the field of complex networks. [...] Read more.

Community detection can help analyze the structural features and functions of complex networks, and plays important roles in many aspects such as project recommendation and network evolution analysis. Therefore, community detection has always been a hot topic in the field of complex networks. Although various community-detection methods have been proposed, how to improve their accuracy and efficiency is still an ambition pursued by researchers. In view of this, this paper proposes a community-detection method for complex networks based on node influence analysis. First, the influence of nodes is represented as a vector composed by neighborhood degree centrality, betweennes centrality and clustering coefficient. Then, Pareto dominance is used to rank the influence of nodes. After that, the community centers are selected by comprehensively considering the node influence and crowding degree. Finally, the remaining nodes are allocated to different communities using a labeling algorithm. The proposed method in this paper is applied to several actual networks. The comparison results with other methods demonstrate the effectiveness of the proposed method. Full article

(This article belongs to the Section Mathematics)

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14 pages, 3762 KiB

Open AccessArticle

Design and Optimization of a Mid-Field Wireless Power Transfer System for Enhanced Energy Transfer Efficiency

by Daud Khan, Ashfaq Ahmad and Dong-you Choi

Symmetry 2024, 16(6), 753; https://doi.org/10.3390/sym16060753 - 17 Jun 2024

Viewed by 1274

Abstract

Mid-field wireless power transfer (WPT) offers a compelling solution for delivering power to miniature implantable medical devices deep within the human body. Despite its potential, the current power delivery levels remain constrained, and the design of a compact source structure to focus the [...] Read more.

Mid-field wireless power transfer (WPT) offers a compelling solution for delivering power to miniature implantable medical devices deep within the human body. Despite its potential, the current power delivery levels remain constrained, and the design of a compact source structure to focus the transmitter field on such implants presents significant challenges. In this paper, a novel miniaturized transmitter antenna operating at 1.71 GHz is proposed. Leveraging the antenna proximity-coupled feeding technique, we achieve optimal current distribution for efficient power transfer. Additionally, a receiver integrated within the human body is proposed, comprising a slotted ground and a meandering slotted radiating element. This receiver is excited via a coaxial feedline with a truncated ground. Our findings demonstrate wireless power transfer of −23 dB (0.501%) at a distance of 30 mm between the transmitter and receiver, alongside a peak gain of −20 dB with an impedance bandwidth of 39.61%. These results highlight promising advancements in enhancing energy transfer efficiency for deep-implant applications. Full article

(This article belongs to the Special Issue Symmetric/Asymmetric Design in Microwave Communication Systems & Embedded Systems for Emerging Wireless Technologies)

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22 pages, 796 KiB

Open AccessArticle

A Clustering Model for Three-Way Asymmetric Proximities: Unveiling Origins and Destinations

by Laura Bocci and Donatella Vicari

Symmetry 2024, 16(6), 752; https://doi.org/10.3390/sym16060752 - 16 Jun 2024

Viewed by 937

Abstract

In many real-world situations, the available data consist of a set of several asymmetric pairwise proximity matrices that collect directed exchanges between pairs of objects measured or observed in a number of occasions (three-way data). To unveil patterns of exchange, a clustering model [...] Read more.

In many real-world situations, the available data consist of a set of several asymmetric pairwise proximity matrices that collect directed exchanges between pairs of objects measured or observed in a number of occasions (three-way data). To unveil patterns of exchange, a clustering model is proposed that accounts for the systematic differences across occasions. Specifically, the goal is to identify the groups of objects that are primarily origins or destinations of the directed exchanges, and, together, to measure the extent to which these clusters differ across occasions. The model is based on two clustering structures for the objects, which are linked one-to-one and common to all occasions. The first structure assumes a standard partition of the objects to fit the average amounts of the exchanges, while the second one fits the imbalances using an “incomplete” partition of the objects, allowing some to remain unassigned. In addition, to account for the heterogeneity of the occasions, the amounts and directions of exchange between clusters are modeled by occasion-specific weights. An Alternating Least-Squares algorithm is provided. Results from artificial data and a real application on international student mobility show the capability of the model to identify origin and/or destination clusters with common behavior across occasions. Full article

(This article belongs to the Section Mathematics)

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26 pages, 1418 KiB

Open AccessArticle

A Novel Three-Parameter Nadarajah Haghighi Model: Entropy Measures, Inference, and Applications

by Etaf Alshawarbeh, Fatimah M. Alghamdi, Mohammed Amine Meraou, Hassan M. Aljohani, Mahmoud Abdelraouf, Fathy H. Riad, Sara Mohamed Ahmed Alsheikh and Meshayil M. Alsolmi

Symmetry 2024, 16(6), 751; https://doi.org/10.3390/sym16060751 - 16 Jun 2024

Cited by 1 | Viewed by 787

Abstract

The fitting and modeling of skewed, complex, symmetric, and asymmetric datasets is an exciting research topic in many fields of applied sciences: notably, lifetime, medical, and financial sciences. This paper introduces a heavy-tailed Nadarajah Haghighi model by compounding the heavy-tailed family and Nadarajah [...] Read more.

The fitting and modeling of skewed, complex, symmetric, and asymmetric datasets is an exciting research topic in many fields of applied sciences: notably, lifetime, medical, and financial sciences. This paper introduces a heavy-tailed Nadarajah Haghighi model by compounding the heavy-tailed family and Nadarajah Haghighi distribution. The model obtained has three parameters that account for the scale and shape of the distribution. The proposed distribution’s fundamental characteristics, such as the probability density, cumulative distribution, hazard rate, and survival functions, are provided, several key statistical properties are established, and several entropy information measures are proposed. Estimation of model parameters is performed via a maximum likelihood estimator procedure. Further, different simulation experiments are conducted to demonstrate the proposed estimator’s performance using measures like the average estimate, the average bias, and the associated mean square error. Finally, we apply our proposed model to analyze three different real datasets. In our illustration, we compare the practicality of the recommended model with several well-known competing models. Full article

(This article belongs to the Special Issue Symmetric or Asymmetric Distributions and Its Applications)

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15 pages, 4988 KiB

Open AccessArticle

Symmetrical Modeling of Physical Properties of Flexible Structure of Silicone Materials for Control of Pneumatic Soft Actuators

by Eduard Muratbakeev, Yuriy Kozhubaev, Yao Yiming and Shehzad Umar

Symmetry 2024, 16(6), 750; https://doi.org/10.3390/sym16060750 - 16 Jun 2024

Viewed by 1186

Abstract

With the ongoing advancements in material technology, the domain of soft robotics has garnered increasing attention. Soft robots, in contrast to their rigid counterparts, offer superior adaptability to the environment, enhanced flexibility, and improved safety, rendering them highly suitable for complex application scenarios [...] Read more.

With the ongoing advancements in material technology, the domain of soft robotics has garnered increasing attention. Soft robots, in contrast to their rigid counterparts, offer superior adaptability to the environment, enhanced flexibility, and improved safety, rendering them highly suitable for complex application scenarios such as rescue operations and medical interventions. In this paper, a new type of pneumatic software actuator is proposed. The actuator adopts a combination of a soft structure and pneumatic control, which is highly flexible and versatile. By using the flow of gas inside the soft structure, high-precision and flexible motion control is realized. In the design process, the extensibility and adaptability of the structure are considered, so that the actuator can adapt to different working environments and task requirements. The experimental results show that the pneumatic soft actuator exhibits excellent performance in terms of accuracy, response speed, and controllability. This research provides new ideas and methods for the development of the field of pneumatic actuators and has wide application prospects. The main research content of this paper is as follows: first, the soft pneumatic actuator is modeled and simulated, the structure is optimized on the basis of simulation, and finally, the performance of the actuator is tested. Full article

(This article belongs to the Special Issue Advanced Materials, Structures, Symmetrical Design and Mechanism in Mechanical Engineering)

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46 pages, 10310 KiB

Open AccessArticle

An Intelligent Connected Vehicle Material Distribution Route Model Based on k-Center Spatial Cellular Clustering and an Improved Cockroach Optimization Algorithm

by Xiao Zhou, Jun Wang, Wenbing Liu, Juan Pan, Taiping Zhao, Fan Jiang and Rui Li

Symmetry 2024, 16(6), 749; https://doi.org/10.3390/sym16060749 - 15 Jun 2024

Viewed by 913

Abstract

Based on the analysis of the problems in material distribution routes, we propose the idea of integrating the intelligent connected vehicle system with material distribution, and construct an intelligent connected vehicle material distribution route model based on k-center spatial cellular clustering and [...] Read more.

Based on the analysis of the problems in material distribution routes, we propose the idea of integrating the intelligent connected vehicle system with material distribution, and construct an intelligent connected vehicle material distribution route model based on k-center spatial cellular clustering and an improved cockroach optimization algorithm. Firstly, we set the research scope to include the distribution center, the distribution points and the geographical environment. A cellular spatial model of distribution points is constructed to quantify and visualize the neighborhood relationship between the distribution centers and distribution points. On this basis, we construct an intelligent connected vehicle material distribution route model based on the improved cockroach optimization algorithm, and the optimal material distribution center is determined by searching for the corresponding optimal distribution route of each distribution center. In the experiment, we use the concept of symmetry to design routes that start from the initial points. The route passes through the distribution point, and finally reaches the destination. In this mode, the experiment generates symmetrically round-trip routes and generates different distribution time schedules. Case studies and comparative experiments show that the proposed algorithm has a total distance cost 1.2 km lower than the distance cost generated by the Baidu Map method and 2.7 km lower than the distance cost generated by the 360 Map method. In terms of the total time cost of the proposed algorithm, it is 0.06 h lower than the time cost generated by the Baidu Map method and 0.135 h lower than the time cost generated by the 360 Map method. Compared with the commonly used Dijkstra algorithm and the A* algorithm for route optimization, our proposed algorithm also generates a lower cost than the two other types of optimization algorithms. In the case study, the distance generated by the proposed algorithm is 1.8 km lower than that of the Dijkstra algorithm, and the total time cost is 0.09 h lower than that of the Dijkstra algorithm. The distance generated by the proposed algorithm is 1.6 km lower than that of the A* algorithm, and the total time cost is 0.08 h lower than that of the A* algorithm. Meanwhile, the proposed algorithm has a lower time complexity than the two commonly used optimization algorithms. Therefore, our proposed algorithm can find the distribution route with the lowest transportation cost. Compared to the commonly used electronic maps and the optimization algorithms for distribution route planning, our proposed algorithm can output distribution routes with lower costs under the same distribution sequence, and reduce the transportation costs for intelligent connected vehicle material distribution systems to the maximum extent. Full article

(This article belongs to the Special Issue Symmetry in Computing Algorithms and Applications)

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Symmetry, Volume 16, Issue 6 (June 2024) – 143 articles

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