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Symmetry, Volume 16, Issue 6 (June 2024) – 131 articles

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25 pages, 8482 KiB  
Article
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 (registering DOI) - 18 Jun 2024
Viewed by 51
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)
23 pages, 2637 KiB  
Article
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 (registering DOI) - 18 Jun 2024
Viewed by 54
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
23 pages, 1001 KiB  
Article
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 (registering DOI) - 18 Jun 2024
Viewed by 71
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(n2) 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(n2) 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(nlogn) 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  
Review
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
Viewed by 76
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, rreHta, where H is the Hubble parameter. For H0, this symmetry corresponds to the conventional invariance of Minkowski spacetime under translations rra. 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, Shor=4πKA, where K=1/(16πG). 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=df/dR. 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  
Article
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 112
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  
Article
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 106
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  
Article
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 126
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  
Correction
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 62
Abstract
Addition of an author and his email [...] Full article
39 pages, 8597 KiB  
Article
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 265
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  
Article
Moment Problems and Integral Equations
by Cristian Octav Olteanu
Symmetry 2024, 16(6), 757; https://doi.org/10.3390/sym16060757 - 17 Jun 2024
Viewed by 226
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 III)
18 pages, 432 KiB  
Article
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
Viewed by 194
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
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21 pages, 2209 KiB  
Article
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 220
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  
Article
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 247
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  
Article
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 220
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
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22 pages, 809 KiB  
Article
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 216
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)
26 pages, 1410 KiB  
Article
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
Viewed by 183
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)
15 pages, 4988 KiB  
Article
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 348
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
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46 pages, 6469 KiB  
Article
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 226
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)
13 pages, 241 KiB  
Article
An Efficient Solution of Multiplicative Differential Equations through Laguerre Polynomials
by Hatice Yalman Kosunalp, Selcuk Bas and Selahattin Kosunalp
Symmetry 2024, 16(6), 748; https://doi.org/10.3390/sym16060748 - 15 Jun 2024
Viewed by 150
Abstract
The field of multiplicative analysis has recently garnered significant attention, particularly in the context of solving multiplicative differential equations (MDEs). The symmetry concept in MDEs facilitates the determination of invariant solutions and the reduction of these equations by leveraging their intrinsic symmetrical properties. [...] Read more.
The field of multiplicative analysis has recently garnered significant attention, particularly in the context of solving multiplicative differential equations (MDEs). The symmetry concept in MDEs facilitates the determination of invariant solutions and the reduction of these equations by leveraging their intrinsic symmetrical properties. This study is motivated by the need for efficient methods to address MDEs, which are critical in various applications. Our novel contribution involves leveraging the fundamental properties of orthogonal polynomials, specifically Laguerre polynomials, to derive new solutions for MDEs. We introduce the definitions of Laguerre multiplicative differential equations and multiplicative Laguerre polynomials. By applying the power series method, we construct these multiplicative Laguerre polynomials and rigorously prove their basic properties. The effectiveness of our proposed solution is validated through illustrative examples, demonstrating its practical applicability and potential for advancing the field of multiplicative analysis. Full article
(This article belongs to the Special Issue Computational Mathematics and Its Applications in Numerical Analysis)
17 pages, 2049 KiB  
Article
Lump, Breather, Ma-Breather, Kuznetsov–Ma-Breather, Periodic Cross-Kink and Multi-Waves Soliton Solutions for Benney–Luke Equation
by Miguel Vivas-Cortez, Sajawal Abbas Baloch, Muhammad Abbas, Moataz Alosaimi and Guo Wei
Symmetry 2024, 16(6), 747; https://doi.org/10.3390/sym16060747 - 15 Jun 2024
Viewed by 155
Abstract
The goal of this research is to utilize some ansatz forms of solutions to obtain novel forms of soliton solutions for the Benney–Luke equation. It is a mathematically valid approximation that describes the propagation of two-way water waves in the presence of surface [...] Read more.
The goal of this research is to utilize some ansatz forms of solutions to obtain novel forms of soliton solutions for the Benney–Luke equation. It is a mathematically valid approximation that describes the propagation of two-way water waves in the presence of surface tension. By using ansatz forms of solutions, with an appropriate set of parameters, the lump soliton, periodic cross-kink waves, multi-waves, breather waves, Ma-breather, Kuznetsov–Ma-breather, periodic waves and rogue waves solutions can be obtained. Breather waves are confined, periodic, nonlinear wave solutions that preserve their amplitude and shape despite alternating between compression and expansion. For some integrable nonlinear partial differential equations, a lump soliton is a confined, stable solitary wave solution. Rogue waves are unusually powerful and sharp ocean surface waves that deviate significantly from the surrounding wave pattern. They pose a threat to maritime safety. They typically show up in solitary, seemingly random circumstances. Periodic cross-kink waves are a particular type of wave pattern that has frequent bends or oscillations that cross at right angles. These waves provide insights into complicated wave dynamics and arise spontaneously in a variety of settings. In order to predict the wave dynamics, certain 2D, 3D and contour profiles are also analyzed. Since these recently discovered solutions contain certain arbitrary constants, they can be used to describe the variation in the qualitative characteristics of wave phenomena. Full article
(This article belongs to the Special Issue Symmetry in Nonlinear Partial Differential Equations and Rogue Waves)
13 pages, 269 KiB  
Article
Combinatorial Identities Concerning Binomial Quotients
by Yulei Chen and Dongwei Guo
Symmetry 2024, 16(6), 746; https://doi.org/10.3390/sym16060746 - 14 Jun 2024
Viewed by 167
Abstract
Making use of a telescoping approach, three types of sums of binomial quotients are examined. The summation terms of the two types of alternating sums have symmetry (i.e., their numerators and denominators are completely symmetric). We obtained a series of their explicit sums. [...] Read more.
Making use of a telescoping approach, three types of sums of binomial quotients are examined. The summation terms of the two types of alternating sums have symmetry (i.e., their numerators and denominators are completely symmetric). We obtained a series of their explicit sums. Furthermore, by means of binomial relations, three recurrence relations of the sums are derived. In addition, series of double summation formulae involving binomial quotients are established. Full article
(This article belongs to the Section Mathematics)
44 pages, 858 KiB  
Review
Isospin Symmetry Breaking in Atomic Nuclei
by Javid A. Sheikh, Syed P. Rouoof, Raja N. Ali, Niyaz Rather, Chandan Sarma and Praveen C. Srivastava
Symmetry 2024, 16(6), 745; https://doi.org/10.3390/sym16060745 - 14 Jun 2024
Viewed by 206
Abstract
In this paper, the importance of isospin symmetry and its breaking in elucidating the properties of atomic nuclei is reviewed. The quark mass splitting and the electromagnetic origin of the isospin symmetry breaking (ISB) for the nuclear many-body problem is discussed. The experimental [...] Read more.
In this paper, the importance of isospin symmetry and its breaking in elucidating the properties of atomic nuclei is reviewed. The quark mass splitting and the electromagnetic origin of the isospin symmetry breaking (ISB) for the nuclear many-body problem is discussed. The experimental data on isobaric analogue states cannot be described only with the Coulomb interaction, and ISB terms in the nucleon–nucleon interaction are needed to discern the observed properties. In the present work, the ISB terms are explicitly considered in nuclear energy density functional and spherical shell model approaches, and a detailed investigation of the analogue states and other properties of nuclei is performed. It is observed that isospin mixing is largest for the N = Z system in the density functional approach Full article
(This article belongs to the Special Issue Restoration of Broken Symmetries in the Nuclear Many-Body Problem)
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13 pages, 284 KiB  
Article
On Symmetries of Integrable Quadrilateral Equations
by Junwei Cheng, Jin Liu and Da-jun Zhang
Symmetry 2024, 16(6), 744; https://doi.org/10.3390/sym16060744 - 14 Jun 2024
Viewed by 165
Abstract
In the paper, we describe a method for deriving generalized symmetries for a generic discrete quadrilateral equation that allows a Lax pair. Its symmetry can be interpreted as a flow along the tangent direction of its solution evolving with a Lie group parameter [...] Read more.
In the paper, we describe a method for deriving generalized symmetries for a generic discrete quadrilateral equation that allows a Lax pair. Its symmetry can be interpreted as a flow along the tangent direction of its solution evolving with a Lie group parameter t. Starting from the spectral problem of the quadrilateral equation and assuming the eigenfunction evolves with the parameter t, one can obtain a differential-difference equation hierarchy, of which the flows are proved to be commuting symmetries of the quadrilateral equation. We prove this result by using the zero-curvature representations of these flows. As an example, we apply this method to derive symmetries for the lattice potential Korteweg–de Vries equation. Full article
(This article belongs to the Special Issue Symmetry in Integrable Systems: Topics and Advances)
20 pages, 540 KiB  
Article
Study on Neutrosophic Graph with Application on Earthquake Response Center in Japan
by Wadei Faris AL-Omeri and M. Kaviyarasu
Symmetry 2024, 16(6), 743; https://doi.org/10.3390/sym16060743 - 14 Jun 2024
Viewed by 313
Abstract
A mathematical method of combining several elements has emerged in recent times, providing a more comprehensive approach. Adhering to the foregoing mathematical methodology, we fuse two extremely potent methods, namely graph theory and neutrosophic sets, and present the concept of neutrosophic graphs ( [...] Read more.
A mathematical method of combining several elements has emerged in recent times, providing a more comprehensive approach. Adhering to the foregoing mathematical methodology, we fuse two extremely potent methods, namely graph theory and neutrosophic sets, and present the concept of neutrosophic graphs (G). Next, we outline many ideas, such as union, join, and composition of Gs, which facilitate the straightforward manipulation of Gs in decision-making scenarios. We provide a few scenarios to clarify these activities. The homomorphisms of Gs are also described. Lastly, understanding neutrosophic graphs and how Japan responds to earthquakes can help develop more resilient and adaptable disaster management plans, which can eventually save lives and lessen the effects of seismic disasters. With the support of using an absolute score function value, Hokkaido (H) and Saitama (SA) were the optimized locations. Because of its location in the Pacific Ring of Fire, Japan is vulnerable to regular earthquakes. As such, it is critical to customize reaction plans to the unique difficulties and features of Japan’s seismic activity. Examining neutrosophic graphs within the framework of earthquake response centers might offer valuable perspectives on tailoring and enhancing response tactics, particularly for Japan’s requirements. Full article
(This article belongs to the Section Mathematics)
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18 pages, 740 KiB  
Article
The Local Convergence of a Three-Step Sixth-Order Iterative Approach with the Basin of Attraction
by Kasmita Devi, Prashanth Maroju, Eulalia Martínez and Ramandeep Behl
Symmetry 2024, 16(6), 742; https://doi.org/10.3390/sym16060742 - 14 Jun 2024
Viewed by 229
Abstract
In this study, we introduce an iterative approach exhibiting sixth-order convergence for the solution of nonlinear equations. The method attains sixth-order convergence by using three evaluations of the function and two evaluations of the first-order derivative per iteration. We examined the theoretical convergence [...] Read more.
In this study, we introduce an iterative approach exhibiting sixth-order convergence for the solution of nonlinear equations. The method attains sixth-order convergence by using three evaluations of the function and two evaluations of the first-order derivative per iteration. We examined the theoretical convergence of our method through the convergence theorem, which substantiates the convergence order. Furthermore, we analyzed the local convergence of our proposed technique by employing a hypothesis that involves the first-order derivative of the function Θ alongside the Lipschitz conditions. To evaluate the performance and efficacy of our iterative method, we provide a comparative analysis against existing methods based on various standard numerical problems. Finally, graphical comparisons employing basins of attraction are presented to illustrate the dynamic behavior of the iterative method in the complex plane. Full article
(This article belongs to the Section Mathematics)
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23 pages, 10849 KiB  
Article
Study of Non-Smooth Symmetry Collision of Rolling Bodies of Localized Functional-Slot Cage-Less Ball Bearings Considering Lubrication Flow
by Jingwei Zhang, Yibo Wang, Linting Guan, Yuan Zhang and Shanping Yang
Symmetry 2024, 16(6), 741; https://doi.org/10.3390/sym16060741 - 14 Jun 2024
Viewed by 249
Abstract
This article presents a vibration model of neighboring rolling parts that takes into account non-smooth symmetric collisions. This model was used to examine the motion state of the rolling element and the collision force between nearby rolling elements. It also determined the motion [...] Read more.
This article presents a vibration model of neighboring rolling parts that takes into account non-smooth symmetric collisions. This model was used to examine the motion state of the rolling element and the collision force between nearby rolling elements. It also determined the motion posture and overall collision form of the rolling element after setting the functional slot. Afterwards, the level of disorderly movement and the structure of the moving object were examined and confirmed through the use of a phase diagram of the motion system in relation to zero symmetry, the Lyapunov exponent, and a platform for measuring irregular vibrations in the bearing. This work aims to clarify the factors that contribute to the persistent chaotic state of rolling elements in bearing vibration. Full article
(This article belongs to the Section Engineering and Materials)
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17 pages, 715 KiB  
Article
Dynamics of Symmetrical Discontinuous Hopfield Neural Networks with Poisson Stable Rates, Synaptic Connections and Unpredictable Inputs
by Marat Akhmet, Zakhira Nugayeva and Roza Seilova
Symmetry 2024, 16(6), 740; https://doi.org/10.3390/sym16060740 - 13 Jun 2024
Viewed by 155
Abstract
The purpose of this paper is to study the dynamics of Hopfield neural networks with impulsive effects, focusing on Poisson stable rates, synaptic connections, and unpredictable external inputs. Through the symmetry of impulsive and differential compartments of the model, we follow and extend [...] Read more.
The purpose of this paper is to study the dynamics of Hopfield neural networks with impulsive effects, focusing on Poisson stable rates, synaptic connections, and unpredictable external inputs. Through the symmetry of impulsive and differential compartments of the model, we follow and extend the principal dynamical ideas of the founder. Specifically, the research delves into the phenomena of unpredictability and Poisson stability, which have been examined in previous studies relating to models of continuous and discontinuous neural networks with constant components. We extend the analysis to discontinuous models characterized by variable impulsive actions and structural ingredients. The method of included intervals based on the B-topology is employed to investigate the networks. It is a novel approach that addresses the unique challenges posed by the sophisticated recurrence. Full article
(This article belongs to the Special Issue Application of Symmetry in Equations)
17 pages, 482 KiB  
Article
A Unified Approach and Related Fixed-Point Theorems for Suzuki Contractions
by Kastriot Zoto, Vesna Šešum-Čavić, Mirjana Pantović, Vesna Todorčević, Marsela Zoto and Stojan Radenović
Symmetry 2024, 16(6), 739; https://doi.org/10.3390/sym16060739 - 13 Jun 2024
Viewed by 176
Abstract
This paper aims to give an extended class of contractive mappings combining types of Suzuki contractions α-admissible mapping and Wardowski F-contractions in b-metric-like spaces. Our results cover and generalize many of the recent advanced results on the existence and uniqueness [...] Read more.
This paper aims to give an extended class of contractive mappings combining types of Suzuki contractions α-admissible mapping and Wardowski F-contractions in b-metric-like spaces. Our results cover and generalize many of the recent advanced results on the existence and uniqueness of fixed points and fulfill the Suzuki-type nonlinear hybrid contractions on various generalized metrics. Full article
(This article belongs to the Special Issue Symmetry in Metric Spaces and Topology)
19 pages, 787 KiB  
Article
Nonexpansiveness and Fractal Maps in Hilbert Spaces
by María A. Navascués
Symmetry 2024, 16(6), 738; https://doi.org/10.3390/sym16060738 - 13 Jun 2024
Viewed by 206
Abstract
Picard iteration is on the basis of a great number of numerical methods and applications of mathematics. However, it has been known since the 1950s that this method of fixed-point approximation may not converge in the case of nonexpansive mappings. In this paper, [...] Read more.
Picard iteration is on the basis of a great number of numerical methods and applications of mathematics. However, it has been known since the 1950s that this method of fixed-point approximation may not converge in the case of nonexpansive mappings. In this paper, an extension of the concept of nonexpansiveness is presented in the first place. Unlike the classical case, the new maps may be discontinuous, adding an element of generality to the model. Some properties of the set of fixed points of the new maps are studied. Afterwards, two iterative methods of fixed-point approximation are analyzed, in the frameworks of b-metric and Hilbert spaces. In the latter case, it is proved that the symmetrically averaged iterative procedures perform well in the sense of convergence with the least number of operations at each step. As an application, the second part of the article is devoted to the study of fractal mappings on Hilbert spaces defined by means of nonexpansive operators. The paper considers fractal mappings coming from φ-contractions as well. In particular, the new operators are useful for the definition of an extension of the concept of α-fractal function, enlarging its scope to more abstract spaces and procedures. The fractal maps studied here have quasi-symmetry, in the sense that their graphs are composed of transformed copies of itself. Full article
(This article belongs to the Special Issue Symmetry in Geometric Theory of Analytic Functions)
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20 pages, 280 KiB  
Article
On the Inverse of the Linearization Coefficients of Bessel Polynomials
by Mohamed Jalel Atia
Symmetry 2024, 16(6), 737; https://doi.org/10.3390/sym16060737 - 13 Jun 2024
Viewed by 225
Abstract
In this contribution, we first present a new recursion relation fulfilled by the linearization coefficients of Bessel polynomials (LCBPs), which is different than the one presented by Berg and Vignat in 2008. We will explain why this new recursion formula is as important [...] Read more.
In this contribution, we first present a new recursion relation fulfilled by the linearization coefficients of Bessel polynomials (LCBPs), which is different than the one presented by Berg and Vignat in 2008. We will explain why this new recursion formula is as important as Berg and Vignat’s. We introduce the matrix linearization coefficients of Bessel polynomials (MLCBPs), and we present some new results and some conjectures on these matrices. Second, we present the inverse of the connection coefficients with an application involving the modified Bessel function of the second kind. Finally, we introduce the inverse of the matrix of the linearization coefficients of the Bessel polynomials (IMLCBPs), and we present some open problems related to these IMLCBPs. Full article
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