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Symmetry
Volume 16
Issue 6
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Symmetry, Volume 16, Issue 6 (June 2024) – 50 articles

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18 pages, 508 KiB  
Article
New Order 2.0 Simplified Weak Itô–Taylor Symmetrical Scheme for Stochastic Delay Differential Equations
by Yang Li, Qianhai Xu, Yifei Xin and Yu Zhang
Symmetry 2024, 16(6), 685; https://doi.org/10.3390/sym16060685 (registering DOI) - 3 Jun 2024
Abstract
In this article, we construct a new order 2.0 simplified weak Itô–Taylor symmetrical scheme for stochastic delay differential equations. By the new local weak convergence lemma and the connection inequality, we theoretically prove the global weak convergence theorem in two parts on the [...] Read more.
In this article, we construct a new order 2.0 simplified weak Itô–Taylor symmetrical scheme for stochastic delay differential equations. By the new local weak convergence lemma and the connection inequality, we theoretically prove the global weak convergence theorem in two parts on the basis of Malliavin stochastic analysis. Meanwhile, numerical examples are presented to illustrate the error and convergence results. Furthermore, the obtained results display the influence of the delay coefficient on global errors. Full article
(This article belongs to the Section Mathematics)
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36 pages, 1038 KiB  
Article
Design Procedure for Real-Time Cyber–Physical Systems Tolerant to Cyberattacks
by Carlos M. Paredes, Diego Martínez Castro, Apolinar González Potes, Andrés Rey Piedrahita and Vrani Ibarra Junquera
Symmetry 2024, 16(6), 684; https://doi.org/10.3390/sym16060684 (registering DOI) - 3 Jun 2024
Abstract
Modern industrial automation supported by Cyber–Physical Systems (CPSs) requires high flexibility, which is achieved through increased interconnection between modules. This interconnection introduces a layer of symmetry into the design and operation of CPSs, balancing the distribution of tasks and resources across the system [...] Read more.
Modern industrial automation supported by Cyber–Physical Systems (CPSs) requires high flexibility, which is achieved through increased interconnection between modules. This interconnection introduces a layer of symmetry into the design and operation of CPSs, balancing the distribution of tasks and resources across the system and streamlining the flow of information. However, this adaptability also exposes control systems to security threats, particularly through novel communication links that are vulnerable to cyberattacks. Traditional strategies may have limitations in these applications. This research proposes a design approach for control applications supported by CPSs that incorporates cyberattack detection and tolerance strategies. Using a modular and adaptive approach, the system is partitioned into microservices for scalability and resilience, allowing structural symmetry to be maintained. Schedulability assessments ensure that critical timing constraints are met, improving overall system symmetry and performance. Advanced cyberattack detection and isolation systems generate alarms and facilitate rapid response with replicas of affected components. These replicas enable the system to recover from and tolerate cyberattacks, maintaining uninterrupted operation and preserving the balanced structure of the system. In conclusion, the proposed approach addresses the security challenges in CPS-based control applications and provides an integrated and robust approach to protect industrial automation systems from cyber threats. A case study conducted at a juice production facility in Colima, México, demonstrated how the architecture can be applied to complex processes such as pH control, from simulation to industrial implementation. The study highlighted a plug-and-play approach, starting with component definitions and relationships, and extending to technology integration, thereby reinforcing symmetry and efficiency within the system. Full article
(This article belongs to the Special Issue Symmetry Application in the Control Design of Cyber-Physical Systems)
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14 pages, 10703 KiB  
Article
Symmetry-Enhanced Fuzzy Logic Analysis in Parallel and Cross-Road Scenarios: Optimizing Direction and Distance Weights for Map Matching
by Weicheng Zhou, Huilin Ge and Muhammad Awais Ashraf
Symmetry 2024, 16(6), 683; https://doi.org/10.3390/sym16060683 (registering DOI) - 3 Jun 2024
Abstract
This study addresses the challenges of setting segmentation points in the membership function and determining appropriate weights for different types of information within a fuzzy logic algorithm for map matching. We use linear fitting to derive an empirical formula for setting segmentation points [...] Read more.
This study addresses the challenges of setting segmentation points in the membership function and determining appropriate weights for different types of information within a fuzzy logic algorithm for map matching. We use linear fitting to derive an empirical formula for setting segmentation points for the information membership function. Furthermore, we evaluate the effects of various weights for direction and distance information in parallel and cross-road scenarios. The research identified the optimal distance that achieves the highest matching accuracy and provided insights into how the weights of connection, direction, and distance information affect this accuracy. The simulations confirmed the critical importance of precise segmentation point settings and weight determinations in enhancing the accuracy of fuzzy logic algorithms for map matching. The results underscore the potency of our tailored parameter-setting strategy and contribute to knowledge of symmetry, offering practical insights for implementing fuzzy logic in map matching with a particular emphasis on the principle of symmetry in algorithm design and information processing. 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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15 pages, 4062 KiB  
Article
Hypergolic Ignition by Off-Center Binary Collision of Monoethanolamine-NaBH4 and Hydrogen Peroxide Droplets
by Dawei Zhang, Siduo Song, Dehai Yu, Yueming Yuan, Hongmei Liu, Xuedong Liu and Xuejun Fan
Symmetry 2024, 16(6), 682; https://doi.org/10.3390/sym16060682 (registering DOI) - 2 Jun 2024
Abstract
Hypergolic ignition of H2O2 and MEA-NaBH4 by off-center collision of their droplets was experimentally studied, focusing on the characteristics and mechanism of droplet mixing, droplet heating and evaporation, and gas-phase ignition. The whole collision ignition process was divided into [...] Read more.
Hypergolic ignition of H2O2 and MEA-NaBH4 by off-center collision of their droplets was experimentally studied, focusing on the characteristics and mechanism of droplet mixing, droplet heating and evaporation, and gas-phase ignition. The whole collision ignition process was divided into five stages, which were compared, respectively, with that of head-on collision. Under the condition of a slightly off-center collision (for cases where B < 0.35), H2O2 droplets penetrate MEA-NaBH4 droplets after the collision and coalesce with it, but the internal H2O2 drop inside the MEA-NaBH4 droplet does not form a stable sphere. Instead, it rotates and expands inside the mixed droplet. With B increasing to 0.59, the droplets no longer coalesce after collision but separate away, forming satellite droplets. In such cases, multi-ignition mode is observed. When B increases to a certain extent, specifically, 0.85, a grazing collision is observed such that no mass transfer exists during the interaction of droplets, which leads to ignition failure. A theoretical model quantifying droplet swelling rate was established to calculate the volume change of the droplet. It was found that the swelling can be attributed to the flash boiling of superheated internal H2O2 fluid. Meanwhile, the ignition delay time was found to linearly decrease with B at various Wes until the extent where the chemical reaction takes over control, leading to an almost constant time delay defined as RDT. Additionally, the regime of ignition modes corresponding to different droplet mixing features is summarized in the We-B parametric space. Full article
(This article belongs to the Special Issue Symmetry in Aerospace Sciences and Applications)
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25 pages, 719 KiB  
Review
Handwritten Recognition Techniques: A Comprehensive Review
by Husam Ahmad Alhamad, Mohammad Shehab, Mohd Khaled Y. Shambour, Muhannad A. Abu-Hashem, Ala Abuthawabeh, Hussain Al-Aqrabi, Mohammad Sh. Daoud and Fatima B. Shannaq
Symmetry 2024, 16(6), 681; https://doi.org/10.3390/sym16060681 (registering DOI) - 2 Jun 2024
Abstract
Given the prevalence of handwritten documents in human interactions, optical character recognition (OCR) for documents holds immense practical value. OCR is a field that empowers the translation of various document types and images into data that can be analyzed, edited, and searched. In [...] Read more.
Given the prevalence of handwritten documents in human interactions, optical character recognition (OCR) for documents holds immense practical value. OCR is a field that empowers the translation of various document types and images into data that can be analyzed, edited, and searched. In handwritten recognition techniques, symmetry can be crucial to improving accuracy. It can be used as a preprocessing step to normalize the input data, making it easier for the recognition algorithm to identify and classify characters accurately. This review paper aims to summarize the research conducted on character recognition for handwritten documents and offer insights into future research directions. Within this review, the research articles focused on handwritten OCR were gathered, synthesized, and examined, along with closely related topics, published between 2019 and the first quarter of 2024. Well-established electronic databases and a predefined review protocol were utilized for article selection. The articles were identified through keyword, forward, and backward reference searches to comprehensively cover all relevant literature. Following a rigorous selection process, 116 articles were included in this systematic literature review. This review article presents cutting-edge achievements and techniques in OCR and underscores areas where further research is needed. Full article
(This article belongs to the Section Computer)
23 pages, 1777 KiB  
Article
Effective Video Summarization Using Channel Attention-Assisted Encoder–Decoder Framework
by Faisal Alharbi, Shabana Habib, Waleed Albattah, Zahoor Jan, Meshari D. Alanazi and Muhammad Islam
Symmetry 2024, 16(6), 680; https://doi.org/10.3390/sym16060680 (registering DOI) - 1 Jun 2024
Abstract
A significant number of cameras regularly generate massive amounts of data, demanding hardware, time, and labor resources to acquire, process, and monitor. Asymmetric frames within videos pose a challenge to automatic summarization of videos, making it challenging to capture key content. Developments in [...] Read more.
A significant number of cameras regularly generate massive amounts of data, demanding hardware, time, and labor resources to acquire, process, and monitor. Asymmetric frames within videos pose a challenge to automatic summarization of videos, making it challenging to capture key content. Developments in computer vision have accelerated the seamless capture and analysis of high-resolution video content. Video summarization (VS) has garnered considerable interest due to its ability to provide concise summaries of lengthy videos. The current literature mainly relies on a reduced set of representative features implemented using shallow sequential networks. Therefore, this work utilizes an optimal feature-assisted visual intelligence framework for representative feature selection and summarization. Initially, the empirical analysis of several features is performed, and ultimately, we adopt a fine-tuning InceptionV3 backbone for feature extraction, deviating from conventional approaches. Secondly, our strategic encoder–decoder module captures complex relationships with five convolutional blocks and two convolution transpose blocks. Thirdly, we introduced a channel attention mechanism, illuminating interrelations between channels and prioritizing essential patterns to grasp complex refinement features for final summary generation. Additionally, comprehensive experiments and ablation studies validate our framework's exceptional performance, consistently surpassing state-of-the-art networks on two benchmarks (TVSum and SumMe) datasets. Full article
(This article belongs to the Special Issue New Trends in Symmetry/Asymmetry of Image Processing and Computer Vision)
25 pages, 1974 KiB  
Article
Power Transformer On-Load Capacity-Regulating Control and Optimization Based on Load Forecasting and Hesitant Fuzzy Control
by Dexu Zou, Xinyu Sun, Hao Quan, Jianhua Yin, Qingjun Peng, Shan Wang, Weiju Dai and Zhihu Hong
Symmetry 2024, 16(6), 679; https://doi.org/10.3390/sym16060679 (registering DOI) - 1 Jun 2024
Abstract
The operational stability of a power transformer exerts an extremely important impact on the power symmetry, balance, and security of power systems. When the grid load fluctuates greatly, if the load factor of the transformer cannot be maintained within a reasonable range, it [...] Read more.
The operational stability of a power transformer exerts an extremely important impact on the power symmetry, balance, and security of power systems. When the grid load fluctuates greatly, if the load factor of the transformer cannot be maintained within a reasonable range, it leads to increased instability in grid operation. Adjusting the transformer capacity based on load changes is of great significance. The existing control methods for on-load capacity-regulating (OLCR) transformers have low timeliness, and the daily switching frequency of the capacity-regulating switch is not controlled. To ensure the safe and stable operation of transformers, this paper proposes a control method for OLCR transformers based on load prediction and fuzzy control. Firstly, the operating principle of OLCR transformers is analyzed, and a multi-strategy enhanced dung beetle optimizer (MSDBO) combined with a CNN−LSTM model is proposed for load forecasting. On this basis, the daily switching frequency of the capacity-regulating transformer is introduced, and hesitant fuzzy control is used to select the optimal capacity-regulating strategy relying on three factors: loss, economy, and switching frequency. Finally, simulation models are constructed using the MATLAB/SIMULINK platform and simulation analysis is conducted to verify the effectiveness and superiority of the proposed control method. For the three scenarios in this paper, the method reduces daily power loss by 28.5% to 56.3% and daily operating costs by 25.4% to 50.8%. The method used in this paper can sacrifice 3.5% to 9.2% of the loss reduction capability in exchange for reducing the number of switch operations by 28.6% to 57.1%, significantly extending the lifespan of the switches and thereby increasing the operational lifespan of the transformer. Full article
(This article belongs to the Special Issue Symmetry/Asymmetry Studies in Modern Power Systems)
8 pages, 237 KiB  
Article
Solving Second-Order Homogeneous Linear Differential Equations in Terms of the Tri-Confluent Heun’s Function
by Shayea Aldossari
Symmetry 2024, 16(6), 678; https://doi.org/10.3390/sym16060678 (registering DOI) - 31 May 2024
Abstract
In this paper, we state an algorithm that checks whether a given second-order linear differential equation can be reduced to the tri-confluent Heun’s equation. The algorithm provides a method for finding solutions of the form [...] Read more.
In this paper, we state an algorithm that checks whether a given second-order linear differential equation can be reduced to the tri-confluent Heun’s equation. The algorithm provides a method for finding solutions of the form exp(∫r(x)dx)·HeunT(q,α,γ,δ,ϵ,f(x)), where the parameters α,β,λ∈C, the functions r,f∈C(x), and f are not constant. Full article
(This article belongs to the Section Mathematics)
17 pages, 1309 KiB  
Article
Timelike Constant Axis Ruled Surface Family in Minkowski 3-Space
by Areej A. Almoneef and Rashad A. Abdel-Baky
Symmetry 2024, 16(6), 677; https://doi.org/10.3390/sym16060677 (registering DOI) - 31 May 2024
Abstract
A timelike (TL) constant axis ruled surface in E13 (Minkowski 3-space), as determined by its ruling, forms a constant dual angle with its Disteli-axis (striction axis or curvature axis). In this article, we employ the symmetry through point geometry [...] Read more.
A timelike (TL) constant axis ruled surface in E13 (Minkowski 3-space), as determined by its ruling, forms a constant dual angle with its Disteli-axis (striction axis or curvature axis). In this article, we employ the symmetry through point geometry of Lorentzian dual curves and the line geometry of TL ruled surfaces. This produces the capability to expound a set of curvature functions that specify the local configurations of TL ruled surfaces. Then, we gain some new constant axis ruled surfaces in Lorentzian line space and their geometrical illustrations. Further, we also earn several organizations among a TL constant axis ruled surface and its striction curve. Full article
(This article belongs to the Section Mathematics)
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18 pages, 1347 KiB  
Article
Modeling the Nonmonotonic Immune Response in a Tumor–Immune System Interaction
by Yu Liu, Yuhang Ma, Cuihong Yang, Zhihang Peng, Yasuhiro Takeuchi, Malay Banerjee and Yueping Dong
Symmetry 2024, 16(6), 676; https://doi.org/10.3390/sym16060676 (registering DOI) - 31 May 2024
Abstract
Tumor–immune system interactions are very complicated, being highly nonlinear and not well understood. A large number of tumors can potentially weaken the immune system through various mechanisms such as secreting cytokines that suppress the immune response. In this paper, we propose a tumor–immune [...] Read more.
Tumor–immune system interactions are very complicated, being highly nonlinear and not well understood. A large number of tumors can potentially weaken the immune system through various mechanisms such as secreting cytokines that suppress the immune response. In this paper, we propose a tumor–immune system interaction model with a nonmonotonic immune response function and adoptive cellular immunotherapy (ACI). The model has a tumor-free equilibrium and at most three tumor-presence equilibria (low, moderate and high ones). The stability of all equilibria is studied by analyzing their characteristic equations. The consideration of nonmonotonic immune response results in a series of bifurcations such as the saddle-node bifurcation, transcritical bifurcation, Hopf bifurcation and Bogdanov–Takens bifurcation. In addition, numerical simulation results show the coexistence of periodic orbits and homoclinic orbits. Interestingly, along with various bifurcations, we also found two bistable scenarios: the coexistence of a stable tumor-free as well as a high-tumor-presence equilibrium and the coexistence of a stable-low as well as a high-tumor-presence equilibrium, which can show symmetric and antisymmetric properties in a range of model parameters and initial cell concentrations. The new findings indicate that under ACI, patients can possibly reach either a stable tumor-free state or a low-tumor-presence state in the presence of nonmonotonic immune response once the immune system is activated. Full article
(This article belongs to the Special Issue Mathematical Modeling in Biology and Life Sciences)
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15 pages, 326 KiB  
Article
Solitons of η-Ricci–Bourguignon Type on Submanifolds in (LCS)m Manifolds
by Lixu Yan, Vandana, Aliya Naaz Siddiqui, Halil Ibrahim Yoldas and Yanlin Li
Symmetry 2024, 16(6), 675; https://doi.org/10.3390/sym16060675 (registering DOI) - 31 May 2024
Abstract
In this research article, we concentrate on the exploration of submanifolds in an (LCS)m-manifold B˜. We examine these submanifolds in the context of two distinct vector fields, namely, the characteristic vector field and the concurrent [...] Read more.
In this research article, we concentrate on the exploration of submanifolds in an (LCS)m-manifold B˜. We examine these submanifolds in the context of two distinct vector fields, namely, the characteristic vector field and the concurrent vector field. Initially, we consider some classifications of η-Ricci–Bourguignon (in short, η-RB) solitons on both invariant and anti-invariant submanifolds of B˜ employing the characteristic vector field. We establish several significant findings through this process. Furthermore, we investigate additional results by using η-RB solitons on invariant submanifolds of B˜ with concurrent vector fields, and discuss a supporting example. Full article
(This article belongs to the Special Issue Symmetry and Its Application in Differential Geometry and Topology III)
19 pages, 359 KiB  
Article
A New Adaptive Levenberg–Marquardt Method for Nonlinear Equations and Its Convergence Rate under the Hölderian Local Error Bound Condition
by Yang Han and Shaoping Rui
Symmetry 2024, 16(6), 674; https://doi.org/10.3390/sym16060674 (registering DOI) - 30 May 2024
Abstract
The Levenberg–Marquardt (LM) method is one of the most significant methods for solving nonlinear equations as well as symmetric and asymmetric linear equations. To improve the method, this paper proposes a new adaptive LM algorithm by modifying the LM parameter, combining the trust [...] Read more.
The Levenberg–Marquardt (LM) method is one of the most significant methods for solving nonlinear equations as well as symmetric and asymmetric linear equations. To improve the method, this paper proposes a new adaptive LM algorithm by modifying the LM parameter, combining the trust region technique and the non-monotone technique. It is interesting that the new algorithm is constantly optimized by adaptively choosing the LM parameter. To evaluate the effectiveness of the new algorithm, we conduct tests using various examples. To extend the convergence results, we prove the convergence of the new algorithm under the Hölderian local error bound condition rather than the commonly used local error bound condition. Theoretical analysis and numerical results show that the new algorithm is stable and effective. Full article
(This article belongs to the Special Issue Computational Mathematics and Its Applications in Numerical Analysis)
27 pages, 9799 KiB  
Article
On the Solvatochromism of Fluorescein Sodium
by Corina Cheptea, Alexandru Zara, Ecaterina Ambrosi, Ana Cezarina Morosanu, Maria Diaconu, Mihaela Miron, Dana Ortansa Dorohoi and Dan Gheorghe Dimitriu
Symmetry 2024, 16(6), 673; https://doi.org/10.3390/sym16060673 (registering DOI) - 30 May 2024
Abstract
Fluorescein sodium is a very important compound for a wide spectrum of applications, from which medical applications prevail. Despite this, there are very few studies in the literature related to the structure and fundamental properties of fluorescein sodium and its solutions, with most [...] Read more.
Fluorescein sodium is a very important compound for a wide spectrum of applications, from which medical applications prevail. Despite this, there are very few studies in the literature related to the structure and fundamental properties of fluorescein sodium and its solutions, with most of the studies dealing with fluorescein. The purpose of the present article is to determine some parameters of the fluorescein sodium molecule approaching the quantum-mechanical modeling and experimental solvatochromism in both binary and ternary solutions. For data analysis, several theoretical models were applied. The results highlight the intermolecular interactions involved in the spectral shift of the electronic absorption band of fluorescein sodium when dissolved in different solvents or binary solvents and allowed the estimation of the difference between the interaction energy in molecular pairs of the type of fluorescein sodium − solvent 1 and fluorescein sodium − solvent 2. By applying a variational method, the dipole moment in the first excited state of the fluorescein sodium molecule and the angle between the dipole moments in the ground and excited states, respectively, were estimated. These results are useful for a better understanding of the behavior of fluorescein sodium when dissolved in different solvents or combinations of solvents, to develop new practical applications. Full article
(This article belongs to the Special Issue Chemistry: Symmetry/Asymmetry—Feature Papers and Reviews)
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27 pages, 4016 KiB  
Article
Symmetrical Data Recovery: FPGA-Based Multi-Dimensional Elastic Recovery Acceleration for Multiple Block Failures in Ceph Systems
by Fan Lei, Yong Wang, Junqi Chen and Sijie Yang
Symmetry 2024, 16(6), 672; https://doi.org/10.3390/sym16060672 (registering DOI) - 30 May 2024
Abstract
In the realm of Ceph distributed storage systems, ensuring swift and symmetrical data recovery during severe data corruption scenarios is pivotal for data reliability and system stability. This paper introduces an innovative FPGA-based Multi-Dimensional Elastic Recovery Acceleration method, termed AMDER-Ceph. Utilizing FPGA technology, [...] Read more.
In the realm of Ceph distributed storage systems, ensuring swift and symmetrical data recovery during severe data corruption scenarios is pivotal for data reliability and system stability. This paper introduces an innovative FPGA-based Multi-Dimensional Elastic Recovery Acceleration method, termed AMDER-Ceph. Utilizing FPGA technology, this method is a pioneer in accelerating erasure code data recovery within such systems symmetrically. By harnessing the parallel computing power of FPGAs and optimizing Cauchy matrix binary operations, AMDER-Ceph significantly enhances data recovery speed and efficiency symmetrically. Our evaluations in real-world Ceph environments show that AMDER-Ceph achieves up to 4.84 times faster performance compared with traditional methods, especially evident in the standard 4 MB block size configurations of Ceph systems. Full article
(This article belongs to the Section Computer)
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18 pages, 319 KiB  
Article
A Singular Tempered Sub-Diffusion Fractional Model Involving a Non-Symmetrically Quasi-Homogeneous Operator
by Xinguang Zhang, Peng Chen, Lishuang Li and Yonghong Wu
Symmetry 2024, 16(6), 671; https://doi.org/10.3390/sym16060671 (registering DOI) - 30 May 2024
Viewed by 26
Abstract
In this paper, we focus on the existence of positive solutions for a singular tempered sub-diffusion fractional model involving a quasi-homogeneous nonlinear operator. By using the spectrum theory and computing the fixed point index, some new sufficient conditions for the existence of positive [...] Read more.
In this paper, we focus on the existence of positive solutions for a singular tempered sub-diffusion fractional model involving a quasi-homogeneous nonlinear operator. By using the spectrum theory and computing the fixed point index, some new sufficient conditions for the existence of positive solutions are derived. It is worth pointing out that the nonlinearity of the equation contains a tempered fractional sub-diffusion term, and is allowed to possess strong singularities in time and space variables. In particular, the quasi-homogeneous operator is a nonlinear and non-symmetrical operator. Full article
(This article belongs to the Special Issue Symmetry in Geometric Theory of Analytic Functions)
23 pages, 924 KiB  
Article
Advancing Sustainable Urban Development: Navigating Complexity with Spherical Fuzzy Decision Making
by Mohd Anjum, Hong Min, Gaurav Sharma and Zubair Ahmed
Symmetry 2024, 16(6), 670; https://doi.org/10.3390/sym16060670 (registering DOI) - 29 May 2024
Viewed by 233
Abstract
This study explores the complexities of urban planning and addresses major issues by carefully weighing four options for smart city technology, community-based development, green infrastructure investment, and transit-oriented development. Unlike traditional evaluations, our study applies the novel SWARA-WASPAS model to spherical fuzzy sets [...] Read more.
This study explores the complexities of urban planning and addresses major issues by carefully weighing four options for smart city technology, community-based development, green infrastructure investment, and transit-oriented development. Unlike traditional evaluations, our study applies the novel SWARA-WASPAS model to spherical fuzzy sets (SFSs), thus identifying and navigating the uncertainty present in decision making. This methodological approach improves the accuracy of our assessment by providing detailed information about the advantages and disadvantages of each option. Our study offers useful insights for urban policymakers and planners using carefully weighted criteria and employing a methodical ranking procedure. The aim is to provide insights for decisions that promote equity, environmental consciousness, resilience, and symmetry in urban environments. The application of the SWARA-WASPAS approach not only advances the field but also provides a strong basis for informed decision making. This improves the accuracy of our evaluations and provides detailed insights into each option’s pros and cons. Our study uses weighted criteria and systematic ranking to advise urban policymakers and planners. Our main goal is to help urban populations make resilient, environmentally responsible, equitable, and symmetrical decisions. Our research aims to further the conversation on sustainable urban development by offering a framework based on data that addresses the difficulties associated with dynamic urban environments. In the end, we want our humanized viewpoint to speak to a wider audience and inspire a shared dedication to creating cities that flourish in the face of changing urban environments. Full article
(This article belongs to the Special Issue Recent Developments on Fuzzy Sets Extensions)
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22 pages, 420 KiB  
Article
Estimation of Marshall–Olkin Extended Generalized Extreme Value Distribution Parameters under Progressive Type-II Censoring by Using a Genetic Algorithm
by Rasha Abd El-Wahab Attwa, Shimaa Wasfy Sadk and Taha Radwan
Symmetry 2024, 16(6), 669; https://doi.org/10.3390/sym16060669 (registering DOI) - 29 May 2024
Viewed by 175
Abstract
In this article, we consider the statistical analysis of the parameter estimation of the Marshall–Olkin extended generalized extreme value under liner normalization distribution (MO-GEVL) within the context of progressively type-II censored data. The progressively type-II censored data are considered for three specific distribution [...] Read more.
In this article, we consider the statistical analysis of the parameter estimation of the Marshall–Olkin extended generalized extreme value under liner normalization distribution (MO-GEVL) within the context of progressively type-II censored data. The progressively type-II censored data are considered for three specific distribution patterns: fixed, discrete uniform, and binomial random removal. The challenge lies in the computation of maximum likelihood estimations (MLEs), as there is no straightforward analytical solution. The classical numerical methods are considered inadequate for solving the complex MLE equation system, leading to the necessity of employing artificial intelligence algorithms. This article utilizes the genetic algorithm (GA) to overcome this difficulty. This article considers parameter estimation through both maximum likelihood and Bayesian methods. For the MLE, the confidence intervals of the parameters are calculated using the Fisher information matrix. In the Bayesian estimation, the Lindley approximation is applied, considering LINEX loss functions and square error loss, suitable for both non-informative and informative contexts. The effectiveness and applicability of these proposed methods are demonstrated through numerical simulations and practical real-data examples. Full article
(This article belongs to the Special Issue Mathematical Analysis and Its Applications from Decision Theory to Extreme Values)
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14 pages, 8143 KiB  
Article
Estimation of Pointing Errors of Large Radio Telescopes under Solar Radiation Based on Digital Twin
by Shanxiang Wei, Deqing Kong, Binlan Wang, Lianbo Fu, Wenrong Xiao, Zongming Yin, Yongxiang Li and Zhouzhou Xiao
Symmetry 2024, 16(6), 668; https://doi.org/10.3390/sym16060668 (registering DOI) - 29 May 2024
Viewed by 150
Abstract
The pointing accuracy of large radio telescopes is affected by antenna structure errors, installation errors, servo errors, gravity, and varying environmental factors. Although an on-line pointing model had been developed in the past for several large radio telescopes to correct these effects, it [...] Read more.
The pointing accuracy of large radio telescopes is affected by antenna structure errors, installation errors, servo errors, gravity, and varying environmental factors. Although an on-line pointing model had been developed in the past for several large radio telescopes to correct these effects, it is also valuable to explore new ways to correct these effects. Therefore, in order to estimate the dynamic pointing error of large radio telescopes under solar radiation, a new way based on digital twin (DT) is used in this paper. Digital models of the Wuqing 70-m radio telescope (WRT70) are created based on the DT operational framework. Finally, the reliability of the WRT70’s DT system is verified, and the dynamic pointing error of WRT70 (staying at the position of the elevation angle of 90° and the azimuth angle of 180°) on two sunny days in different seasons is estimated by the created DT system. The research results show that the pointing error of large radio telescopes under solar radiation fluctuates greatly and the seasonal differences are very striking. The maximum elevation pointing error of WRT70 under solar radiation around the winter solstice is over 40 arcsec, which is equal to 4/11 of the beam width for WRT70 operating at 8 GHz. In this paper, it is feasible to estimate the time-varying pointing errors of large radio telescopes at rest under solar radiation by constructing a DT system, but it is not effective to estimate the dynamic pointing errors of large radio telescopes in operation. It is expected to establish a dynamic pointing error model and calibrate the dynamic pointing errors of large radio telescopes in operation by DT technology in the future. Full article
(This article belongs to the Section Physics)
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11 pages, 1315 KiB  
Article
Numerical Solution for the Heat Conduction Model with a Fractional Derivative and Temperature-Dependent Parameters
by Rafał Brociek, Edyta Hetmaniok and Damian Słota
Symmetry 2024, 16(6), 667; https://doi.org/10.3390/sym16060667 - 28 May 2024
Viewed by 249
Abstract
This paper presents the numerical solution of the heat conduction model with a fractional derivative of the Riemann–Liouville type with respect to the spatial variable. The considered mathematical model assumes the dependence on temperature of the material parameters (such as specific heat, density, [...] Read more.
This paper presents the numerical solution of the heat conduction model with a fractional derivative of the Riemann–Liouville type with respect to the spatial variable. The considered mathematical model assumes the dependence on temperature of the material parameters (such as specific heat, density, and thermal conductivity) of the model. In the paper, the boundary conditions of the first and second types are considered. If the heat flux equal to zero is assumed on the left boundary, then the thermal symmetry is obtained, which results in a simplification of the problem and the possibility of considering only half the area. The numerical examples presented in the paper illustrate the effectiveness and convergence of the discussed computational method. Full article
(This article belongs to the Special Issue Advanced Analytical and Numerical Methods for Fractional Initial and Boundary Value Problems with Symmetry/Asymmetry)
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15 pages, 2323 KiB  
Article
The Thermoelastic Dynamic Response of a Rod Due to a Moving Heat Source under the Fractional-Order Thermoelasticity Theory
by Fengjun Liu, Pengjie Shi and Ying Guo
Symmetry 2024, 16(6), 666; https://doi.org/10.3390/sym16060666 - 28 May 2024
Viewed by 194
Abstract
In this paper, the thermoelastic behavior of a rod made of an isotropic material under the action of a moving heat source was investigated using a new theory of thermoelasticity related to fractional-order time with two relaxation times. A mathematical model of the [...] Read more.
In this paper, the thermoelastic behavior of a rod made of an isotropic material under the action of a moving heat source was investigated using a new theory of thermoelasticity related to fractional-order time with two relaxation times. A mathematical model of the one-dimensional thermoelasticity problem was established based on the new thermoelasticity theory. We considered the symmetry of the material, and the fractional-order thermoelasticity control equation was given. Subsequently, the control equations were solved and analyzed using the Laplace transform and its inverse transform. This study examined the effects of fractional-order parameters, time, two thermal relaxation times, and the speed of movement of the heat source on the displacement, temperature, and stress distribution patterns in the rod. Full article
(This article belongs to the Section Engineering and Materials)
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17 pages, 297 KiB  
Article
A Note on the Application of the Double Sumudu–Generalized Laplace Decomposition Method and 1+1- and 2+1-Dimensional Time-Fractional Boussinesq Equations
by Hassan Eltayeb and Said Mesloub
Symmetry 2024, 16(6), 665; https://doi.org/10.3390/sym16060665 - 28 May 2024
Viewed by 182
Abstract
The current paper concentrates on discovering the exact solutions of the singular time-fractional Boussinesq equation and coupled time-fractional Boussinesq equation by presenting a new technique known as the double Sumudu–generalized Laplace and Adomian decomposition method. Here, two main theorems are addressed that are [...] Read more.
The current paper concentrates on discovering the exact solutions of the singular time-fractional Boussinesq equation and coupled time-fractional Boussinesq equation by presenting a new technique known as the double Sumudu–generalized Laplace and Adomian decomposition method. Here, two main theorems are addressed that are very useful in this work. Moreover, the mentioned method is effective in solving several problems. Some examples are presented to check the precision and symmetry of the technique. The outcomes show that the proposed technique is precise and gives better solutions as compared to existing methods in the literature. Full article
(This article belongs to the Special Issue Discussion of Properties and Applications of Integral Transform)
18 pages, 951 KiB  
Article
A Ciphertext Reduction Scheme for Garbling an S-Box in an AES Circuit with Minimal Online Time
by Xu Yan, Bin Lian, Yunhao Yang, Xiaotie Wang, Jialin Cui, Xianghong Zhao, Fuqun Wang and Kefei Chen
Symmetry 2024, 16(6), 664; https://doi.org/10.3390/sym16060664 - 28 May 2024
Viewed by 199
Abstract
The secure computation of symmetric encryption schemes using Yao’s garbled circuits, such as AES, allows two parties, where one holds a plaintext block m and the other holds a key k, to compute Enc(k,m) without [...] Read more.
The secure computation of symmetric encryption schemes using Yao’s garbled circuits, such as AES, allows two parties, where one holds a plaintext block m and the other holds a key k, to compute Enc(k,m) without leaking m and k to one another. Due to its wide application prospects, secure AES computation has received much attention. However, the evaluation of AES circuits using Yao’s garbled circuits incurs substantial communication overhead. To further improve its efficiency, this paper, upon observing the special structures of AES circuits and the symmetries of an S-box, proposes a novel ciphertext reduction scheme for garbling an S-box in the last SubBytes step. Unlike the idea of traditional Yao’s garbled circuits, where the circuit generator uses the input wire labels to encrypt the corresponding output wire labels, our garbling scheme uses the input wire labels of an S-box to encrypt the corresponding “flip bit strings”. This approach leads to a significant performance improvement in our garbling scheme, which necessitates only 28 ciphertexts to garble an S-box and a single invocation of a cryptographic primitive for decryption compared to the best result in previous work that requires 8×28 ciphertexts to garble an S-box and multiple invocations of a cryptographic primitive for decryption. Crucially, the proposed scheme provides a new idea to improve the performance of Yao’s garbled circuits. We analyze the security of the proposed scheme in the semi-honest model and experimentally verify its efficiency. Full article
(This article belongs to the Special Issue New Advances in Symmetric Cryptography)
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18 pages, 1214 KiB  
Article
Characterizations of Minimal Dominating Sets in γ-Endowed and Symmetric γ-Endowed Graphs with Applications to Structure-Property Modeling
by Sakander Hayat, Raman Sundareswaran, Marayanagaraj Shanmugapriya, Asad Khan, Venkatasubramanian Swaminathan, Mohamed Hussian Jabarullah and Mohammed J. F. Alenazi
Symmetry 2024, 16(6), 663; https://doi.org/10.3390/sym16060663 - 27 May 2024
Viewed by 199
Abstract
Claude Berge (1987) introduced the concept of k-extendable graphs, wherein any independent set of size k is inherently a constituent of a maximum independent set within a graph H=(V,E). Graphs possessing the property of being [...] Read more.
Claude Berge (1987) introduced the concept of k-extendable graphs, wherein any independent set of size k is inherently a constituent of a maximum independent set within a graph H=(V,E). Graphs possessing the property of being 1-extendable are termedas Berge graphs. This introduction gave rise to the notion of well-covered graphs and well-dominated graphs. A graph is categorized as well-covered if each of its maximal independent sets is, in fact, a maximum independent set. Similarly, a graph attains the classification of well-dominated if every minimal dominating set (DS) within it is a minimum dominating set. In alignment with the concept of k-extendable graphs, the framework of (k,γ)-endowed graphs and symmetric (k,γ)-endowed graphs are established. In these graphs, each DS of size k encompasses a minimum DS of the graph. In this article, a study of γ-endowed dominating sets is initiated. Various results providing a deep insight into γ-endowed dominating sets in graphs such as those characterizing the ones possessing a unique minimum DS are proven. We also introduce and study the symmetric γ-endowed graphs and minimality of dominating sets in them. In addition, we give a solution to an open problem in the literature. which seeks to find a domination-based parameter that has a correlation coefficient of ρ>0.9967 with the total π-electronic energy of lower benzenoid hydrocarbons. We show that the upper dominating number Γ(H) studied in this paper delivers a strong prediction potential. Full article
(This article belongs to the Special Issue Symmetry and Graph Theory)
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16 pages, 355 KiB  
Article
Sufficient Conditions for Linear Operators Related to Confluent Hypergeometric Function and Generalized Bessel Function of the First Kind to Belong to a Certain Class of Analytic Functions
by Saiful R. Mondal, Manas Kumar Giri and Raghavendar Kondooru
Symmetry 2024, 16(6), 662; https://doi.org/10.3390/sym16060662 - 27 May 2024
Viewed by 173
Abstract
Geometric function theory has extensively explored the geometric characteristics of analytic functions within symmetric domains. This study analyzes the geometric properties of a specific class of analytic functions employing confluent hypergeometric functions and generalized Bessel functions of the first kind. Specific constraints are [...] Read more.
Geometric function theory has extensively explored the geometric characteristics of analytic functions within symmetric domains. This study analyzes the geometric properties of a specific class of analytic functions employing confluent hypergeometric functions and generalized Bessel functions of the first kind. Specific constraints are imposed on the parameters to ensure the inclusion of the confluent hypergeometric function within the analytic function class. The coefficient bound of the class is used to determine the inclusion properties of integral operators involving generalized Bessel functions of the first kind. Different results are observed for these operators, depending on the specific values of the parameters. The results presented here include some previously published findings as special cases. Full article
(This article belongs to the Special Issue Symmetries of Difference Equations, Special Functions and Orthogonal Polynomials II)
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19 pages, 1108 KiB  
Article
Particle Swarm Optimization Algorithm Using Velocity Pausing and Adaptive Strategy
by Kezong Tang and Chengjian Meng
Symmetry 2024, 16(6), 661; https://doi.org/10.3390/sym16060661 - 27 May 2024
Viewed by 285
Abstract
Particle swarm optimization (PSO) as a swarm intelligence-based optimization algorithm has been widely applied to solve various real-world optimization problems. However, traditional PSO algorithms encounter issues such as premature convergence and an imbalance between global exploration and local exploitation capabilities when dealing with [...] Read more.
Particle swarm optimization (PSO) as a swarm intelligence-based optimization algorithm has been widely applied to solve various real-world optimization problems. However, traditional PSO algorithms encounter issues such as premature convergence and an imbalance between global exploration and local exploitation capabilities when dealing with complex optimization tasks. To address these shortcomings, an enhanced PSO algorithm incorporating velocity pausing and adaptive strategies is proposed. By leveraging the search characteristics of velocity pausing and the terminal replacement mechanism, the problem of premature convergence inherent in standard PSO algorithms is mitigated. The algorithm further refines and controls the search space of the particle swarm through time-varying inertia coefficients, symmetric cooperative swarms concepts, and adaptive strategies, balancing global search and local exploitation. The performance of VASPSO was validated on 29 standard functions from Cec2017, comparing it against five PSO variants and seven swarm intelligence algorithms. Experimental results demonstrate that VASPSO exhibits considerable competitiveness when compared with 12 algorithms. The relevant code can be found on our project homepage. Full article
(This article belongs to the Special Issue Symmetry in Computing Algorithms and Applications)
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19 pages, 848 KiB  
Article
Enhancing Integer Time Series Model Estimations through Neural Network-Based Fuzzy Time Series Analysis
by Mohammed H. El-Menshawy, Mohamed S. Eliwa, Laila A. Al-Essa, Mahmoud El-Morshedy and Rashad M. EL-Sagheer
Symmetry 2024, 16(6), 660; https://doi.org/10.3390/sym16060660 - 27 May 2024
Viewed by 232
Abstract
This investigation explores the effects of applying fuzzy time series (FTSs) based on neural network models for estimating a variety of spectral functions in integer time series models. The focus is particularly on the skew integer autoregressive of order one (NSINAR(1)) model. To [...] Read more.
This investigation explores the effects of applying fuzzy time series (FTSs) based on neural network models for estimating a variety of spectral functions in integer time series models. The focus is particularly on the skew integer autoregressive of order one (NSINAR(1)) model. To support this estimation, a dataset consisting of NSINAR(1) realizations with a sample size of n = 1000 is created. These input values are then subjected to fuzzification via fuzzy logic. The prowess of artificial neural networks in pinpointing fuzzy relationships is harnessed to improve prediction accuracy by generating output values. The study meticulously analyzes the enhancement in smoothing of spectral function estimators for NSINAR(1) by utilizing both input and output values. The effectiveness of the output value estimates is evaluated by comparing them to input value estimates using a mean-squared error (MSE) analysis, which shows how much better the output value estimates perform. Full article
(This article belongs to the Topic Fuzzy Number, Fuzzy Difference, Fuzzy Differential: Theory and Applications)
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39 pages, 1207 KiB  
Article
The Additive Xgamma-Burr XII Distribution: Properties, Estimation and Applications
by Hebatalla H. Mohammad, Faten S. Alamri, Heba N. Salem and Abeer A. EL-Helbawy
Symmetry 2024, 16(6), 659; https://doi.org/10.3390/sym16060659 - 27 May 2024
Viewed by 247
Abstract
This paper introduces a new four-parameter additive model, named xgamma-Burr XII distribution, by considering two competing risks: the former has the xgamma distribution and the latter has the Burr XII distribution. A graphical description of the xgamma-Burr XII distribution is presented, including plots [...] Read more.
This paper introduces a new four-parameter additive model, named xgamma-Burr XII distribution, by considering two competing risks: the former has the xgamma distribution and the latter has the Burr XII distribution. A graphical description of the xgamma-Burr XII distribution is presented, including plots of the probability density function, hazard rate and reversed hazard rate functions. The xgamma-Burr XII density has different shapes such as decreasing, unimodal, approximately symmetric and decreasing-unimodal. The main statistical properties of the proposed model are studied. The unknown model parameters, reliability, hazard rate and reversed hazard rate functions are estimated via the maximum likelihood method. The asymptotic confidence intervals of the parameters, reliability function, hazard rate function and reversed hazard rate function are also obtained. A simulation study is carried out to evaluate the performance of the maximum likelihood estimates. In addition, three real data are applied to show the superiority of the xgamma-Burr XII distribution over some known distributions in real-life applications. Full article
(This article belongs to the Section Mathematics)
5 pages, 204 KiB  
Editorial
The Nuclear Physics of Neutron Stars
by Charalampos Moustakidis
Symmetry 2024, 16(6), 658; https://doi.org/10.3390/sym16060658 - 27 May 2024
Viewed by 298
Abstract
Neutron stars are considered extraordinary astronomical laboratories for the physics of nuclear matter as they have the most fascinating constitution of energy and matter in the Universe [...] Full article
(This article belongs to the Special Issue The Nuclear Physics of Neutron Stars)
27 pages, 2290 KiB  
Review
The Scale-Invariant Vacuum Paradigm: Main Results and Current Progress Review (Part II)
by Vesselin G. Gueorguiev and Andre Maeder
Symmetry 2024, 16(6), 657; https://doi.org/10.3390/sym16060657 - 26 May 2024
Viewed by 196
Abstract
This is a summary of the main results within the Scale-Invariant Vacuum (SIV) paradigm based on Weyl integrable geometry. We also review the mathematical framework and utilize alternative derivations of the key equations based on the reparametrization invariance as well. The main results [...] Read more.
This is a summary of the main results within the Scale-Invariant Vacuum (SIV) paradigm based on Weyl integrable geometry. We also review the mathematical framework and utilize alternative derivations of the key equations based on the reparametrization invariance as well. The main results discussed are related to the early universe; that is, applications to inflation, Big Bang Nucleosynthesis, and the growth of the density fluctuations within the SIV. Some of the key SIV results for the early universe are a natural exit from inflation within the SIV in a later time texit with value related to the parameters of the inflationary potential along with the possibility for the density fluctuations to grow sufficiently fast within the SIV without the need for dark matter to seed the growth of structure in the universe. In the late-time universe, the applications of the SIV paradigm are related to scale-invariant dynamics of galaxies, MOND, dark matter, and dwarf spheroidals, where one can find MOND to be a peculiar case of the SIV theory. Finally, within the recent time epoch, we highlight that some of the change in the length-of-the-day (LOD), about 0.92 cm/yr, can be accounted for by SIV effects in the Earth–Moon system. Full article
(This article belongs to the Special Issue Nature and Origin of Dark Matter and Dark Energy II)
19 pages, 306 KiB  
Article
On the Reducibility of a Class Nonlinear Almost Periodic Hamiltonian Systems
by Nina Xue and Yanmei Sun
Symmetry 2024, 16(6), 656; https://doi.org/10.3390/sym16060656 - 26 May 2024
Viewed by 275
Abstract
Inthis paper, we consider the reducibility of a class of nonlinear almost periodic Hamiltonian systems. Under suitable hypothesis of analyticity, non-resonant conditions and non-degeneracy conditions, by using KAM iteration, it is shown that the considered Hamiltonian system is reducible to an almost periodic [...] Read more.
Inthis paper, we consider the reducibility of a class of nonlinear almost periodic Hamiltonian systems. Under suitable hypothesis of analyticity, non-resonant conditions and non-degeneracy conditions, by using KAM iteration, it is shown that the considered Hamiltonian system is reducible to an almost periodic Hamiltonian system with zero equilibrium points for most small enough parameters. As an example, we discuss the reducibility and stability of an almost periodic Hill’s equation. Full article
(This article belongs to the Special Issue Symmetry in Integrable Systems and Soliton Theories)
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