Journal Description
Symmetry
Symmetry
is an international, peer-reviewed, open access journal covering research on symmetry/asymmetry phenomena wherever they occur in all aspects of natural sciences. Symmetry is published monthly online by MDPI.
- Open Access— free for readers, with article processing charges (APC) paid by authors or their institutions.
- High Visibility: indexed within Scopus, SCIE (Web of Science), CAPlus / SciFinder, Inspec, Astrophysics Data System, and other databases.
- Journal Rank: JCR - Q2 (Multidisciplinary Sciences) / CiteScore - Q1 (General Mathematics); Q1 (Physics and Astronomy); Q1 (Computer Science)
- Rapid Publication: manuscripts are peer-reviewed and a first decision is provided to authors approximately 16.2 days after submission; acceptance to publication is undertaken in 3.5 days (median values for papers published in this journal in the second half of 2023).
- Recognition of Reviewers: reviewers who provide timely, thorough peer-review reports receive vouchers entitling them to a discount on the APC of their next publication in any MDPI journal, in appreciation of the work done.
- Testimonials: See what our editors and authors say about Symmetry.
Impact Factor:
2.7 (2022);
5-Year Impact Factor:
2.7 (2022)
Latest Articles
Estimation of the Domain of Attraction on Controlled Nonlinear Neutral Complex Networks via Razumikhin Approach
Symmetry 2024, 16(6), 643; https://doi.org/10.3390/sym16060643 - 22 May 2024
Abstract
This paper is devoted to dealing with the issue of the estimation of the domain of attraction (DOA) for highly nonlinear neutral complex networks (HNNCNs) with time delays. Firstly, by the Razumikhin approach, we establish several novel lemmas on the estimation of DOA
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This paper is devoted to dealing with the issue of the estimation of the domain of attraction (DOA) for highly nonlinear neutral complex networks (HNNCNs) with time delays. Firstly, by the Razumikhin approach, we establish several novel lemmas on the estimation of DOA for highly nonlinear neutral differential systems. The cases of bounded non-differentiable delays and unbounded proportional delays are discussed, respectively. Subsequently, by utilizing the proposed lemmas, combining the Lyapunov stability theory and inequality technique, the estimation of DOA on HNNCNs with bounded delays or proportional delays is derived when the chosen control gain is sufficiently large. If initial values start from DOA, then the states of systems will exponentially or polynomially converge to the equilibrium point, which means that the local exponential or polynomial synchronization of HNNCNs is realized. Additionally, the weighted outer-coupling matrix of complex networks is not required to be symmetric, which means that the derived results can be applied to both the undirected networks and directed networks. Finally, several numerical examples are provided to illustrate the feasibility of theoretical findings.
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(This article belongs to the Section Mathematics)
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Mean-Field Stochastic Linear Quadratic Optimal Control for Jump-Diffusion Systems with Hybrid Disturbances
by
Chao Tang, Xueqin Li and Qi Wang
Symmetry 2024, 16(6), 642; https://doi.org/10.3390/sym16060642 - 22 May 2024
Abstract
A mean-field linear quadratic stochastic (MF-SLQ for short) optimal control problem with hybrid disturbances and cross terms in a finite horizon is concerned. The state equation is a systems driven by the Wiener process and the Poisson random martingale measure disturbed by some
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A mean-field linear quadratic stochastic (MF-SLQ for short) optimal control problem with hybrid disturbances and cross terms in a finite horizon is concerned. The state equation is a systems driven by the Wiener process and the Poisson random martingale measure disturbed by some stochastic perturbations. The cost functional is also disturbed, which means more general cases could be characterized, especially when extra environment perturbations exist. In this paper, the well-posedness result on the jump diffusion systems is obtained by the fixed point theorem and also the solvability of the MF-SLQ problem. Actually, by virtue of adjoint variables, classic variational calculus, and some dual representation, an optimal condition is derived. Throughout our research, in order to connect the optimal control and the state directly, two Riccati differential equations, a BSDE with random jumps and an ordinary equation (ODE for short) on disturbance terms are obtained by a decoupling technique, which provide an optimal feedback regulator. Meanwhile, the relationship between the two Riccati equations and the so-called mean-field stochastic Hamilton system is established. Consequently, the optimal value is characterized by the initial state, disturbances, and original value of the Riccati equations. Finally, an example is provided to illustrate our theoretic results.
Full article
(This article belongs to the Section Engineering and Materials)
Open AccessArticle
An Adaptive Search Algorithm for Multiplicity Dynamic Flexible Job Shop Scheduling with New Order Arrivals
by
Linshan Ding, Zailin Guan, Dan Luo, Mudassar Rauf and Weikang Fang
Symmetry 2024, 16(6), 641; https://doi.org/10.3390/sym16060641 - 22 May 2024
Abstract
In today’s customer-centric economy, the demand for personalized products has compelled corporations to develop manufacturing processes that are more flexible, efficient, and cost-effective. Flexible job shops offer organizations the agility and cost-efficiency that traditional manufacturing processes lack. However, the dynamics of modern manufacturing,
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In today’s customer-centric economy, the demand for personalized products has compelled corporations to develop manufacturing processes that are more flexible, efficient, and cost-effective. Flexible job shops offer organizations the agility and cost-efficiency that traditional manufacturing processes lack. However, the dynamics of modern manufacturing, including machine breakdown and new order arrivals, introduce unpredictability and complexity. This study investigates the multiplicity dynamic flexible job shop scheduling problem (MDFJSP) with new order arrivals. To address this problem, we incorporate the fluid model to propose a fluid randomized adaptive search (FRAS) algorithm, comprising a construction phase and a local search phase. Firstly, in the construction phase, a fluid construction heuristic with an online fluid dynamic tracking policy generates high-quality initial solutions. Secondly, in the local search phase, we employ an improved tabu search procedure to enhance search efficiency in the solution space, incorporating symmetry considerations. The results of the numerical experiments demonstrate the superior effectiveness of the FRAS algorithm in solving the MDFJSP when compared to other algorithms. Specifically, the proposed algorithm demonstrates a superior quality of solution relative to existing algorithms, with an average improvement of 29.90%; and exhibits an acceleration in solution speed, with an average increase of 1.95%.
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(This article belongs to the Special Issue Symmetry in Computing Algorithms and Applications)
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Nonlinear Transport through Parity–Time Symmetric Lattice Potentials
by
Wei Mao and Yongping Zhang
Symmetry 2024, 16(6), 640; https://doi.org/10.3390/sym16060640 - 22 May 2024
Abstract
We study nonlinear transports of a light field through finite parity–time symmetric lattice potentials. The initial light field is trapped in a source reservoir and is released to expand toward the lattice potentials along the transverse direction due to the nonlinearity. We identify
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We study nonlinear transports of a light field through finite parity–time symmetric lattice potentials. The initial light field is trapped in a source reservoir and is released to expand toward the lattice potentials along the transverse direction due to the nonlinearity. We identify the transports that can be classified into in-band and in-gap transports. In the in-band transport, the light field can tunnel through the lattices into the sink reservoir, and in the in-gap transport, the light field is self-trapped inside the lattices to form a solitary wave.
Full article
(This article belongs to the Special Issue Symmetry-Related Quantum Phases in Exciton-Polariton Condensates)
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An Online Review-Driven Picture Fuzzy Multi-Criteria Group Decision-Making Approach for Evaluating the Online Medical Service Quality of Doctors
by
Kaiwen Shi and Juanjuan Peng
Symmetry 2024, 16(6), 639; https://doi.org/10.3390/sym16060639 - 21 May 2024
Abstract
In order to further investigate the level of online medical services in China and improve the medical experience of patients, this study aims to establish an online review-driven picture fuzzy multi-criteria group decision-making (MCGDM) approach for the online medical service evaluation of doctors.
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In order to further investigate the level of online medical services in China and improve the medical experience of patients, this study aims to establish an online review-driven picture fuzzy multi-criteria group decision-making (MCGDM) approach for the online medical service evaluation of doctors. First, based on the Aczel–Alsina t-norm and t-conorm, the normal picture fuzzy Aczel–Alsina operations involving a variable parameter are defined to make the corresponding operations more flexible than other operations. Second, two picture fuzzy Aczel–Alsina aggregation operators are developed, and the corresponding properties are discussed as well. Third, combined with the online review information of China’s medical platform Haodaifu, the online review-driven evaluation attributes and their corresponding weights are obtained, which can make the evaluation model more objective. Fourth, an extended normal picture fuzzy complex proportional assessment (COPRAS) decision-making method for the service quality evaluation of online medical services is proposed. Finally, an empirical example is presented to verify the feasibility and validity of the proposed method. A sensitivity analysis and a comparison analysis are also conducted to demonstrate the effectiveness and flexibility of the proposed approach.
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(This article belongs to the Special Issue Fuzzy Set Theory and Uncertainty Theory—Volume III)
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Strange Things in Bottom-to-Strange Decays: The Standard Model Turned Upside Down?
by
Martin Andersson, Alexander Mclean Marshall, Konstantinos A. Petridis and Eluned Smith
Symmetry 2024, 16(6), 638; https://doi.org/10.3390/sym16060638 - 21 May 2024
Abstract
The flavour anomalies are a set of experimental deviations from the Standard Model (SM) predictions in several observables involving decays of bottom quarks. In particular, tensions between theory and experiment in measurements involving a bottom quark decaying into a strange quark and a
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The flavour anomalies are a set of experimental deviations from the Standard Model (SM) predictions in several observables involving decays of bottom quarks. In particular, tensions between theory and experiment in measurements involving a bottom quark decaying into a strange quark and a pair of muons have motivated much theoretical work to explore possible new physics explanations. This review summarises the tumultuous evolution of these tensions, focusing on the most recent experimental results and their implications for physics beyond the SM. We also discuss the prospects for future measurements and tests of the flavour anomalies at the LHC and other facilities.
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(This article belongs to the Special Issue Symmetries and Anomalies in Flavour Physics)
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A Necessary Optimality Condition on the Control of a Charged Particle
by
Nigar Yildirim Aksoy, Ercan Celik and Merve Zengin
Symmetry 2024, 16(6), 637; https://doi.org/10.3390/sym16060637 - 21 May 2024
Abstract
We consider an optimal control problem with the boundary functional for a Schrödinger equation describing the motion of a charged particle. By using the existence of an optimal solution, we search the necessary optimality conditions for the examined control problem. First, we constitute
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We consider an optimal control problem with the boundary functional for a Schrödinger equation describing the motion of a charged particle. By using the existence of an optimal solution, we search the necessary optimality conditions for the examined control problem. First, we constitute an adjoint problem by a Lagrange multiplier that is related to constraints of theory on symmetries and conservation laws. The adjoint problem obtained is a boundary value problem with a nonhomogeneous boundary condition. We prove the existence and uniqueness of the solution of the adjoint problem. Then, we demonstrate the differentiability of the objective functional in the sense of Frechet and get a formula for its gradient. Finally, we give a necessary optimality condition in the form of a variational inequality.
Full article
(This article belongs to the Special Issue Advanced Symmetry Methods for Dynamics, Control, Optimization and Applications in 2023)
Open AccessArticle
Real-Time Control of Sintering Moisture Based on Temporal Fusion Transformers
by
Xinping Chen, Jinyang Cheng, Ziyun Zhou, Xinyu Lu, Binghui Ye and Yushan Jiang
Symmetry 2024, 16(6), 636; https://doi.org/10.3390/sym16060636 - 21 May 2024
Abstract
The quality of sintered ore, which serves as the primary raw material for blast furnace ironmaking, is directly influenced by the moisture in the sintering mixture. In order to improve the precision of water addition in the sintering process, this paper proposes an
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The quality of sintered ore, which serves as the primary raw material for blast furnace ironmaking, is directly influenced by the moisture in the sintering mixture. In order to improve the precision of water addition in the sintering process, this paper proposes an intelligent model for predicting water-filling volume based on Temporal Fusion Transformer (TFT), whose symmetry enables it to effectively capture long-term dependencies in time series data. Utilizing historical sintering data to develop a prediction model for the amount of mixing and water addition, the results indicate that the TFT model can achieve the R squared of 0.9881, and the root mean square error (RMSE) of 3.5951. When compared to the transformer, long short-term memory (LSTM), and particle swarm optimization–long short-term memory (PSO-LSTM), it is evident that the TFT model outperforms the other models, improving the RMSE by 8.5403, 6.9852, and 0.453, respectively. As an application, the TFT model provides an effective interval reference for moisture control in normal sintering processes, which ensures that the error is within 1 t.
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(This article belongs to the Topic Intelligent Control in Smart Energy Systems)
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PSD and Cross-PSD of Responses of Seven Classes of Fractional Vibrations Driven by fGn, fBm, Fractional OU Process, and von Kármán Process
by
Ming Li
Symmetry 2024, 16(5), 635; https://doi.org/10.3390/sym16050635 - 20 May 2024
Abstract
This paper gives its contributions in four stages. First, we propose the analytical expressions of power spectrum density (PSD) responses and cross-PSD responses to seven classes of fractional vibrators driven by fractional Gaussian noise (fGn). Second, we put forward the analytical expressions of
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This paper gives its contributions in four stages. First, we propose the analytical expressions of power spectrum density (PSD) responses and cross-PSD responses to seven classes of fractional vibrators driven by fractional Gaussian noise (fGn). Second, we put forward the analytical expressions of PSD and cross-PSD responses to seven classes of fractional vibrators excited by fractional Brownian motion (fBm). Third, we present the analytical expressions of PSD and cross-PSD responses to seven classes of fractional vibrators driven by the fractional Ornstein–Uhlenbeck (OU) process. Fourth, we bring forward the analytical expressions of PSD and cross-PSD responses to seven classes of fractional vibrators excited by the von Kármán process. We show that the statistical dependences of the responses to seven classes of fractional vibrators follow those of the excitation of fGn, fBm, the OU process, or the von Kármán process. We also demonstrate the obvious effects of fractional orders on the responses to seven classes of fractional vibrations. In addition, we newly introduce class VII fractional vibrators, their frequency transfer function, and their impulse response in this research.
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(This article belongs to the Special Issue Symmetry in the Advanced Mechanics of Systems)
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A New Three-Parameter Inverse Rayleigh Distribution: Simulation and Application to Real Data
by
Muzafer Shala and Faton Merovci
Symmetry 2024, 16(5), 634; https://doi.org/10.3390/sym16050634 - 20 May 2024
Abstract
In this paper, we introduce a new three-parameter inverse Rayleigh distribution that extends the inverse Rayleigh distribution, constructed based on the generalized transmuted family of distributions proposed by Alizadeh, Merovci, and Hamedani. We explore statistical properties such as the quantile function, moments, harmonic
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In this paper, we introduce a new three-parameter inverse Rayleigh distribution that extends the inverse Rayleigh distribution, constructed based on the generalized transmuted family of distributions proposed by Alizadeh, Merovci, and Hamedani. We explore statistical properties such as the quantile function, moments, harmonic mean, mean deviation, stress–strength reliability, and entropy. Parameter estimation is performed using various methods, including maximum likelihood, least squares, the method of the maximum product of spacings, and the method of Cramér–von Mises. The usefulness of the new three-parameter inverse Rayleigh distribution is illustrated by modeling a real dataset, demonstrating its superior fit compared to several other distributions.
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(This article belongs to the Special Issue Symmetric or Asymmetric Distributions and Its Applications)
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Calibrated Empirical Neutrosophic Cumulative Distribution Function Estimation for Both Symmetric and Asymmetric Data
by
Hareem Abbasi, Usman Shahzad, Walid Emam, Muhammad Hanif, Nasir Ali and Mubeen Mukhtar
Symmetry 2024, 16(5), 633; https://doi.org/10.3390/sym16050633 - 20 May 2024
Abstract
The traditional stratification weight is widely used in survey sampling for estimation under stratified random sampling (StRS). A neutrosophic calibration approach is proposed under neutrosophic statistics for the first time with the aim of improving conventional stratification weight. This addresses the challenge of
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The traditional stratification weight is widely used in survey sampling for estimation under stratified random sampling (StRS). A neutrosophic calibration approach is proposed under neutrosophic statistics for the first time with the aim of improving conventional stratification weight. This addresses the challenge of estimating the empirical cumulative distribution function (CDF) of a finite population using the neutrosophic technique. The neutrosophic technique extends traditional statistics, dealing with indeterminate, vague, and uncertain values. Thus, using additional information, we are able to obtain an effective estimate of the neutrosophic CDF. The suggested estimator yields an interval range in which the population empirical CDF is likely to exist rather than a single numerical value. The proposed family of neutrosophic estimators will be defined under suitable calibration constraints. A simulation study is also computed in order to assess the effectiveness of the suggested and adapted neutrosophic estimators using real-life symmetric and asymmetric datasets.
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(This article belongs to the Section Mathematics)
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Statistical Mechanics Approaches for Studying Temperature and Rate Effects in Multistable Systems
by
Andrea Cannizzo and Stefano Giordano
Symmetry 2024, 16(5), 632; https://doi.org/10.3390/sym16050632 - 20 May 2024
Abstract
Systems with a multistable energy landscape are widespread in physics, biophysics, technology, and materials science. They are strongly influenced by thermal fluctuations and external mechanical actions that can be applied at different rates, moving the system from equilibrium to non-equilibrium regimes. In this
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Systems with a multistable energy landscape are widespread in physics, biophysics, technology, and materials science. They are strongly influenced by thermal fluctuations and external mechanical actions that can be applied at different rates, moving the system from equilibrium to non-equilibrium regimes. In this paper, we focus on a simple system involving a single breaking phenomenon to describe the various theoretical approaches used to study these problems. To begin with, we propose the exact solution at thermodynamic equilibrium based on the calculation of the partition function without approximations. We then introduce the technique of spin variables, which is able to simplify the treatment even for systems with a large number of coordinates. We then analyze the energy balance of the system to better understand its underlying physics. Finally, we introduce a technique based on transition state theory useful for studying the non-equilibrium dynamical regimes of these systems. This method is appropriate for the evaluation of rate effects and hysteresis loops. These approaches are developed for both the Helmholtz ensemble (prescribed extension) and the Gibbs ensemble (applied force) of statistical mechanics. The symmetry and duality of these two ensembles is discussed in depth. While these techniques are used here for a simple system with theoretical purposes, they can be applied to complex systems of interest for several physical, biophysical, and technological applications.
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(This article belongs to the Special Issue Feature Papers in Section "Engineering and Materials" 2024)
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Pseudo-Spin Symmetry and the Hints for Unstable and Superheavy Nuclei
by
Jing Geng, Zhiheng Wang, Jia Liu, Jiajie Li and Wenhui Long
Symmetry 2024, 16(5), 631; https://doi.org/10.3390/sym16050631 - 20 May 2024
Abstract
The pseudo-spin symmetry (PSS) provides an important angle to understand nuclear microscopic structure and the novel phenomena found in unstable nuclei. The relativistic Hartree–Fock (RHF) theory, that takes the important degrees of freedom associated with the -meson and -tensor (
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The pseudo-spin symmetry (PSS) provides an important angle to understand nuclear microscopic structure and the novel phenomena found in unstable nuclei. The relativistic Hartree–Fock (RHF) theory, that takes the important degrees of freedom associated with the -meson and -tensor ( -T) couplings into account, provides an appropriate description of the PSS restoration in realistic nuclei, particularly for the pseudo-spin (PS) doublets with high angular momenta ( ). The investigations of the PSS within the RHF theory are recalled in this paper by focusing on the effects of the Fock terms. Aiming at common artificial shell closures appearing in previous relativistic mean-field calculations, the mechanism responsible for the PSS restoration of high- orbits is stressed, revealing the manifestation of nuclear in-medium effects on the PSS, and thus, providing qualitative guidance on modeling the in-medium balance between nuclear attractions and repulsions. Moreover, the essential role played by the -T coupling, that contributes mainly via the Fock terms, is introduced as combined with the relations between the PSS and various nuclear phenomena, including the shell structure and the evolution, novel halo and bubble-like phenomena, and the superheavy magicity. As the consequences of the nuclear force in complicated nuclear many-body systems, the PSS itself and the mechanism therein can not only deepen our understanding of nuclear microscopic structure and relevant phenomena, but also provide special insight into the nature of the nuclear force, which can further enrich our knowledge of nuclear physics.
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(This article belongs to the Special Issue Restoration of Broken Symmetries in the Nuclear Many-Body Problem)
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Fault-Tolerant Phototaxis of a Modular System Inspired by Gonium pectorale Using Phase-Based Control
by
Kohei Nishikawa, Yuki Origane, Hiroki Etchu and Daisuke Kurabayashi
Symmetry 2024, 16(5), 630; https://doi.org/10.3390/sym16050630 - 19 May 2024
Abstract
In this study, we proposed a model for modular robots in which autonomous decentralized modules adaptively organize their behavior. The phototaxis of Gonium pectorale, a species of volvocine algae, was modeled as a modular system, and a fault-tolerant modular control method of
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In this study, we proposed a model for modular robots in which autonomous decentralized modules adaptively organize their behavior. The phototaxis of Gonium pectorale, a species of volvocine algae, was modeled as a modular system, and a fault-tolerant modular control method of phototaxis was proposed for it. The proposed method was based on the rotation phase of the colony and adaptively adjusted an internal response-related parameter to enhance the fault tolerance of the system. Compared to a constant parameter approach, the simulation results demonstrated a significant improvement in the phototaxis time for positive and negative phototaxis during module failures. This method contributes to achieving autonomous, decentralized, and purposeful mediation of the modules necessary for controlling modular robots.
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(This article belongs to the Special Issue Symmetry in Robot Design and Application)
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Features, Paradoxes and Amendments of Perturbative Non-Hermitian Quantum Mechanics
by
Miloslav Znojil
Symmetry 2024, 16(5), 629; https://doi.org/10.3390/sym16050629 - 19 May 2024
Abstract
Quantum mechanics of unitary systems is considered in quasi-Hermitian representation and in the dynamical regime in which one has to take into account the ubiquitous presence of perturbations, random or specific. In this paper, it is shown that multiple technical obstacles encountered in
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Quantum mechanics of unitary systems is considered in quasi-Hermitian representation and in the dynamical regime in which one has to take into account the ubiquitous presence of perturbations, random or specific. In this paper, it is shown that multiple technical obstacles encountered in such a context can be circumvented via just a mild amendment of the so-called Rayleigh–Schrödinger perturbation–expansion approach. In particular, the quasi-Hermitian formalism characterized by an enhancement of flexibility is shown to remain mathematically tractable while, on the phenomenological side, opening several new model-building horizons. It is emphasized that they include, i.a., the study of generic random perturbations and/or of multiple specific non-Hermitian toy models. In parallel, several paradoxes and open questions are shown to survive.
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(This article belongs to the Special Issue Quantum Mechanics: Concepts, Symmetries, and Recent Developments)
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Short-Term Electrical Load Forecasting Using an Enhanced Extreme Learning Machine Based on the Improved Dwarf Mongoose Optimization Algorithm
by
Haocheng Wang, Yu Zhang and Lixin Mu
Symmetry 2024, 16(5), 628; https://doi.org/10.3390/sym16050628 - 18 May 2024
Abstract
Accurate short-term electrical load forecasting is crucial for the stable operation of power systems. Given the nonlinear, periodic, and rapidly changing characteristics of short-term power load forecasts, this paper introduces a novel forecasting method employing an Extreme Learning Machine (ELM) enhanced by an
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Accurate short-term electrical load forecasting is crucial for the stable operation of power systems. Given the nonlinear, periodic, and rapidly changing characteristics of short-term power load forecasts, this paper introduces a novel forecasting method employing an Extreme Learning Machine (ELM) enhanced by an improved Dwarf Mongoose Optimization Algorithm (Local escape Dwarf Mongoose Optimization Algorithm, LDMOA). This method addresses the significant prediction errors of conventional ELM models and enhances prediction accuracy. The enhancements to the Dwarf Mongoose Optimization Algorithm include three key modifications: initially, a dynamic backward learning strategy is integrated at the early stages of the algorithm to augment its global search capabilities. Subsequently, a cosine algorithm is employed to locate new food sources, thereby expanding the search scope and avoiding local optima. Lastly, a “madness factor” is added when identifying new sleeping burrows to further widen the search area and effectively circumvent local optima. Comparative analyses using benchmark functions demonstrate the improved algorithm’s superior convergence and stability. In this study, the LDMOA algorithm optimizes the weights and thresholds of the ELM to establish the LDMOA-ELM prediction model. Experimental forecasts utilizing data from China’s 2016 “The Electrician Mathematical Contest in Modeling” demonstrate that the LDMOA-ELM model significantly outperforms the original ELM model in terms of prediction error and accuracy.
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(This article belongs to the Special Issue Evolutionary Computation, Metaheuristics, Nature-Inspired Algorithms, and Symmetry)
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Best Proximity Point Results via Simulation Function with Application to Fuzzy Fractional Differential Equations
by
Ghada Ali, Nawab Hussain and Abdelhamid Moussaoui
Symmetry 2024, 16(5), 627; https://doi.org/10.3390/sym16050627 - 17 May 2024
Abstract
In this study, we prove the existence and uniqueness of a best proximity point in the setting of non-Archimedean modular metric spaces via the concept of simulation functions. A non-Archimedean metric modular is shaped as a parameterized family of classical metrics; therefore, for
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In this study, we prove the existence and uniqueness of a best proximity point in the setting of non-Archimedean modular metric spaces via the concept of simulation functions. A non-Archimedean metric modular is shaped as a parameterized family of classical metrics; therefore, for each value of the parameter, the positivity, the symmetry, the triangle inequality, or the continuity is ensured. Also, we demonstrate how analogous theorems in modular metric spaces may be used to generate the best proximity point results in triangular fuzzy metric spaces. The utility of our findings is further demonstrated by certain examples, illustrated consequences, and an application to fuzzy fractional differential equations.
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(This article belongs to the Special Issue Symmetry in Metric Spaces and Topology)
Open AccessArticle
Sedenion Algebra Model as an Extension of the Standard Model and Its Link to SU(5)
by
Qiang Tang and Jau Tang
Symmetry 2024, 16(5), 626; https://doi.org/10.3390/sym16050626 - 17 May 2024
Abstract
In the Standard Model, ad hoc hypotheses assume the existence of three generations of point-like leptons and quarks, which possess a point-like structure and follow the Dirac equation involving four anti-commutative matrices. In this work, we consider the sedenion hypercomplex algebra as an
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In the Standard Model, ad hoc hypotheses assume the existence of three generations of point-like leptons and quarks, which possess a point-like structure and follow the Dirac equation involving four anti-commutative matrices. In this work, we consider the sedenion hypercomplex algebra as an extension of the Standard Model and show its close link to SU(5), which is the underlying symmetry group for the grand unification theory (GUT). We first consider the direct-product quaternion model and the eight-element octonion algebra model. We show that neither the associative quaternion model nor the non-associative octonion model could generate three fermion generations. Instead, we show that the sedenion model, which contains three octonion sub-algebras, leads naturally to precisely three fermion generations. Moreover, we demonstrate the use of basis sedenion operators to construct twenty-four 5 × 5 generalized lambda matrices representing SU(5) generators, in analogy to the use of octonion basis operators to generate Gell-Mann’s eight 3 × 3 lambda-matrix generators for SU(3). Thus, we provide a link between the sedenion algebra and Georgi and Glashow’s SU(5) GUT model that unifies the electroweak and strong interactions for the Standard Model’s elementary particles, which obey SU(3)SU(2)U(1) symmetry.
Full article
(This article belongs to the Special Issue Symmetry in Geometric Mechanics and Mathematical Physics)
Open AccessArticle
Inference for Compound Exponential XLindley Model with Applications to Lifetime Data
by
Fatimah M. Alghamdi, Mohammed Amine Meraou, Hassan M. Aljohani, Amani Alrumayh, Fathy H. Riad, Sara Mohamed Ahmed Alsheikh and Meshayil M. Alsolmi
Symmetry 2024, 16(5), 625; https://doi.org/10.3390/sym16050625 - 17 May 2024
Abstract
The creating of novel models essentially stems from the requirement to appropriate describe survival cases. In this study, a novel lifetime model with two parameters is proposed and studied for modeling more types of data used in different study cases, including symmetric, asymmetric,
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The creating of novel models essentially stems from the requirement to appropriate describe survival cases. In this study, a novel lifetime model with two parameters is proposed and studied for modeling more types of data used in different study cases, including symmetric, asymmetric, skewed, and complex datasets. The proposed model is obtained by compounding the exponential and XLindley distributions, and it is regarded as a strong competitor for the widely applied symmetrical and non-symmetrical models. Several characteristics and statistical properties are investigated. The unknown parameters of the recommended model for the complete sample are estimated using two estimation methods; notably, maximum likelihood estimation and Bayes techniques based on several loss functions as well as an approximate tool are used to construct the confidence intervals for the unknown parameters of the suggested model. The estimation procedures are compared using a Monte Carlo simulation experiment to demonstrate their effectiveness. In the end, the applicability and flexibility of the recommended model are conducted using two real lifetime datasets. In our illustration, we compare the practicality of the recommended model with several well-known competing distributions.
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(This article belongs to the Section Mathematics)
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An Effective Method for the Evaluation of the Enantiomeric Purity of 1,2-Diacyl-sn-glycero-3-phosphocholine-Based Lipids by NMR Analysis
by
Antonia Di Mola, Lorenzo de Ferra, Mauro Anibaldi, Guglielmo Monaco and Antonio Massa
Symmetry 2024, 16(5), 624; https://doi.org/10.3390/sym16050624 - 17 May 2024
Abstract
In this article, we report a very efficient method for the determination of the enantiopurity of 1,2-diacyl-sn-glycero-3-phosphocholine by 1H NMR analysis using a readily available chiral derivatizing boronic acid (CDA), (R)-(2-(((1-phenylethyl)amino)methyl)phenyl)boronic acid. After the removal of the acyl
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In this article, we report a very efficient method for the determination of the enantiopurity of 1,2-diacyl-sn-glycero-3-phosphocholine by 1H NMR analysis using a readily available chiral derivatizing boronic acid (CDA), (R)-(2-(((1-phenylethyl)amino)methyl)phenyl)boronic acid. After the removal of the acyl groups of 1,2-diacyl-sn-glycero-3-phosphocholine via methanolysis and washing fatty acid byproducts with CHCl3, the obtained sn-glycero-3-phosphocholine (GPC) with the free diol moiety is derivatized by the chiral boronic acid and analyzed by 1H NMR analysis. The choline methyl resonance of each diastereomer is observed at distinctive chemical shifts in the 1H NMR spectrum. Integration of the respective resonances allows direct determination of the enantiomeric purity. The procedure was tested successfully using 1,2-dipalmitoyl-sn-glycero-3-phosphocholine (DPPC) with different enantiomeric purities and with commercially available 1,2-dimyristoyl-sn-glycero-3-phosphocholine (DMPC) and 1,2-distearoyl-sn-glycero-3-phosphocholine (DSPC).
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(This article belongs to the Special Issue Symmetry and Asymmetry in Medicinal Chemistry)
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