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
Symmetry and Symmetry-Breaking in Fluid Dynamics
Symmetry 2024, 16(5), 621; https://doi.org/10.3390/sym16050621 (registering DOI) - 17 May 2024
Abstract
It may seem that the heading of this Special Issue of Symmetry—though narrower than the famous all-inclusive title of an essay by Jean-Paul Sartre, Being and Nothingness—encompasses most, if not all, fluid phenomena [...]
Full article
(This article belongs to the Special Issue Symmetry and Symmetry-Breaking in Fluid Dynamics)
Open AccessArticle
Conical-Shaped Shells of Non-Uniform Thickness Vibration Analysis Using Higher-Order Shear Deformation Theory
by
Saira Javed
Symmetry 2024, 16(5), 620; https://doi.org/10.3390/sym16050620 (registering DOI) - 16 May 2024
Abstract
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The aim of this research is to investigate the frequency of conical-shaped shells, consisting of different materials, based on higher-order shear deformation theory (HSDT). The shells are of non-uniform thickness, consisting of two to six symmetric cross-ply layers. Simply supported boundary conditions were
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The aim of this research is to investigate the frequency of conical-shaped shells, consisting of different materials, based on higher-order shear deformation theory (HSDT). The shells are of non-uniform thickness, consisting of two to six symmetric cross-ply layers. Simply supported boundary conditions were used to analyse the frequency of conical-shaped shells. The differential equations, consisting of displacement and rotational functions, were approximated using spline approximation. A generalised eigenvalue problem was obtained and solved numerically for an eigenfrequency parameter and associated eigenvector of spline coefficients. The frequency of shells was analysed by varying the geometric parameters such as length of shell, cone angle, node number in circumference direction and number of layers, as well as three thickness variations such as linear, sinusoidal and exponential. It was also evident that by varying geometrical parameters, the mechanical parameters such as stress, moment and shear resultants were affected. Research results concluded that for three different thickness variations, as the number of layers of conical shells increases, the frequency values decrease. Moreover, by varying length ratios and cone angles, shells with variable thickness had lower frequency values compared to shells of constant thickness. The numerical results obtained were verified through the already existing literature. It is evident that the present results are very close to the already existing literature.
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Open AccessArticle
Effect of Salt Solution Tracer Dosage on the Transport and Mixing of Tracer in a Water Model of Asymmetrical Gas-Stirred Ladle with a Moderate Gas Flowrate
by
Linbo Li, Chao Chen, Xin Tao, Hongyu Qi, Tao Liu, Qiji Yan, Feng Deng, Arslan Allayev, Wanming Lin and Jia Wang
Symmetry 2024, 16(5), 619; https://doi.org/10.3390/sym16050619 - 16 May 2024
Abstract
In previous research simulating steelmaking ladles using cold water models, the dosage/volume of the salt tracer solution is one of the factors that has been overlooked by researchers to a certain extent. Previous studies have demonstrated that salt tracers may influence the flow
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In previous research simulating steelmaking ladles using cold water models, the dosage/volume of the salt tracer solution is one of the factors that has been overlooked by researchers to a certain extent. Previous studies have demonstrated that salt tracers may influence the flow and measured mixing time of fluids in water models. Based on a water model scaled down from an industrial 130-ton ladle by a ratio of 1:3, this study investigates the impact of salt tracer dosage on the transport and mixing of tracers in the water model of gas-stirred ladle with a moderate gas flow rate. A preliminary uncertainty analysis of the experimental mixing time is performed, and the standard deviations were found to be less than 15%. It was observed in the experiments that the transport paths of tracers in the ladle can be classified into two trends. A common trend is that the injected salt solution tracer is asymmetrically transported towards the left sidewall of the ladle by the main circulation. In another trend, the injected salt solution tracer is transported both by the main circulation to the left side wall and by downward flow towards the gas column. The downward flow may be accelerated and become a major flow pattern when the tracer volume increases. For the dimensionless concentration curve, the sinusoidal type, which represents a rapid mixing, is observed at the top surface monitoring points, while the parabolic type is observed at the bottom monitoring points. An exception is the monitoring point at the right-side bottom (close to the asymmetric gas nozzle area), where both sinusoidal-type and parabolic-type curves are observed. Regarding the effect of tracer volume on the curve and mixing time, the curves at the top surface monitoring points are less influenced but curves at the bottom monitoring points are noticeably influenced by the tracer volume. A trend of decreasing and then increasing as the tracer volume increases was found at the top surface monitoring points, while the mixing times at the bottom monitoring points decrease with the increase in the tracer volume.
Full article
(This article belongs to the Special Issue Symmetry and Its Applications in Experimental Fluid Mechanics)
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Open AccessArticle
The Dynamical and Kinetic Equations of Four-Five-Six-Wave Resonance for Ocean Surface Gravity Waves in Water with a Finite Depth
by
Guobin Lin
Symmetry 2024, 16(5), 618; https://doi.org/10.3390/sym16050618 - 16 May 2024
Abstract
Based on the Hamilton canonical equations for ocean surface waves with four-five-six-wave resonance conditions , the determinate dynamical equation of four-five-six-wave resonances for ocean surface gravity waves in water with a finite depth is established, thus leading to the elimination of the nonresonant
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Based on the Hamilton canonical equations for ocean surface waves with four-five-six-wave resonance conditions , the determinate dynamical equation of four-five-six-wave resonances for ocean surface gravity waves in water with a finite depth is established, thus leading to the elimination of the nonresonant second-, third-, fourth-, and fifth-order nonlinear terms though a suitable canonical transformation. The four kernels of the equation and the 18 coefficients of the transformation are expressed in explicit form in terms of the expansion coefficients of the gravity wave Hamiltonian in integral-power series in normal variables. The possibilities of the existence of integrals of motion for the wave momentum and the wave action are discussed, particularly the special integrals for the latter. For ocean surface capillary–gravity waves on a fluid with a finite depth, the sixth-order expansion coefficients of the Hamiltonian in integral-power series in normal variables are concretely provided, thus naturally including the classical fifth-order kinetic energy expansion coefficients given by Krasitskii.
Full article
(This article belongs to the Special Issue Symmetrical Mathematical Computation in Fluid Dynamics)
Open AccessArticle
High-Order Extended Kalman Filter for State Estimation of Nonlinear Systems
by
Linwang Ding and Chenglin Wen
Symmetry 2024, 16(5), 617; https://doi.org/10.3390/sym16050617 - 16 May 2024
Abstract
In general, the extended Kalman filter (EKF) has a wide range of applications, aiming to minimize symmetric loss function (mean square error) and improve the accuracy and efficiency of state estimation. As the nonlinear model complexity increases, rounding errors gradually amplify, leading to
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In general, the extended Kalman filter (EKF) has a wide range of applications, aiming to minimize symmetric loss function (mean square error) and improve the accuracy and efficiency of state estimation. As the nonlinear model complexity increases, rounding errors gradually amplify, leading to performance degradation. After multiple iterations, divergence may occur. The traditional extended Kalman filter cannot accurately estimate the nonlinear model, and these errors still have an impact on the accuracy. To improve the filtering performance of the extended Kalman filter (EKF), this paper proposes a new extended Kalman filter (REKF) method that utilizes the statistical properties of the rounding error to enhance the estimation accuracy. After establishing the state model and measurement model, the residual term is used to replace the higher-order term in the Taylor expansion, and the least squares method is applied to identify the residual term step by step. Then, the iterative process of updating the extended Kalman filter is carried out. Within the Kalman filter framework, a higher-order rounding error-based extended Kalman filter (REKF) is designed for the joint estimation of rounding error and random variables, and the solution method for the rounding error is considered for the multilevel approximation of the original function. Through numerical simulations on a general nonlinear model, the higher-order rounding error-based extended Kalman filter (REKF) achieves better estimation results than the extended Kalman filter (EKF) and improves the filtering accuracy by utilizing the higher-order rounding error information, which also proves the effectiveness of the proposed method.
Full article
(This article belongs to the Section Engineering and Materials)
Open AccessArticle
A Transformer and LSTM-Based Approach for Blind Well Lithology Prediction
by
Danyan Xie, Zeyang Liu, Fuhao Wang and Zhenyu Song
Symmetry 2024, 16(5), 616; https://doi.org/10.3390/sym16050616 - 16 May 2024
Abstract
Petrographic prediction is crucial in identifying target areas and understanding reservoir lithology in oil and gas exploration. Traditional logging methods often rely on manual interpretation and experiential judgment, which can introduce subjectivity and constraints due to data quality and geological variability. To enhance
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Petrographic prediction is crucial in identifying target areas and understanding reservoir lithology in oil and gas exploration. Traditional logging methods often rely on manual interpretation and experiential judgment, which can introduce subjectivity and constraints due to data quality and geological variability. To enhance the precision and efficacy of lithology prediction, this study employed a Savitzky–Golay filter with a symmetric window for anomaly data processing, coupled with a residual temporal convolutional network (ResTCN) model tasked with completing missing logging data segments. A comparative analysis against the support vector regression and random forest regression model revealed that the ResTCN achieves the smallest MAE, at 0.030, and the highest coefficient of determination, at 0.716, which are indicative of its proximity to the ground truth. These methodologies significantly enhance the quality of the training data. Subsequently, a Transformer–long short-term memory (T-LS) model was applied to identify and classify the lithology of unexplored wells. The input layer of the Transformer model follows an embedding-like principle for data preprocessing, while the encoding block encompasses multi-head attention, Add & Norm, and feedforward components, integrating the multi-head attention mechanism. The output layer interfaces with the LSTM layer through dropout. A performance evaluation of the T-LS model against established rocky prediction techniques such as logistic regression, k-nearest neighbor, and random forest demonstrated its superior identification and classification capabilities. Specifically, the T-LS model achieved a precision of 0.88 and a recall of 0.89 across nine distinct lithology features. A Shapley analysis of the T-LS model underscored the utility of amalgamating multiple logging data sources for lithology classification predictions. This advancement partially addresses the challenges associated with imprecise predictions and limited generalization abilities inherent in traditional machine learning and deep learning models applied to lithology identification, and it also helps to optimize oil and gas exploration and development strategies and improve the efficiency of resource extraction.
Full article
(This article belongs to the Special Issue Advances in Computer Vision, Pattern Recognition, Machine Learning and Symmetry)
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Open AccessArticle
A Systematic Formulation into Neutrosophic Z Methodologies for Symmetrical and Asymmetrical Transportation Problem Challenges
by
Muhammad Kamran, Manal Elzain Mohamed Abdalla, Muhammad Nadeem, Anns Uzair, Muhammad Farman, Lakhdar Ragoub and Ismail Naci Cangul
Symmetry 2024, 16(5), 615; https://doi.org/10.3390/sym16050615 - 15 May 2024
Abstract
This study formulates a multi-objective, multi-item solid transportation issue with parameters that are neutrosophic Z-number fuzzy variables such as transportation costs, supplies, and demands. This work covers two scenarios where uncertainty in the problem can arise: the fuzzy solid transportation problem and the
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This study formulates a multi-objective, multi-item solid transportation issue with parameters that are neutrosophic Z-number fuzzy variables such as transportation costs, supplies, and demands. This work covers two scenarios where uncertainty in the problem can arise: the fuzzy solid transportation problem and the interval solid transportation problem. The first scenario arises when we represent data problems as intervals instead of exact values, while the second scenario arises when the information is not entirely clear. We address both models when the uncertainty alone impacts the constraint set. In order to find a solution for the interval case, we generate an additional problem. Since this auxiliary problem is typical of solid transportation, we can resolve it using the effective techniques currently in use. In the fuzzy scenario, a parametric method is used to discover a fuzzy solution to the earlier issue. Parametric analysis identifies that the best parameterized approaches to complementary problems are characterized by the application of parametric analysis. We present a suggested algorithm for determining the stability set. Finally, we provide a numerical example and sensitivity analysis for the transportation problem, which is both symmetrical and asymmetrical.
Full article
(This article belongs to the Special Issue Symmetry/Asymmetry in Operations Research)
Open AccessArticle
Belief Reliability Modeling Method for Wind Farms Considering Two-Directional Rotor Equivalent Wind Speed
by
Shuyu Li, Rui Kang, Meilin Wen and Tianpei Zu
Symmetry 2024, 16(5), 614; https://doi.org/10.3390/sym16050614 - 15 May 2024
Abstract
Compared to conventional energy sources, wind power is a clean energy source with high intermittence and uncertainty. As a system that converts wind energy into electricity, wind farms inevitably face severe reliability issues. In this paper, based on reliability theory, a new reliability
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Compared to conventional energy sources, wind power is a clean energy source with high intermittence and uncertainty. As a system that converts wind energy into electricity, wind farms inevitably face severe reliability issues. In this paper, based on reliability theory, a new reliability modeling method for wind farms is proposed. Firstly, a belief reliability model for wind farms is constructed. Then, a power generation model based on two-directional rotor equivalent wind speed is established to represent the wind farm performance in the belief reliability model. Finally, several numerical studies are conducted to verify the power generation model under different wind speeds and directions, to demonstrate the belief reliability model with different levels of uncertainty, and to compare the belief reliability considering two-directional rotor equivalent wind speed with other methods.
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(This article belongs to the Special Issue Advances and Applications of Uncertainty Theory in Reliability and Systems Engineering)
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On Neutrosophic Fuzzy Metric Space and Its Topological Properties
by
Samriddhi Ghosh, Sonam, Ramakant Bhardwaj and Satyendra Narayan
Symmetry 2024, 16(5), 613; https://doi.org/10.3390/sym16050613 - 15 May 2024
Abstract
The present research introduces a novel concept termed “neutrosophic fuzzy metric space”, which extends the traditional metric space framework by incorporating the notion of neutrosophic fuzzy sets. A thorough investigation of various structural and topological properties within this newly proposed generalization of metric
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The present research introduces a novel concept termed “neutrosophic fuzzy metric space”, which extends the traditional metric space framework by incorporating the notion of neutrosophic fuzzy sets. A thorough investigation of various structural and topological properties within this newly proposed generalization of metric space has been conducted. Additionally, counterparts of well-known theorems such as the Uniform Convergence Theorem and the Baire Category Theorem have been established for this generalized metric space. Through rigorous analysis, a detailed understanding of its fundamental characteristics has been attained, illuminating its potential applications and theoretical significance.
Full article
(This article belongs to the Special Issue Research on Fuzzy Logic and Mathematics with Applications II)
Open AccessArticle
Based on Symmetric Jump Risk Market: Study on the Ruin Problem of a Risk Model with Liquid Reserves and Proportional Investment
by
Chunwei Wang, Shujing Wang, Jiaen Xu and Shaohua Li
Symmetry 2024, 16(5), 612; https://doi.org/10.3390/sym16050612 - 15 May 2024
Abstract
In order to deal with complex risk scenarios involving claims, uncertainty, and investments, we consider the ruin problems in a compound Poisson risk model with liquid reserves and proportional investments and study the expected discounted penalty function under threshold dividend strategies. Firstly, the
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In order to deal with complex risk scenarios involving claims, uncertainty, and investments, we consider the ruin problems in a compound Poisson risk model with liquid reserves and proportional investments and study the expected discounted penalty function under threshold dividend strategies. Firstly, the integral differential equation of the expected discounted penalty function is derived. Secondly, since the closed-form solution of the equation cannot be obtained, a sinc method is used to obtain the numerical approximation solution of the equation. Finally, the feasibility and superiority of the sinc method are illustrated by error analysis. In addition, based on a symmetric jump risk market, we discuss the influence of some parameters on the ruin probability with some examples. This study can help actuaries develop more robust risk management strategies and ensure the long-term stability and profitability of insurance companies. It provides a theoretical basis for actuaries to carry out risk management.
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(This article belongs to the Section Mathematics)
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A New Modification of the Weibull Distribution: Model, Theory, and Analyzing Engineering Data Sets
by
Huda M. Alshanbari, Zubair Ahmad, Abd Al-Aziz Hosni El-Bagoury, Omalsad Hamood Odhah and Gadde Srinivasa Rao
Symmetry 2024, 16(5), 611; https://doi.org/10.3390/sym16050611 - 15 May 2024
Abstract
Symmetrical as well as asymmetrical statistical models play a prominent role in describing and predicting the real-world phenomena of nature. Among other fields, these models are very useful for modeling data in the sector of civil engineering. Due to the applicability of the
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Symmetrical as well as asymmetrical statistical models play a prominent role in describing and predicting the real-world phenomena of nature. Among other fields, these models are very useful for modeling data in the sector of civil engineering. Due to the applicability of the statistical models in civil engineering and other related sectors, this paper offers a statistical methodology to improve the distributional flexibility of traditional models. The suggested method/approach is called the extended-X family of distributions. The proposed method has the ability to generate symmetrical and asymmetrical probability distributions. Based on the extended-X family approach, an updated version of the Weibull model, namely, the extended Weibull model, is studied. The proposed model is very flexible and has the ability to capture the symmetrical and asymmetrical shapes of its density function. For the extended-X method, the estimation of parameters, a simulation study, and some mathematical properties are derived. Finally, the practical illustration/usefulness of the suggested model is shown by analyzing two data sets taken from the field of engineering. Both data sets represent the fracture toughness of alumina (Al2O3).
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(This article belongs to the Special Issue Skewed (Asymmetrical) Probability Distributions and Applications across Disciplines III)
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On the Maximum Likelihood Estimators’ Uniqueness and Existence for Two Unitary Distributions: Analytically and Graphically, with Application
by
Gadir Alomair, Yunus Akdoğan, Hassan S. Bakouch and Tenzile Erbayram
Symmetry 2024, 16(5), 610; https://doi.org/10.3390/sym16050610 - 14 May 2024
Abstract
Unit distributions, exhibiting inherent symmetrical properties, have been extensively studied across various fields. A significant challenge in these studies, particularly evident in parameter estimations, is the existence and uniqueness of estimators. Often, it is challenging to demonstrate the existence of a unique estimator.
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Unit distributions, exhibiting inherent symmetrical properties, have been extensively studied across various fields. A significant challenge in these studies, particularly evident in parameter estimations, is the existence and uniqueness of estimators. Often, it is challenging to demonstrate the existence of a unique estimator. The major issue with maximum likelihood and other estimator-finding methods that use iterative methods is that they need an initial value to reach the solution. This dependency on initial values can lead to local extremes that fail to represent the global extremities, highlighting a lack of symmetry in solution robustness. This study applies a very simple, and unique, estimation method for unit Weibull and unit Burr XII distributions that both attain the global maximum value. Therefore, we can conclude that the findings from the obtained propositions demonstrate that both the maximum likelihood and graphical methods are symmetrically similar. In addition, three real-world data applications are made to show that the method works efficiently.
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(This article belongs to the Section Mathematics)
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Open AccessArticle
Delay Effects on Plant Stability and Symmetry-Breaking Pattern Formation in a Klausmeier-Gray-Scott Model of Semiarid Vegetation
by
Ikram Medjahdi, Fatima Zohra Lachachi, María Ángeles Castro and Francisco Rodríguez
Symmetry 2024, 16(5), 609; https://doi.org/10.3390/sym16050609 - 14 May 2024
Abstract
The Klausmeier–Gray–Scott model of vegetation dynamics consists of a system of two partial differential equations relating plant growth and soil water. It is capable of reproducing the characteristic spatial patterns of vegetation found in plant ecosystems under water limitations. Recently, a discrete delay
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The Klausmeier–Gray–Scott model of vegetation dynamics consists of a system of two partial differential equations relating plant growth and soil water. It is capable of reproducing the characteristic spatial patterns of vegetation found in plant ecosystems under water limitations. Recently, a discrete delay was incorporated into this model to account for the lag between water infiltration into the soil and the following water uptake by plants. In this work, we consider a more ecologically realistic distributed delay to relate plant growth and soil water availability and analyse the effects of different delay types on the dynamics of both mean-field and spatial Klausmeier–Gray–Scott models. We consider distributed delays based on Gamma kernels and use the so-called linear chain trick to analyse the stability of the uniformly vegetated equilibrium. It is shown that the presence of delays can lead to the loss of stability in the constant equilibrium and to a reduction of the parameter region where steady-state vegetation patterns can arise through symmetry-breaking by diffusion-driven instability. However, these effects depend on the type of delay, and they are absent for distributed delays with weak kernels when vegetation mortality is low.
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(This article belongs to the Special Issue Mathematical Modeling in Biology and Life Sciences)
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Analyzing Dynamics: Lie Symmetry Approach to Bifurcation, Chaos, Multistability, and Solitons in Extended (3 + 1)-Dimensional Wave Equation
by
Muhammad Bilal Riaz, Adil Jhangeer, Faisal Z. Duraihem and Jan Martinovic
Symmetry 2024, 16(5), 608; https://doi.org/10.3390/sym16050608 - 14 May 2024
Abstract
The examination of new (3 + 1)-dimensional wave equations is undertaken in this study. Initially, the identification of the Lie symmetries of the model is carried out through the utilization of the Lie symmetry approach. The commutator and adjoint table of the symmetries
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The examination of new (3 + 1)-dimensional wave equations is undertaken in this study. Initially, the identification of the Lie symmetries of the model is carried out through the utilization of the Lie symmetry approach. The commutator and adjoint table of the symmetries are presented. Subsequently, the model under discussion is transformed into an ordinary differential equation using these symmetries. The construction of several bright, kink, and dark solitons for the suggested equation is then achieved through the utilization of the new auxiliary equation method. Subsequently, an analysis of the dynamical nature of the model is conducted, encompassing various angles such as bifurcation, chaos, and sensitivity. Bifurcation occurs at critical points within a dynamical system, accompanied by the application of an outward force, which unveils the emergence of chaotic phenomena. Two-dimensional plots, time plots, multistability, and Lyapunov exponents are presented to illustrate these chaotic behaviors. Furthermore, the sensitivity of the investigated model is executed utilizing the Runge–Kutta method. This analysis confirms that the stability of the solution is minimally affected by small changes in initial conditions. The attained outcomes show the effectiveness of the presented methods in evaluating solitons of multiple nonlinear models.
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(This article belongs to the Special Issue Symmetry in the Soliton Theory)
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Open AccessConference Report
Analogies between Lattice QCD and the Truncated Nambu–Jona-Lasinio Model
by
Mitja Rosina
Symmetry 2024, 16(5), 607; https://doi.org/10.3390/sym16050607 - 14 May 2024
Abstract
A modified Nambu–Jona-Lasinio Model with lattice structure is very instructive. It shows several similar problems and their solutions as the Lattice QCD. We study the limits of the large box size, small cell size and realistic pion mass. In particular, we study the
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A modified Nambu–Jona-Lasinio Model with lattice structure is very instructive. It shows several similar problems and their solutions as the Lattice QCD. We study the limits of the large box size, small cell size and realistic pion mass. In particular, we study the relation of the discrete (bound state) solutions to the physical scattering states, for example the pion–pion scattering.
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(This article belongs to the Special Issue Selected Papers from ACHT 2021: Perspectives in Particle, Cosmo- and Astroparticle Theory)
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Adaptive Fuzzy Fixed-Time Control for Nonlinear Systems with Unmodeled Dynamics
by
Rongzheng Luo, Lu Zhang, You Li and Jiwei Shen
Symmetry 2024, 16(5), 606; https://doi.org/10.3390/sym16050606 - 14 May 2024
Abstract
This article concentrates on the problem of fixed-time tracking control for a certain class of nonlinear systems with unmodeled dynamics. Unmodeled dynamics are prevalent in practical engineering systems, such as axially symmetric systems like robotic arms, spacecraft, and missiles. In this paper, the
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This article concentrates on the problem of fixed-time tracking control for a certain class of nonlinear systems with unmodeled dynamics. Unmodeled dynamics are prevalent in practical engineering systems, such as axially symmetric systems like robotic arms, spacecraft, and missiles. In this paper, the fuzzy-logic systems (FLSs) are implemented to address the challenge of accurately approximating the unknown nonlinear terms that arise during the derived control algorithm process. By employing fixed-time command filters (FTCF), the “explosion of complexity” issues encountered in traditional backstepping methods will be effectively resolved. Moreover, error compensation mechanisms are derived to effectively mitigate the filtering errors that may arise from the FTCFs. The computational burden associated with FLSs is reduced through the utilization of the weight vector estimation method based on the maximal norm and an adaptive approach. A fixed-time adaptive fuzzy tracking controller is developed within the backstepping control framework to ensure the boundedness of all signals and achieve fixed-time convergence of the tracking error for the controlled system. Illustrative examples are conducted to illustrate the viability of the derived controller.
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(This article belongs to the Special Issue Recent Progress in Robot Control Systems: Theory and Applications, Volume II)
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Open AccessArticle
Emergence of Novel WEDEx-Kerberotic Cryptographic Framework to Strengthen the Cloud Data Security against Malicious Attacks
by
Syeda Wajiha Zahra, Muhammad Nadeem, Ali Arshad, Saman Riaz, Waqas Ahmed, Muhammad Abu Bakr and Amerah Alabrah
Symmetry 2024, 16(5), 605; https://doi.org/10.3390/sym16050605 - 13 May 2024
Abstract
Researchers have created cryptography algorithms that encrypt data using a public or private key to secure it from intruders. It is insufficient to protect the data by using such a key. No research article has identified an algorithm capable of protecting both the
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Researchers have created cryptography algorithms that encrypt data using a public or private key to secure it from intruders. It is insufficient to protect the data by using such a key. No research article has identified an algorithm capable of protecting both the data and the associated key, nor has any mechanism been developed to determine whether access to the data is permissible or impermissible based on the authentication of the key. This paper presents a WEDEx-Kerberotic Framework for data protection, in which a user-defined key is firstly converted to a cipher key using the “Secure Words on Joining Key (SWJK)” algorithm. Subsequently, a WEDEx-Kerberotic encryption mechanism is created to protect the data by encrypting it with the cipher key. The first reason for making the WEDEx-Kerberotic Framework is to convert the user-defined key into a key that has nothing to do with the original key, and the length of the cipher key is much shorter than the original key. The second reason is that each ciphertext and key value are interlinked. When an intruder utilizes the snatching mechanism to obtain data, the attacker obtains data or a key unrelated to the original data. No matter how efficient the algorithm is, an attacker cannot access the data when these methods and algorithms are used to protect it. Finally, the proposed algorithm is compared to the previous approaches to determine the uniqueness of the algorithm and assess its superiority to the previous algorithms.
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(This article belongs to the Section Computer)
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Open AccessArticle
Advancing Survey Sampling Efficiency under Stratified Random Sampling and Post-Stratification: Leveraging Symmetry for Enhanced Estimation Accuracy in the Prediction of Exam Scores
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Gullinkala Ramya Venkata Triveni, Faizan Danish and Olayan Albalawi
Symmetry 2024, 16(5), 604; https://doi.org/10.3390/sym16050604 - 13 May 2024
Abstract
This pioneering investigation introduces two innovative estimators crafted to evaluate the finite population distribution function of a study variable, employing auxiliary variables within the framework of stratified random sampling and post-stratification while emphasizing symmetry in the sampling process. The derivation of mathematical expressions
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This pioneering investigation introduces two innovative estimators crafted to evaluate the finite population distribution function of a study variable, employing auxiliary variables within the framework of stratified random sampling and post-stratification while emphasizing symmetry in the sampling process. The derivation of mathematical expressions for bias and the mean square error up to the first degree of approximation fortifies the credibility of the proposed estimators. Drawing from three distinct datasets, including real-world data capturing student behaviors and exam performances from 500 students, this research highlights the superior efficiency of the proposed estimators compared to existing methods across both sampling schemes. Employing the proposed estimator, we effectively forecast students’ exam scores based on their study hours, backed by empirical evidence showcasing its precision in terms of mean square error and percentage relative efficiency. This study not only introduces inventive solutions to enduring challenges in survey sampling but also provides practical insights into enhancing predictive accuracy in educational assessments.
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(This article belongs to the Section Mathematics)
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Open AccessArticle
Modeling Renewable Warranties and Post-Warranty Replacements for Self-Announcing Failure Products Subject to Mission Cycles
by
Lijun Shang, Jianhui Chen, Baoliang Liu, Cong Lin and Li Yang
Symmetry 2024, 16(5), 603; https://doi.org/10.3390/sym16050603 - 13 May 2024
Abstract
The number of failures serves as a critical indicator that dynamically impacts the reliability of self-announcing failure products, making it highly practical to incorporate the failure count into reliability management throughout the entire product life cycle. This paper investigates comprehensive methodologies for effectively
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The number of failures serves as a critical indicator that dynamically impacts the reliability of self-announcing failure products, making it highly practical to incorporate the failure count into reliability management throughout the entire product life cycle. This paper investigates comprehensive methodologies for effectively managing the reliability of self-announcing failure products throughout both the warranty and post-warranty stages, taking into account factors such as the failure count, mission cycles, and limited time duration. Three renewable warranty strategies are introduced alongside proposed models for post-warranty replacements. By analyzing variables like the failure number, mission cycles, and time constraints, these proposed warranties provide practical frameworks for efficient reliability management during the warranty stage. Additionally, the introduced warranties utilize cost and time metrics to extract valuable insights that inform decision making and enable effective reliability management during the warranty stage. Moreover, this study establishes cost and time metrics for key post-warranty replacements, facilitating the development of individual cost rates and model applications in other post-warranty scenarios. Analyses of the renewable free-repair–replacement warranties demonstrate that establishing an appropriate number of failures as the replacement threshold can effectively reduce warranty-servicing costs and extend the coverage duration.
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(This article belongs to the Special Issue Advances and Applications of Uncertainty Theory in Reliability and Systems Engineering)
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A Deterministic and Stochastic Fractional-Order ILSR Rumor Propagation Model Incorporating Media Reports and a Nonlinear Inhibition Mechanism
by
Xuefeng Yue and Weiwei Zhu
Symmetry 2024, 16(5), 602; https://doi.org/10.3390/sym16050602 - 13 May 2024
Abstract
Nowadays, rumors spread more rapidly than before, leading to more panic and instability in society. Therefore, it is essential to seek out propagation law in order to prevent rumors from spreading further and avoid unnecessary harm. There is a connection between rumor models
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Nowadays, rumors spread more rapidly than before, leading to more panic and instability in society. Therefore, it is essential to seek out propagation law in order to prevent rumors from spreading further and avoid unnecessary harm. There is a connection between rumor models and symmetry. The consistency of a system or model is referred to as the level of symmetry under certain transformations. For this purpose, we propose a fractional-order Ignorant–Latent–Spreader–Remover (ILSR) rumor propagation model that incorporates media reports and a nonlinear inhibition mechanism. Firstly, the boundedness and non-negativeness of the solutions are derived under fractional differential equations. Secondly, the threshold is used to evaluate and illustrate the stability both locally and globally. Finally, by utilizing Pontryagin’s maximum principle, we obtain the necessary conditions for the optimal control in the fractional-order rumor propagation model, and we also obtain the associated optimal solutions. Furthermore, the numerical results indicate that media reports can decrease the spread of rumors in different dynamic regions, but they cannot completely prevent rumor dissemination. The results are also exhibited and corroborated by replicating the model with specific hypothetical parameter values. It can be inferred that fractional order yields more favorable outcomes when rumor permanence in the population is higher. The presented method facilitates the acquisition of profound insights into the dissemination dynamics and subsequent consequences of rumors within a societal network.
Full article
(This article belongs to the Section Mathematics)
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