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
Existence Results for Tempered-Hilfer Fractional Differential Problems on Hölder Spaces
Symmetry 2024, 16(6), 700; https://doi.org/10.3390/sym16060700 (registering DOI) - 5 Jun 2024
Abstract
This paper considers a nonlinear fractional-order boundary value problem
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This paper considers a nonlinear fractional-order boundary value problem for , , , with appropriate integral boundary conditions on the Hölder spaces. Here, f is a real-valued function that satisfies the Hölder condition, and represents the tempered-Hilfer fractional derivative of order with parameter and type . The corresponding integral problem is introduced in the study of this issue. This paper addresses a fundamental issue in the field, namely the circumstances under which differential and integral problems are equivalent. This approach enables the study of differential problems using integral operators. In order to achieve this, tempered fractional calculus and the equivalence problem of the studied problems are introduced and studied. The selection of an appropriate function space is of fundamental importance. This paper investigates the applicability of these operators on Hölder spaces and provides a comprehensive rationale for this choice.
Full article
(This article belongs to the Special Issue Symmetry in Differential Equations and Integral Operators)
Open AccessArticle
Research on Decomposition and Offloading Strategies for Complex Divisible Computing Tasks in Computing Power Networks
by
Ping He, Jiayue Cang, Huaying Qi and Hui Li
Symmetry 2024, 16(6), 699; https://doi.org/10.3390/sym16060699 (registering DOI) - 5 Jun 2024
Abstract
With the continuous emergence of intelligent network applications and complex tasks for mobile terminals, the traditional single computing model often fails to meet the greater requirements of computing and network technology, thus promoting the formation of a new computing power network architecture, of
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With the continuous emergence of intelligent network applications and complex tasks for mobile terminals, the traditional single computing model often fails to meet the greater requirements of computing and network technology, thus promoting the formation of a new computing power network architecture, of ‘cloud, edge and end’ three-level heterogeneous computing. For complex divisible computing tasks in the network, task decomposition and offloading help to realize a distributed execution of tasks, thus reducing the overall running time and improving the utilization of fragmented resources in the network. However, in the process of task decomposition and offloading, there are problems, such as there only being a single method of task decomposition; that too large or too small decomposition granularity will lead to an increase in transmission delay; and the pursuit of low-delay and low-energy offloading requirements. Based on this, a complex divisible computing task decomposition and offloading scheme is proposed. Firstly, the computational task is decomposed into multiple task elements based on code partitioning, and then a density-peak-clustering algorithm with an improved adaptive truncation distance and clustering center (ATDCC-DPC) is proposed to cluster the task elements into subtasks based on the task elements themselves and the dependencies between the task elements. Secondly, taking the subtasks as the offloading objects, the improved Double Deep Q-Network subtask offloading algorithm (ISO-DDQN) is proposed to find the optimal offloading scheme that minimizes the delay and energy consumption. Finally, the proposed algorithms are verified by simulation experiments, and the scheme in this paper can effectively reduce the task delay and energy consumption and improve the service experience.
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(This article belongs to the Section Computer)
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Improving the Robustness of the Theil-Sen Estimator Using a Simple Heuristic-Based Modification
by
Artur Bal
Symmetry 2024, 16(6), 698; https://doi.org/10.3390/sym16060698 (registering DOI) - 5 Jun 2024
Abstract
One of the most widely used robust regression methods for solving simple linear regression problems is the Theil-Sen (TS) estimator. This estimator has some notable advantages; however, it does not belong to the most robust estimation methods (called high-breakdown estimators) and is prone
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One of the most widely used robust regression methods for solving simple linear regression problems is the Theil-Sen (TS) estimator. This estimator has some notable advantages; however, it does not belong to the most robust estimation methods (called high-breakdown estimators) and is prone to outliers whose distribution is highly asymmetric with respect to the correct data points. This paper presents a modification of the TS estimator, the Robustified Theil-Sen (RTS) estimator. The new method uses a heuristic-based selection procedure to reduce the number of initial estimates of the regression function parameters computed with at least one outlier, thereby improving the regression results. The use of this heuristic procedure only slightly increases the computational time required for using the RTS estimator compared to the TS estimator. Preliminary results of two numerical experiments presented in the paper show that the RTS estimator outperforms other comparable estimators, i.e., the TS estimator and the repeated median estimator, in terms of robustness. The results presented also suggest that the breakpoint value (which is a measure of the robustness of estimators) of the RTS estimator is higher than the breakpoint value of the TS estimator and equal to the breakpoint value of the high-breakpoint estimators.
Full article
(This article belongs to the Special Issue Symmetrical and Asymmetrical Distributions in Statistics and Data Science II)
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A Knowledge-Guided Multi-Objective Shuffled Frog Leaping Algorithm for Dynamic Multi-Depot Multi-Trip Vehicle Routing Problem
by
Yun Zhao, Xiaoning Shen and Zhongpei Ge
Symmetry 2024, 16(6), 697; https://doi.org/10.3390/sym16060697 - 5 Jun 2024
Abstract
Optimization algorithms have a wide range of applications in symmetry problems, such as graphs, networks, and pattern recognition. In this paper, a dynamic periodic multi-depot multi-trip vehicle routing model for scheduling test samples is constructed, which considers the differences in testing unit price
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Optimization algorithms have a wide range of applications in symmetry problems, such as graphs, networks, and pattern recognition. In this paper, a dynamic periodic multi-depot multi-trip vehicle routing model for scheduling test samples is constructed, which considers the differences in testing unit price and testing capacity of various agencies and introduces a cross-depot collaborative transport method. Both the cost and the testing time are minimized by determining the optimal sampling routes and testing agencies, subjecting to the constraints of vehicle capacity, number of vehicles, and delivery time. To solve the model, a knowledge-guided multi-objective shuffled frog leaping algorithm (KMOSFLA) is proposed. KMOSFLA adopts a convertible encoding mechanism to realize the diversified search in different search spaces. Three novel strategies are designed: the population initialization with historical information reuse, the leaping rule based on the greedy crossover and genetic recombination, and the objective-driven enhanced search. Systematic experimental studies are implemented. First, feasibility analyses of the model are carried out, where effectiveness of the cross-depot collaborative transport is validated and sensitivity analyses on two parameters (vehicle capacity and proportion of the third-party testing agencies) are performed. Then, the proposed algorithm KMOSFLA is compared with five state-of-the-art algorithms. Experimental results indicate that KMOSFLA can provide a set of non-dominated schedules with lower cost and shorter testing time in each scheduling period, which provides a reference for the dispatcher to make a final decision.
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(This article belongs to the Section Computer)
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Magneto Axisymmetric Vibration of FG-GPLs Reinforced Annular Sandwich Plates with an FG Porous Core Using DQM and a New Shear Deformation Theory
by
Aamna H. K. Al-Ali, Fatemah H. H. Al Mukahal and Mohammed Sobhy
Symmetry 2024, 16(6), 696; https://doi.org/10.3390/sym16060696 - 5 Jun 2024
Abstract
Based on the differential quadrature procedure (DQP), the vibrational response of functionally graded (FG) sandwich annular plates enhanced with graphene platelets (GPLs) and with an FG porous core is illustrated in this paper. The current annular plate is assumed to deform axisymmetrically and
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Based on the differential quadrature procedure (DQP), the vibrational response of functionally graded (FG) sandwich annular plates enhanced with graphene platelets (GPLs) and with an FG porous core is illustrated in this paper. The current annular plate is assumed to deform axisymmetrically and expose to a radial magnetic field. The Lorentz magnetic body force is deduced via Maxwell’s relations. The effective physical properties of the upper and lower layers of the sandwich plate are obtained by employing the Halpin–Tsai model. Our technique depends on a new four-unknown shear deformation theory to depict the displacements. In addition, the motion equations are established via Hamilton’s principle. The motion equations are solved by employing the DQP. In order to study the convergence of the DQ method, the minimum number of grid points needed for a converged solution is ascertained. In addition, the current theory’s outcomes are compared with those of previous higher-order theories. The effects of the porosity distribution type, porosity factor, GPLs distribution pattern, GPLs weight fraction, inner-to-outer radius ratio, outer radius-to-thickness ratio, magnetic field parameters, core thickness, and elastic substrate parameters on the nondimensional vibration frequencies are discussed.
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(This article belongs to the Section Mathematics)
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The Influence of the Interface on the Micromechanical Behavior of Unidirectional Fiber-Reinforced Ceramic Matrix Composites: An Analysis Based on the Periodic Symmetric Boundary Conditions
by
Wei Yan, Shilun Shi, Longcheng Xiao, Xiulun Li and Jian Xu
Symmetry 2024, 16(6), 695; https://doi.org/10.3390/sym16060695 - 5 Jun 2024
Abstract
The long-term periodicity and uncontrollable interface properties during the preparation process for silicon carbide fiber reinforced silicon carbide-based composites (SiCf/SiC CMC) make it difficult to thoroughly investigate their mechanical damage behavior under complex loading conditions. To delve deeper into the influence
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The long-term periodicity and uncontrollable interface properties during the preparation process for silicon carbide fiber reinforced silicon carbide-based composites (SiCf/SiC CMC) make it difficult to thoroughly investigate their mechanical damage behavior under complex loading conditions. To delve deeper into the influence of the interface strength and toughness on the mechanical response of microscopic representative volume element (RVE) models under complex loading conditions, in this work, based on numerical simulation methods, a microscale representative volume element (RVE) with periodic symmetric boundary conditions for the material is constructed. The phase-field fracture theory and cohesive zone model are coupled to capture the brittle cracking of the matrix and the debonding behavior at the fiber/matrix interface. Simulation analysis is conducted for tensile, compressive, and shear loading as well as combined loading, and the validity of the model is verified based on the Chamis theory. Further investigation is conducted into the mechanical response behavior of the microscale RVE model under complex loading conditions in relation to the interface strength and interface toughness. The results indicate that under uniaxial loading, increasing the interface strength leads to a tighter bond between the fiber and matrix, suppressing crack initiation and propagation, and significantly increasing the material’s fracture strength. However, compared to the transverse compressive strength, increasing the interface strength does not continuously enhance the strength under other loading conditions. Meanwhile, under the condition of strong interface strength of 400 MPa, an increase in the interface toughness significantly increases the transverse compressive strength of the material. When it increases from 2 J/m2 to 20 J/m2, the transverse compressive strength increases by 28.49%. Under biaxial combined loading, increasing the interface strength significantly widens the failure envelope space under σ2-τ23 combined loading; with the transition from transverse compressive stress to tensile stress, the transverse shear strength shows a trend of first increasing and then decreasing, and when the ratio of transverse shear displacement to transverse tensile/compressive displacement is −1, it reaches the maximum. This study provides strong numerical support for the investigation of the interface properties and mechanical behavior of SiCf/SiC composites under complex loading conditions, offering important references for engineering design and material performance optimization.
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(This article belongs to the Special Issue Asymmetry and Symmetry in Dynamical Systems)
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On Generalized Fibospinomials: Generalized Fibonacci Polynomial Spinors
by
Ece Gülşah Çolak, Nazmiye Gönül Bilgin and Yüksel Soykan
Symmetry 2024, 16(6), 694; https://doi.org/10.3390/sym16060694 - 5 Jun 2024
Abstract
Spinors are important objects in physics, which have found their place more and more after the discovery that particles have an intrinsic angular momentum shape and Cartan’s mathematical expression of this situation. Recent studies using special number sequences have also revealed a new
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Spinors are important objects in physics, which have found their place more and more after the discovery that particles have an intrinsic angular momentum shape and Cartan’s mathematical expression of this situation. Recent studies using special number sequences have also revealed a new approach to the use of spinors in mathematics and have provided a different perspective for spinor research that can be used as a source for future physics studies. The purpose of this work is to expand the generalized Fibonacci quaternion polynomials to the generalized Fibonacci polynomial spinors by associating spinors with quaternions, and to introduce and investigate a new polynomial sequence that can be used to benefit from the potential advantages of spinors in physical applications, and thus, to provide mathematical arguments, such as new polynomials, for studies using spinors and quaternions in quantum mechanics. Starting from this point of view, in this paper we introduce and investigate a new family of sequences called generalized Fibospinomials (or generalized Fibonacci polynomial spinors or Horadam polynomial spinors). Being particular cases, we use -Fibonacci and -Lucas polynomial spinors. We present Binet’s formulas, generating functions and the summation formulas for these polynomials. In addition, we obtain some special identities of these new sequences and matrices related to these polynomials. The importance of this study is that generalized Fibospinomials are currently the most generalized sequence in the literature when moving from Fibonacci quaternions to spinor structure, and that a wide variety of new spinor sequences can be obtained from this particular polynomial sequence.
Full article
(This article belongs to the Special Issue Asymmetric and Symmetric Study on Number Theory and Cryptography)
Open AccessArticle
Covering-Based Intuitionistic Hesitant Fuzzy Rough Set Models and Their Application to Decision-Making Problems
by
Muhammad Kamraz Khan, Kamran, Muhammad Sajjad Ali Khan, Ahmad Aloqaily and Nabil Mlaiki
Symmetry 2024, 16(6), 693; https://doi.org/10.3390/sym16060693 - 4 Jun 2024
Abstract
In this paper, we present four categories of covering-based intuitionistic hesitant fuzzy rough set (CIHFRS) models using intuitionistic hesitant fuzzy -neighborhoods (IHF -neighborhoods) and intuitionistic hesitant fuzzy complementary -neighborhoods (IHFC -neighborhoods. Through theoretical analysis of covering-based IHFRS models, we
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In this paper, we present four categories of covering-based intuitionistic hesitant fuzzy rough set (CIHFRS) models using intuitionistic hesitant fuzzy -neighborhoods (IHF -neighborhoods) and intuitionistic hesitant fuzzy complementary -neighborhoods (IHFC -neighborhoods. Through theoretical analysis of covering-based IHFRS models, we propose the intuitionistic hesitant fuzzy TOPSIS (IHF-TOPSIS) technique for order of preference by similarity to an ideal solution, addressing multicriteria decision-making (MCDM) challenges concerning the assessment of IHF data. A compelling example aptly showcases the suggested approach. Furthermore, we address MCDM problems regarding the assessment of IHF information based on CIHFRS models. Through comparison and analysis, it is evident that addressing MCDM problems by assessing IHF data using CIHFRS models proves more effective than utilizing intuitionistic fuzzy data with CIFRS models or hesitant fuzzy information with CHFRS models. IHFS emerges as a unique and superior tool for addressing real-world challenges. Additionally, covering-based rough sets (CRSs) have been successfully applied to decision problems due to their robust capability in handling unclear data. In this study, by combining CRSs with IHFS, four classes of CIFRS versions are established using IHF -neighborhoods and IHFC -neighborhoods. A corresponding approximation axiomatic system is developed for each. The roughness and precision degrees of CBIHFRS models are specifically talked about. The relationship among these four types of IHFRS versions and existing related versions is presented based on theoretical investigations. A method for MCDM problems through IHF information, namely, IHF-TOPSIS, is introduced to further demonstrate its effectiveness and applicability. By conducting a comparative study, the effectiveness of the suggested approach is evaluated.
Full article
(This article belongs to the Special Issue Fuzzy Covering Rough Set and Its Applications)
Open AccessArticle
Control of Three-Dimensional Natural Convection of Graphene–Water Nanofluids Using Symmetrical Tree-Shaped Obstacle and External Magnetic Field
by
Walid Aich, Inès Hilali-Jaghdam, Amnah Alshahrani, Chemseddine Maatki, Badr M. Alshammari and Lioua Kolsi
Symmetry 2024, 16(6), 692; https://doi.org/10.3390/sym16060692 - 4 Jun 2024
Abstract
This numerical investigation explores the enhanced control of the 3D natural convection (NC) within a cubic cavity filled with graphene–water nanofluids, utilizing a bottom-center-located tree-shaped obstacle and a horizontal magnetic field (MF). The analysis includes the effects of the Rayleigh number (Ra), the
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This numerical investigation explores the enhanced control of the 3D natural convection (NC) within a cubic cavity filled with graphene–water nanofluids, utilizing a bottom-center-located tree-shaped obstacle and a horizontal magnetic field (MF). The analysis includes the effects of the Rayleigh number (Ra), the solid volume fraction of graphene ( ), the Hartmann number (Ha), and the fins’ length (W). The results show complex flow patterns and thermal behavior within the cavity, indicating the interactive effects of nanofluid properties, the tree-shaped obstacle, and magnetic field effects. The MHD effects reduce the convection, while the addition of graphene improves the thermal conductivity of the fluid, which enhances the heat transfer observed with increasing Rayleigh numbers. The increase in the fins’ length on the heat transfer efficiency is found to be slightly negative, which is attributed to the complex interplay between the enhanced heat transfer surface area and fluid flow disruption. This study presents an original combination of non-destructive methods (magnetic field) and a destructive method (tree-shaped obstacle) for the control of the fluid flow and heat transfer characteristics in a 3D cavity filled with graphene–water nanofluids. In addition, it provides valuable information for optimizing heat transfer control strategies, with applications in electronic cooling, renewable energy systems, and advanced thermal management solutions. The application of a magnetic field was found to reduce the maximum velocity and total entropy generation by about 82% and 76%, respectively. The addition of graphene nanoparticles was found to reduce the maximum velocity by about 5.5% without the magnetic field and to increase it by 1.12% for Ha = 100. Varying the obstacles’ length from W = 0.2 to W = 0.8 led to a reduction in velocity by about 23.6%.
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(This article belongs to the Special Issue Symmetry in Thermal Fluid Sciences and Energy Applications)
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Relation-Preserving Functional Contractions Involving a Triplet of Auxiliary Functions with an Application to Integral Equations
by
Doaa Filali and Faizan Ahmad Khan
Symmetry 2024, 16(6), 691; https://doi.org/10.3390/sym16060691 - 4 Jun 2024
Abstract
This article addresses certain fixed-point results in a metric space equipped with a locally transitive binary relation under a functional contraction containing three auxiliary functions. The findings proved herein enrich and improve a number of existing results. In order to prove the credibility
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This article addresses certain fixed-point results in a metric space equipped with a locally transitive binary relation under a functional contraction containing three auxiliary functions. The findings proved herein enrich and improve a number of existing results. In order to prove the credibility of our findings, an illustrative example is provided. Making use of our findings, we study the genuineness of the unique solution to a Fredholm integral equation.
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(This article belongs to the Special Issue Elementary Fixed Point Theory and Common Fixed Points II)
Open AccessArticle
A Novel Constraint-Aware Flexible Model with Ant Colony Optimization for Symmetrical Travel Recommendation
by
Mohammed Alatiyyah
Symmetry 2024, 16(6), 690; https://doi.org/10.3390/sym16060690 - 4 Jun 2024
Abstract
This paper proposes a flexible travel recommender model (FTRM) that emphasizes the symmetry between user preferences and travel constraints, addressing key challenges in the field such as the integration of diverse constraint types and the customization of travel itineraries. The key contribution of
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This paper proposes a flexible travel recommender model (FTRM) that emphasizes the symmetry between user preferences and travel constraints, addressing key challenges in the field such as the integration of diverse constraint types and the customization of travel itineraries. The key contribution of the proposed model lies in its integration with the item constraints data model (ICDM), which effectively manages a plethora of constraint types. Additionally, this study develops a novel algorithm inspired by ant colony optimization (ACO) principles, demonstrating performance metrics that are comparable to state-of-the-art algorithms in this field. A comprehensive set of systematic experimental analyses is conducted, employing various models across diverse situational contexts, with the primary goal of illustrating the capabilities of the proposed symmetrical FTRM using real-world data from the Durham dataset. The obtained results highlight the model’s ability to accommodate diverse constraint types, facilitating the customization of travel itineraries to suit individual user preferences and achieve a balanced and symmetrical travel experience. Specifically, our model outperforms existing models in terms of flexibility and customization, showing significant improvements in user satisfaction and itinerary efficiency.
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(This article belongs to the Section Computer)
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Investigation on the Influence of Film Cooling Structure on the Flow and Heat Transfer Characteristics of Axisymmetric Plug Nozzle
by
Zhuang Ma, Bo Zhang and Yun Bai
Symmetry 2024, 16(6), 689; https://doi.org/10.3390/sym16060689 - 4 Jun 2024
Abstract
Some numerical simulations were used to study the effects of blowing ratio (0.25–0.5), hole diameters(0.65~1 mm), and hole inclination angle (30~60°) of the film cooling structure on the cooling and aerodynamic characteristics of the axisymmetric plug nozzle under the condition of transonic. The
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Some numerical simulations were used to study the effects of blowing ratio (0.25–0.5), hole diameters(0.65~1 mm), and hole inclination angle (30~60°) of the film cooling structure on the cooling and aerodynamic characteristics of the axisymmetric plug nozzle under the condition of transonic. The results showed that the bow shocks appear near the film holes on the plug wall in the supersonic region, which cause the wall cooling effectiveness of the plug to decrease. Compared with the baseline plug, the blowing ratio ranged from 0.25 to 0.5, the wall average temperature of the rear plug decreased by 34.4~48.1%, the thrust coefficient and total pressure recovery coefficient decreased by 0.31~0.61% and 0.52~0.93%, respectively. When the perforated percentage is constant, the wall cooling effectiveness increases with the decrease of the hole diameters. The increase in the inclination angle of the film holes lead to the decrease in cooling effectiveness and aerodynamic performance. This is because the penetration ability of the cooling air to the mainstream is enhanced, and the obstruction to the mainstream boundary layer is increased, resulting in the increase of bow shock intensity near the film holes in the supersonic region.
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(This article belongs to the Special Issue Advances in Heat and Mass Transfer with Symmetry)
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Bogdanov–Takens Bifurcation of Kermack–McKendrick Model with Nonlinear Contact Rates Caused by Multiple Exposures
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Jun Li and Mingju Ma
Symmetry 2024, 16(6), 688; https://doi.org/10.3390/sym16060688 - 4 Jun 2024
Abstract
In this paper, we consider the influence of a nonlinear contact rate caused by multiple contacts in classical SIR model. In this paper, we unversal unfolding a nilpotent cusp singularity in such systems through normal form theory, we reveal that the system undergoes
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In this paper, we consider the influence of a nonlinear contact rate caused by multiple contacts in classical SIR model. In this paper, we unversal unfolding a nilpotent cusp singularity in such systems through normal form theory, we reveal that the system undergoes a Bogdanov-Takens bifurcation with codimension 2. During the bifurcation process, numerous lower codimension bifurcations may emerge simultaneously, such as saddle-node and Hopf bifurcations with codimension 1. Finally, employing the Matcont and Phase Plane software, we construct bifurcation diagrams and topological phase portraits. Additionally, we emphasize the role of symmetry in our analysis. By considering the inherent symmetries in the system, we provide a more comprehensive understanding of the dynamical behavior. Our findings suggest that if this occurrence rate is applied to the SIR model, it would yield different dynamical phenomena compared to those obtained by reducing a 3-dimensional dynamical model to a planar system by neglecting the disease mortality rate, which results in a stable nilpotent cusp singularity with codimension 2. We found that in SIR models with the same occurrence rate, both stable and unstable Bogdanov-Takens bifurcations occur, meaning both stable and unstable limit cycles appear in this system.
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(This article belongs to the Special Issue Symmetry/Asymmetry of Differential Equations in Biomathematics)
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Dynamical Analysis and Synchronization of Complex Network Dynamic Systems under Continuous-Time
by
Rui Yang, Huaigu Tian, Zhen Wang, Wei Wang and Yang Zhang
Symmetry 2024, 16(6), 687; https://doi.org/10.3390/sym16060687 (registering DOI) - 4 Jun 2024
Abstract
In multilayer complex networks, the uncertainty in node states leads to intricate behaviors. It is, therefore, of great importance to be able to estimate the states of target nodes in these systems, both for theoretical advancements and practical applications. This paper introduces a
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In multilayer complex networks, the uncertainty in node states leads to intricate behaviors. It is, therefore, of great importance to be able to estimate the states of target nodes in these systems, both for theoretical advancements and practical applications. This paper introduces a state observer-based approach for the state estimation of such networks, focusing specifically on a class of complex dynamic networks with nodes that correspond one-to-one. Initially, a chaotic system is employed to model the dynamics of each node and highlight the essential state components for analysis and derivation. A network state observer is then constructed using a unique diagonal matrix, which underpins the driver and response-layer networks. By integrating control theory and stability function analysis, the effectiveness of the observer in achieving synchronization between complex dynamic networks and target systems is confirmed. Additionally, the efficacy and precision of the proposed method are validated through simulation.
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(This article belongs to the Special Issue Symmetry in Nonlinear Dynamics and Chaos II)
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Several Symmetric Identities of the Generalized Degenerate Fubini Polynomials by the Fermionic p-Adic Integral on
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Maryam Salem Alatawi, Waseem Ahmad Khan and Ugur Duran
Symmetry 2024, 16(6), 686; https://doi.org/10.3390/sym16060686 - 3 Jun 2024
Abstract
After constructions of p-adic q-integrals, in recent years, these integrals with some of their special cases have not only been utilized as integral representations of many special numbers, polynomials, and functions but have also given the chance for deep analysis of
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After constructions of p-adic q-integrals, in recent years, these integrals with some of their special cases have not only been utilized as integral representations of many special numbers, polynomials, and functions but have also given the chance for deep analysis of many families of special polynomials and numbers, such as Bernoulli, Fubini, Bell, and Changhee polynomials and numbers. One of the main applications of these integrals is to obtain symmetric identities for the special polynomials. In this study, we focus on a novel extension of the degenerate Fubini polynomials and on obtaining some symmetric identities for them. First, we introduce the two-variable degenerate w-torsion Fubini polynomials by means of their exponential generating function. Then, we provide a fermionic p-adic integral representation of these polynomials. By this representation, we derive some new symmetric identities for these polynomials, using some special p-adic integral techniques. Lastly, by using some series manipulation techniques, we obtain more identities of symmetry for the two variable degenerate w-torsion Fubini polynomials.
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(This article belongs to the Special Issue Symmetries of Difference Equations, Special Functions and Orthogonal Polynomials II)
Open AccessArticle
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 - 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
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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.
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(This article belongs to the Section Mathematics)
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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 - 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
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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.
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(This article belongs to the Special Issue Symmetry Application in the Control Design of Cyber-Physical Systems)
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Symmetry-Enhanced Fuzzy Logic Analysis in Parallel and Cross-Road Scenarios: Optimizing Direction and Distance Weights for Map Matching
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Weicheng Zhou, Huilin Ge and Muhammad Awais Ashraf
Symmetry 2024, 16(6), 683; https://doi.org/10.3390/sym16060683 - 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
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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.
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(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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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 - 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
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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.
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(This article belongs to the Special Issue Symmetry in Aerospace Sciences and Applications)
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Open AccessReview
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 - 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
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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.
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(This article belongs to the Section Computer)
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Algorithms, Axioms, Fractal Fract, Mathematics, Symmetry
Fractal and Design of Multipoint Iterative Methods for Nonlinear Problems
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Research on Data Mining of Electronic Health Records Using Deep Learning Methods
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Symmetry in Hamiltonian Dynamical Systems
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Global and Local Scale Symmetry in Gravitation and Cosmology
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