期刊名：Symmetry

期刊主页：https://www.mdpi.com/journal/symmetry

对称理论、泛函分析与计算数学持续为非线性系统、动力学建模、优化算法、工程仿真提供底层理论支撑。本专题汇集发表于 Symmetry 的系列研究，系统展现现代数学理论与数值方法的前沿进展，研究范畴涵盖无穷积分方程组、分数阶微积分、四元数与对偶四元数矩阵方程、不动点理论、演化偏微分系统、李群分析、图论哈密顿问题、元胞自动机、ζ 函数逼近、分形几何；同时包含高维统计建模、强化学习收敛性分析、混沌控制、洛伦兹不变理论、张量方程数值求解、k 近邻条件过程理论、贝叶斯参数估计、无人机路径优化、生物系统稳定性、熔岩流分形特征以及人体体脂测算模型等方向。成果融合基础数学理论推导、高效数值算法实现与多领域工程应用，完整呈现对称思想、非线性分析与计算方法赋能数理科学、信息科学、生命科学及复杂系统研究的广阔前景。

1. Asymptotically Stable Solutions of Infinite Systems of Quadratic Hammerstein Integral Equations

渐近稳定解：二次哈默斯坦积分方程

http://www.mdpi.com/2073-8994/16/1/107

Bana?, J.; Madej, J. Asymptotically Stable Solutions of Infinite Systems of Quadratic Hammerstein Integral Equations. Symmetry 2024, 16, 107.

2. Semi-Separable Potentials as Solutions to the 3D Inverse Problem of Newtonian Dynamics

半可分离势：牛顿动力学三维逆问题的解

http://www.mdpi.com/2073-8994/16/2/198

Kotoulas, T. Semi-Separable Potentials as Solutions to the 3D Inverse Problem of Newtonian Dynamics. Symmetry 2024, 16, 198.

3. g.ridge: An R Package for Generalized Ridge Regression for Sparse and High-Dimensional Linear Models

g.ridge：适用于稀疏高维线性模型的广义岭回归 R 程序包

http://www.mdpi.com/2073-8994/16/2/223

Emura, T.; Matsumoto, K.; Uozumi, R.; Michimae, H. g.ridge: An R Package for Generalized Ridge Regression for Sparse and High-Dimensional Linear Models. Symmetry 2024, 16, 223.

4. Numerical Algorithms for Approximation of Fractional Integrals and Derivatives Based on Quintic Spline Interpolation

基于五次样条插值的分数积分与微分数值算法

http://www.mdpi.com/2073-8994/16/2/252

Ciesielski, M. Numerical Algorithms for Approximation of Fractional Integrals and Derivatives Based on Quintic Spline Interpolation. Symmetry 2024, 16, 252.

5. Dual Quaternion Matrix Equation AXB = C with Applications

双四元数矩阵方程 AXB=C 及其应用

http://www.mdpi.com/2073-8994/16/3/287

Chen, Y.; Wang, Q.-W.; Xie, L.-M. Dual Quaternion Matrix Equation AXB = C with Applications. Symmetry 2024, 16, 287.

6. Partial Control and Beyond: Controlling Chaotic Transients with the Safety Function

偏控制及拓展：基于安全函数抑制混沌暂态

http://www.mdpi.com/2073-8994/16/3/338

Capeáns, R.; Sanjuan, M.A.F. Partial Control and Beyond: Controlling Chaotic Transients with the Safety Function. Symmetry 2024, 16, 338.

7. The Hermitian Solution to a New System of Commutative Quaternion Matrix Equations

一类新型交换四元数矩阵方程的厄米特解

http://www.mdpi.com/2073-8994/16/3/361

Zhang, Y.; Wang, Q.-W.; Xie, L.-M. The Hermitian Solution to a New System of Commutative Quaternion Matrix Equations. Symmetry 2024, 16, 361.

8. The General Solution to a Classical Matrix Equation AXB = C over the Dual Split Quaternion Algebra

对偶分裂四元数代数上经典矩阵方程 AXB=C 的通解

http://www.mdpi.com/2073-8994/16/4/491

Si, K.-W.; Wang, Q.-W. The General Solution to a Classical Matrix Equation AXB = C over the Dual Split Quaternion Algebra. Symmetry 2024, 16, 491.

9. Evolution of Hybrid Cellular Automata for Density Classification Problem

面向密度分类问题的混合元胞自动机演化研究

http://www.mdpi.com/2073-8994/16/5/599

Anghelescu, P. Evolution of Hybrid Cellular Automata for Density Classification Problem. Symmetry 2024, 16, 599.

10. Nonexpansiveness and Fractal Maps in Hilbert Spaces

希尔伯特空间中的非扩张映射与分形映射

http://www.mdpi.com/2073-8994/16/6/738

Navascués, M.A. Nonexpansiveness and Fractal Maps in Hilbert Spaces. Symmetry 2024, 16, 738.

11. A Factory of Fractional Derivatives

分数导数统一构造框架

http://www.mdpi.com/2073-8994/16/7/814

Ortigueira, M.D. A Factory of Fractional Derivatives. Symmetry 2024, 16, 814.

12. Anthropometric Formulas Repurposed to Predict Body Fat Content from Ultrasound Measurements

人体测量公式改良：基于超声皮下脂肪厚度测算体脂率

http://www.mdpi.com/2073-8994/16/8/962

Muntean, P.; Miclos-Balica, M.; Macavei, G.A.; Munteanu, O.; Neagu, A.; Neagu, M. Anthropometric Formulas Repurposed to Predict Body Fat Content from Ultrasound Measurements of Subcutaneous Fat Thickness. Symmetry 2024, 16, 962.

13. Symmetries and Invariant Solutions of Higher-Order Evolution Systems

高阶演化系统的对称与不变解

http://www.mdpi.com/2073-8994/16/8/1023

Tracinà, R. Symmetries and Invariant Solutions of Higher-Order Evolution Systems. Symmetry 2024, 16, 1023.

14. New Fixed Point Theorems for Generalized Meir–Keeler Type Nonlinear Mappings

广义 Meir–Keeler 型非线性映射的新型不动点定理及其应用

http://www.mdpi.com/2073-8994/16/8/1088

Huang, S.-Y.; Du, W.-S. New Fixed Point Theorems for Generalized Meir–Keeler Type Nonlinear Mappings with Applications to Fixed Point Theory. Symmetry 2024, 16, 1088.

15. Three-Dimensional Lorentz-Invariant Velocities

三维洛伦兹不变速度场研究

http://www.mdpi.com/2073-8994/16/9/1133

Hill, J.M. Three-Dimensional Lorentz-Invariant Velocities. Symmetry 2024, 16, 1133.

16. Spectral Properties of Dual Unit Gain Graph

对偶单位增益图的谱特性分析

http://www.mdpi.com/2073-8994/16/9/1142

Cui, C.; Lu, Y.; Qi, L.; Wang, L. Spectral Properties of Dual Unit Gain Graphs. Symmetry 2024, 16, 1142.

17. The BiCG Algorithm for Solving the Minimal Frobenius Norm Solution of Generalized Sylvester Tensor Equation

双共轭梯度法求解广义西尔维斯特张量最小 Frobenius 范数解

http://www.mdpi.com/2073-8994/16/9/1167

Xie, M.; Wang, Q.-W.; Zhang, Y. The BiCG Algorithm for Solving the Minimal Frobenius Norm Solution of Generalized Sylvester Tensor Equation over the Quaternions. Symmetry 2024, 16, 1167.

18. Solving the Dual Generalized Commutative Quaternion Matrix Equation AXB = C

对偶交换四元数矩阵方程 AXB=C 求解

http://www.mdpi.com/2073-8994/16/10/1359

Shi, L.; Wang, Q.-W.; Xie, L.-M.; Zhang, X.-F. Solving the Dual Generalized Commutative Quaternion Matrix Equation AXB = C. Symmetry 2024, 16, 1359.

19. Uniform Consistency and Weak Convergence of k-NN Single Index Conditional U-Processes

含函数混合数据的 k 近邻单指标条件过程与 U 过程：一致邻域收敛与弱收敛性

http://www.mdpi.com/2073-8994/16/12/1576

Bouzebda, S. Uniform in Number of Neighbor Consistency and Weak Convergence of k-Nearest Neighbor Single Index Conditional Processes and k-Nearest Neighbor Single Index Conditional U-Processes Involving Functional Mixing Data. Symmetry 2024, 16, 1576.

20. Joint Approximation by the Riemann and Hurwitz Zeta-Functions in Short Intervals

小区间内黎曼 ζ 函数与赫尔维茨 ζ 函数联合逼近

http://www.mdpi.com/2073-8994/16/12/1707

Laurin?ikas, A. Joint Approximation by the Riemann and Hurwitz Zeta-Functions in Short Intervals. Symmetry 2024, 16, 1707.

21. The One-Fault Dimension-Balanced Hamiltonian Problem in Toroidal Mesh Graphs

环面网格图单故障维度均衡哈密顿问题

http://www.mdpi.com/2073-8994/17/1/93

Juan, J.S.-T.; Ciou, H.-C.; Lin, M.-J. The One-Fault Dimension-Balanced Hamiltonian Problem in Toroidal Mesh Graphs. Symmetry 2025, 17, 93.

22. Bi-Symmetric Polyhedral Cages with Maximally Connected Faces

面连通度最大化的双对称多面体笼结构

http://www.mdpi.com/2073-8994/17/1/101

Piette, B.; Lukács, Á. Bi-Symmetric Polyhedral Cages with Maximally Connected Faces and Small Holes. Symmetry 2025, 17, 101.

23. Estimation and Bayesian Prediction for the Generalized Exponential Distribution Under Type-II Censoring

第二类截尾下广义指数分布的参数估计与贝叶斯预测

http://www.mdpi.com/2073-8994/17/2/222

Wang, W.; Gui, W. Estimation and Bayesian Prediction for the Generalized Exponential Distribution Under Type-II Censoring. Symmetry 2025, 17, 222.

24. Discrete-Time Dynamical Systems on Structured State Spaces: State-Transition Laws in Finite-Dimensional Lie Algebras

结构化状态空间离散动力系统：有限维李代数状态转移规律

http://www.mdpi.com/2073-8994/17/3/463

Fiori, S. Discrete-Time Dynamical Systems on Structured State Spaces: State-Transition Laws in Finite-Dimensional Lie Algebras. Symmetry 2025, 17, 463.

25. Convergence Analysis of Reinforcement Learning Algorithms Using Generalized Weak Contraction Mappings

基于广义弱压缩映射的强化学习算法收敛性分析

http://www.mdpi.com/2073-8994/17/5/750

Belhenniche, A.; Chertovskih, R.; Gonçalves, R. Convergence Analysis of Reinforcement Learning Algorithms Using Generalized Weak Contraction Mappings. Symmetry 2025, 17, 750.

Symmetry 2025, 17, 750.

26. Lie Group Classification for a Reduced Burgers System

简化伯格斯方程组的李群分类研究

http://www.mdpi.com/2073-8994/17/5/763

Sophocleous, C.; Tracinà, R. Lie Group Classification for a Reduced Burgers System. Symmetry 2025, 17, 763.

27. 3D UAV Route Optimization in Complex Environments Using an Enhanced Artificial Lemming Algorithm

基于改进人工旅鼠算法的复杂环境无人机三维航迹优化

http://www.mdpi.com/2073-8994/17/6/946

Xie, Y.; Sun, Z.; Yuan, K.; Sun, Z. 3D UAV Route Optimization in Complex Environments Using an Enhanced Artificial Lemming Algorithm. Symmetry 2025, 17, 946.

28. Stability Analysis of Biological Systems Under Threshold Conditions

阈值约束下生物系统的稳定性分析

http://www.mdpi.com/2073-8994/17/8/1193

Mahbuba, J.E.; Wang, X.-S. Stability Analysis of Biological Systems Under Threshold Conditions. Symmetry 2025, 17, 1193.

29. Fractal Complexity and Symmetry in Lava Flow Emplacement

熔岩堆积过程的分形复杂度与对称特性研究

http://www.mdpi.com/2073-8994/17/9/1502

Miguel, A.F. Fractal Complexity and Symmetry in Lava Flow Emplacement. Symmetry 2025, 17, 1502.

期刊介绍

主编：Sergei D. Odintsov, Institute of Space Sciences (IEEC-CSIC), Spain

荣誉主编：蔡荣根教授，宁波大学；张继平教授，北京大学

期刊主题涵盖了所有科学研究中有关对称/非对称现象的理论和应用研究，主要包括数学、计算机、工程与材料、物理学、生命科学、化学等领域的最新进展。期刊已被 Scopus、SCIE (Web of Science)、CAPlus/SciFinder 等多家知名数据库收录。

2025 Impact Factor 2.2

2025 CiteScore 5.2

Time to First Decision 16.3 Days

Acceptance to Publication 2.9 Days