IF 2.6 2区数学

Studies in Applied Mathematics Pub Date : 2025-07-04 DOI: 10.1111/sapm.70079

Zihan Yin, Jing Kang, Changzheng Qu

{"title":"Dispersive Revival Phenomena for Two-Dimensional Dispersive Evolution Equations","authors":"Zihan Yin, Jing Kang, Changzheng Qu","doi":"10.1111/sapm.70079","DOIUrl":"https://doi.org/10.1111/sapm.70079","url":null,"abstract":"<div>\u0000 \u0000 <p>In this paper, we investigate dispersive revival phenomena of two-dimensional linear spatially periodic dispersive evolution equations, defined on a rectangle with periodic boundary conditions and discontinuous initial profiles. We begin by studying the periodic initial-boundary value problem for general two-dimensional dispersive evolution equations. We prove that, when posed on a periodic rational torus, two-dimensional linear dispersive equations with homogeneous power integral binary polynomial dispersion relations exhibit the standard dispersive revival effect at rational times. This means that the resulting solution can be expressed as a finite linear combination of translates of the initial data. Next, we explore a novel revival phenomenon in two-dimensional equations with nonpolynomial dispersion relations, in the concrete case of the periodic initial-boundary value problem for the linear Kadomtsev–Petviashvili equation on a square with step function initial data. In this scenario, the revival phenomenon exhibits a novel characteristic that there are radically different qualitative behaviors in the <span></span><math>\u0000 <semantics>\u0000 <mi>x</mi>\u0000 <annotation>$x$</annotation>\u0000 </semantics></math>- and <span></span><math>\u0000 <semantics>\u0000 <mi>y</mi>\u0000 <annotation>$y$</annotation>\u0000 </semantics></math>-directions. We provide an analytic description of this dichotomous revival phenomenon and present illustrative numerical simulations.</p></div>","PeriodicalId":51174,"journal":{"name":"Studies in Applied Mathematics","volume":"155 1","pages":""},"PeriodicalIF":2.6,"publicationDate":"2025-07-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144551215","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

The determinant of the adjacency matrix of a quaternion unit gain graph 四元数单位增益图邻接矩阵的行列式

IF 0.7 3区数学

Discrete Mathematics Pub Date : 2025-07-04 DOI: 10.1016/j.disc.2025.114659

Ivan I. Kyrchei , Eran Treister , Volodymyr O. Pelykh

{"title":"The determinant of the adjacency matrix of a quaternion unit gain graph","authors":"Ivan I. Kyrchei , Eran Treister , Volodymyr O. Pelykh","doi":"10.1016/j.disc.2025.114659","DOIUrl":"10.1016/j.disc.2025.114659","url":null,"abstract":"<div><div>In this paper, we present a combinatorial description of the determinant of the adjacency matrix of a quaternion unit gain graph using recently introduced row-column noncommutative determinants by one of the authors. We define a quaternion unit gain graph as a graph in which each edge's orientation is assigned a quaternion unit, and its opposite orientation is assigned the inverse of this quaternion unit. Initially, we provide detailed combinatorial descriptions of the determinants of the adjacency matrices for a single cycle and a path graph with quaternion unit gains. Subsequently, we investigate the determinant of the adjacency matrix for quaternion unit gain graphs whose underlying graphs consist of multiple cycles and/or path graphs. We introduce a decomposition procedure for such graphs involving reductions obtained by cutting off edges associated with branch vertices so that each reduction's adjacency matrix is equal to the direct sum of its components' adjacency matrices. Our resulting theorem offers a combinatorial description for obtaining the determinant of an adjacency matrix in terms of cycle and graph path adjacency determinants on which they are decomposed. The obtained results are novel for quaternion unit gain graphs and complex ones, and they could be applied to various types of gain graphs, not just those with unit gains.</div></div>","PeriodicalId":50572,"journal":{"name":"Discrete Mathematics","volume":"349 1","pages":"Article 114659"},"PeriodicalIF":0.7,"publicationDate":"2025-07-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144557029","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Topological Incremental Fast Fourier transform on time–frequency domain feature extraction for equipment fault diagnosis 基于拓扑增量快速傅立叶变换的设备故障诊断时频特征提取

IF 5.3 1区数学

Chaos Solitons & Fractals Pub Date : 2025-07-04 DOI: 10.1016/j.chaos.2025.116761

Yang Han , Ruiyao Jia , Hanju Cai , Wenpeng Luan, Bochao Zhao, Bo liu

{"title":"Topological Incremental Fast Fourier transform on time–frequency domain feature extraction for equipment fault diagnosis","authors":"Yang Han , Ruiyao Jia , Hanju Cai , Wenpeng Luan, Bochao Zhao, Bo liu","doi":"10.1016/j.chaos.2025.116761","DOIUrl":"10.1016/j.chaos.2025.116761","url":null,"abstract":"<div><div>Equipment fault diagnosis is crucial to ensure safe operation of industrial systems. The development of artificial intelligence has led to increasing applications of data-driven methods for fault diagnosis. However, such methods often require a large amount of labeled data for training and are tend to be sensitive to noise. To address these challenges, a novel model using topological data analysis (TDA)—-topological incremental fast Fourier transform(TIFF)—-for equipment fault diagnosis is proposed in this paper, leveraging the capability of TDA in extracting geometric features of dataset after continuous deformations of topology space. First, for time series signal of equipment operation, persistent homology fluctuating series is constructed by calculating the topological Wasserstein distance between two successive windows of the raw signal, which contains more condensed information on its fault pattern. Then, the time–frequency domain features of the raw signals are obtained by concatenating the frequency domain features derived from fast Fourier transformation and time domain features derived from statistical analysis on both of the persistent homology fluctuating and the raw signal series. Finally, a machine learning based equipment fault diagnosis framework is proposed. By feeding the time–frequency domain features extracted by TDA method, a model based on support vector machine(SVM) classifier after supervised training is established to give identification result for type of fault. The proposed method is tested on two publicly available datasets under different conditions and the results prove that it outperforms three state-of-the-art benchmarks in noisy settings and with few-shot.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"199 ","pages":"Article 116761"},"PeriodicalIF":5.3,"publicationDate":"2025-07-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144557616","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Solution of three-dimensional steady state Stokes flow problems with exit boundary conditions by the boundary element method 边界元法求解具有出口边界条件的三维稳态Stokes流动问题

IF 2.9 2区数学

Computers & Mathematics with Applications Pub Date : 2025-07-04 DOI: 10.1016/j.camwa.2025.06.031

Kunj Sankhla, Sandipan Kumar Das

{"title":"Solution of three-dimensional steady state Stokes flow problems with exit boundary conditions by the boundary element method","authors":"Kunj Sankhla, Sandipan Kumar Das","doi":"10.1016/j.camwa.2025.06.031","DOIUrl":"10.1016/j.camwa.2025.06.031","url":null,"abstract":"<div><div>This paper explores the Boundary Element formulation of “exit” boundary conditions for three-dimensional steady state Stokes flows. A previous investigation had formulated it for two- dimensional situations. The current study is a natural extension of that research. Specifically, the boundaries that have the normal-velocity gradient specified as zero or that have the pressure specified as any value can now be tackled in three dimensions. This would open up the Boundary Element Method (BEM) to a wide variety of Stokes flow problems. The procedure for both the boundary conditions begins with the creation of a replica of the exit plane at a small distance inside the domain. A discretization of the relevant mathematical quantities within the integration terms would result in the generation of the BEM equations that would include the above boundary conditions. This paper articulates all the mathematical intricacies of the procedure, especially for the more important specified-pressure boundary condition. The remainder of this paper demonstrates the new boundary conditions for a couple of relatively simple Stokes flow problems that were hitherto unsolvable by the standard BEM procedure. The BEM predictions matched excellently with the available analytical solutions. The article rounds off with concluding statements and possible research directions in the future.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"195 ","pages":"Pages 1-13"},"PeriodicalIF":2.9,"publicationDate":"2025-07-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144562866","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Consensus of multi-agent systems with noise-based delayed communications under dynamic Denial-of-Service attacks 基于噪声的延迟通信多智能体系统在动态拒绝服务攻击下的一致性

IF 5.3 1区数学

Chaos Solitons & Fractals Pub Date : 2025-07-04 DOI: 10.1016/j.chaos.2025.116783

Sen Li , Yuhang Zheng , Junhao Hu , Wenxue Li

{"title":"Consensus of multi-agent systems with noise-based delayed communications under dynamic Denial-of-Service attacks","authors":"Sen Li , Yuhang Zheng , Junhao Hu , Wenxue Li","doi":"10.1016/j.chaos.2025.116783","DOIUrl":"10.1016/j.chaos.2025.116783","url":null,"abstract":"<div><div>This work formulates stochastic consensus with probability one (SC-PO) of multi-agent systems (MSs) by proposing noise-based delayed communication protocols under dynamic Denial-of-Service (D-DoS) attacks. The developed consensus protocols are composed of two cases: (1) interference attacker induces transmission defeats on full inter-agent communication; (2) the attacker interrupts a subset of communication links. During activation period, the communication from neighbors of each agent can be successfully jammed in a certain probability, that is, the Denial-of-Service attacker acts randomly, which fits better to the reality. Different from existing results about the SC-PO of MSs incorporating noise and time delays, this paper delves into the SC-PO through creating a delay-free companion system, which removes the underlying assumption of mean square consensus. By leveraging Lyapunov method, graph theory and stochastic analysis, SC-PO criteria are formulated, which is intricately connected with topology structure, noise intensity, D-DoS frequency and the probability of successful attack. Moreover, on the basis of the criterion, bounds on the attack parameters that can be tolerated and the communication delay are estimated. It is demonstrated that the noise in our work plays a positive role in consensus. Finally, a numerical simulation case for a specific class of robot manipulators is provided to authenticate the feasibility and validity of the theoretical derivations.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"199 ","pages":"Article 116783"},"PeriodicalIF":5.3,"publicationDate":"2025-07-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144549663","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

A nonparametric approach to nonsmooth vector fractional interval-valued optimization problems 非光滑矢量分数阶区间值优化问题的非参数方法

IF 5.3 1区数学

Chaos Solitons & Fractals Pub Date : 2025-07-04 DOI: 10.1016/j.chaos.2025.116638

Tadeusz Antczak , Nisha Pokharna

{"title":"A nonparametric approach to nonsmooth vector fractional interval-valued optimization problems","authors":"Tadeusz Antczak , Nisha Pokharna","doi":"10.1016/j.chaos.2025.116638","DOIUrl":"10.1016/j.chaos.2025.116638","url":null,"abstract":"<div><div>Interval programming is a useful tool that provides an easier way to handle uncertainty in various classes of optimization problems. Therefore, we investigate in the paper a new type of nondifferentiable vector interval-valued fractional optimization problems in which the functions involved possess a new generalized convexity property introduced in this paper for interval-valued functions. Namely, we study optimality conditions for (weak) LU-Pareto solutions of vector fractional optimization problems with interval-valued objective functions in their numerators and denominators by using the nonparametric approach. Thus, we derive both the nonparametric necessary optimality conditions of Fritz John type and, assuming additionally the Slater constraint qualification, the nonparametric type necessary optimality conditions of Karush-Kuhn-Tucker type for a feasible point of the aforesaid nonsmooth vector fractional interval-valued optimization problem to be its weakly LU-Pareto solution. The sufficient optimality conditions for a weak LU-Pareto solution and a LU-Pareto solution are also proven assuming additionally nonsmooth generalized convexity of the functions involved in the aforesaid vector optimization problem. Further, the nondifferentiable multicriteria nonparametric Mond-Weir dual problem is also formulated for the studied nondifferentiable multiobjective fractional interval-valued optimization problem. Then, dual theorems are proven for these two nondifferentiable multicriteria fractional optimization problems with interval-valued objectives in their nominators and denominators also assuming generalized convexity hypotheses.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"199 ","pages":"Article 116638"},"PeriodicalIF":5.3,"publicationDate":"2025-07-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144549764","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

A novel rule for cooperation in the spatial public goods game: Second-order social learning 空间公共物品博弈中一种新的合作规则：二阶社会学习

IF 5.3 1区数学

Chaos Solitons & Fractals Pub Date : 2025-07-04 DOI: 10.1016/j.chaos.2025.116795

Nanrong He , Qiuxiang Lu , Fang Yan , Qiang Wang

{"title":"A novel rule for cooperation in the spatial public goods game: Second-order social learning","authors":"Nanrong He , Qiuxiang Lu , Fang Yan , Qiang Wang","doi":"10.1016/j.chaos.2025.116795","DOIUrl":"10.1016/j.chaos.2025.116795","url":null,"abstract":"<div><div>In real-world contexts, sustaining cooperation is often challenging; however, the learning rule by which individuals learn from their peers may dramatically reshape evolutionary dynamics. In reality, imitation-based traditional social learning (TSL) is inherently constrained by its reliance on copying only immediate neighbors, which limits the depth of information sampling. To overcome this, we introduce a novel second-order social learning (SOSL) rule that broadens the horizon of social information sampling. Specifically, SOSL employs a two-step information sampling process: instead of directly copying the strategy of the successful neighbor, individual adopts the strategy that their successful neighbor has identified as optimal through TSL rule. Using Monte Carlo simulations of the public goods game on a lattice-structured population, compared with the TSL rule, we find that the SOSL rule markedly lowers the conditions of the critical synergy factor for the emergence of cooperation and full cooperation. Even when the synergy factor is too low for cooperation to emerge under the TSL rule, the SOSL rule sustains cooperative clusters and accelerates the transition from defection to widespread cooperation. Furthermore, by introducing a strategy-preference coevolutionary framework that allows individuals to adapt their learning mode, we show that the population converges overwhelmingly to the SOSL rule under moderate synergy factors. Finally, the cooperative advantage of the SOSL rule holds across diverse network structures and persists even under noisy parameter conditions.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"199 ","pages":"Article 116795"},"PeriodicalIF":5.3,"publicationDate":"2025-07-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144549763","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Robustness of reliability bounds for (n,k)-star networks （n,k）星网络可靠性界的鲁棒性

IF 1 3区数学

Discrete Applied Mathematics Pub Date : 2025-07-04 DOI: 10.1016/j.dam.2025.06.064

Hao Li , Hongwei Qiao , Eminjan Sabir

{"title":"Robustness of reliability bounds for (n,k)-star networks","authors":"Hao Li , Hongwei Qiao , Eminjan Sabir","doi":"10.1016/j.dam.2025.06.064","DOIUrl":"10.1016/j.dam.2025.06.064","url":null,"abstract":"<div><div>The sub-network reliability, SNR for short, of a network is the probability that a healthy sub-network of a certain scale is operational in the network when faults occurs. It is surprisingly found that some networks’ SNR are different even though they have the same cardinality of processors. Hereby, we conduct comparative analysis for a pair of distinct topologies of <span><math><mrow><mo>(</mo><mi>n</mi><mo>,</mo><mi>k</mi><mo>)</mo></mrow></math></span>-star networks <span><math><msub><mrow><mi>S</mi></mrow><mrow><mi>n</mi><mo>,</mo><mi>k</mi></mrow></msub></math></span> with same cardinality of processors to assess the robustness of their SNR bounds. We demonstrate analytically that SNR in <span><math><msub><mrow><mi>S</mi></mrow><mrow><mi>n</mi><mo>,</mo><mi>k</mi></mrow></msub></math></span> is proportional to <span><math><mi>n</mi></math></span> when sub-networks are of the same cardinality of processors. This study presents a theoretical framework for selecting the more reliable topology among <span><math><msub><mrow><mi>S</mi></mrow><mrow><mi>n</mi><mo>,</mo><mi>k</mi></mrow></msub></math></span>s of the same cardinality of processors. We also conduct numerical simulations to verify our theoretical findings.</div></div>","PeriodicalId":50573,"journal":{"name":"Discrete Applied Mathematics","volume":"377 ","pages":"Pages 51-65"},"PeriodicalIF":1.0,"publicationDate":"2025-07-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144550026","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

A flux solver based on discrete Boltzmann method for compressible flows with nonequilibrium effects 基于离散玻尔兹曼方法的非平衡可压缩流通量求解器

IF 2.9 2区数学

Computers & Mathematics with Applications Pub Date : 2025-07-04 DOI: 10.1016/j.camwa.2025.06.036

Chuandong Lin , Chang Shu

{"title":"A flux solver based on discrete Boltzmann method for compressible flows with nonequilibrium effects","authors":"Chuandong Lin , Chang Shu","doi":"10.1016/j.camwa.2025.06.036","DOIUrl":"10.1016/j.camwa.2025.06.036","url":null,"abstract":"<div><div>A flux solver based upon the discrete Boltzmann method (DBM) is presented for simulating compressible flows that encompass both hydrodynamic and thermodynamic behaviors. The kinetic model utilizes discrete distribution functions expressed through the discrete equilibrium distribution function that is calculated via the inverse matrix method. Unlike the DBM using discrete Boltzmann equations, our approach solves the conservation equations of mass, momentum, and energy by calculating flux terms from the summation of discrete distribution functions. This method significantly enhances computational efficiency and numerical robustness compared to DBM, by employing fewer governing equations and allowing for larger time steps. The approach is validated through five standard benchmarks: sound wave, thermal Couette flow, Sod shock tube, Lax shock tube, and Kelvin–Helmholtz instability. Two discrete velocity sets at the Euler and Navier–Stokes levels are employed in the simulations. It is demonstrated that the flux solver effectively integrates the strengths of both hydrodynamic solvers and the DBM, offering a powerful tool for simulating and analyzing compressible flows with complex nonequilibrium features in diverse scientific and engineering applications.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"195 ","pages":"Pages 14-27"},"PeriodicalIF":2.9,"publicationDate":"2025-07-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144562865","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

An improved proximal alternating linearized minimization algorithm and its inertial Bregman extension for structured nonconvex nonsmooth optimization problems on Riemannian manifold 黎曼流形上结构非凸非光滑优化问题的改进近端交替线性化最小化算法及其惯性Bregman扩展

IF 2.1 2区数学

Journal of Computational and Applied Mathematics Pub Date : 2025-07-04 DOI: 10.1016/j.cam.2025.116886

Jiawei Xu , Bo He , Zheng Peng , Xu Zhang

{"title":"An improved proximal alternating linearized minimization algorithm and its inertial Bregman extension for structured nonconvex nonsmooth optimization problems on Riemannian manifold","authors":"Jiawei Xu , Bo He , Zheng Peng , Xu Zhang","doi":"10.1016/j.cam.2025.116886","DOIUrl":"10.1016/j.cam.2025.116886","url":null,"abstract":"<div><div>In this paper, we study a class of nonconvex and nonsmooth optimization problems with a specific structure. The objective function consists of the following components: a nonsmooth function in Euclidean space, a smooth function on a manifold, and a smooth coupling function linking of these two variables. By exploiting problem’s composite structure, we propose an improved version of the proximal alternating linearized minimization method. This algorithm employs a splitting technique, where the nonsmooth subproblem defined in the Euclidean space is solved using a forward–backward operator, and the smooth manifold subproblem is addressed using a Riemannian gradient step. We further extend this algorithm by introducing an inertial Bregman variant, which incorporates inertial step and Bregman regularization to improve both efficiency and robustness. We provide a theoretical analysis of the proposed algorithms and establish their iteration complexity for obtaining an <span><math><mi>ϵ</mi></math></span>-stationary point under mild assumptions. Finally, we present numerical experiments on sparse principal component analysis to verify the effectiveness of the proposed algorithms.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"473 ","pages":"Article 116886"},"PeriodicalIF":2.1,"publicationDate":"2025-07-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144563363","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

数学最新文献