Mathematical Methods in the Applied Sciences最新文献

{"title":"Normalized Solutions for a SchröDinger Equation With Van Der Waals Type Potentials and External Potential: Mass Supercritical","authors":"Jianqing Chen,&nbsp;Zhewen Chen","doi":"10.1002/mma.10636","DOIUrl":"https://doi.org/10.1002/mma.10636","url":null,"abstract":"<div>\u0000 \u0000 <p>We study the existence of ground states with prescribed \u0000<span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <msup>\u0000 <mrow>\u0000 <mi>L</mi>\u0000 </mrow>\u0000 <mrow>\u0000 <mn>2</mn>\u0000 </mrow>\u0000 </msup>\u0000 </mrow>\u0000 <annotation>$$ {L}^2 $$</annotation>\u0000 </semantics></math>-norm for the mass supercritical Schrödinger equation with van der Waals type potentials (that is, two-body potentials with different width) in the presence of nonsymmetric negative potentials. We prove the existence of normalized ground states at positive energy level under mild assumptions on external potential.</p>\u0000 </div>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"48 5","pages":"5781-5789"},"PeriodicalIF":2.1,"publicationDate":"2024-12-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143595661","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}

{"title":"Semi-Analytical Solutions of the Multi-Dimensional Time-Fractional Solitary Water Wave Equations Using RPS Method","authors":"Rakesh Kumar Meena,&nbsp;Sushil Kumar","doi":"10.1002/mma.10665","DOIUrl":"https://doi.org/10.1002/mma.10665","url":null,"abstract":"<div>\u0000 \u0000 <p>This article concerns the use of the residual power series (RPS) approach to get the semi-analytical solutions of multi-dimensional Korteweg-de Vries (KdV), that is, shallow water wave equations with any arbitrary time-fractional order (\u0000<span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>γ</mi>\u0000 </mrow>\u0000 <annotation>$$ gamma $$</annotation>\u0000 </semantics></math>). The time-fractional derivative is considered in the Caputo sense. The solutions of the fractional KdV equation obtained using the RPS method for \u0000<span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>γ</mi>\u0000 <mo>=</mo>\u0000 <mn>1</mn>\u0000 </mrow>\u0000 <annotation>$$ gamma =1 $$</annotation>\u0000 </semantics></math> are compared with the exact solutions of the integer-order KdV equation to show the RPS method's effectiveness, accuracy, and convergence. Some examples are also solved to study the effects of the fractional derivative \u0000<span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mi>γ</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$$ left(gamma right) $$</annotation>\u0000 </semantics></math> on the wave's amplitude.</p>\u0000 </div>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"48 5","pages":"6208-6221"},"PeriodicalIF":2.1,"publicationDate":"2024-12-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143595662","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}

{"title":"The Equivalence Canonical Forms of Two Sets of Five Quaternion Matrices With Applications","authors":"Zhuo-Heng He,&nbsp;Yun-Ze Xu,&nbsp;Qing-Wen Wang,&nbsp;Chong-Quan Zhang","doi":"10.1002/mma.10613","DOIUrl":"https://doi.org/10.1002/mma.10613","url":null,"abstract":"<div>\u0000 \u0000 <p>In this paper, the equivalence canonical forms of two sets of five quaternion matrices are considered. The simultaneous decompositions of these two sets of quaternion matrices are established. Some practical algorithms for computing the decompositions are also presented. Using the equivalence canonical forms, some practical solvability conditions for two systems of generalized Sylvester-type quaternion matrix equations are derived in terms of the ranks of the coefficient matrices. The general solutions to the systems are also provided. Some numerical examples are given to illustrate the results. The proposed simultaneous decompositions are applied to construct a new framework of color watermarks embedding. In this framework, five color watermarks can be embedded into one host image simultaneously with high efficiency. Moreover, a counterexample for the existence of the equivalence canonical form of the general matrix quaternity with the same row or column numbers is presented. The results extend the existing findings on the equivalence canonical forms of general matrix arrays.</p>\u0000 </div>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"48 5","pages":"5483-5505"},"PeriodicalIF":2.1,"publicationDate":"2024-12-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143595666","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}

{"title":"Balancing Polynomial for Solution Nonlinear Stochastic Itô–Volterra Integral Equations","authors":"Zahra Beyranvand,&nbsp;Taher Lotfi","doi":"10.1002/mma.10667","DOIUrl":"https://doi.org/10.1002/mma.10667","url":null,"abstract":"<div>\u0000 \u0000 <p>This paper introduces an innovative method for solving nonlinear stochastic Itô–Volterra integral equations using balancing polynomials and their associated operational matrices. This approach effectively transforms these complex stochastic equations into a system of nonlinear algebraic equations that can be solved using the Newton method. Balancing polynomials are chosen for their ability to enhance stability and convergence, providing a more reliable and manageable framework for tackling challenging stochastic problems. The paper also includes a convergence analysis and error estimation for the proposed method. Additionally, the effectiveness of this approach is demonstrated through four numerical examples. The results obtained from this method are compared with the exact solution and those from other established techniques, including the block-pulse function method, the shifted Jacobi operational matrix (SJOM) method, and the shifted Jacobi spectral Galerkin (SJSG) method. These comparisons highlight the superior performance and accuracy of the proposed method. All numerical computations were performed using MATLAB.</p>\u0000 </div>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"48 5","pages":"6230-6246"},"PeriodicalIF":2.1,"publicationDate":"2024-12-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143595664","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}

{"title":"Discretization of the Wave Equation on a Metric Graph","authors":"Sergei A. Avdonin,&nbsp;Alexander S. Mikhaylov,&nbsp;Victor S. Mikhaylov,&nbsp;Abdon E. Choque-Rivero","doi":"10.1002/mma.10630","DOIUrl":"https://doi.org/10.1002/mma.10630","url":null,"abstract":"<div>\u0000 \u0000 <p>The question of what conditions should be set at the nodes of a discrete graph for the wave equation with discrete time is investigated. The variational method for the derivation of these conditions is used. A parallel with the continuous case is also drawn. As an example, the problem of shape controllability from the boundary is studied.</p>\u0000 </div>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"48 5","pages":"5708-5717"},"PeriodicalIF":2.1,"publicationDate":"2024-12-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143595457","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}

{"title":"Novel Stability and Stabilization Conditions for Fractional-Order Systems With Mixed Delays","authors":"Yi-Nan Chen,&nbsp;Jun-Guo Lu,&nbsp;Qing-Hao Zhang,&nbsp;Zhen Zhu","doi":"10.1002/mma.10668","DOIUrl":"https://doi.org/10.1002/mma.10668","url":null,"abstract":"<div>\u0000 \u0000 <p>This paper investigates the stability and stabilization of the fractional-order systems with mixed delays (FOSMDs), including discrete delays and distributed delays. At first, an order-dependent stability condition for FOSMDs is derived with the use of small gain theorem. Then, based on the stability condition, a robust stability condition for the uncertain FOSMDs with polytopic uncertainties is proposed. Next, with the robust stability condition and the designed state feedback controllers, a robust stabilization condition for the uncertain FOSMDs is proposed. At last, several numerical examples are put forward to manifest the effectiveness of the obtained results.</p>\u0000 </div>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"48 6","pages":"6253-6262"},"PeriodicalIF":2.1,"publicationDate":"2024-12-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143622677","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}

{"title":"Exponential Quasi-Synchronization of Nonautonomous Complex Dynamical Networks With Conformable Fractional-Order Derivatives","authors":"Baizeng Bao,&nbsp;Liguang Xu","doi":"10.1002/mma.10645","DOIUrl":"https://doi.org/10.1002/mma.10645","url":null,"abstract":"<div>\u0000 \u0000 <p>This paper studies the exponential quasi-synchronization of nonautonomous conformable fractional-order complex dynamical networks (NCFCDNs) via means of the periodically intermittent pinning control (PIPC). First, a nonautonomous conformable fractional-order error systems are established, which include stable and unstable subsystems. Second, for the cases where the existing results are invalid to handle switched nonautonomous terms, a new conformable fractional-order Halanay inequality is obtained, which serves as a powerful tool in the analysis of quasi-synchronization of NCFCDNs. Then, by virtue of the obtained Halanay inequality, Lyapunov method, and periodically intermittent controller, sufficient conditions of exponential quasi-synchronization of NCFCDNs are derived. Our results allow nonautonomous terms to be switched during work time and rest time, which is more relaxing than the previous results. Finally, a simulation example is included to show the feasibility of the derived results.</p>\u0000 </div>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"48 5","pages":"5906-5919"},"PeriodicalIF":2.1,"publicationDate":"2024-12-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143595692","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}

{"title":"Long Time Existence of Smooth Solutions to 3D Euler–Poisson System of Electrons With Nonzero Vorticity","authors":"Li Shiyu","doi":"10.1002/mma.10652","DOIUrl":"https://doi.org/10.1002/mma.10652","url":null,"abstract":"<div>\u0000 \u0000 <p>In this paper, we investigate the long-term stability of classical solution to 3D one-fluid Euler–Poisson system of electrons with nonzero vorticity. It is shown that the classical solution is well-posed for a lifesapn \u0000<span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <msub>\u0000 <mrow>\u0000 <mi>T</mi>\u0000 </mrow>\u0000 <mrow>\u0000 <mi>δ</mi>\u0000 </mrow>\u0000 </msub>\u0000 </mrow>\u0000 <annotation>$$ {T}_{delta } $$</annotation>\u0000 </semantics></math> at least \u0000<span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mfrac>\u0000 <mrow>\u0000 <mi>ε</mi>\u0000 </mrow>\u0000 <mrow>\u0000 <mi>δ</mi>\u0000 </mrow>\u0000 </mfrac>\u0000 </mrow>\u0000 <annotation>$$ frac{varepsilon }{delta } $$</annotation>\u0000 </semantics></math>, where \u0000<span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>ε</mi>\u0000 <mo>&gt;</mo>\u0000 <mn>0</mn>\u0000 </mrow>\u0000 <annotation>$$ varepsilon &gt;0 $$</annotation>\u0000 </semantics></math> is the size of the initial perturbed density and velocity, \u0000<span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>δ</mi>\u0000 <mo>&gt;</mo>\u0000 <mn>0</mn>\u0000 </mrow>\u0000 <annotation>$$ delta &gt;0 $$</annotation>\u0000 </semantics></math> is the size of the initial vorticity. This implies that the lifespan \u0000<span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <msub>\u0000 <mrow>\u0000 <mi>T</mi>\u0000 </mrow>\u0000 <mrow>\u0000 <mi>δ</mi>\u0000 </mrow>\u0000 </msub>\u0000 </mrow>\u0000 <annotation>$$ {T}_{delta } $$</annotation>\u0000 </semantics></math> only essentially depends on the size \u0000<span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>δ</mi>\u0000 </mrow>\u0000 <annotation>$$ delta $$</annotation>\u0000 </semantics></math> of the initial vorticity.</p>\u0000 </div>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"48 5","pages":"6019-6034"},"PeriodicalIF":2.1,"publicationDate":"2024-12-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143595694","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}

{"title":"Fixed-Time Bipartite Synchronization of Stochastic Multiplex Signed Networks Via Quantized Generalized Intermittent Control","authors":"Xuejiao Qin,&nbsp;Haijun Jiang,&nbsp;Jianlong Qiu,&nbsp;Cheng Hu,&nbsp;Yue Ren","doi":"10.1002/mma.10629","DOIUrl":"https://doi.org/10.1002/mma.10629","url":null,"abstract":"<div>\u0000 \u0000 <p>This study is dedicated to the fixed-time (FDT) bipartite synchronization of stochastic multiplex signed networks via quantized generalized intermittent control (QGIC). Firstly, a multiplex network including signed graphs and stochastic disturbances is introduced. Secondly, a new lemma of FDT stability is established by using reduction to absurdity and mathematical induction. Thirdly, based on the proposed FDT stability and the stochastic analysis techniques, several sufficient conditions on FDT bipartite synchronization are derived by designing a novel QGIC strategy. Significantly, the designed controller is a unified form of periodic and aperiodic cases and is only activated in the work interval. At last, two numerical simulations are offered to validate the superiority and effectiveness of the theoretical findings.</p>\u0000 </div>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"48 5","pages":"5692-5707"},"PeriodicalIF":2.1,"publicationDate":"2024-12-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143595697","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}

{"title":"Elasticity of Substitution and Economic Growth: Some New Results","authors":"Constantin Chilarescu","doi":"10.1002/mma.10644","DOIUrl":"https://doi.org/10.1002/mma.10644","url":null,"abstract":"<div>\u0000 \u0000 <p>The main aim of this paper is to improve some recent results on the impact of the elasticity of substitution on economic growth. We proved the existence, uniqueness, and asymptotic stability of the balanced growth equilibrium and then study the effect of the elasticity of substitution on the long-run equilibrium and on the steady state. We also show that a higher elasticity of substitution increases per capita income, the relative share of physical capital, the common growth rate, and the share of human capital allocated to the production sector.</p>\u0000 <p><b>MSC Classification:</b> C61, C62, E21, O41</p>\u0000 </div>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"48 5","pages":"5896-5905"},"PeriodicalIF":2.1,"publicationDate":"2024-12-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143595696","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}