Mathematical Methods in the Applied Sciences最新文献

{"title":"Sampling in Shift-Invariant Spaces Generated by Hilbert Space-Valued Functions","authors":"Md Hasan Ali Biswas, Rohan Joy, Felix Krahmer, Ramakrishnan Radha","doi":"10.1002/mma.10710","DOIUrl":"https://doi.org/10.1002/mma.10710","url":null,"abstract":"<div>\u0000 \u0000 <p>In this paper, we investigate the problem of sampling and reconstruction in principal shift-invariant spaces generated by Hilbert space-valued functions. Given any signal \u0000<span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>f</mi>\u0000 </mrow>\u0000 <annotation>$$ f $$</annotation>\u0000 </semantics></math> and data point \u0000<span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <msub>\u0000 <mrow>\u0000 <mi>x</mi>\u0000 </mrow>\u0000 <mrow>\u0000 <mi>k</mi>\u0000 </mrow>\u0000 </msub>\u0000 <mo>∈</mo>\u0000 <mi>ℝ</mi>\u0000 </mrow>\u0000 <annotation>$$ {x}_kin mathbb{R} $$</annotation>\u0000 </semantics></math>, the sample \u0000<span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>f</mi>\u0000 <mo>(</mo>\u0000 <msub>\u0000 <mrow>\u0000 <mi>x</mi>\u0000 </mrow>\u0000 <mrow>\u0000 <mi>k</mi>\u0000 </mrow>\u0000 </msub>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$$ fleft({x}_kright) $$</annotation>\u0000 </semantics></math> is stored along a sequence of directions \u0000<span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <msub>\u0000 <mrow>\u0000 <mo>{</mo>\u0000 <msub>\u0000 <mrow>\u0000 <mi>ν</mi>\u0000 </mrow>\u0000 <mrow>\u0000 <mi>k</mi>\u0000 <mi>m</mi>\u0000 </mrow>\u0000 </msub>\u0000 <mo>}</mo>\u0000 </mrow>\u0000 <mrow>\u0000 <mi>m</mi>\u0000 <mo>∈</mo>\u0000 <mi>ℤ</mi>\u0000 </mrow>\u0000 </msub>\u0000 </mrow>\u0000 <annotation>$$ {left{{nu}_{km}right}}_{min mathbb{Z}} $$</annotation>\u0000 </semantics></math>. Specifically, the inner products \u0000<span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mo>⟨</mo>\u0000 <mi>f</mi>\u0000 <mo>(</mo>\u0000 <msub>\u0000 <mrow>\u0000 <mi>x</mi>\u0000 </mrow>\u0000 <mrow>\u0000 <mi>k</mi>\u0000 </mrow>\u0000 </msub>\u0000 <mo>)</mo>\u0000 <mo>,</mo>\u0000 <msub>\u0000 <mrow>\u0000 <mi>ν</mi>\u0000 </mrow>\u0000 <mrow>\u0000 <mi>k</mi>\u0000 ","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"48 6","pages":"6717-6733"},"PeriodicalIF":2.1,"publicationDate":"2025-01-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143622708","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":"Existence of Solutions for a Class of Volterra Integral Equations on Time Scales","authors":"Wafaa Salih Ramadan,&nbsp;Svetlin G. Georgiev,&nbsp;Waleed Al-Hayani","doi":"10.1002/mma.10702","DOIUrl":"https://doi.org/10.1002/mma.10702","url":null,"abstract":"<div>\u0000 \u0000 <p>In this paper, we investigate a class of Volterra integral equations for existence of global classical solutions. We give conditions under which the considered equations have at least one and at least two classical solutions. To prove our main results, we propose a new approach based upon recent theoretical results. More precisely, we give a suitable integral representation of the solutions of the considered Volterra integral equation. Then, we construct two operators for which any fixed point of their sum is a solution of the considered Volterra integral equation.</p>\u0000 </div>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"48 6","pages":"6647-6653"},"PeriodicalIF":2.1,"publicationDate":"2025-01-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143622693","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":"Bifurcation and Chaos Control of Mixed Rayleigh-LiéNard Oscillator With Two Periodic Excitations and Mixed Delays","authors":"Hongzhen Zhao,&nbsp;Jing Li,&nbsp;Shaotao Zhu,&nbsp;Yufeng Zhang,&nbsp;Bo Sun","doi":"10.1002/mma.10621","DOIUrl":"https://doi.org/10.1002/mma.10621","url":null,"abstract":"<div>\u0000 \u0000 <p>This paper investigates the bifurcation, chaos, and active control of a mixed Rayleigh-Liénard oscillator with mixed time delays. First, the effects of system parameters on the supercritical pitchfork bifurcations are discussed in detail by applying the fast-slow separation method. Second, it is rigorously proved by the Melnikov method that chaotic vibration exists when the parameters of the uncontrolled system are selected above the threshold of chaos occurrence. By fine-tuning the system parameters, a criterion for designing the control parameters to make the Melnikov function non-zero is derived. In addition, the routes to chaos in controlled system are explored by bifurcation diagrams, largest Lyapunov exponents, phase portraits, Poincaré maps, basins of attraction, frequency spectra, and displacement time series. The results indicate that by properly adjusting the displacement feedback coefficient and the amplitude of parameter excitation, the chaotic motion caused by increasing of the amplitude of external excitation and strength of distributed time delay can be effectively suppressed. This research result can provide theoretical support for exploring the potential chaotic motion of other types of oscillators.</p>\u0000 </div>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"48 5","pages":"5586-5601"},"PeriodicalIF":2.1,"publicationDate":"2025-01-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143595421","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":"Two-Grid Finite Element Method for the Time-Fractional Allen–Cahn Equation With the Logarithmic Potential","authors":"Jiyu Zhang,&nbsp;Xiaocui Li,&nbsp;Wenyan Ma","doi":"10.1002/mma.10704","DOIUrl":"https://doi.org/10.1002/mma.10704","url":null,"abstract":"<div>\u0000 \u0000 <p>In this paper, we propose a two-grid finite element method for solving the time-fractional Allen–Cahn equation with the logarithmic potential. Firstly, with the L1 method to approximate Caputo fractional derivative, we solve the fully discrete time-fractional Allen–Cahn equation on a coarse grid with mesh size \u0000<span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>H</mi>\u0000 </mrow>\u0000 <annotation>$$ H $$</annotation>\u0000 </semantics></math> and time step size \u0000<span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>τ</mi>\u0000 </mrow>\u0000 <annotation>$$ tau $$</annotation>\u0000 </semantics></math>. Then, we solve the linearized system with the nonlinear term replaced by the value of the first step on a fine grid with mesh size \u0000<span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>h</mi>\u0000 </mrow>\u0000 <annotation>$$ h $$</annotation>\u0000 </semantics></math> and the same time step size \u0000<span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>τ</mi>\u0000 </mrow>\u0000 <annotation>$$ tau $$</annotation>\u0000 </semantics></math>. We obtain the energy stability of the two-grid finite element method and the optimal order of convergence of the two-grid finite element method in the L2 norm when the mesh size satisfies \u0000<span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>h</mi>\u0000 <mo>=</mo>\u0000 <mi>O</mi>\u0000 <mo>(</mo>\u0000 <msup>\u0000 <mrow>\u0000 <mi>H</mi>\u0000 </mrow>\u0000 <mrow>\u0000 <mn>2</mn>\u0000 </mrow>\u0000 </msup>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$$ h&amp;#x0003D;Oleft({H}&amp;#x0005E;2right) $$</annotation>\u0000 </semantics></math>. The theoretical results are confirmed by arithmetic examples, which indicate that the two-grid finite element method can keep the same convergence rate and save the CPU time.</p>\u0000 </div>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"48 6","pages":"6654-6663"},"PeriodicalIF":2.1,"publicationDate":"2025-01-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143622697","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":"A Model of the Deformations of a Cross-Section of the Spinal Cord Due to Periodic Pressure Loadings","authors":"Paul J. Harris,&nbsp;Jenny Venton","doi":"10.1002/mma.10666","DOIUrl":"https://doi.org/10.1002/mma.10666","url":null,"abstract":"<p>Changes in the pressure of the cerebrospinal fluid that surrounds the spinal cord can cause deformations of the spinal cord, which, in turn, may lead to the cord being damaged. In addition, the changes in the pressure of the surrounding cerebrospinal fluid can cause changes to the pressure of the extracellular fluid which saturates the spinal cord. The finite element method can be used to solve the differential equations, which describe both how the cord deforms and changes in the pressure of the extracellular fluid but often this requires a large number of time-steps to obtain an accurate and stable numerical solution. We present an alternative approach that uses a Fourier series method that avoids the need for using a time-stepping scheme and that can model how a pressure pulse affects the spinal cord.</p>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"48 5","pages":"6222-6229"},"PeriodicalIF":2.1,"publicationDate":"2025-01-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/mma.10666","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143595429","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Two-Dimensional Jet Flows for Compressible Full Euler System With General Vorticity","authors":"Yan Li","doi":"10.1002/mma.10676","DOIUrl":"https://doi.org/10.1002/mma.10676","url":null,"abstract":"<div>\u0000 \u0000 <p>In this paper, we consider the well-posedness theory of two-dimensional compressible subsonic jet flows for steady full Euler system with general vorticity. We show that the stream function formulation for such system admits a variational structure. Then the existence and uniqueness of a smooth subsonic jet flow can be established by the variational method developed by Alt, Caffarelli and Friedman. Furthermore, the far fields behavior of the flow and the existence of a critical upstream pressure are also obtained.</p>\u0000 </div>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"48 6","pages":"6342-6360"},"PeriodicalIF":2.1,"publicationDate":"2025-01-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143622431","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":"Stabilization for Coupled Hyperbolic System With Memory Effects Via Minimal State Variable","authors":"Mengxian Lv,&nbsp;Junmin Wang","doi":"10.1002/mma.10674","DOIUrl":"https://doi.org/10.1002/mma.10674","url":null,"abstract":"<div>\u0000 \u0000 <p>In this work, we investigate the stabilization of a coupled PDE's system consisting of one Kirchhoff plate and one wave equation with memory effects. Three different cases are considered where the frictional infinite memory occurs in both equations or in one of the equations. First, we achieve the existence and uniqueness of the solution, utilizing the concept of minimal state variable. Moreover, it is shown that the coupled system is forced to polynomially decay. And by frequency domain analysis, the explicit decay rates are established, which only depend on the place of memory effect.</p>\u0000 </div>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"48 6","pages":"6323-6334"},"PeriodicalIF":2.1,"publicationDate":"2025-01-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143622432","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":"Regularization of the Time-Fractional Order SchröDinger Problem by Using the Mollification Regularization Method","authors":"Lan Yang,&nbsp;Lin Zhu,&nbsp;Shangqin He,&nbsp;Bingxin Zhao","doi":"10.1002/mma.10716","DOIUrl":"https://doi.org/10.1002/mma.10716","url":null,"abstract":"<div>\u0000 \u0000 <p>This study investigates the solution of an ill-posed time-fractional order Schrödinger equation using a mollification regularization technique of the Dirichlet kernel. The Dirichlet regularized solution is obtained through convolution of the Dirichlet kernel with real measured data. Estimations of convergence are derived based on parameter selection criteria of a priori and a posteriori. The efficiency of the methodology was successfully verified by simulation tests.</p>\u0000 </div>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"48 6","pages":"6799-6817"},"PeriodicalIF":2.1,"publicationDate":"2025-01-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143622699","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":"On the Inversion of Generalized V-Line Transform of a Vector Field in \u0000ℝ2","authors":"Rahul Bhardwaj,&nbsp;Rohit Kumar Mishra,&nbsp;Manmohan Vashisth","doi":"10.1002/mma.10689","DOIUrl":"https://doi.org/10.1002/mma.10689","url":null,"abstract":"<div>\u0000 \u0000 <p>This article studies the inverse problem of recovering a vector field supported in \u0000<span></span><math>\u0000 <mrow>\u0000 <msub>\u0000 <mrow>\u0000 <mi>𝔻</mi>\u0000 </mrow>\u0000 <mrow>\u0000 <mi>R</mi>\u0000 </mrow>\u0000 </msub>\u0000 </mrow></math>, the disk of radius \u0000<span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>R</mi>\u0000 </mrow>\u0000 <annotation>$$ R $$</annotation>\u0000 </semantics></math> centered at the origin, through a set of generalized broken ray/V-line transforms, namely, longitudinal and transverse V-line transforms. Geometrically, we work with broken lines that start from the boundary of a disk and break at a fixed angle after traveling a distance along the diameter. We derive two inversion formulas to recover a vector field in \u0000<span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <msup>\u0000 <mrow>\u0000 <mi>ℝ</mi>\u0000 </mrow>\u0000 <mrow>\u0000 <mn>2</mn>\u0000 </mrow>\u0000 </msup>\u0000 </mrow>\u0000 <annotation>$$ {mathbb{R}}&amp;#x0005E;2 $$</annotation>\u0000 </semantics></math> from the knowledge of its longitudinal and transverse V-line transforms over two different subsets of aforementioned broken lines in \u0000<span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <msup>\u0000 <mrow>\u0000 <mi>ℝ</mi>\u0000 </mrow>\u0000 <mrow>\u0000 <mn>2</mn>\u0000 </mrow>\u0000 </msup>\u0000 </mrow>\u0000 <annotation>$$ {mathbb{R}}&amp;#x0005E;2 $$</annotation>\u0000 </semantics></math>.</p>\u0000 </div>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"48 6","pages":"6512-6520"},"PeriodicalIF":2.1,"publicationDate":"2025-01-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143622470","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":"Jacobian-Free Vectorial Iterative Scheme to Find Simple Several Solutions Simultaneously","authors":"Alicia Cordero,&nbsp;Juan R. Torregrosa,&nbsp;Paula Triguero-Navarro","doi":"10.1002/mma.10631","DOIUrl":"https://doi.org/10.1002/mma.10631","url":null,"abstract":"<p>This manuscript is devoted to a derivative-free parametric iterative step to obtain roots simultaneously for both nonlinear systems and equations. We prove that when it is added to an arbitrary scheme, it doubles the convergence order of the original procedure and defines a new algorithm that obtains several solutions simultaneously. Different numerical experiments are carried out to check the behavior of the iterative methods by changing the value of the parameter and the initial guesses. Also, it performs a numerical example where the dynamical planes are carried out to see and compare the basins of attraction.</p>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"48 5","pages":"5718-5730"},"PeriodicalIF":2.1,"publicationDate":"2025-01-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/mma.10631","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143595362","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}