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Applications of Mathematics最新文献

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The direct and inverse problem for sub-diffusion equations with a generalized impedance subregion 具有广义阻抗子区域的子扩散方程的正逆问题
IF 0.7 4区 数学
Applications of Mathematics Pub Date : 2021-11-16 DOI: 10.21136/AM.2021.0107-20
Isaac Harris
{"title":"The direct and inverse problem for sub-diffusion equations with a generalized impedance subregion","authors":"Isaac Harris","doi":"10.21136/AM.2021.0107-20","DOIUrl":"10.21136/AM.2021.0107-20","url":null,"abstract":"<div><p>In this paper, we consider the direct and inverse problem for time-fractional diffusion in a domain with an impenetrable subregion. Here we assume that on the boundary of the subregion the solution satisfies a generalized impedance boundary condition. This boundary condition is given by a second order spatial differential operator imposed on the boundary. A generalized impedance boundary condition can be used to model corrosion and delimitation. The well-posedness for the direct problem is established where the Laplace transform is used to study the time dependent boundary value problem. The inverse impedance problem of determining the parameters from the Cauchy data is also studied provided the boundary of the subregion is known. The uniqueness of recovering the boundary parameters from the Neumann to Dirichlet mapping is proven.</p></div>","PeriodicalId":55505,"journal":{"name":"Applications of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2021-11-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50032347","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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 new iteration methods for solving absolute value equations 求解绝对值方程的新迭代方法
IF 0.7 4区 数学
Applications of Mathematics Pub Date : 2021-11-11 DOI: 10.21136/AM.2021.0055-21
Rashid Ali, Kejia Pan
{"title":"The new iteration methods for solving absolute value equations","authors":"Rashid Ali,&nbsp;Kejia Pan","doi":"10.21136/AM.2021.0055-21","DOIUrl":"10.21136/AM.2021.0055-21","url":null,"abstract":"<div><p>Many problems in operations research, management science, and engineering fields lead to the solution of absolute value equations. In this study, we propose two new iteration methods for solving absolute value equations <i>Ax — |x| = b</i>, where <i>A</i> ∈ ℝ<sup><i>n×n</i></sup> is an <i>M</i>-matrix or strictly diagonally dominant matrix, <i>b</i> ∈ ℝ<sup><i>n</i></sup> and <i>x</i> ∈ ℝ<sup><i>n</i></sup> is an unknown solution vector. Furthermore, we discuss the convergence of the proposed two methods under suitable assumptions. Numerical experiments are given to verify the feasibility, robustness and effectiveness of our methods.</p></div>","PeriodicalId":55505,"journal":{"name":"Applications of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2021-11-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50020333","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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: 7
Dewetting Dynamics of Anisotropic Particles: A Level Set Numerical Approach 各向异性颗粒的脱湿动力学:水平集数值方法
IF 0.7 4区 数学
Applications of Mathematics Pub Date : 2021-11-01 DOI: 10.21136/AM.2021.0040-21
Siddharth Gavhale, Karel Švadlenka
{"title":"Dewetting Dynamics of Anisotropic Particles: A Level Set Numerical Approach","authors":"Siddharth Gavhale,&nbsp;Karel Švadlenka","doi":"10.21136/AM.2021.0040-21","DOIUrl":"10.21136/AM.2021.0040-21","url":null,"abstract":"<div><p>We extend thresholding methods for numerical realization of mean curvature flow on obstacles to the anisotropic setting where interfacial energy depends on the orien- tation of the interface. This type of schemes treats the interface implicitly, which supports natural implementation of topology changes, such as merging and splitting, and makes the approach attractive for applications in material science. The main tool in the new scheme are convolution kernels developed in previous studies that approximate the given anisotropy in a nonlocal way. We provide a detailed report on the numerical properties of the proposed algorithm.</p></div>","PeriodicalId":55505,"journal":{"name":"Applications of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2021-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50000787","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Extrapolated positive definite and positive semi-definite splitting methods for solving non-Hermitian positive definite linear systems 求解非厄米正定线性系统的外推正定和正半定分裂方法
IF 0.7 4区 数学
Applications of Mathematics Pub Date : 2021-10-25 DOI: 10.21136/AM.2021.0256-20
Raheleh Shokrpour, Ghodrat Ebadi
{"title":"Extrapolated positive definite and positive semi-definite splitting methods for solving non-Hermitian positive definite linear systems","authors":"Raheleh Shokrpour,&nbsp;Ghodrat Ebadi","doi":"10.21136/AM.2021.0256-20","DOIUrl":"10.21136/AM.2021.0256-20","url":null,"abstract":"<div><p>Recently, Na Huang and Changfeng Ma in (2016) proposed two kinds of typical practical choices of the PPS method. In this paper, we extrapolate two versions of the PPS iterative method, and we introduce the extrapolated Hermitian and skew-Hermitian positive definite and positive semi-definite splitting (EHPPS) iterative method and extrapolated triangular positive definite and positive semi-definite splitting (ETPPS) iterative method. We also investigate convergence analysis and consistency of the proposed iterative methods. Then, we study upper bounds for the spectral radius of iteration matrices and give upper bounds for the extrapolation parameter of the methods. Moreover, the optimal parameters which minimize upper bounds of the spectral radius are obtained. Finally, several numerical examples are given to show the efficiency of the presented method.</p></div>","PeriodicalId":55505,"journal":{"name":"Applications of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2021-10-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50047151","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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 interior-point algorithm for semidefinite least-squares problems 半定最小二乘问题的内点算法
IF 0.7 4区 数学
Applications of Mathematics Pub Date : 2021-10-20 DOI: 10.21136/AM.2021.0217-20
Chafia Daili, Mohamed Achache
{"title":"An interior-point algorithm for semidefinite least-squares problems","authors":"Chafia Daili,&nbsp;Mohamed Achache","doi":"10.21136/AM.2021.0217-20","DOIUrl":"10.21136/AM.2021.0217-20","url":null,"abstract":"<div><p>We propose a feasible primal-dual path-following interior-point algorithm for semidefinite least squares problems (SDLS). At each iteration, the algorithm uses only full Nesterov-Todd steps with the advantage that no line search is required. Under new appropriate choices of the parameter <i>β</i> which defines the size of the neighborhood of the central-path and of the parameter <i>θ</i> which determines the rate of decrease of the barrier parameter, we show that the proposed algorithm is well defined and converges to the optimal solution of SDLS. Moreover, we obtain the currently best known iteration bound for the algorithm with a short-update method, namely, <span>({cal O}(sqrt n log (n/varepsilon)))</span>. Finally, we report some numerical results to illustrate the efficiency of our proposed algorithm.</p></div>","PeriodicalId":55505,"journal":{"name":"Applications of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2021-10-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50094681","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Continuous dependence of 2D large scale primitive equations on the boundary conditions in oceanic dynamics 海洋动力学中二维大尺度原始方程对边界条件的连续依赖
IF 0.7 4区 数学
Applications of Mathematics Pub Date : 2021-10-20 DOI: 10.21136/AM.2021.0076-20
Yuanfei Li, Shengzhong Xiao
{"title":"Continuous dependence of 2D large scale primitive equations on the boundary conditions in oceanic dynamics","authors":"Yuanfei Li,&nbsp;Shengzhong Xiao","doi":"10.21136/AM.2021.0076-20","DOIUrl":"10.21136/AM.2021.0076-20","url":null,"abstract":"<div><p>In this paper, we consider an initial boundary value problem for the two-dimensional primitive equations of large scale oceanic dynamics. Assuming that the depth of the ocean is a positive constant, we establish rigorous a priori bounds of the solution to problem. With the aid of these a priori bounds, the continuous dependence of the solution on changes in the boundary terms is obtained.</p></div>","PeriodicalId":55505,"journal":{"name":"Applications of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2021-10-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50039180","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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: 1
Application of Rothe’s Method to a Parabolic Inverse Problem with Nonlocal Boundary Condition Rothe方法在非局部边界条件抛物型反问题中的应用
IF 0.7 4区 数学
Applications of Mathematics Pub Date : 2021-10-19 DOI: 10.21136/AM.2021.0029-21
Yong-Hyok Jo, Myong-Hwan Ri
{"title":"Application of Rothe’s Method to a Parabolic Inverse Problem with Nonlocal Boundary Condition","authors":"Yong-Hyok Jo,&nbsp;Myong-Hwan Ri","doi":"10.21136/AM.2021.0029-21","DOIUrl":"10.21136/AM.2021.0029-21","url":null,"abstract":"<div><p>We consider an inverse problem for the determination of a purely time-dependent source in a semilinear parabolic equation with a nonlocal boundary condition. An approximation scheme for the solution together with the well-posedness of the problem with the initial value <i>u</i><sub>0</sub> ∈ <i>H</i><sup>1</sup>(Ω) is presented by means of the Rothe time-discretization method. Further approximation scheme via Rothe’s method is constructed for the problem when <i>u</i><sub>0</sub> ∈ <i>L</i><sup>2</sup>(Ω) and the integral kernel in the nonlocal boundary condition is symmetric.</p></div>","PeriodicalId":55505,"journal":{"name":"Applications of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2021-10-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50037822","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Some remarks on comparison of predictors in seemingly unrelated linear mixed models 对看似不相关的线性混合模型中预测因子比较的几点评述
IF 0.7 4区 数学
Applications of Mathematics Pub Date : 2021-10-18 DOI: 10.21136/AM.2021.0366-20
Nesrin Güler, Melek Eriş Büyükkaya
{"title":"Some remarks on comparison of predictors in seemingly unrelated linear mixed models","authors":"Nesrin Güler,&nbsp;Melek Eriş Büyükkaya","doi":"10.21136/AM.2021.0366-20","DOIUrl":"10.21136/AM.2021.0366-20","url":null,"abstract":"<div><p>In this paper, we consider a comparison problem of predictors in the context of linear mixed models. In particular, we assume a set of <i>m</i> different seemingly unrelated linear mixed models (SULMMs) allowing correlations among random vectors across the models. Our aim is to establish a variety of equalities and inequalities for comparing covariance matrices of the best linear unbiased predictors (BLUPs) of joint unknown vectors under SULMMs and their combined model. We use the matrix rank and inertia method for establishing equalities and inequalities. We also give an extensive approach for seemingly unrelated regression models (SURMs) by applying the results obtained for SULMMs to SURMs.</p></div>","PeriodicalId":55505,"journal":{"name":"Applications of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2021-10-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.21136/AM.2021.0366-20.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50036956","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
Option valuation under the VG process by a DG method 用DG方法对VG过程下的期权进行估值
IF 0.7 4区 数学
Applications of Mathematics Pub Date : 2021-10-06 DOI: 10.21136/AM.2021.0345-20
Jiří Hozman, Tomáš Tichý
{"title":"Option valuation under the VG process by a DG method","authors":"Jiří Hozman,&nbsp;Tomáš Tichý","doi":"10.21136/AM.2021.0345-20","DOIUrl":"10.21136/AM.2021.0345-20","url":null,"abstract":"<div><p>The paper presents a discontinuous Galerkin method for solving partial integrodifferential equations arising from the European as well as American option pricing when the underlying asset follows an exponential variance gamma process. For practical purposes of numerical solving we introduce the modified option pricing problem resulting from a localization to a bounded domain and an approximation of small jumps, and we discuss the related error estimates. Then we employ a robust numerical procedure based on piecewise polynomial generally discontinuous approximations in the spatial domain. This technique enables a simple treatment of the American early exercise constraint by a direct encompassing it as an additional nonlinear source term to the governing equation. Special attention is paid to the proper discretization of non-local jump integral components, which is based on splitting integrals with respect to the domain according to the size of the jumps. Moreover, to preserve sparsity of resulting linear algebraic systems the pricing equation is integrated in the temporal variable by a semi-implicit Euler scheme. Finally, the numerical results demonstrate the capability of the numerical scheme presented within the reference benchmarks.</p></div>","PeriodicalId":55505,"journal":{"name":"Applications of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2021-10-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50021947","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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 effect of a magnetic field on the onset of Bénard convection in variable viscosity couple-stress fluids using classical Lorenz model 用经典洛伦兹模型研究了变黏度耦合应力流体中磁场对对流起始的影响
IF 0.7 4区 数学
Applications of Mathematics Pub Date : 2021-09-16 DOI: 10.21136/AM.2021.0010-21
Venkatesh Ramachandramurthy, Nagasundar Kavitha, Agrahara Sanjeevmurthy Aruna
{"title":"The effect of a magnetic field on the onset of Bénard convection in variable viscosity couple-stress fluids using classical Lorenz model","authors":"Venkatesh Ramachandramurthy,&nbsp;Nagasundar Kavitha,&nbsp;Agrahara Sanjeevmurthy Aruna","doi":"10.21136/AM.2021.0010-21","DOIUrl":"10.21136/AM.2021.0010-21","url":null,"abstract":"<div><p>The Rayleigh-Bénard convection for a couple-stress fluid with a thermorheological effect in the presence of an applied magnetic field is studied using both linear and non-linear stability analysis. This problem discusses the three important mechanisms that control the onset of convection; namely, suspended particles, an applied magnetic field, and variable viscosity. It is found that the thermorheological parameter, the couple-stress parameter, and the Chandrasekhar number influence the onset of convection. The effect of an increase in the thermorheological parameter leads to destabilization in the system, while the Chandrasekhar number and the couple-stress parameter have the opposite effect. The generalized Lorenz’s model of the problem is essentially the classical Lorenz model but with coefficients involving the impact of three mechanisms as discussed earlier. The classical Lorenz model is a fifth-order autonomous system and found to be analytically intractable. Therefore, the Lorenz system is solved numerically using the Runge-Kutta method in order to quantify heat transfer. An effect of increasing the thermorheological parameter is found to enhance heat transfer, while the couple-stress parameter and the Chandrasekhar number diminishes the same.</p></div>","PeriodicalId":55505,"journal":{"name":"Applications of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2021-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50034136","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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: 1
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