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  • Herbivore harvesting and alternative steady states in coral reefs
    Appl. Math. (IF 0.544) Pub Date : 2020-12-16
    Ikbal Hossein Sarkar, Joydeb Bhattacharyya, Samares Pal

    Coral reefs can undergo relatively rapid changes in the dominant biota, a phenomenon referred to as phase shift. Degradation of coral reefs is often associated with changes in community structure towards a macroalgae-dominated reef ecosystem due to the reduction in herbivory caused by overfishing. We investigate the coral-macroalgal phase shift due to the effects of harvesting of herbivorous reef fish

  • A spatially sixth-order hybrid L 1-CCD method for solving time fractional Schrödinger equations
    Appl. Math. (IF 0.544) Pub Date : 2020-12-16
    Chun-Hua Zhang, Jun-Wei Jin, Hai-Wei Sun, Qin Sheng

    We consider highly accurate schemes for nonlinear time fractional Schrödinger equations (NTFSEs). While an L1 strategy is employed for approximating the Caputo fractional derivative in the temporal direction, compact CCD finite difference approaches are incorporated in the space. A highly effective hybrid L1-CCD method is implemented successfully. The accuracy of this linearized scheme is order six

  • Regularity criterion for a nonhomogeneous incompressible Ginzburg-Landau-Navier-Stokes system
    Appl. Math. (IF 0.544) Pub Date : 2020-12-14
    Nana Pan, Jishan Fan, Yong Zhou

    We prove a regularity criterion for a nonhomogeneous incompressible Ginzburg-Landau-Navier-Stokes system with the Coulomb gauge in ℝ3. It is proved that if the velocity field in the Besov space satisfies some integral property, then the solution keeps its smoothness.

  • A sensitivity result for quadratic second-order cone programming and its application
    Appl. Math. (IF 0.544) Pub Date : 2020-12-14
    Qi Zhao, Wenhao Fu, Zhongwen Chen

    In this paper, we present a sensitivity result for quadratic second-order cone programming under the weak form of second-order sufficient condition. Based on this result, we analyze the local convergence of an SQP-type method for nonlinear second-order cone programming. The subproblems of this method at each iteration are quadratic second-order cone programming problems. Compared with the local convergence

  • An improved regularity criteria for the MHD system based on two components of the solution
    Appl. Math. (IF 0.544) Pub Date : 2020-12-04
    Zujin Zhang, Yali Zhang

    As observed by Yamazaki, the third component b3 of the magnetic field can be estimated by the corresponding component u3 of the velocity field in Lλ (2 ⩽ λ ⩽ 6) norm. This leads him to establish regularity criterion involving u3, j3 or u3, ω3. Noticing that λ can be greater than 6 in this paper, we can improve previous results.

  • Incompressible limit of a fluid-particle interaction model
    Appl. Math. (IF 0.544) Pub Date : 2020-11-27
    Hongli Wang, Jianwei Yang

    The incompressible limit of the weak solutions to a fluid-particle interaction model is studied in this paper. By using the relative entropy method and refined energy analysis, we show that, for well-prepared initial data, the weak solutions of the compressible fluid-particle interaction model converge to the strong solution of the incompressible Navier-Stokes equations as long as the Mach number goes

  • Isocanted Alcoved Polytopes
    Appl. Math. (IF 0.544) Pub Date : 2020-10-21
    María Jesús de la Puente, Pedro Luis Clavería

    Through tropical normal idempotent matrices, we introduce isocanted alcoved polytopes, computing their f-vectors and checking the validity of the following five conjectures: Bárány, unimodality, 3d, flag and cubical lower bound (CLBC). Isocanted alcoved polytopes are centrally symmetric, almost simple cubical polytopes. They are zonotopes. We show that, for each dimension, there is a unique combinatorial

  • Block Matrix Approximation Via Entropy Loss Function
    Appl. Math. (IF 0.544) Pub Date : 2020-11-02
    Malwina Janiszewska, Augustyn Markiewicz, Monika Mokrzycka

    The aim of the paper is to present a procedure for the approximation of a symmetric positive definite matrix by symmetric block partitioned matrices with structured off-diagonal blocks. The entropy loss function is chosen as approximation criterion. This procedure is applied in a simulation study of the statistical problem of covariance structure identification.

  • Modifying the Tropical Version of Stickel’s Key Exchange Protocol
    Appl. Math. (IF 0.544) Pub Date : 2020-10-27
    Any Muanalifah, Sergeĭ Sergeev

    A tropical version of Stickel’s key exchange protocol was suggested by Grigoriev and Shpilrain (2014) and successfully attacked by Kotov and Ushakov (2018). We suggest some modifications of this scheme that use commuting matrices in tropical algebra and discuss some possibilities of attacks on these new modifications. We suggest some simple heuristic attacks on one of our new protocols, and then we

  • Guaranteed Two-Sided Bounds on All Eigenvalues of Preconditioned Diffusion and Elasticity Problems Solved By the Finite Element Method
    Appl. Math. (IF 0.544) Pub Date : 2020-10-21
    Martin Ladecký, Ivana Pultarová, Jan Zeman

    A method of characterizing all eigenvalues of a preconditioned discretized scalar diffusion operator with Dirichlet boundary conditions has been recently introduced in Gergelits, Mardal, Nielsen, and Strakoš (2019). Motivated by this paper, we offer a slightly different approach that extends the previous results in some directions. Namely, we provide bounds on all increasingly ordered eigenvalues of

  • Kinetic BGK Model for a Crowd: Crowd Characterized By a State of Equilibrium
    Appl. Math. (IF 0.544) Pub Date : 2020-10-21
    Abdelghani El Mousaoui, Pierre Argoul, Mohammed El Rhabi, Abdelilah Hakim

    This article focuses on dynamic description of the collective pedestrian motion based on the kinetic model of Bhatnagar-Gross-Krook. The proposed mathematical model is based on a tendency of pedestrians to reach a state of equilibrium within a certain time of relaxation. An approximation of the Maxwellian function representing this equilibrium state is determined. A result of the existence and uniqueness

  • Dirichlet Boundary Value Problem for an Impulsive Forced Pendulum Equation with Viscous and Dry Frictions
    Appl. Math. (IF 0.544) Pub Date : 2020-10-21
    Martina Pavlačková, Pavel Ženčák

    Sufficient conditions are given for the solvability of an impulsive Dirichlet boundary value problem to forced nonlinear differential equations involving the combination of viscous and dry frictions. Apart from the solvability, also the explicit estimates of solutions and their derivatives are obtained. As an application, an illustrative example is given, and the corresponding numerical solution is

  • Distance Matrices Perturbed by Laplacians
    Appl. Math. (IF 0.544) Pub Date : 2020-09-04
    Balaji Ramamurthy, Ravindra Bhalchandra Bapat, Shivani Goel

    Let T be a tree with n vertices. To each edge of T we assign a weight which is a positive definite matrix of some fixed order, say, s. Let Dij denote the sum of all the weights lying in the path connecting the vertices i and j of T. We now say that Dij is the distance between i and j. Define D ≔ [Dij], where Dii is the s × s null matrix and for i ≠ j, Dij is the distance between i and j. Let G be an

  • Convergence Acceleration of Shifted LR Transformations for Totally Nonnegative Hessenberg Matrices
    Appl. Math. (IF 0.544) Pub Date : 2020-09-07
    Akiko Fukuda, Yusaku Yamamoto, Masashi Iwasaki, Emiko Ishiwata, Yoshimasa Nakamura

    We design shifted LR transformations based on the integrable discrete hungry Toda equation to compute eigenvalues of totally nonnegative matrices of the banded Hessenberg form. The shifted LR transformation can be regarded as an extension of the extension employed in the well-known dqds algorithm for the symmetric tridiagonal eigenvalue problem. In this paper, we propose a new and effective shift strategy

  • Interval Matrices with Monge Property
    Appl. Math. (IF 0.544) Pub Date : 2020-09-04
    Martin Černý

    We generalize the Monge property of real matrices for interval matrices. We define two classes of interval matrices with the Monge property—in a strong and a weak sense. We study the fundamental properties of both types. We show several different characterizations of the strong Monge property. For the weak Monge property, we give a polynomial description and several sufficient and necessary conditions

  • Complexity of Computing Interval Matrix Powers for Special Classes of Matrices
    Appl. Math. (IF 0.544) Pub Date : 2020-09-07
    David Hartman, Milan Hladík

    Computing powers of interval matrices is a computationally hard problem. Indeed, it is NP-hard even when the exponent is 3 and the matrices only have interval components in one row and one column. Motivated by this result, we consider special types of interval matrices where the interval components occupy specific positions. We show that computing the third power of matrices with only one column occupied

  • Partial Sum of Eigenvalues of Random Graphs
    Appl. Math. (IF 0.544) Pub Date : 2020-09-04
    Israel Rocha

    Let G be a graph on n vertices and let λ1 ⩾ λ2 ⩾ ‣ ⩾ λn be the eigenvalues of its adjacency matrix. For random graphs we investigate the sum of eigenvalues \({s_k} = \sum\limits_{i = 1}^k {{\lambda _i}},\) for 1 ⩾ k ⩾ n, and show that a typical graph has Sk ⩾ (e(G) + k2)/(0.99n)1/2, where e(G) is the number of edges of G. We also show bounds for the sum of eigenvalues within a given range in terms

  • Lanczos-Like Algorithm for the Time-Ordered Exponential: The *-Inverse Problem
    Appl. Math. (IF 0.544) Pub Date : 2020-09-24
    Pierre-Louis Giscard, Stefano Pozza

    The time-ordered exponential of a time-dependent matrix A(t) is defined as the function of A(t) that solves the first-order system of coupled linear differential equations with non-constant coefficients encoded in A(t). The authors have recently proposed the first Lanczos-like algorithm capable of evaluating this function. This algorithm relies on inverses of time-dependent functions with respect to

  • Complete Solution of Tropical Vector Inequalities Using Matrix Sparsification
    Appl. Math. (IF 0.544) Pub Date : 2020-09-16
    Nikolai Krivulin

    We examine the problem of finding all solutions of two-sided vector inequalities given in the tropical algebra setting, where the unknown vector multiplied by known matrices appears on both sides of the inequality. We offer a solution that uses sparse matrices to simplify the problem and to construct a family of solution sets, each defined by a sparse matrix obtained from one of the given matrices

  • Optimization Problem under Two-Sided (max, +)/(min, +) Inequality Constraints
    Appl. Math. (IF 0.544) Pub Date : 2020-09-15
    Karel Zimmermann

    (max, +)-linear functions are functions which can be expressed as the maximum of a finite number of linear functions of one variable having the form f(x1, …, xh) = max(aj + xj), where aj, j = 1, …, h, are real numbers. Similarly (min, +)-linear functions are defined. We will consider optimization problems in which the set of feasible solutions is the solution set of a finite inequality system, where

  • On The Vectors Associated with the Roots of Max-Plus Characteristic Polynomials
    Appl. Math. (IF 0.544) Pub Date : 2020-09-15
    Yuki Nishida, Sennosuke Watanabe, Yoshihide Watanabe

    We discuss the eigenvalue problem in the max-plus algebra. For a max-plus square matrix, the roots of its characteristic polynomial are not its eigenvalues. In this paper, we give the notion of algebraic eigenvectors associated with the roots of characteristic polynomials. Algebraic eigenvectors are the analogues of the usual eigenvectors in the following three senses: (1) An algebraic eigenvector

  • The Generalized Finite Volume SUSHI Scheme for the Discretization of the Peaceman Model
    Appl. Math. (IF 0.544) Pub Date : 2020-09-15
    Mohamed Mandari, Mohamed Rhoudaf, Ouafa Soualhi

    We demonstrate some a priori estimates of a scheme using stabilization and hybrid interfaces applying to partial differential equations describing miscible displacement in porous media. This system is made of two coupled equations: an anisotropic diffusion equation on the pressure and a convection-diffusion-dispersion equation on the concentration of invading fluid. The anisotropic diffusion operators

  • Asymptotic Lower Bounds for Eigenvalues of the Steklov Eigenvalue Problem with Variable Coefficients
    Appl. Math. (IF 0.544) Pub Date : 2020-09-09
    Yu Zhang, Hai Bi, Yidu Yang

    In this paper, using a new correction to the Crouzeix-Raviart finite element eigenvalue approximations, we obtain asymptotic lower bounds of eigenvalues for the Steklov eigenvalue problem with variable coefficients on d-dimensional domains (d = 2, 3). In addition, we prove that the corrected eigenvalues converge to the exact ones from below. The new result removes the conditions of eigenfunction being

  • A phase-field method applied to interface tracking for blood clot formation
    Appl. Math. (IF 0.544) Pub Date : 2020-07-09
    Marek Čapek

    The high shear rate thrombus formation was only recently recognized as another way of thrombosis. Models proposed in Weller (2008), (2010) take into account this type of thrombosis. This work uses the phase-field method to model these evolving interface problems. A loosely coupled iterative procedure is introduced to solve the coupled system of equations. Convergence behavior on two levels of refinement

  • Boundary exact controllability for a porous elastic Timoshenko system
    Appl. Math. (IF 0.544) Pub Date : 2020-07-03
    Manoel J. Santos; Carlos A. Raposo; Leonardo R. S. Rodrigues

    In this paper, we consider a one-dimensional system governed by two partial differential equations. Such a system models phenomena in engineering, such as vibrations in beams or deformation of elastic bodies with porosity. By using the HUM method, we prove that the system is boundary exactly controllable in the usual energy space. We will also determine the minimum time allowed by the method for the

  • Beyond the Mattriad Conferences
    Appl. Math. (IF 0.544) Pub Date : 2020-07-01
    Jan Hauke, Augustyn Markiewicz, Simo Puntanen

    In this article we present a short history of the MatTriad Conferences, a series of international conferences on matrix analysis and its applications. The name MatTriad originally comes from the phrase Three Days Full of Matrices. The first MatTriad was held in the Mathematical Research and Conference Center of the Institute of Mathematics of the Polish Academy of Sciences in Będlewo, near Poznań,

  • The Collatz-Wielandt Quotient for Pairs of Nonnegative Operators
    Appl. Math. (IF 0.544) Pub Date : 2020-06-30
    Shmuel Friedland

    In this paper we consider two versions of the Collatz-Wielandt quotient for a pair of nonnegative operators A, B that map a given pointed generating cone in the first space into a given pointed generating cone in the second space. If the two spaces and two cones are identical, and B is the identity operator, then one version of this quotient is the spectral radius of A. In some applications, as commodity

  • On the local convergence of Kung-Traub’s two-point method and its dynamics
    Appl. Math. (IF 0.544) Pub Date : 2020-06-30
    Parandoosh Ataei Delshad; Taher Lotfi

    In this paper, the local convergence analysis of the family of Kung-Traub’s two-point method and the convergence ball for this family are obtained and the dynamical behavior on quadratic and cubic polynomials of the resulting family is studied. We use complex dynamic tools to analyze their stability and show that the region of stable members of this family is vast. Numerical examples are also presented

  • Periodic solutions of nonlinear differential systems by the method of averaging
    Appl. Math. (IF 0.544) Pub Date : 2020-06-30
    Zhanyong Li; Qihuai Liu; Kelei Zhang

    In many engineering problems, when studying the existence of periodic solutions to a nonlinear system with a small parameter via the local averaging theorem, it is necessary to verify some properties of the fundamental solution matrix to the corresponding linearized system along the periodic solution of the unperturbed system. But sometimes, it is difficult or it requires a lot of calculations. In

  • Linear Complementarity Problems and Bi-Linear Games
    Appl. Math. (IF 0.544) Pub Date : 2020-06-25
    Gokulraj Sengodan, Chandrashekaran Arumugasamy

    In this paper, we define bi-linear games as a generalization of the bimatrix games. In particular, we generalize concepts like the value and equilibrium of a bimatrix game to the general linear transformations defined on a finite dimensional space. For a special type of Z-transformation we observe relationship between the values of the linear and bi-linear games. Using this relationship, we prove some

  • Incompressible inviscid limit for the full magnetohydrodynamic flows on expanding domains
    Appl. Math. (IF 0.544) Pub Date : 2020-06-25
    Young-Sam Kwon

    In this paper we study the incompressible inviscid limit of the full magnetohydrodynamic flows on expanding domains with general initial data. By applying the relative energy method and carrying out detailed analysis on the oscillation part of the velocity, we prove rigorously that the gradient part of the weak solutions of the full magnetohydrodynamic flows converges to the strong solution of the

  • On complete moment convergence for weighted sums of negatively superadditive dependent random variables
    Appl. Math. (IF 0.544) Pub Date : 2020-06-15
    Haiwu Huang; Xuewen Lu

    In this work, the complete moment convergence and complete convergence for weighted sums of negatively superadditive dependent (NSD) random variables are studied, and some equivalent conditions of these strong convergences are established. These main results generalize and improve the corresponding theorems of Baum and Katz (1965) and Chow (1988) to weighted sums of NSD random variables without the

  • Exponential stability of a flexible structure with history and thermal effect
    Appl. Math. (IF 0.544) Pub Date : 2020-06-15
    Roberto Díaz; Jaime Muñoz; Carlos Martínez; Octavio Vera

    In this paper we study the asymptotic behavior of a system composed of an integro-partial differential equation that models the longitudinal oscillation of a beam with a memory effect to which a thermal effect has been given by the Green-Naghdi model type III, being physically more accurate than the Fourier and Cattaneo models. To achieve this goal, we will use arguments from spectral theory, considering

  • Notion of Information and Independent Component Analysis
    Appl. Math. (IF 0.544) Pub Date : 2020-05-25
    Una Radojičić; Klaus Nordhausen; Hannu Oja

    Partial orderings and measures of information for continuous univariate random variables with special roles of Gaussian and uniform distributions are discussed. The information measures and measures of non-Gaussianity including the third and fourth cumulants are generally used as projection indices in the projection pursuit approach for the independent component analysis. The connections between information

  • Empirical Regression Quantile Processes
    Appl. Math. (IF 0.544) Pub Date : 2020-05-25
    Jana Jurečková; Jan Picek; Martin Schindler

    We address the problem of estimating quantile-based statistical functionals, when the measured or controlled entities depend on exogenous variables which are not under our control. As a suitable tool we propose the empirical process of the average regression quantiles. It partially masks the effect of covariates and has other properties convenient for applications, e.g. for coherent risk measures of

  • Scatter Halfspace Depth: Geometric Insights
    Appl. Math. (IF 0.544) Pub Date : 2020-05-25
    Stanislav Nagy

    Scatter halfspace depth is a statistical tool that allows one to quantify the fitness of a candidate covariance matrix with respect to the scatter structure of a probability distribution. The depth enables simultaneous robust estimation of location and scatter, and nonparametric inference on these. A handful of remarks on the definition and the properties of the scatter halfspace depth are provided

  • Changepoint Estimation for Dependent and Non-Stationary Panels
    Appl. Math. (IF 0.544) Pub Date : 2020-05-25
    Michal Pešta; Barbora Peštová; Matúš Maciak

    The changepoint estimation problem of a common change in panel means for a very general panel data structure is considered. The observations within each panel are allowed to be generally dependent and non-stationary. Simultaneously, the panels are weakly dependent and non-stationary among each other. The follow up period can be extremely short and the changepoint magnitudes may differ across the panels

  • Discrete Random Processes with Memory: Models and Applications
    Appl. Math. (IF 0.544) Pub Date : 2020-05-25
    Tomáš Kouřim; Petr Volf

    The contribution focuses on Bernoulli-like random walks, where the past events significantly affect the walk’s future development. The main concern of the paper is therefore the formulation of models describing the dependence of transition probabilities on the process history. Such an impact can be incorporated explicitly and transition probabilities modulated using a few parameters reflecting the

  • On the Optimality of the Max-Depth and Max-Rank Classifiers for Spherical Data
    Appl. Math. (IF 0.544) Pub Date : 2020-05-25
    Ondřej Vencálek; Houyem Demni; Amor Messaoud; Giovanni C. Porzio

    The main goal of supervised learning is to construct a function from labeled training data which assigns arbitrary new data points to one of the labels. Classification tasks may be solved by using some measures of data point centrality with respect to the labeled groups considered. Such a measure of centrality is called data depth. In this paper, we investigate conditions under which depth-based classifiers

  • Behaviour of Higher-Order Approximations of the Tests in the Single Parameter Cox Proportional Hazards Model
    Appl. Math. (IF 0.544) Pub Date : 2020-05-21
    Aneta Andrášiková; Eva Fišerová

    Survival analysis is applied in a wide range of sectors (medicine, economy, etc.), and its main idea is based on evaluating the time until the occurrence of an event of interest. The effect of some particular covariates on survival time is usually described by the Cox proportional hazards model and the statistical significance of the impact of covariates is verified by the likelihood ratio test, the

  • Some Consistent Exponentiality Tests Based on Puri-Rubin and Desu Characterizations
    Appl. Math. (IF 0.544) Pub Date : 2020-05-21
    Marija Cuparić; Bojana Milošević; Yakov Yu. Nikitin; Marko Obradović

    We present new goodness-of-fit tests for the exponential distribution based on equidistribution type characterizations. For the construction of the test statistics, we employ an L2-distance between the corresponding V-empirical distribution functions. The resulting test statistics are V-statistics, free of the scale parameter.The quality of the tests is assessed through local Bahadur efficiencies as

  • A Convergence Result and Numerical Study for a Nonlinear Piezoelectric Material in a Frictional Contact Process with a Conductive Foundation
    Appl. Math. (IF 0.544) Pub Date : 2020-05-14
    El-Hassan Benkhira, Rachid Fakhar, Youssef Mandyly

    We consider two static problems which describe the contact between a piezoelectric body and an obstacle, the so-called foundation. The constitutive relation of the material is assumed to be electro-elastic and involves the nonlinear elastic constitutive Hencky’s law. In the first problem, the contact is assumed to be frictionless, and the foundation is nonconductive, while in the second it is supposed

  • Stability of unique pseudo almost periodic solutions with measure
    Appl. Math. (IF 0.544) Pub Date : 2020-04-06
    Boulbaba Ghanmi; Mohsen Miraoui

    By means of the fixed-point methods and the properties of the μ-pseudo almost periodic functions, we prove the existence, uniqueness, and exponential stability of the μ-pseudo almost periodic solutions for some models of recurrent neural networks with mixed delays and time-varying coefficients, where μ is a positive measure. A numerical example is given to illustrate our main results.

  • A Blow-up Criterion for the Strong Solutions to the Nonhomogeneous Navier-Stokes-Korteweg Equations in Dimension Three
    Appl. Math. (IF 0.544) Pub Date : 2020-04-06
    Huanyuan Li Zhengzhou

    This paper proves a Serrin’s type blow-up criterion for the 3D density-dependent Navier-Stokes-Korteweg equations with vacuum. It is shown that if the density ϱ and velocity field u satisfy \(\parallel\triangledown\varrho\parallel_{{L^\infty}(0,T;W^{1,q})}+\parallel{u}\parallel_{{L^s}(0,T;L_\omega^r)}<\infty\) for some q > 3 and any (r, s) satisfying 2/s + 3/r ⩽ 1, 3, < r ⩽ ∞, then the strong solutions

  • A comparison of approaches for the construction of reduced basis for stochastic Galerkin matrix equations
    Appl. Math. (IF 0.544) Pub Date : 2020-03-12
    Michal Béreš

    We examine different approaches to an efficient solution of the stochastic Galerkin (SG) matrix equations coming from the Darcy flow problem with different, uncertain coefficients in apriori known subdomains. The solution of the SG system of equations is usually a very challenging task. A relatively new approach to the solution of the SG matrix equations is the reduced basis (RB) solver, which looks

  • An adaptive s -step conjugate gradient algorithm with dynamic basis updating
    Appl. Math. (IF 0.544) Pub Date : 2020-02-29
    Erin Claire Carson

    The adaptive s-step CG algorithm is a solver for sparse symmetric positive definite linear systems designed to reduce the synchronization cost per iteration while still achieving a user-specified accuracy requirement. In this work, we improve the adaptive s-step conjugate gradient algorithm by the use of iteratively updated estimates of the largest and smallest Ritz values, which give approximations

  • On polynomial robustness of flux reconstructions
    Appl. Math. (IF 0.544) Pub Date : 2020-02-26
    Miloslav Vlasák

    We deal with the numerical solution of elliptic not necessarily self-adjoint problems. We derive a posteriori upper bound based on the flux reconstruction that can be directly and cheaply evaluated from the original fluxes and we show for one-dimensional problems that local efficiency of the resulting a posteriori error estimators depends on p1/2 only, where p is the discretization polynomial degree

  • Domain decomposition methods coupled with parareal for the transient heat equation in 1 and 2 spatial dimensions
    Appl. Math. (IF 0.544) Pub Date : 2020-02-26
    Ladislav Foltyn; Dalibor Lukáš; Ivo Peterek

    We present a parallel solution algorithm for the transient heat equation in one and two spatial dimensions. The problem is discretized in space by the lowest-order conforming finite element method. Further, a one-step time integration scheme is used for the numerical solution of the arising system of ordinary differential equations. For the latter, the parareal method decomposing the time interval

  • Optimal Packings for Filled Rings of Circles
    Appl. Math. (IF 0.544) Pub Date : 2020-02-02
    Dinesh B. Ekanayake; Manjula Mahesh Ranpatidewage; Douglas J. LaFountain

    General circle packings are arrangements of circles on a given surface such that no two circles overlap except at tangent points. In this paper, we examine the optimal arrangement of circles centered on concentric annuli, in what we term rings. Our motivation for this is two-fold: first, certain industrial applications of circle packing naturally allow for filled rings of circles; second, any packing

  • Solvability of a Dynamic Rational Contact with Limited Interpenetration for Viscoelastic Plates
    Appl. Math. (IF 0.544) Pub Date : 2020-01-31
    Jiří Jarušek

    Solvability of the rational contact with limited interpenetration of different kind of viscolastic plates is proved. The biharmonic plates, von Kármán plates, Reissner-Mindlin plates, and full von Kármán systems are treated. The viscoelasticity can have the classical (“short memory”) form or the form of a certain singular memory. For all models some convergence of the solutions to the solutions of

  • A Continuity Result for a Quasilinear Elliptic Free Boundary Problem
    Appl. Math. (IF 0.544) Pub Date : 2020-01-31
    Abdeslem Lyaghfouri

    We investigate a two dimensional quasilinear free boundary problem, and show that the free boundary is a union of graphs of continuous functions.

  • Global Strong Solutions of a 2-D New Magnetohydrodynamic System
    Appl. Math. (IF 0.544) Pub Date : 2020-01-29
    Ruikuan Liu; Jiayan Yang

    The main objective of this paper is to study the global strong solution of the parabolic-hyperbolic incompressible magnetohydrodynamic model in the two dimensional space. Based on Agmon, Douglis, and Nirenberg’s estimates for the stationary Stokes equation and Solonnikov’s theorem on Lp-Lq-estimates for the evolution Stokes equation, it is shown that this coupled magnetohydrodynamic equations possesses

  • Inverse Eigenvalue Problem for Constructing a Kind of Acyclic Matrices with Two Eigenpairs
    Appl. Math. (IF 0.544) Pub Date : 2020-01-20
    Maryam Babaei Zarch; Seyed Abolfazl Shahzadeh Fazeli; Seyed Mehdi Karbassi

    We investigate an inverse eigenvalue problem for constructing a special kind of acyclic matrices. The problem involves the reconstruction of the matrices whose graph is an m-centipede. This is done by using the (2m − 1)st and (2m)th eigenpairs of their leading principal submatrices. To solve this problem, the recurrence relations between leading principal submatrices are used.

  • A Recovery-Based a Posteriori Error Estimator for the Generalized Stokes Problem
    Appl. Math. (IF 0.544) Pub Date : 2020-01-09
    Pengzhan Huang; Qiuyu Zhang

    A recovery-based a posteriori error estimator for the generalized Stokes problem is established based on the stabilized P1 − P0 (linear/constant) finite element method. The reliability and efficiency of the error estimator are shown. Through theoretical analysis and numerical tests, it is revealed that the estimator is useful and efficient for the generalized Stokes problem.

  • Theoretical and numerical studies of the P N P M DG schemes in one space dimension
    Appl. Math. (IF 0.544) Pub Date : 2019-11-20
    Abdulatif Badenjki; Gerald Warnecke

    We give a proof of the existence of a solution of reconstruction operators used in the PNPM DG schemes in one space dimension. Some properties and error estimates of the projection and reconstruction operators are presented. Then, by applying the PNPM DG schemes to the linear advection equation, we study their stability obtaining maximal limits of the Courant numbers for several PNPM DG schemes mostly

  • Fractional-order Bessel functions with various applications
    Appl. Math. (IF 0.544) Pub Date : 2019-11-18
    Haniye Dehestani; Yadollah Ordokhani; Mohsen Razzaghi

    We introduce fractional-order Bessel functions (FBFs) to obtain an approximate solution for various kinds of differential equations. Our main aim is to consider the new functions based on Bessel polynomials to the fractional calculus. To calculate derivatives and integrals, we use Caputo fractional derivatives and Riemann-Liouville fractional integral definitions. Then, operational matrices of fractional-order

  • Solving second-order singularly perturbed ODE by the collocation method based on energetic Robin boundary functions
    Appl. Math. (IF 0.544) Pub Date : 2019-10-31
    Chein-Shan Liu; Botong Li

    for a second-order singularly perturbed ordinary differential equation (ODE) under the Robin type boundary conditions, we develop an energetic Robin boundary functions method (ERBFM) to find the solution, which automatically satisfies the Robin boundary conditions. For the non-singular ODE the Robin boundary functions consist of polynomials, while the normalized exponential trial functions are used

  • The anti-disturbance property of a closed-loop system of 1-d wave equation with boundary control matched disturbance
    Appl. Math. (IF 0.544) Pub Date : 2019-10-30
    Xiao-Rui Wang; Gen-Qi Xu

    We study the anti-disturbance problem of a 1-d wave equation with boundary control matched disturbance. In earlier literature, the authors always designed the controller such as the sliding mode control and the active disturbance rejection control to stabilize the system. However, most of the corresponding closed-loop systems are boundedly stable. In this paper we show that the linear feedback control

  • The adaptation of the k -means algorithm to solving the multiple ellipses detection problem by using an initial approximation obtained by the DIRECT global optimization algorithm
    Appl. Math. (IF 0.544) Pub Date : 2019-10-29
    Rudolf Scitovski; Kristian Sabo

    We consider the multiple ellipses detection problem on the basis of a data points set coming from a number of ellipses in the plane not known in advance, whereby an ellipse E is viewed as a Mahalanobis circle with center S, radius r, and some positive definite matrix Σ. A very efficient method for solving this problem is proposed. The method uses a modification of the k-means algorithm for Mahalanobis-circle

  • DG Method for Pricing European Options under Merton Jump-Diffusion Model
    Appl. Math. (IF 0.544) Pub Date : 2019-10-01
    Jiří Hozman; Tomáš Tichý; Miloslav Vlasák

    Under real market conditions, there exist many cases when it is inevitable to adopt numerical approximations of option prices due to non-existence of analytical formulae. Obviously, any numerical technique should be tested for the cases when the analytical solution is well known. The paper is devoted to the discontinuous Galerkin method applied to European option pricing under the Merton jump-diffusion

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