Let h be a polynomial in four variables with the singular Hessian Hh and the gradient ▽h and R be a nonzero relation of ▽h. Set H = ▽R（▽h）. We prove that the components of H are linearly dependent when rkHh ≤ 2...Let h be a polynomial in four variables with the singular Hessian Hh and the gradient ▽h and R be a nonzero relation of ▽h. Set H = ▽R（▽h）. We prove that the components of H are linearly dependent when rkHh ≤ 2 and give a necessary and sufficient condition for the components of H to be linearly dependent when rkHh = 3.展开更多
In this paper, we improve the algorithm and rewrite the function make- Pairing for computing a Gorni-Zampieri pair of a homogeneous polynomial map. As an application, some counterexamples to PLDP （dependence problem ...In this paper, we improve the algorithm and rewrite the function make- Pairing for computing a Gorni-Zampieri pair of a homogeneous polynomial map. As an application, some counterexamples to PLDP （dependence problem for power lin- car maps） are obtained, including one in the lowest dimension （n = 48） in all suchcounterexamples one has found up to now.展开更多
The stability in L∞-norm is considered for the Ritz-Volterra projection and some applications are presented in this paper. As a result, point-wise error estimates are established for the finite element approximation ...The stability in L∞-norm is considered for the Ritz-Volterra projection and some applications are presented in this paper. As a result, point-wise error estimates are established for the finite element approximation for the parabolic integrodifferential equation, Sobolev equations, and a diffusion equation with non-local boundary value problem.展开更多
Many engineering structures exhibit frequency dependent characteristics and analyses of these structures lead to frequency dependent eigenvalue problems.This paper presents a novel perturbative iteration(PI)algorithm ...Many engineering structures exhibit frequency dependent characteristics and analyses of these structures lead to frequency dependent eigenvalue problems.This paper presents a novel perturbative iteration(PI)algorithm which can be used to effectively and efficiently solve frequency dependent eigenvalue problems of general frequency dependent systems.Mathematical formulations of the proposed method are developed and based on these formulations,a computer algorithm is devised.Extensive numerical case examples are given to demonstrate the practicality of the proposed method.When all modes are included,the method is exact and when only a subset of modes are used,very accurate results are obtained.展开更多
基金The Scientific Research Foundation (2012QD05X) of Civil Aviation University of Chinathe Fundamental Research Funds(3122014K011)for the Central Universities of China
文摘Let h be a polynomial in four variables with the singular Hessian Hh and the gradient ▽h and R be a nonzero relation of ▽h. Set H = ▽R（▽h）. We prove that the components of H are linearly dependent when rkHh ≤ 2 and give a necessary and sufficient condition for the components of H to be linearly dependent when rkHh = 3.
基金The"985 Project"and"211 Project"of Jilin Universitythe Basis Scientific Research Fund(200903286)of Ministry of Education of China+1 种基金the NSF(11126044,11071097)of ChinaShandong Postdoctoral Science Foundation(201003054),Innovation Program
文摘In this paper, we improve the algorithm and rewrite the function make- Pairing for computing a Gorni-Zampieri pair of a homogeneous polynomial map. As an application, some counterexamples to PLDP （dependence problem for power lin- car maps） are obtained, including one in the lowest dimension （n = 48） in all suchcounterexamples one has found up to now.
文摘The stability in L∞-norm is considered for the Ritz-Volterra projection and some applications are presented in this paper. As a result, point-wise error estimates are established for the finite element approximation for the parabolic integrodifferential equation, Sobolev equations, and a diffusion equation with non-local boundary value problem.
文摘Many engineering structures exhibit frequency dependent characteristics and analyses of these structures lead to frequency dependent eigenvalue problems.This paper presents a novel perturbative iteration(PI)algorithm which can be used to effectively and efficiently solve frequency dependent eigenvalue problems of general frequency dependent systems.Mathematical formulations of the proposed method are developed and based on these formulations,a computer algorithm is devised.Extensive numerical case examples are given to demonstrate the practicality of the proposed method.When all modes are included,the method is exact and when only a subset of modes are used,very accurate results are obtained.
