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LOCAL APPROXIMATE SOLUTIONS OF A CLASS OF NONLINEAR DIFFUSION POPULATION MODELS
Guang Chong Yang,Xia Chen,Lan Xiao 경남대학교 수학교육과 2021 Nonlinear Functional Analysis and Applications Vol.26 No.1
This paper studies approximate solutions for a class of nonlinear diffusion population models. Our methods are to use the fundamental solution of heat equations to construct integral forms of the models and the well-known Banach compression map theorem to prove the existence of positive solutions of integral equations. Non-steady-state local approximate solutions for suitable harvest functions are obtained by utilizing the approximation theorem of multivariate continuous functions.
YANG, GUANG CHONG 한국전산응용수학회 2006 Journal of applied mathematics & informatics Vol.20 No.1
For any fixed $\lambda\leq-\frac{1}{2}$, there exists $f(\eta){\in}C^1[0,+\infty)$ which satisfies the following nonlinear boundary value problem f'+ff'+$\lambda(l-f'^2)=0$ a.e.in $(0,+\infty)$, f(0)=0, f'(0) = 0, $f'(+\infty)=1$, which arises in boundary layer theory in fluid mechanics.
A MATRIX INEQUALITY ON SCHUR COMPLEMENTS
YANG, ZHONG-PENG,CAO, CHONG-GUANG,ZHANG, XIAN 한국전산응용수학회 2005 Journal of applied mathematics & informatics Vol.18 No.1
We investigate a matrix inequality on Schur complements defined by {1}-generalized inverses, and obtain simultaneously a necessary and sufficient condition under which the inequality turns into an equality. This extends two existing matrix inequalities on Schur complements defined respectively by inverses and Moore-Penrose generalized inverses (see Wang et al. [Lin. Alg. Appl., 302-303(1999)163-172] and Liu and Wang [Lin. Alg. Appl., 293(1999)233-241]). Moreover, the non-uniqueness of $\{1\}$-generalized inverses yields the complicatedness of the extension.
INEQUALITIES INVOLVING KHATRI-RAO PRODUCTS OF HERMITIAN MATRICES
Yang, Zhong-Peng,Zhang, Xian,Cao, Chong-Guang 한국전산응용수학회 2002 The Korean journal of computational & applied math Vol.9 No.1
Recently, Several inequalities Khatri-Rao Products of two four partitioned blocks positive definite real symmetry matrices are established by Liu in[Lin. Alg. Appl. 289(1999): 267-277]. We extend these results in two ways. First, the results are extended to two any partitioned blocks Hermitian matrices. Second, necessary and sufficient conditions under which these inequalities become equalities are presented.
A matrix inequality on Schur complements
Zhong-peng Yang,Chong-guang Cao,Xian Zhang 한국전산응용수학회 2005 Journal of applied mathematics & informatics Vol.18 No.1-2
We investigate a matrix inequality on Schur complements de- fined by {1}-generalized inverses, and obtain simultaneously a necessary and sufficient condition under which the inequality turns into an equality. This extends two existing matrix inequalities on Schur complements de- fined respectively by inverses and Moore-Penrose generalized inverses (see Wang et al. [Lin. Alg. Appl., 302-303(1999)163-172] and Liu and Wang [Lin. Alg. Appl., 293(1999)233-241]). Moreover, the non-uniqueness of {1}-generalized inverses yields the complicatedness of the extension.
LMI Stability Criterion with Less Variables for Time-delay Systems
Xun-Lin Zhu,Tao Li,Chong Lin,Lei Guo,Guang-Hong Yang 제어·로봇·시스템학회 2009 International Journal of Control, Automation, and Vol.7 No.4
Slack variables approach is an important technique for tackling the delay-dependent stability problem for systems with time-varying delay. In this paper, a new delay-dependent stability criterion is presented without introducing any slack variable. The technique is based on a simply integral inequal-ity. The result is shown to be equivalent to some existing ones but includes the least number of vari-ables. Thus, redundant selection and computation can be avoided so that the computational burden can be largely reduced. Numerical examples are given to illustrate the effectiveness of the proposed stabil-ity conditions.