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Matlab Methods for Roots of characteristic equation of Cylindrical Bessel equation Eigenvalue Problems on General Interval

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Chinese Quarterly Journal of Mathematics 2009年第1期24卷 145-150页

作者： ZHAO Xi-lai CUI Qun-fa Department of Mathematics Bast China Normal University Shanghai 200241 China Department of Mathematics Hebi Vocational Institute of Technology Hebi 450030 China Anyang Normal University Anyang 455000 China

Root of characteristic equation for cylindrical Bessel equation eigenvalue problems on general interval is of great real physical importance at engineering and physical. First, the characteristic equation of cylindrical Bessel equation eigenvalue problem on general interval is given, second, by mean of compared method, we obtaining roots of characteristic equation with Matlab program is discussed.

关键词： cylindrical Bessel equation characteristic equation method of Matlab

Synchronization of two coupled pendula in absence of escapement

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Applied Mathematics and Mechanics(English Edition) 2016年第12期37卷 1721-1738页

作者： F.TALAMUCCI DIMAI Dipartimento di Matematica e Informatica "Ulisse Dini"Università degli Studi di Firenze

A model of two oscillating pendula placed on a mobile support is studied. Once an overall scheme of equations, under general assumptions, is formulated via the Lagrangian equations of motion, the specific case of absence of escapement is examined. The mechanical model consists of two coupled pendula both oscillating on a moving board attached to a spring. The final result performs selection among the peculiar parameters of the physical process （the length, the ratio of masses, the friction and damping coefficients, and the stiffness of the spring）, providing a tendency to synchronization.

关键词： synchronization coupled pendula characteristic equation eigenvalue lo-calization

SINGULAR INTEGRAL equationS ALONG AN OPEN ARC WITH SOLUTIONS HAVING SINGULARITIES OF HIGHER ORDER

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Acta Mathematica Scientia 2005年第2期25卷 193-200页

作者：钟寿国 School of Mathematics and Statistics Wuhan University Wuhan 430072 China

In this paper, the difficulties on calculation in solving singular integral equations are overcome when the restriction of curve of integration to be a closed contour is cancelled. When the curve is an open arc and the solutions for singular integral equations possess singularities of higher order, the solution and the solvable condition for characteristic equations as well as the generalized Noether theorem for complete equations are given.

关键词： Open arc singular integral equation solutions with singularity of higher order Noether theorem characteristic equation

A SPECIAL METHOD OF FOURIER SERIES WHICH IS EQUAL TO THE METHOD OF SEPARATION OF VARIABLES ON BOUNDARY VALUE PROBLEM

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Acta Mechanica Solida Sinica 1997年第3期10卷 255-261页

作者： Yan Xianggan Wu Jike, Department of Mechanics, Peking Unirersity, Bejing 100871. China BEIJING UNIV DEPT MECHBEIJING 100871PEOPLES R CHINA

By the separation of singularity, a special Fourier series solution of the boundary value problem for plane is obtained, which can satisfy all boundary conditions and converges rapidly. II is proved that the solution is equal to the result of separation of variables. As a result, the non-linear characteristic equations resulting from the method of separation of variables are transformed into polynomial equations that can provide a foundation for approximate computation and asymptotic analysis.

关键词： separation of singularity series resolution method of separation of variables boundary value problem characteristic equation

RATIO-DEPENDENT PREDATOR-PREY MODEL WITH STAGE STRUCTURE AND TIME DELAY

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International Journal of Biomathematics 2012年第4期5卷 15-37页

作者： LIJUAN ZHA JING-AN CUI XUEYONG ZHOU School of Mathematical Sciences Nanjing Normal University Nanjing 210046 Jiangsu P. R. China School of Science Beijing University of Civil Engineering and Architecture Beijing 100044 P. R. China

Ratio-dependent predator prey models are favored by many animal ecologists recently as more suitable ones for predator-prey interactions where predation involves searching process. In this paper, a ratio-dependent predator prey model with stage structure and time delay for prey is proposed and analyzed. In this model, we only consider the stage structure of immature and mature prey species and not consider the stage structure of predator species. We assume that the predator only feed on the mature prey and the time for prey from birth to maturity represented by a constant time delay. At first, we investigate the permanence and existence of the proposed model and sufficient conditions are derived. Then the global stability of the nonnegative equilibria are derived. We also get the sufficient criteria for stability switch of the positive equilibrium. Finally, some numerical simulations are carried out for supporting the analytic results.

关键词： Ratio-dependent stage structure time delay characteristic equation globally asymptotical stability.

Method of characteristic for Functional equations in Polynomial Form

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Acta Mathematica Sinica,English Series 1997年第3期13卷 421-432页

作者： Janusz Matkowski (Department of Mathematics,Technical University of Bielsko-Biala 43-309 Bielsko-Biala,Poland)Zhang Weinian (Department of Mathematics,Sichung Union University,East Area,Chengdu 610041,China) Department of Mathematics Technical University of Bielsko-Biala Department of Mathematics Sichung Union University

Properties of continuous solutions of a second order polynomial-like iterated functional equation are given by considering its characteristic.A useful method to discuss the general case is described indeed in this pro... 详细信息

关键词： Functional equation Iterative root characteristic equation Recursive construction

Compound structure analysis of a new chaotic system

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Journal of Southeast University(English Edition) 2004年第4期20卷 477-481页

作者：刘文波陈关荣南京航空航天大学自动化学院南京210016 香港城市大学电子工程系

This paper analyzes the compound attractor structure of a new three-dimensional autonomous chaotic system. First, it is found that there exist five equilibria in the chaotic system, and the stabilities of these equilibria are discussed under a constant scalar control input parameter m. Secondly, the trajectories of the attractors on a y-z plane are examined, the reasons why these trajectories can exist or disappear are also described. Finally, the forming procedure of the different scrolls chaotic attractor is explored by computer simulations when the parameter m is varied. It is shown that the new chaotic attractor has a compound structure, it can evolve to other three-dimensional autonomous chaotic systems. The results of theoretical analysis and simulation are helpful for better understanding of other similar chaotic systems.

关键词： three-dimensional autonomous system chaos equilibrium attractor characteristic equation compound structure

Generalized Cayley-Hamilton theorem for core-EP inverse matrix and DMP inverse matrix

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Journal of Southeast University(English Edition) 2018年第1期34卷 135-138页

作者： Wang Hongxing Chen Jianlong Yan Guanjie School of Mathematics Southeast UniversityNanjing 211189China School of Science Guangxi University for NationalitiesNanning 530006China

By using the classical Cayley-Hamilton theorem,the polynomial equations of the core-EP inverse matrix and Drazin-Moore-Penrose(DMP)inverse matrix are given,*** the characteristic polynomial of the singular matrix A,p A(s)=det(s E n-A)=s n+a n-1 s n-1+…+a 1 s,is given,then f A(A)=0 and f A(A d,+)=0 in which f A(A)=a 1 x n+a 2 x n-1+…+a n-1 x 2+x,and A and A d,+are the core-EP inverse and the DMP inverse of A,***,some properties of the characteristic polynomials of A D∈C n,n and A∈C n,n are derived.

关键词： Cayley-Hamilton theorem characteristic equation Drazin inverse Drazin-Moore-Penrose(DMP)inverse core-EP inverse

THE ASYMPTOTIC STABILITY REGION TO A CLASS OF HIGHER ORDER DELAY LINEAR DIFFERENCE equationS

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Annals of Differential equations 2014年第1期30卷 33-53页

作者： Hongshan Ren Institute of Math.Science Heilongjiang University

In this paper, we establish necessary and sufficient conditions for the zero solution to a class of higher order delay linear difference equations to be asymptotically stable, which are easy to be verified and to be a... 详细信息

关键词： delay difference equation asymptotic stability characteristic equation