作者机构：
[Zhang, Xiaoming] Beijing Normal Univ, Dept Phys, Beijing 100875, Peoples R China.;Nanhua Univ, Sch Phys & Mat, Hengyang 421001, Peoples R China.;Beijing Univ Posts & Telecommun, Sch Sci, Beijing 100876, Peoples R China.;Chinese Ctr Adv Sci & Technol, World Lab, Beijing 8730, Peoples R China.;Beijing Normal Univ Branch, Beijing Hong Kong Singapore Joint Ctr Nonlinear &, Beijing, Peoples R China.
通讯机构：
[Zhang, Xiaoming] B;Beijing Normal Univ, Dept Phys, Beijing 100875, Peoples R China.
摘要：
Pattern formation in spatiotemporal chaotic systems is investigated. Temporally chaotic and spatially ordered patterns are observed by varying the coupling strength. Spatial orderings emerge spontaneously due to self-organization of partial and nonlocal chaos synchronization, governed by various types of spatial symmetries. The first and secondary bifurcations from spatially disordered chaos to chaos with different levels of spatial orderings are observed and the scaling behaviors associated with these bifurcations are statistically analyzed.
关键词：
complete symmetric function;Schur-convexity;theory of majorization
摘要：
This paper investigates Schur-convexity of the complete symmetric function c(r)(x) = Sigma(i1+...+in=r)x(1)(i1)...x(n)(in) and the function phi(r)(x) = C-r(x)/Cr-1(x), where i(1),...i(n) are non-negative integers and r >= 1. Some inequalities, including Ky Fan type inequality, are established by use of the theory of majorization. It is also concerned with an open problem proposed by Menon [1].
摘要：
The complex permittivity of hydrogen plasma in single wall carbon nanotubes (SWNTs), which were grown by iron-catalyzed high-pressure disproportionation (HiPco), is deduced using double-fluid theory and phenomenological model. We calculate the absorptional attenuations of microwave in HiPco SWNTs in the range of 300 MHz–30 GHz under different conditions. The experimental phenomenon of strong microwave absorption (around 2.45 GHz) by hydrogen plasma in HiPco SWNTs can be explained numerically. The influences of the liberal electron density and electronic effective collision frequency on microwave absorption are presented theoretically.
摘要：
By introducing a new norm which is equivalent to the usual norm in the phase space, we prove that for n-dimensional second order dissipative lattices of coupled oscillators with external periodic forces under Dirichlet, Neumann and periodic boundary conditions, if the system is bounded dissipative and the coupled coefficients are both large enough, the asymptotic synchronization will occur. And we give a concrete bounded dissipative second order lattices system. Our results show that the bounds of the difference between the components of any solution are directly proportional to mn/2 and inversely proportional to the coupled coefficients, where m is the mesh size and n is the space dimension of lattice points.
期刊：
JOURNAL OF INEQUALITIES AND APPLICATIONS,2006年2006(1):1-9 ISSN：1029-242X
通讯作者：
Guan, KZ
作者机构：
[Guan, Kaizhong] Department of Mathematics and Physics, Nanhua University, Hengyang, China
通讯机构：
[Guan, KZ ] ;Nanhua Univ, Dept Math & Phys, Hengyang 421001, Hunan, Peoples R China.
摘要：
We prove that the complete elementary symmetric function c(r) = c(r) (x) = C-n([r]) (x) = Sigma i(1+...+in= r) x(1)(i1)...x(n)(in) and the function phi(r)(x) = c(r)(x)/c(r-1)(x) are Schur-convex functions in R-+(n) = {(x(1), x(2),...,x(n)) vertical bar x(i) > 0}, where i(1), i(2),...,i(n) are nonnegative integers, r is an element of N = {1, 2,...}, i = 1, 2,...,n. For which, some inequalities are established by use of the theory of majorization. A problem given by K. V. Menon (Duke Mathematical Journal 35 (1968), 37-45) is also solved. Copyright (C) 2006 Kaizhong Guan. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
期刊：
Journal of Mathematical Analysis and Applications,2005年312(2):555-563 ISSN：0022-247X
通讯作者：
Li, XY
作者机构：
[Li, XY] Nanhua Univ, Sch Math & Phys, Hengyang 421001, Hunan, Peoples R China.
通讯机构：
[Li, XY] N;Nanhua Univ, Sch Math & Phys, Hengyang 421001, Hunan, Peoples R China.
关键词：
Global asymptotic stability;Length of semicycle;Rational difference equation;Semicycle;Trajectory structure
摘要：
In this paper, we use a method different from the known literature to investigate the global behavior of the following fourth-order rational difference equation: x(n+1) = x(n-1)x(n-2)x(n-3)+x(n-1)+x(n-2)+x(n-3)+a/x(n-1)x(n-2)+x(n-1)x(n-3)+x(n-2)x(n-3)+1+a, n = 0, 1, 2, . , where a is an element of [0, infinity) and the initial values x(-3), x(-2), x(-1), x(0) E (0, infinity). The rule of the trajectory structure for the solutions of the equation is clearly described out. The successive lengths of positive and negative semicycles of nontrivial solutions of the above equation is found to periodically occur. However, the order for them to occur is completely different although there is the same prime period 7. The rule is 3(+), 1(-), 1(+), 2(-) or 3(-), 1(+), 1-, 2(+) in a period. By using the rule, the positive equilibrium point of the equation is verified to be globally asymptotically stable. (c) 2005 Elsevier Inc. All rights reserved.
摘要：
In this paper, we use a method different from the known literature to investigate the qualitative properties of the following fourth-order rational difference equation: [GRAPHICS] where a is an element of [0, infinity) and the initial values x(-3), x(-2), X-1, X-0 is an element of (0, infinity). The successive lengths of positive and negative semicycles of nontrivial solutions of the above equation is found to periodically occur, that is,..., 3(+), 2(-),1(+), 1(-), 3(+), 2(-), 1(+), 1(-), 3(+), 2(-), 1(+), 1(-), 3(+), 2(-), 1(+), 1(-).... or,.... 2(+),1(-), 1(+), 3(-),2(+), 1(-), 1(+),3(-),2(+), 1(-),1(+), 3(-),2(+), 1(-),1(+),3(-),2(+), 1(-), 1(+), 3(-),.... By using the rule, the positive equilibrium point of the equation is verified to be globally asymptotically stable. (c) 2005 Elsevier Inc. All rights reserved.
摘要：
Some sufficient conditions and some sufficient and necessary conditions are established for the oscillation of a class of odd-order delay parabolic differential equations of the form ∂Nu(x,t)∂tN-a(t)Δu+∑i=1npi(x,t)u(x,t-σi)-∑j=1mqi(x,t)u(x,t-τj)+h(t)f(u(x,t-r1),…,u(x,t-rl))=0,(x,t)∈Ω×[t0,+∞)≡G,t0∈R,where N is an odd integer, Ω is a bounded domain in RM with a smooth boundary ∂Ω, and Δ is the Laplacian operation with three different boundary conditions. To some extent, our results extended and improved the oscillatory results of some references. Meanwhile, we corrected some mistakes in a main conclusion of reference (J. Comput. Appl. Math. 147 (2002) 263).
摘要：
In this paper, we investigate the existence of multiple positive periodic solutions to a class of functional difference equations. We answer the open problems proposed by Y. Raffoul in [Electron. J. Differential Equations 55 (2002) 1-8] and the conditions obtained improve some recent results established there. (c) 2004 Elsevier Inc. All rights reserved.
