Let G be a connected graph. We denote by σ(G,x) and δ(G) respectively the σ-polynomial and the edge-density of G,where δ(G)=|E(G)||V(G)|2. If σ(G,x) has at least an unreal root,then G is said to be a σ-unreal gr...Let G be a connected graph. We denote by σ(G,x) and δ(G) respectively the σ-polynomial and the edge-density of G,where δ(G)=|E(G)||V(G)|2. If σ(G,x) has at least an unreal root,then G is said to be a σ-unreal graph.Let δ(n) be the minimum edge-density over all n vertices graphs with σ-unreal roots. In this paper,by using the theory of adjoint polynomials, a negative answer to a problem posed by Brenti et al. is given and the following results are obtained:For any positive integer a and rational number 0≤c≤1,there exists at least a graph sequence {G i} 1≤i≤a such that G i is σ-unreal and δ(G i)→c as n→∞ for all 1≤i≤a,and moreover, δ(n)→0 as n→∞.展开更多
Based on the computerized symbolic computation, some new exact travelling wave solutions to three nonlinear evolution equations are explicitly obtained by replacing the tanhξ in tanh-function method with the solution...Based on the computerized symbolic computation, some new exact travelling wave solutions to three nonlinear evolution equations are explicitly obtained by replacing the tanhξ in tanh-function method with the solutions of a new auxiliary ordinary differential equation.展开更多
It is necessary to test for varying dispersion in generalized nonlinear models.Wei,et al(1998) developed a likelihood ratio test,a score test and their adjustments to test for varying dispersion in continuous exponent...It is necessary to test for varying dispersion in generalized nonlinear models.Wei,et al(1998) developed a likelihood ratio test,a score test and their adjustments to test for varying dispersion in continuous exponential family nonlinear models.This type of problem in the framework of general discrete exponential family nonlinear models is discussed.Two types of varying dispersion,which are random coefficients model and random effects model,are proposed,and corresponding score test statistics are constructed and expressed in simple,easy to use,matrix formulas.展开更多
This paper investigates the effects of postponing retirement on economic growth in an aging society by using the infinite overlapping generations model constructed by Blanchard (1985) in a simple endogenous growth fra...This paper investigates the effects of postponing retirement on economic growth in an aging society by using the infinite overlapping generations model constructed by Blanchard (1985) in a simple endogenous growth framework.It shows that postponing retirement may decelerate economic growth.展开更多
基金Supported by the National Natural Science Foundation of China(1 0 0 6 1 0 0 3 ) and the Science Founda-tion of the State Education Ministry of China
文摘Let G be a connected graph. We denote by σ(G,x) and δ(G) respectively the σ-polynomial and the edge-density of G,where δ(G)=|E(G)||V(G)|2. If σ(G,x) has at least an unreal root,then G is said to be a σ-unreal graph.Let δ(n) be the minimum edge-density over all n vertices graphs with σ-unreal roots. In this paper,by using the theory of adjoint polynomials, a negative answer to a problem posed by Brenti et al. is given and the following results are obtained:For any positive integer a and rational number 0≤c≤1,there exists at least a graph sequence {G i} 1≤i≤a such that G i is σ-unreal and δ(G i)→c as n→∞ for all 1≤i≤a,and moreover, δ(n)→0 as n→∞.
基金Supported by the Natural Science Foundation and the High Education Science Research ProgramNJ0 2 0 35 of Inner Mongoli
文摘Based on the computerized symbolic computation, some new exact travelling wave solutions to three nonlinear evolution equations are explicitly obtained by replacing the tanhξ in tanh-function method with the solutions of a new auxiliary ordinary differential equation.
基金Supported by the National Natural Science Foundations of China( 1 9631 0 4 0 ) and SSFC( o2 BTJ0 0 1 ) .
文摘It is necessary to test for varying dispersion in generalized nonlinear models.Wei,et al(1998) developed a likelihood ratio test,a score test and their adjustments to test for varying dispersion in continuous exponential family nonlinear models.This type of problem in the framework of general discrete exponential family nonlinear models is discussed.Two types of varying dispersion,which are random coefficients model and random effects model,are proposed,and corresponding score test statistics are constructed and expressed in simple,easy to use,matrix formulas.
文摘This paper investigates the effects of postponing retirement on economic growth in an aging society by using the infinite overlapping generations model constructed by Blanchard (1985) in a simple endogenous growth framework.It shows that postponing retirement may decelerate economic growth.
