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
The two-parameter exponential distribution is proposed to be an underlying model,and prediction bounds for future observations are obtained by using Bayesian approach.Prediction intervals are derived for unobserved li...The two-parameter exponential distribution is proposed to be an underlying model,and prediction bounds for future observations are obtained by using Bayesian approach.Prediction intervals are derived for unobserved lifetimes in one-sample prediction and two-sample prediction based on type Ⅱ doubly censored samples.A numerical example is given to illustrate the procedures,prediction intervals are investigated via Monte Carlo method,and the accuracy of prediction intervals is presented.展开更多
For a graph G,P(G,λ)denotes the chromatic polynomial of G.Two graphs G and H are said to be chromatically equivalent,denoted by G～H,if P(G,λ)=p(H,λ).Let [G]={H|H～G}.If [G]={G},then G is said to be chromaticall...For a graph G,P(G,λ)denotes the chromatic polynomial of G.Two graphs G and H are said to be chromatically equivalent,denoted by G～H,if P(G,λ)=p(H,λ).Let [G]={H|H～G}.If [G]={G},then G is said to be chromatically unique.For a complete 5 partite graph G with 5n vertices, define θ(G)=(α(G,6)-2 n+1 -2 n-1 + 5)/2 n-2 ,where α(G,6) denotes the number of 6 independent partition s of G.In this paper, the authors show that θ(G)≥0 and determine all g raphs with θ(G)=0,1,2,5/2,7/2,4,17/4.By using these results the chromaticity of 5 partite graphs of the form G-S with θ(G)=0,1,2,5/2,7/2,4,17/4 is inve stigated,where S is a set of edges of G.Many new chromatically unique 5 partite graphs are obtained.展开更多
The notion of w-density for the graphs with positive weights on vertices and nonnegative weights on edges is introduced.A weighted graph is called w-balanced if its w-density is no less than the w-density of any subgr...The notion of w-density for the graphs with positive weights on vertices and nonnegative weights on edges is introduced.A weighted graph is called w-balanced if its w-density is no less than the w-density of any subgraph of it.In this paper,a good characterization of w-balanced weighted graphs is given.Applying this characterization,many large w-balanced weighted graphs are formed by combining smaller ones.In the case where a graph is not w-balanced,a polynomial-time algorithm to find a subgraph of maximum w-density is proposed.It is shown that the w-density theory is closely related to the study of SEW(G,w) games.展开更多
Hiding efficiency of traditional audio information hiding methods is always low since the sentience similarity cannot be guaranteed. A new audio information hiding method is proposed in this letter which can impose th...Hiding efficiency of traditional audio information hiding methods is always low since the sentience similarity cannot be guaranteed. A new audio information hiding method is proposed in this letter which can impose the insensitivity with the audio phase for auditory and realize the information hiding through specific algorithm in order to modify local phase within the auditory perception. The algorithm is to introduce the operation of "set 1" and "set 0" for every phase vectors, then the phases must lie on the boundary of a phase area after modified. If it lies on "1" boundary, it comes by set 1 operation. If it lies on "0" boundary, it comes by set 0 operation. The results show that, compared with the legacy method, the proposed method has better auditory similarity, larger information embedding capacity and lower code error rate. As a kind of blind detect method, it fits for application scenario without channel interference.展开更多
In this paper, some new classes of integral graphs are given in two new ways. It is proved that the problem of finding such integral graphs is equivalent to the problem of solving diophantine equations. Some classes a...In this paper, some new classes of integral graphs are given in two new ways. It is proved that the problem of finding such integral graphs is equivalent to the problem of solving diophantine equations. Some classes are infinite. The discovery of these classes is a new contribution to the search of such integral graphs.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→∞.
文摘The two-parameter exponential distribution is proposed to be an underlying model,and prediction bounds for future observations are obtained by using Bayesian approach.Prediction intervals are derived for unobserved lifetimes in one-sample prediction and two-sample prediction based on type Ⅱ doubly censored samples.A numerical example is given to illustrate the procedures,prediction intervals are investigated via Monte Carlo method,and the accuracy of prediction intervals is presented.
基金Supported by the National Natural Science Foundation of China (1 0 0 61 0 0 3) and the ScienceFoundation of the State Education Ministry of China
文摘For a graph G,P(G,λ)denotes the chromatic polynomial of G.Two graphs G and H are said to be chromatically equivalent,denoted by G～H,if P(G,λ)=p(H,λ).Let [G]={H|H～G}.If [G]={G},then G is said to be chromatically unique.For a complete 5 partite graph G with 5n vertices, define θ(G)=(α(G,6)-2 n+1 -2 n-1 + 5)/2 n-2 ,where α(G,6) denotes the number of 6 independent partition s of G.In this paper, the authors show that θ(G)≥0 and determine all g raphs with θ(G)=0,1,2,5/2,7/2,4,17/4.By using these results the chromaticity of 5 partite graphs of the form G-S with θ(G)=0,1,2,5/2,7/2,4,17/4 is inve stigated,where S is a set of edges of G.Many new chromatically unique 5 partite graphs are obtained.
文摘The notion of w-density for the graphs with positive weights on vertices and nonnegative weights on edges is introduced.A weighted graph is called w-balanced if its w-density is no less than the w-density of any subgraph of it.In this paper,a good characterization of w-balanced weighted graphs is given.Applying this characterization,many large w-balanced weighted graphs are formed by combining smaller ones.In the case where a graph is not w-balanced,a polynomial-time algorithm to find a subgraph of maximum w-density is proposed.It is shown that the w-density theory is closely related to the study of SEW(G,w) games.
文摘Hiding efficiency of traditional audio information hiding methods is always low since the sentience similarity cannot be guaranteed. A new audio information hiding method is proposed in this letter which can impose the insensitivity with the audio phase for auditory and realize the information hiding through specific algorithm in order to modify local phase within the auditory perception. The algorithm is to introduce the operation of "set 1" and "set 0" for every phase vectors, then the phases must lie on the boundary of a phase area after modified. If it lies on "1" boundary, it comes by set 1 operation. If it lies on "0" boundary, it comes by set 0 operation. The results show that, compared with the legacy method, the proposed method has better auditory similarity, larger information embedding capacity and lower code error rate. As a kind of blind detect method, it fits for application scenario without channel interference.
文摘In this paper, some new classes of integral graphs are given in two new ways. It is proved that the problem of finding such integral graphs is equivalent to the problem of solving diophantine equations. Some classes are infinite. The discovery of these classes is a new contribution to the search of such integral graphs.
