The sum of positive eigenvalues and the number of the edges of a graph G are denoted by S(G) and #E(G) respectively. C. Delorme[1] put forward the question: What is the lower bound of S(G) for a given #E(G)? Is it In this paper we give an affirm
The approximate eigenvectors or Ritz vectors obtained by the block Arnoldi method may converge very slowly and even fail to converge even if the approximate eigenvalues do. In order to improve the quality of the Ritz vectors, a modified strategy
In this papert the matrix of equidiagonal-dominance is defined and several theorems about ||A-1||∞ and its evaluation are established. Many interesting numerical examples are given.
The second order approach of local influence (see [15]) is developed and applied to Cox's proportional hazards model, and compared with Cook's local influence approach (see [6] and [13]) which was used in this model. To study local influence, we
In this paper, we study the point process of state transitions in a regular Markov chain.Under a weaker condition, we prove that the point process is a 1-memory self-exciting point process and again obtain four useful formulas of the transition f
In this paper, we study periodic waves in reaction-diffusion systems with limit cycle kinetics and weak diffusion. The results are based on the analysis of a nonlinear partial differential equation which is derived from singular perturbation tech
In this paper, the problem of minimizing a convex function subject to general linear constraints is considered. An algorithm which is an extension of the method described in [4] is presented. And a new dual simplex procedure with lexicographic sc
It is known[5] that an investigation of the up-embeddability of the 3-regular graphs shows a useful approach to that of the general graph. But as far, very few characterizations of the upembeddability are known on the 3-regular graphs. Let G be a
A new ordering method is proposed for automated theorem proving of differential geometry,by which Cartan's moving frame method can be combined with Wu's elimination principle.
This paper gives a sufficient condition for the existence of heteroclinic cycle in the model of competition between n species and a criterion for determining the stability of the heteroclinic cycle. The results given in this paper extend the resu
This paper proves that the Ginzburg-Landan partial differential equation admits an inertial fractal set whose fractal dimension is finite. Purthermore, We produce an exponentially approximating Sequence of localizing compact fractal sets and a fr
In this paper we give an enumeration formula of the outerplanar graphs by means of graph compression, group theory and combinatorial numbers. Some simple examples are exhibited for illustrating the method. The computational results are shown in t
