In connection with he weather forecastiing, we consider the first initial-boundary value problem for the retarded equations (1.6). The weak solutions or smooth solutions are unique, that is found by a means of functional.

Using integral equation methods, we study the existence of multiple periodic plane wave solutions for the Fitzhugh-Nagumo equations. Infinitely many non-constant periodic plane wave solutions are found out under rather general conditions by means of the Browder-Potter fixed point theorem.

In this paper,we study the stability of two classes of large scale dynamical systems with delays by using vector V functions and a vector differential inequality with delays. Some simple algebraic criteria for stability are obtained.

In this paper, the available failure data are the number of system failures in the observable time intervals. We give the lower confidence limits of the reliability and the mission reliability of the repairable systems by means of the nonhomogeneous Poisson process model Similarly, the lower confidence limits of the reliability and the mission reliability of the system may result from observable data of the repairable subsystems by using "bad-as-old" analysis.

In this paper, first we deduce the bound of the absolute smallest eigenvalue of M-matrites introduce the concept of bidiagonally dominant matrices, and obtain a new characterization of M-matrices or generalized strictly diagonally dominant matrices. As applications we give the distribution theorems of eigenvalues of some matrices, and generalize these results to block matrices, thus having improved and generalized the corresponding results of [5]-[11].

This paper proposes a new restricted stepsize algorithm, discusses its convergence properties, and extends it to constrained case.

In this paper, we discuss the asymptotic properties of differential equations by using two Liapunov functions whose derivatives are not negative definite. We extend Marchkov's theorem and the results in [1],[2] and [4].Applying our theorems to some systems, we extend their zones of asymptotic stability.

Weiszfeld first gave a simple iterative algorithm to solve the so-called

type location problem in 1937. Later, it was proved that the algorithm converges globally and, under some conditions; linearly. There is a large literature on this problem. But none of the existent methods have attractive rate.of convergence; in all cases, the rate of convergence is linear at best. Recently, Overton gave an algorithm which is quadratically convergent under certain conditions.But there is no guarantee for its global convergence. In this paper, we provide an algorithm which converges globally and, whenever Weiszfeld's algorithm converges linearly, quadratically.

In this paper we study the.initial boundary value problem of compressible fluids with large parameters. We introduce the technique of norm with weight and the method of factor analysis to make the energy estimation and obtain the existence,and uniqueness for the local C^∞ soluuon.

By the use of Projection Pursuit method, we get two multivariate location parameter tests with two well-known test statistics as indezes, the asymptotic properties of the tests are discussed, and asymptotic rejection regions are obtained by the bootstrap method for the teststatistics.

In this paper, we consider the linear differential equations

and s

where p_j(t)(j=1,2,…,m) are oscillating functions. We obtain some sufficient conditions under which equations(1),(1') are oscillatory. Moreover, we discuss the asymptotic behavior of solutions of (1),(1').

In this paper, we provide a new algorithm of the linearly equality and inequality constrained nonlinear programming problem, The algorithm not only overcomes the disadvantage of the Reduce Gradient algorithm that it is only valid for the linearly equality constrained nonlinear programming problem, but also keeps its advantage of lowering the dimension. Further, the algorithm simplifies Ritter's algorithm in[3].Its convergence is also proved.

In this paper, the concepts of cone quasiconvexity and strong cone quasiconvexity are introduced. By using these concepts and the Minkowski functional, under the condition that the constraint set is compact while the objective function is continuous and strongly cone quasiconvex (cone quasiconvex), we prove the connectedness results of the set of efficient (weakly efficient) solutions to multiobiective optimization problems.

Assume the random variable X has density function f(x-θ),where θ is the location parameter,f(x)=0 when x does not belong to interval [-α,α],and f(x) satisfies some ordinary conditions when x belongs to [-α,α],And X₁,…,X_n is a sample from X,It is proved that for the loss runction L of the form L(d,θ)=W(d-θ),θ_n=1/2[min(X₁,…,X_n)+max(X₁,…,X_n) is the equivariant asymptotic efficient estimator of θ under the group of translations.

Let (U_i COS Co_it+V_i sinco_it),where the joint density of (U₁,V₁,…,U_N,VM_N) is invariant under the transformation

Then X(t) is stationary.Put N_u(T) be the number of upcrossings of the level,u by X(t),0<T≤T,and M(T)=sup {X(t); 0≤t≤T}.Under suitable conditions,we derive the formula of E(N_u(T)) and the limiting theorem of P(M(T)≤u_nT(x)) for T ↑∞,where u_n(x)(n≥1)are all monotone increasing functions.The main results are also extended to the case of infinite sum.

A mong the concepts of solutions concerning non-side payment games,the core is one of the solutions that are studied and used wi?ely.In this paper,a class of quasi-balanced games are studied,which satisfy one of the foiiowing two conditions:
(i) V(M) is a compact set generated by a denumberable set;
(ii) V(M) is an imputation set which is generated from a totallybounded set A.The class of quasi-balanced games has the non-empty core.

This paper investigates the boundedness of solutions of second-order-nonlinear funerional differential equation
(r(t)y')'+f(t,y)+g(t,y_t)=p(t).
It is showed by some examples that the criteria of boundedness given here are applicable of a large class of equations.

This paper has improved Read and Hu's method proposed in[1].A minimally 2-connected graph can be compressed many times until it cannot any longer.These incompressible graphs can be used for enumeration of minimally 2-connected graphs by means of Polya theorem in group theory.A program is presented to give the numbers of all minimally 2-connected graphs of order n≤16.

In this paper we extend a class of singular discounted problems,and obtain the conditions for the existence of the optimal control of the new model.We give the construction of the optimal control when it exists.It acts only when the state reaches the boundaries of some interval and reflects the state into the interval at its boundaries.

In this paper,we define a transformation which transforms a periodic sequence over a finite field F_p to another.The structure of the digraph associated to the set of all periodic sequence under this transformation is discussed,some enumeration results are obtained also.

For nonlinear constraints problems,a famil,of perturbed gradient projection algorithms are given,each of which is globally convergent under very weak conditions.Thus,Du Dingzhu's method [1] is extended without the convexity constraints.

This paper introduces a new concept of strongly extreme stability of the system and obtains a stationary oscillation theorem without using the conditions in Lasalle's theorem [1].The results of [2],[3],[4] are improved and extended.

In this paper,we point out that,for the multiparametric exponential family,any (i,j)-element of the inverse matrix l_n^-1 of Bhattacharyya information matrix with order n has a finite limit when n→∞.Thus the inverse Bh-matrix is introduced,and it can be given in advance.By using the inverse Bh-matrix it is convenient to calculate the variance of the UMVUE of some estimable function.As an example,we give the expression of all elements of the inverse Bh-matrix for normal distributions with unknown mean and variance.

This paper provides a functional equation satisfied by the generating function for enumerating rooted loopless planar maps with vertex partition.A kind of applications to enumerating a type of the rooted loopless planar maps with the maximum valency given is described and the explicit enumerating formulae are found.

The order of an autoregressive sequence x(t) is estimated by calculating the eigenvalues of a matrix with relation to the high order sample covariance matrix,and the strong consistency of the estimate is proved.Assume that the order is known.Then the strong consistency of the high order Yule-Walker estimation of autoregressive parameters is proven and the asymptotic normality of the estimates is studied.

The direction-choice-constraints simplex method (DCCS),a new improvement on the sinmplex method for solving linear programming,is presented.When there are m structural straints constraints in a linear programming problem and only L of them across the optimizing trail,the DCCS saves more than (1-L/M) percent of time and (m²-L²) method.compared with the standard simplex memories.

First we discuss the transformation_between two different equations u_t=K(x,t,u) and v_τ=H(ξ,τ,υ).Then corresponding relations of symmetries and.their Lie algebra are esta blished.Finally,some applications are given.

Under Cox's proportional hazard regression model and in the case of noninformative tensoring, this paper shows that Cox's partial likelihood function is proportional to the likelihood function based on a marginally sufficient statistic for the regression coefficient in the absence of knowledge of baseline havard function with respect to the incomplete samples of the same type. For type Ⅱ censored small samples the relative efficiency of the maximum partial like-lihood estimator versus the maximum likelihood estimator from the exponential case is examined.

We discuss the finite element methods for a nonlinear hyperbolic-parabolic coupled system arising in high temperature fluid dynamics. The optimal order estimates in L₂ and in L_∞ are derived for continuous time Galerkin approximations.

In this paper, the periodic system
x=A(t,x)+b(t,x)
is considered, where the n×n matrix A(t,x) and the,n-vector b(t,x) are continuous in(t,x)∈R×Rⁿ,and A(t+ω,x)=A(t,x);b(t+ω,x)=b(t,x), Using the method of functional analysis, we prove that the above system has ω-periodic solution and give sufficient conditions to guarantee the existence of the unique ω-periodic solution for the following systems.

This paper discusses the properties of a system of controlling equations of pipeline networks, gives a new convex programming method to solve the system of equations with a unique solution, and proves the global convergence. an d the superlinear rate of convergence of the new method. Meanwhile, the paper also establishes a nonlinear programming model for solving the optimization problem of the design and control of the pipeline networks, presents a constrained variable metric algorithm, and proves the.convergence of the algorithm under quite weak conditions.

This paper provides a functional equation satisfied by the generating function for rooted simple planar maps with face partition. As two applications of it, the two functional equations of the generating functions for enumerating the same kind of maps with the valency of the root-face and the number of edges, or the number of non-root-faces as two indices are also deduced respectively. In consequence, the number of rooted plane trees and the number of rooted simple planar maps with the size given are vgain determined explicitly.

This paper does initial research for some applications of parametric random processes (PRP) and doubly random parametric processes (DRPP). There mainly are the competision model and its special case random games; the applications ef PRP in spot derecting of sports competitions and training; The imitating-type fc.recasting and control method;and the selecting material model. Makes some brief discussion about problems of RWIRE, Bayes estimation, and weather forcasts etc.

Different designs (determined by m_i's) give different random one-way models:
y_ij=β+α_i+ε_ij,i=1,…,n,j=1,…,m_i,
and in these models the BAIQUE _D's of linear combination r=f₁θ₁+f₂θ₂ are different.

In this paper, we improve Hormander's lemma in Peter Li and Shing-Tung Yau[1] tend a result in[1].Using Hormander's Lemma, we give some estimates for the eiganvalue problems with discontinuous coefficients.

Analytic functions in one variable are determined uniquely by their local values. As a conjecture, J. L. C. Sanz and T. S. Huang suggested an extrapolation method for one dimension bandlimited functions (or signals), which are some special analytic functions. This conjecture has been proved. In this paper, we discuss the multidimensional problem and obtain the corresponding result.

A predator-Prey system, depending on several parameters, is investigated for the bifurcation of equilibria, Hopf bifurcation, the global bifurcation with saddle connection, and the global existence and nonexistence of limit cycles. We also study the changes of the topological structure of trajectories as the parameters are varied. Finally the biological implications of the mathematical results are discussed.

In this paper we discuss the following boundary value problem:

Here k>0, f(t), g(t) and h(y) are continuous functions on(-∞,+∞) such that the uniqueness of the solution and its condition inpending on the initial value are ensured.