Using the method developed by the author in ^[4-5],we investigate in this paper the existence of a strictly positive(componentwise) periodic solution of the following nonlinear,nonconvolution,Volterra integerodifferential equation with inftnite delay.

This paper considers one of the basic,well studied problems in scheduling theory,that of nonpreemptively scheduling n independent tasks on m identical parallel processors with the objective of minimizing the "makespan".Coffman,Garey and Johnson described an algorithm MULTIFIT,which gives a better worst case performance than the LPT-algorithm.The upper bound 1.22 obtained by them was improved by Yue Minyi,Hans Kellerer and Zhongliang Yu.They gave the bound 1.20 a shorter proof in [3],by means of the weight function.In this paper we will analyse the structure of bin packing directly and give the bound 1.20 a proof without using the weight function.

In this paper,we provide a class of primitive matrices with zero trace which has a continuous exponent set containing the subset{2,3,…,2n-2},and give a series of n×n primitive matrices τ_i1,τ_i2,…,τ_ik whose exponent set satisfies {1,2,3,…2n-2}⊂E(τ_i1)⊂E(τ_i2)⊂E(τ_ik).

In this paper the uniform convergence rate isgiven for two estimators of the inverse correlation function of stationary and invertible time series under fairly general conditions.The asymptotic normality of two estimators is also proved.

In this paper,we discuss the first passage problem of Markov decision programming with incomplete state information.It was shown that the problem can be transformed to Markov decision programming with complete state information.We discuss the existence conditions for existence of an optimal stationary policy.Finally,we discuss the algorithm.

Iterative algorithm proposed by Hoerl and Kennard is an important method for choosing ridge parameter k value in ridge regression estimation,but there are some problems in application and weakness in theory,for this reason.We give the convergence theorem and it's proof,as well as the formula of convergence limit about the iterative algorithm in this paper.

In this paper,the convergence rate of random weighting approximation for the distribution of the partial sum of a stationary linear series is investigated.Under some conditions,it is proved that the cenvergence rate is O(1/√n).In the last section,an AR(p) model is further discussed.

In this paper,we study the equipotential surface problem of equations -Σ_i,j=1ⁿ∂/∂x,(a_ij∂/∂x₁+α₀(x)u=f(x)) in a bounded domain Ω⊂Rⁿ.Using the method of variation,the existence of solutions is proved; finally we obtain its estimation which is applicable.

In this paper,some limit properties of arbitrary binary information sources are studied by using the notion of deviation of entropy density.Some results for the relative entropy densities of arbitrary binary information sources,as corollaries of the main theorems,are obtained.

This paper deals with a type of seasonal integer-valued autoregressive models-SINAR(1).It points out that through the rising dimension method the SINAR(1) serirs can be changed into a multiple stationary aeries.Procedures are developed for the estimatyn of parameters of SINAR(1) with period 2.It is also shown that among the SINAR(1) family vith stationary marginal distribution,the Poisson distributnon is the only distribution with the regresaion function E(x_t-1|x_t) to be a linear function.

In this paper we give approximate unbiased estimates(AUE) of scale parameter σ and location parameter μ of a normal distribution under Ⅰ censoring.Next,we study statistical analysis of accelerated constant stress life test(ACSLT) for lognormal distribution under type Ⅰ censoring anf give AUE of to coefficients in acceleration equation and estimates of various.Finally,a numerical example in computation and usable in application.

A two-dimensional,multicomponent,multiphase,incompressible,compositional reservoir simulator has been developed and applied to micellae/polymer Hooding.The mathematical model of a two dimensional invigorated oil recovery simulation can be described by a system of nonlinear partial differential equations.The pressure and the associated Huid velocity will be approximated by a mixed finite element method,and concentration by a finite element method based on a variant of the method of characteristics.Two such schemes are presented and analyzed for convergence.

It is well known that the transformation parameter estimate is sensitive to the small perturbations in linear regression([4]).In this paper,we apply the local influence approach proposed by Cook([3]) to derive influence measures for assessing the effects of small perturbations arising from the data.The work of Lawrance([6]) is extended to many kinds of perturbationws including case weights,explanatory variables,responses,and the components of one case.Two examples are given to illustrate our results which show that the local influence approach is helpful to the diagnostics of regression transformation models.

In this paper,by combining CAD algorithm with the theoretic proof,we give I_λ-optimal designs of parameter estimation for the additive mixture model of 2-degree on the standard simplex region S_q-1 of,components.On the basis of CAD result,we first give the clues to conjecture that some I_λ-optimal allocations are I_λ-optimal designs,and then by theoretic argumentation we prove the correctness of this conjecture.According to different component numbers q,these designs belong to four respective types.

This paper deals with the conditions for the existence of periodic solutions to different types of differential delay equations with multiple lags.Available criteria are given.

In this paper,we first review some basic definitions and properties of generalized Hamiltonian systems defined on any (finite dimensional Poisson manifolds,and then present some new results on stability of equilibria of generalized Hamiltonian systems.Finally,to illustrate the applications in the qualitatively study of high dimensional differential equations,two examples are given,they are the planar relative motion of three vortices and the biomathematical model of three samples.

In this paper,we consider a new kind of repairable queueing system (RQS) with delay vacations,and give a detailed analysis of the RfaS M^x/G(M/G)/1(M/G) with multiple delay vacation.By the method of Vector Markov Process,we obtain some characteristics of the system,main reliability indices of the service station and important performance measures of the queue.

In this paper,the inverse problem for coefficients ε,μ,in Maxwell system is discussed.Under the condition of σ≡0,by means of two different ways,we separate the inverse problem for two unknown coefficients into two independent inverse problems for one unknown coefficient in the wave equation.Then we prove the existence,uniqueness and extension theorems of the local solutions for the inverse problems.Stability,well-posed property of the solutions a,nd the properties of the solutions at the end points of the largest existence intervals a,re also researched.

In this paper,introducing the variation with weight,making use of the special structure concerning the disspation and double-rotation operators of the MHD equations,we set up the uniform prior estimation,obtain the results as the four parameters Re,Rm (Reynolds number and magnetic Reynolds number)→∞,and prove the existence and unique theorem of the singular limit solution to the Cauchy problem.

We have some results about the bifurcation phenomenon of heteroclinic cycleS⁽ⁿ⁾ with autonomous perturbation.The papeis[1-3]studied the saddle-loop question clearly in case n=1.When n≥2,some sufficient conditions for the bifurcation of S⁽ⁿ⁾ were given with the help of stability in papers [4,5].On the basis of R.I.Bogdanov's thought [6],we get some sufficient conditions and necessary conditons for the bifurcation of S⁽ⁿ⁾ in a Hamiltonian system with autonomous perturbation by studying the change of Hamiltonian function's value along the orbit in this paper.Finally we discuss the problem of uniformity in global bifurcation,and study an example to explain the complexity of bifurcation phenomenon of the heteroclinic cycle.

Let {ξ_n,f_n} be a L^p-mixingale sequence,{a_ni,i≤n} be a double array.We give some sufficient conditions for and obtain the pth-mean and the strong consistency of the least squares estimators of the parameters of linear regressions with L^p-mixingale errors.

In this paper,we discuss the bounds of coherent system reliability in two different ways.The upper and lower bounds of reliability are derived for coherent system with independent components.These bounds improve and perfect the main results of Shathikumar (1986).Some bounds of this paper are better than the bounds of Barlow and Proschan (1981) in certain cases.

In the paper,the spline smoothed bootstrapping for kernel estimator is considered.Under suitable condition,it is shown that spline smoothed bootstrap works for kernel estiomator.The convergence rates regarding the spline smoothed bootstrap for kernel estimator and approximation by the limiting normal distribution are also studied.

In this paper,a class of initial-boundary value problems for nonlinear reaction diffusion integral-differential systems is consider.Under suitable conditions,using the iteration method and the comparison theorem we prove that the initial-boundary value problem has a solution which admits of a uniformly valid asymptotic expansion to any degree of precision.

This paper considers a class of deterministic models of simple food chains with deffusion and group defence.In paper,the influence of diffusion for stablity of simple food chain system is studied,we analysed the conditions which raise the Hopf Bifurcation,discussed the existence of Center-Manifold,and obtained the bifurcating periodic solutions and stable criteria.

The explicit and implicit representations for isospectral and non-iaospectral flows associated with the second-order polynomial spectral problem are presented,and two sets of infinite number of symmetries for the hierarchy of isospectral evolution equations and their Lie algebra structure are constructed.

The approximation properties for spherical functions by the Cesãro means of the spherical harmonic series are studied.The uniform approximation esrimate of the Cesãro means at the critical index and the almost everywhere approximation order of the Cedãro means below the critical index are established.

In this paper,a nonpreemptive priority multiserver queueing system in heavy traffic is considered.We introduce a new system defined as the delayed system".Then using the theory of weak convergence of probability measures we obtain some weak convergence limits for appropriately normalized versions of queueing processes regarding the new system.Therefore,by means of the relation between the new system and the original system,we give limit theorems of the workload processes,the cumulative idleness process and the queue length process for the original system.

In this article, we given a general form of bounded law of iterated logarithm for a sequence of independent B-valued random elements under non-stochastic bounded conditions.As application, we also extendsed some results in (1), (2).

In this paper, we present an additive mullevel Schwarz method for second order elliptic problems in two dimensions, which shows great promise for parallel computers. An alternative linear system, which has the same solution as the finite element equation, is derived. For symmetric, positive elliptic problems, the alternative linear system is solved by using conjugate gradient algorithm with a quite rapid convergent rate. For nonsymmetric or indefinite elliptic problmes, the alternative linear system is solved by using GMRES. and we show that the convergent rate is independent of the number of degrees of freedom and the number of local problems if the subdomains are fine enough. The performance of the our method is illustrated by results of several numerical experiments.

Let F_q be a finite field with q elements, where q is a power of an odd prime. In this paper, the number of subspaces in a transitive set contained in a given subspace of the singular orthogonal geometry over F_q is computed. Then using a class of 1-dimensional isotropic subspaces as elements, some PBIB designs are also constructed.

In this paper we consider the problem of simutanous approximation in Besov spaces by Jackson operators.A new characterization of Besov spaces is given by the error of this approximation process.

By means of two results on linear integral inequalities, components-wise upper bounds are obtained for solutions of some linear and nonlinear two-dimensional systems of ordinary differential equations of first order. These bounds are then applied to derive conditions ensuring boundedness, right-forward continuation of solutions, and the global uniform Lipschitz-stability of the zero solution to the differential systems considered in this paper.

By modifying the method in (3), we remove the limitation "ψ≠Q" in Theorem 3.1 (in [3]) and obtain the necessary and sufficient conditions for the existence of stationary solutions to the doubly stochastic time series AR(1)-MA(3) and general AR(1)-MA(q) modles. We completely overcome the difficulties pointed out by Djψstheim in (2) that the case of MA coefficient processes seems to be difficult to deal with, and our method is helpful in discussing the same problem of AR-AR and multivariate AR-MA models.

The properties of Lie products of vector field generators introduced in Ref. [1] are discussed from which Lie algebra of vector field genegrators can be derived. Based on these, it is shown that the space of time dependent symmetries with exponential terms of time constitutes a Lie subalgebra of Lie algebra of vector fields. Furthermore the commutator relations of Lie algebra of symmetries of this kind are given and thus the isomorphism between it and Lie algebra of vector field generators not depending explicitly on time is presented.

In this paper we investigated the structural properties of linear systems about state feedback and co-state feedback and introduced the geomeeric approach of linear systems in the polynomial matrix descriptions from the abstract module point of view. The structural forms described by polynomial matrices have been given and some important results of linear systems about structural properties have been obtained.