In this paper, we are concerned with the well-posed problem and the construction of a solution for a coupled system of a first order initial boundaryvalue problem. We give an analytic treatment for the existence and uniqueness of a solution as well as its continuous dependence on the external source and the initial-boundary data. The existence problem is based on the method of successive approximations and the contraction mapping theorem. A significant aspect of this method is that it leads to a recursion formula for the calculation of approximate solution as well as error estimates for the approximations.

This paper proposes the concept of a tree game, which may arise from the consideration of a communication system of network of computers, and contributes to an efficient procedure (even when n is large) of finding the kernel and the nucleolus of an n-vertex tree game when it has an empty core; especially it reduces the complicated means of searching for the nucleolus to simplye choosing the lexicographic order minimum from several vectors. A sufficient and necessary condition for a zero-monotonic game to be a tree game and a sufficient condition for a tree game to have an empty core are given. An example is presented at last to carry out in detail the calculation of the kernel and the nucleolus of a tree game with ten vertices.

A river water quality model is described by a 2nd order one-dimensional parabolic system, whose diffusion coefficient is unknown. By means of water quality data observed at a point on a finite time interval, we can identify the diffusion coefficient (a parameter). We prove that the parameter is identifiable under some conditions, i.e. there exists a unique parameter to fift the model and the intput-output model in an admissible parameter set.

Suppose that N_l balls are thrown successively into n_l cells and set x_lj=1 or O according as the jth cell, 1≤j≤n_l, is or is not empty.

In this paper some higher order linear partial differential equations with variable coeffidents and their solutions formulas are given. Since the coeffficients of these equations are general, many linear partial differential equations, which are difficult to solve, can be found in these equations by selecting the variable coefficients and can be solved by the formulas presented, we have solved many linear partial differential equations arising from aerodynamics, elastic vibrations, inhomogeneous wave equation and other fields by means of these formulas. Moreover, the numerical solutions can also be obtained from these formulas by means of a method presented by Feng Kang.

For S a set of n points of E²,the intersection of S with a half-plane is called a Semispace of S, A semispace of S of cardinality k is called a k-subset of S. The number of k-subsets of S is denoted by f_k (S).

The paper proposes a two-step stochastic approximation algorithm with randomly varying truncations for seeking the extremum of a function when its gradient can be observed with random errors which are assumed to belong to a class covering a wide range of correlated noises. The convergence of the algorithm is proved under reasonable conditions a priori requiring neither the boundedness of the algorithm, nor the existence of a Liapounov function.

In this paper,we propose two methods for dividing a given mixture convex polyhedron having lower and upper bound constraints or multiple-component constraints into several subsimplexs that have no common interior points, about a vertex and about the centroid of the polyltedron, respectively. We give the computational procedures for the two division algorithms. For every subsimglex, the simplex-centroid design of 2-degree is performed, and the canonical polynomial of 2-degree is fitted. In this way, we can find mixture components at which the predictor response is optimal in the whole interest region. Examples are included to illustrate the use of these methods.

Given a one-parameter curved exponential family, Efron and Hinkley (1978) proved a significant limit theorem which elucidated the relation between the Fisher information, the observed information and the statistical curvature defined by Efron. In this paper, the theorem is generalized to the multiparameter cass by using a differential geometry approach proposed by Amari (1982) for the curved exponential family. The asymptotic distribution of the related random matrix is studied and the relation between the Fisher information matrix, the observed information matrix and the curvature tencot defined by Amari is exposed. The Edge-worth expansions connected with the random matrix are also obtained to improve the accuracy.

In this paper we deal with the transit specific properties of the resonant pulse jet for the pipeline system connected in series of theoretical fluid. We give the transitive functions of the continuous jet connected in parallel and the export specific properties of the pulse jet system and the resonant pulse jet system.

Let W₁,…,W_m-1 and W_m be independent, where W_i is W_k^-1 (2α_i+k+1,v),with min (α₁,…α_m)≥k/2.Put where W^1/2 is a lower-triangular k×k matrix with positive diagonal elements.The distribution of (W^1/2'W₁W^1/2,…W^1/2'W_m-1W^1/2) is called matrix variate inverse Dirichlet distribution, and its interesting properties are obtained. The applications of this distribution in the Bayes inference are also considered.

The theoretical solutions of the moving boundary problems of the heat equation are hardly applicable in engineering. To encounter this an analytic method is developed here which can lead to easy and simple approximation of the solutions to such problems.

In the present paper an inverse matrix eigenvalue problem related to an inverse scattering problem is studied by the perturbation method. Special application of this method to the discrete inverse Sturm-Liouville problems is considered in detail. Its solution will lead to a solution of a boundary-value problem of a discrete hyperbolic equation with certain boundary conditions, that can be solved in a slightly zigzag but easy way. Numerical examples are included.

This paper gives a simple proof of the following Extreme Theorem. Let f∈L>²(O,T),F_σ={g: (f,g)=0,‖g‖≤σ}.

We consider an n-node overall planning network G=(N, A) in which each are (i,j) represents a process (i.j).To simplify the calculations for the critical path and relative parameters, we define a matrix B=(bij)_(n-1)×n corresponding to G=(N, A) and give calculating formats. Thus calculation of critical path is made easy and network diagram is unnecessary.

In this paper,an asymptotic expansion in the natural apace L[0,r_m] is obtainedaccording to the root subspace of population operator by means of the theory of compactsemigroup.The approximate controllability with regard to the specific fertility β(t) whichis continuous is also proved.

The solitary wave solutions with vibrational properties for modified Davydov equations, which could transport the bound energy along one-dimensional molecular chains (such as α-helix protein molecules) are found by means of the approximation method.

This paper explores the applicability of the optimum partition method (Fisher's clustering method). We introduce a linear model and generalize the optimum partition method to the classification problems of two types of stochastic point sets. The calculation of these methods can be easily realized by computer, and a numerical example is given.

This paper studies the convergence properties of a class of variable metric methods.Under some conditions, the convergences and superlinear convergences of Huang's, Wu and Gui's and Flachs' methods can be proved. In particular, it is shown that a class of variable metric methods without exact line searches is convergent and superlinearly convergent.

This paper give four forms of estimates for the parameters of stationary and invertible ARMA models. For the large sample case, it shows the convergence rate of the estimates.

In this paper we study the oscillation of solutions of the second order differential equations x"(t)+a(t)x(t)=0, t∈[t₀,∞),where a(t) is allowed to change its sign on [T₀, ∞).Three new theorems are established.

In this paper we discuss optimal policies with minimal variance of discounted Markovian decision programming with unbounded rewards discussed in [3].On the basis of the present structure of the set Π^* of optimal policies, we prove that, if the set Π^* is not empty and has at least one optimal policy with finite variance, then, for any ε>0, there exists one stationary policy the optimal policy with E-minimal variance. We give the necessary and sufficient conditions for the existence of optimal policy with minimal variance.

We consider the initial-boundary value problem for a class of system of nonlinear schrödinger equations with magnetic effect and

where β,η are real constants and ε(x,t)=(ε¹(x,t),…,ε³(x,t)),Ω⊂R^m, First the existence of the global solution for problems(1.1)-(1.3) and(1.4)-(1.6) are established.Then, the asymptotic estimations of the solution for problem (1.1)-(1.3) and (1.4)-(1.6) in exterior domains are given Finally, the "blow up" theorems are obtained under some different norms.

Using optimal stopping theory, this paper discusses some maintenance policy problems in reliability theory. In the discrete time case, non-identically distributed systems replacement is dealt with. A sequence of stopping times are defined deductively. Under certain regqiarity conditions, the convergence to optimal stopping time of that sequence is proved. For the total discounted cost criterion, the optimal maintenance policy is then obtained.

In this paper a theorem on infinite 1-critical graphs (i. e. infinite matching covered graphs) is given. It is shown that the number of 1-factors of an infinite locally finite bicritical graph is infinite. Thus a positive answer to Francois Bry's problem^[3] is obtained.

Suppose that the random matrix X has a matrix elliptical distribution and has a density with parameters μ and ∑ or μ⁽¹⁾…μ^(k) and ∑⁽¹⁾…,∑^(k).We wish to test the hypotheses: H₁:μ=0,∑= I; or H₂; μ=0, Σ=σ²I where σ² is an unknown parameter; or H₃:μ⁽¹⁾=…=μ^(k),∑⁽¹⁾=…=∑^(k), It is proved that under some conditions the likelihood ratio tests for the above hypotheses are unbiased.

This paper discusses a class of scheduling problems arising from the real-world. At first we prove that the problem with objective f₁ is NP-complete, then a dynarnic programming approach is developed for finding the optimal solution, at the end a heuristic algorithm is described and the performance guarantee of the algorithm is analysed.

In this paper, the random weighting method is considered for computing the distribution of the error of the sample mean. To estimate the variance of the error of the sample mean, the variance of the random weighting distribution is considered. It is shown that for most population distributions, this random weighting estimate is better than the bootstrapping estimate in small sample cases. Finally, the large sample property of the random weighting method is considered and it is proved that the random weighting method is asymptotically valid.

Let F_q be a finite field, where q=1 (mod 4), All n×n symmetric matrices are taken as the set of treatments. denoted by E, Thus, for different treatments H₁ and H₂,it is defined that (H₁, H₂)=r₁ if H₁-H₂ is congruent to diagonal matrix [I^r, O^(n-r)] and (H₁-H₂)=r_g if H₁-H₂ is congruent to [I^(r-1), O^(n-r)], where g is a generator of multiplicative group F_q^* of F_q.It is shown that E forms an association scheme mith 2n association,classes.

A general Bayesian algorithm with vague prior information (GBV) is provided. This mothod can be used to detect structure change points in abruptly, gradually and temporally changed types of linear models, and has the advantages of applicability to both mufti-parameter-change type and mullti-change type problems for linear models. The calculations can be Pasily realized by computer.

By means of the group representation theory, we discuss the construction of the direct product network and obtain a necessary and sufficient condition under which the direct product network makes the signals noninteract within the system.

Let T be a tournament. A vertex v of T is called a king of T if v can reach every other vertex of T by a path of length at most 2n. We shall always denote the vertex set of T and the set of all kings of T by V(T) and K(T),respectively. Let t and c be nonnegative integers. Ifs for B⊆V(T)-K(T),there exists a supertournament T^* of T and C⊆V(T^*)-V(T) such that|C|=c and K(T^** of T and C⊆V(T^*)-V(T) such that|C|=c and K(T^*)~(K(T)-M)∪B∪C,then we say that T has the strong(t,b,c)-property.

In this paper, we present a subclass of Petri Nets, Pw-nets, which involve time factors. In a Pw-net, each place (not transition) is associated with a non-negative real number, which is different from Time Petri Nets or Timed Petri Nets developed by P. Merlin and C. Ramchandani respectively. A number of essential properties far this kind of Petri nets are indicared. Then a scheme is presented for constructing a Pw-net model for an engineering project. Using the Pw-net model, all reasonable schemes for implementing an engineering project can be obtained. Moreover, the algorithms for solving the above problems can be implemented by computer programs.

In this paper, the general nonlinear differential equations are discussed where f (x, y)

and g(x) satisfy the condition that the point(0, 0) is a singularity of higher order for an equivalent system of (A). A ;sufficient condition for (A) to have chaotic behavior undef a small perturbation and to have subharmonic oscillations is given. The main idea is to transform the original system into one with homoclinic trajectories such that one may use the Melnikov method.

The minimum discrimination information (MDI) problem by Kullback Kullback and Leibler in the unconstrained case, and was studied afterwards by Charnes and Cooper in the linearly constrained case. In this paper the MDI problems with some commonly used nonlinear constraints are discussed. In a special way, other than the Lagrange duality and the conjugate duality, an explicit form of dual problem is derived which has only a nonnegative restriction on a part of dual variables and therefore is easier to be solved than the primal one.Both weak and strong duality theorems are then established. Sensitivity analysis is also made and useful data are listed for calculating the derivatives of all quantities concenrned.

In this paper we study the limit boundary value problems of second-order differential system

on a half-line (c,∞),and give necessary or sufficient condition for each of tliese problems to have a unique solution.

This paper proposes a nzw Lounding technique for the quadratic assignment problem. Computational comparison between this and other existing bounding techniques is carried out through a large number of test problems.