Let N={1,…,n} be the set of all-payers and P(N)={S⊂N|S ≠φN}.A partition B of P(N) is called asymmetric parrion if i.{B₁,…,B_m} and the number of all coalitions S∈B; containing i is cqual to a number k(B₁ indepeadent of i for all i in N and every b₁.We then define a game r (N;v_Y) in terms of a symmetric partition B for every game r:≡v_Y(N)-v(N),v_y(φ)=0; for t1,….m and same r is called a same with svmmetric wartition if theta exists a symmetrtc partttton B suien that (a),v_Y,and (b) the core of r_Y is not empty.A simple expression is obtained for the nucleolus of surh a game.

In the paper,nonlinear parabolic vector-valued obstacle problem (0.1) is discussed via the hole-filling technique and Morry estimation.The C^0,a-and C^1,a-regularity results of the solutions are obtained.

The Cauchy problem is considered for an equation system of nonlinear degenerate parabolic type,which arise in a filtration problem of gas in a porous medium with double porosicy.We obtain the existence,uniqueness and regularity of weak solution.And prove that the interface curves are Lipschitz continuous.

In this paper,Combining Riemann's method with the fixed point theory effectively,we study the initial boundary value problem of the nonlinear equation of the migration of the moisture in soil,that it is in this form:
u_xtx+η(x,t)u_xx=F(x,t,u,u_x,u_t,u_xx,u_xt).
We have obtained existence and uniqueness of the solution under more generalized situation,and we have got the solution by using iterative method and generalize the main results in the references [1]-[3] and so on.

The matched queueing system with a double input is a generalization of the,classical queueing model.There are two Poisson inputs,of which the customers are matched in propertion 1:r and then served in batch.The service time has a PH-distribution.Two.intutive necessary conditions and a necessary and sufficient condition for ergodicity are derived.The stationary distrubution of the queue length is investigated and its computational method is given.

In mechanical engineering there are many problems belonging to dynamical systems with gap.This kind of systems usually produce self-excited oscillation (limit cycle) during operation process.In this paper the existence,uniqueness and stability of such self-excited oscillation are proved.

A class of B-spline curves with an additional parameter n is suggested which converges monotonously to its control polygon to the sense that the sequence of their convex hulls {V₃(n)} is monotonic decreasing and approaches the control polygon as n tends to infinity.The distribution of inflexion and singular points of the planar curves is analysised by using the visual geometric methods different from those in [1-6],avoiding the difficulty in analysis roots of algebraic equations.Some simple and pratical methods of producing the curve that has no singular points or has only one indispensable inflexion are given.

The characteristic finite element and finite difference methods (finite element and finite difference methods are combined with the method of characteristics) to 1-periodic initial-value problems for the nonlinear RLW (Regularised Long Wave) equations are analyzed.Some optimal order error estimates and stabilities are obtained for both methods.We report the numerical results obtained for the solutions of the problems and also compare some of these resuits with those obtained for finite element,finite difference and spectral schemes.

The problem of the linear prediction by p-order time series can be formulated as a linear programming with unrestricted variables.In this paper we consider how to select the optimal p,and give a simplex algorithm for stepwise regression to find the prediction equations and to determine the optimal p.

As another property of spectral estimate like,that of[2],the result of this essay is concerned with the strong consistency of spectral estimate of a certain type of stationary processes.It reads as follows: For the spectral estimate of F[λ],

where ε(1),ε(2),…,ε(N) are observations of the white noise{ε(n),n1},if Eε(1)=0,Eε²(1)=1,Eε⁸²(1)<+∞,then

where
u₄=Eε⁴(1)-3.

In this paper,the multivariate linear functional relationship model

is discussed.The Strong Consistency of estimation in this model is derived withowc the assumption that

where

converges to a limit as n→∞,or is bounded.The assumptions in this paper are aboua equal to that
L=O(nln-αn)
for a certain α>1.

The extremes of a random number of exchangeable random variables are considered.The necessary conditions and the sufficient conditions for the existence of joint asymptotic distributions of upper and lower extremes are obtained.The concrete forms of the limit distributions are gwen.

In 1979 Kedem^[1] studied the relationship between the estimation of the spectra of stationary Gaussian series with zero mean and spectra of corresponding 0-1 series obtained by clipping of zero level.He also generalized the Demoivre-Laplace theorem to the dependent Bernoulli trials in 1977.An et al.^[2] studied the one dimensional time series with finite-state.In this paper we shall generalize the problems mentioned above as in [1] to time series with finite-state and generalize the problem in [2] to the case of multidimension.

In this paper, the discrete constructions and the algorithms are studied for rational B-spline curves. From the point of view of geometry, we introduce the rational discrete B-spline curves by which the convexity theorem and the V-D property are simply proved.

In this paper, according to Huber's M-estimator theory, we propose an M estimate procedure for the.mixed regression model.The consistency and asymptotic normality of the estimates for the mixed regression model are proved.

There is significant economical effect and benefit to employ the technique of Large Area Crop Yield Forecasting. By using the methods of equidistant sampling on the basis of stratification of remote sensing information, meterological model of mufti-variable. statistics, and regression integral of spectral information, a Model for Large Area Wheat Yield Forecasting in Huang Huai Hai Plain is developed. In comparison with the conventional method of yield forecasting, it has the advantages of high accuracy and money-saving. The wheat yield can be forecast before the harvest. This model is quite a new, advanced, and efficient way for large area crop yield forecasting.

The paper proposes some new concepts of higher order feasible (descent) directions, higher order quasifeasible (quasidescent) directions and higher order tangent directions; Using the support functions of these sets of higher order directions, higher order necessary conditions for nonsmooth optimal problem (P) in topological,vector spaces are established. The above set's equivalent presentation and the relations between the sets and the higher order variational sets in [1-3] are discussed under lrrechet differentiability assumptions, with the results higher order necessary conditions for smooth optimal problems (Th 4.2) are obtained which extend nearly all the higher and lower order optimality necessary conditions for smooth problems in [1-9],[12-15].

In the Ernst equation of gravitational fields we give the finite transformations of Virasoro group by means of a formalism of Cauchyl integral equation from the Riemann-Hilbert problem, and establish the reprensentations of the semidirect product of Virasoro and Kac-Moody groups which are non-unitary and of no highest weight. The transformations of the semidirect product group generate new solutions from the known ones. We also assert that many known transformations, such as Neugebauer's Backlund transformation, are subgroups or subsets of the group.

Some sufficient conditions for the convexity of B-B polynomial patch over a rectangle are presented. The convexity relation among function f (X), Bézier net f_N(X) and B-B polynomial B₂^N (X; f) is also discussed.

In this paper, we study the propagation of electromagnetic waves in a class of complicated inhomogeneous media which are axially symmetric. We construct a system of integral equations by means of the method of undetermined functions.

The purpose of this paper is t₀ investigate the optimal properties of the MSE of principle component estimator in the class of reduced. demension estimators. In this paper, it has been proved that the principle component estimator has the μ-m, μ-P. Income, Loss and μ-MB optimal properties. In adition, it has been proved that the principle component estimator is a general best Bayesian estimator of β in the class D.

In this paper, we attempt to discuss the existence of periodic solutions of delay differential equations by using two auxiliary functions and the fixed-point theorem. Several sufficient conditions to ensure the existence of periodic solutions have been obtained. Then we extend the necessary and sufficient condition of the existence of periodic solutions of ordinary differential equations. We have obtained a necessary and sufficient condition of the existence of periodic solutions to the delay differential equations.

In this paper, a new concept of surface interpolation is suggested, naively, region inter-polation. Theoretical and practical methods for constructing interpolation basis are given for a family of maps from Rⁿ to R^m. It provides us with a new access to the noteworthy problem of smooth connection and fillet of free-form surfaces and. the construction of complex surfaces. Practical examples show that this method is convenient and powerful.

In this paper, we show that it requires at least [1/4n²-(1/2n)] arithmetic operations for inverting Toeplitz matrices. Then it immediately follows from Trench's result[4] that the inherent complexity of inverting Toeplitz matrices is O(n²). We consider the relation of computational complexity between inverting Toeplitz matriaces and inverting Hankel matrices and show that the inherent complexity of inverting Hankel matrices is also O(n²),where,is the order of matrices and [x] denotes the integer floor function of x.

Consider the independent variables a_1t,a_2t,…,a_p satisfing a linear regression model, i. e.∑a_ia_it=c.

In this paper, a successive quadratic programming algorithm for solving a nonlinear programming is introduced. Its specialty is that in each iteration of the algorithm, the constraints of the quadratic programming not only are the linear approximations of the original constraints,but also have a perturbation vector. Under certain conditions its locally R-linear rate of convergence is proved. In the final part of the paper, the conditions of its superlinear convergence is discussed.

A new direct search algorithm for unconstrained optimization is given in this paper. It produces step by step a set of search directions from a given direction P_o, when it is applied to a positive definite quadratic function. Well's get, mutually conjugate search directions after (n-1) iterations and the procedure will terminate at a minimum in finite iterations. Moreover, the number of function value evaluations is about 2/3 of that of P_o well's and the number of linear searches is about one half. Furthermore, the convergence, superlinear convergence and second order convergence are shown for different hypotheses. Many numerical examples show that the algorithm is more efficient than P_o well's, and in many cases also more efficient than some analytical methods.

The conditions that the time-dependent coefficient KdV-MKdV-Burgers equation could have Painlevé property are discussed. It is proved that this equation can be transformed to well-known solvable equations if it has Painlevé property.

In this paper we use the method of upper and lower solutions to discuss the periodic boundary value problem of the general second order differential system -x=f(t,x,x), The definition of upper and lower solutions in our paper is an immediate extension of that of scalar equations. Using our results, we can prove the existence of periodic solutions for some second order systems which do not satisfy Nagumo condition. And we can solve the existence problem of periodic solutions for a class of perturbed linear systems.

In this paper we discuss the asymptotic behavior for the following second order neutral functional differential equation

only three types of asymptotic behavior of nonoscillatory solutions satisfying
x(t)[x(t)-cx(t-τ)]>0
are obtained and their criteria are given.

In this paper we study some M-ideal density problems closely related to the best approximations in tensor products. We prove that if X and Y are two Banach spaces such that G is an M-ideal of X and E is a subspace of X.Assume that G∩E is G^*-dense in E. Then (G∩E) Y is (G Y)^*-dense in Y.A similar result is obtained for tensor products of C^*-aigebras.

This paper discusses the problem of best approximations by elements with linear restriction in normed lineal spaces. The existence theorem, characterization theorems and uniqueness theorems are stated Furthermore, as applications, the characterization of best L_p approximations by functions with restricted rariges, and the uniqueness of best L approximations by polynomials having bounded coefficients or restricted ranges of their derivatives are obtained.

We give a gxneral model for nonlinear programming problems with nonlinear constraints and give a condition and a proof of global convergence. We shall see that different alaorirhms are given by different parameters selected. The selection of projection hyperplanes plays an important role in this model.

In this paper, a non-stationary. discounted rZarkovian decision model is investiated under absolute average relatively bounded reward functions. The optimality equations for the model are established. The existence of an E-optimal policy is proved. Necessary and sufficient conditions for the optimality of a policy are derived It is shown that if there is an optimal policy, then there exists an optimal Markovian policy. We also discuss the optimality of a convex combination of these optimal policies. Finally, some properties of these optimal policies are shown.