Let {ξ_n} be a stationary sequence,ξ₁ⁿ≤ξ₂ⁿ≤…≤ξ_nⁿ be the order statistics of ξ₁,…,ξ_n,{ξ_n,j},j=1,2,…,a be the central rank sequences. In this paper,the stable convergence properties of the joint limiting distributions of {ξ_kn,jⁿ},j=1,2,1,2,…,a are determined under some mixing conditions. Further result for distribution of order statistics with random variable ranks is obtained.

In this paper, we discussed the L_p(1≤p≤∞)-Metric Property of Estimates of Error Variance in Linear Models. Our main theorems were similar to those known for classical sums of i.i.d. random variables. It removed、also the results in [1] and [2].

This paper is devoted studying a generalized Euler-Poisson-Darboux equation

The authors have proved the existence and uniqueness of the globol generalized solutions of the mixed problems for the equation by the means of Galerlsin's appeoximations. Moreover, according to the properties of Sobolev space and embeding theorem. the authors obtain the classical solution.

In this paper, we consider the nonlinear programming problem P that minimizes f (x) subject to g(x)≤0, h(x)=0, x∈X, where f :Eⁿ→E^l,g:Eⁿ→E^m,h:Eⁿ→E^l.If X is compact, then under a second order condition that is weaker than MoCormick's second order sufficient condition, we show that a globally exact penalty original problem for a sufficiently large penalty problem is the same as that of the original problem for a sufficienxly large penalty panameter.astly we provide a lower bound on the penalty parameter in terms of I agrangian multipliers at some solutions and the lower bound on the objective function.

In this paper we establish the existence and uniqueness of various kinds of projections for n-parameter product-measurable L log₊^n-1 L bounded stochastic processes, Doléans measures and integrable increasing processes. As it's application, we discuss the equivalence of alternative definitions for optional σ-field O.

In this paper, by studying some curvilinear search methods and "accelarating" algorithms in nonlinear programing, we present the concept of quasi-descent method and extend the important lemma [1, Lemma 3] to quasi-feasible direction methods. On this basis, we give an algorithm model of quasi-feasible direction methods for inequality constrained optimization and show its global convergence under weak conditions. The paper unifies and extends the common feasible direction methods on a larger scale. As a special case of our model, we obtain a class of new. supermemory descent methods for constrained optimization.

In this paper, we consider the nonhomogeneous linear differential equation

where r(t)>0 is an absolutely continuous function on [a,∞),p(t), q₁(t), q₁(a) and f (t) are locally integrable functions on [a, ∞).With the aid of auxiliary functions and inequalities, we obtain some sufficient conditions under which equation(*)belongs to the L.S. or L.S. ∩L.C.

Loop networks are a kind of regular and cyclical digraphs. They are widely used in the design of local area networks, multimodule memory organizations, data alignments in parallel memory systems, and supercomputer architecture. In this paper, we consider the equivalen conditions of the existence of finite diameter of loop network, and also a general algorithm to compute this diameter, specially a simple formula of loop network G(N;s₁,s₂) is obtained.

Based on the concept of element order of diagonally dominant matrices, this paper discusses the factorization processes of ICCG and MICCG. A method of high order truncation is introduced for the computation of Gaussiau elimination to reduce the factorization costs of ICCG and MICCG, and the methods of ICCG and MICCG are improved.

Through the nonlinearization of Lax system of the TD hierarchy, a Bargmann system is obtained and is proved ro be a completely integrable system in Liouville sense. The involutive representations of solutions for the TD hierarchy are given.

In this paper the eigenstructure assignment problem under state feedback is discussed by using Yokoyama-Han canonical form. For every n-dimensional eigenvector (generalized eigenvector) only n₁-subeigenvector is independent. When the given eigenstructure admits of an assignment we give two methods of solving the feedback matrix.

In this paper, we have proved the convergence of the multigrid method using the symmetric Kaczmarz iterauon as its smoothing method for solving the linear systems arising from the discretization of differential equations under the assumption of approximate properties link between the under of smoothing iterauons and the fineness of the coarsest grid in this multigrid method.

In this paper a new method of decision the centre or focus for the singular point O(0,0) of the system shown in the title and decision alues are obtained. This method is bretter than the past ones.

A calss of singularly perzurbed boundary value problems for a higher order elliptic parcial differential equation is considered.

Lee {X_n,n≥1} be an iid sequence with a nondegenerate df F and X_n,1≤…≤X_n,n be the order statistics of X₁,……,X_n.

In this paper we dis cuss a problem proposed from the study of mufti-index stochastic processes:decompose uniquely the Debut of a sub-set S⊂P₊ⁿ=[0,∞[ⁿ into 2ⁿ-1 parts D(S)= D(S)^I called the I-part of D(S),which possesses interior for some |I|-dimension sections but not for higher dimension ones.The special case for n=2 and its usefulness canbe found in [1].

In this paper,some theorems on multivalued mappings are given.By those theorems,we prove that the set of essential games in a game space is a dense residual set,and every game in a game space can be closely approximated arbitrarily by an essential game.

This paper discusses an accurate approximation for Bayesian interval estimation whose xalculation is usually difficult in Bayesian analysis.The method provided in the paper is solwing transcendental equations to obtain Bayes confidence limits and can avoids the difficulty to solve complex equations involving integration.Furthermore the accuracy of the approximation is properly controllable.Using the approach can greatly simplify the calculation for Bayesian interval estimation with non-conjugate prior distributions.It is efficient for some upplied problems.

In the light of the aim of cluster analysis,this paper suggests a new index for PP clustering the mode index.The emphasis is put on the problem of estimating the optimum direction of the mode index.

This paper is a simple disproof of the Eider's conjecture.A family of self orthogonal latin squares of all orders n≠2,3,6 have been constructed in this paper.

This paper studies the existence of global classical solutions of the following initial value problem:

where a>0.This problem describes the linear vibration of certain infinite rods with nonlinear viscoelasticity.It is proved in this paper that under certain conditions of the nonlinear function Q,this problem has a unique global classical solution for any sufficiently smooth initial function ψ(x) and ψ(x) no matter how big they may be.

In this paper,we give a recurrence theorem of LD^*-design,which was first introduced by[1].On the basis of Theorem 6A provided in Ⅲ of[1],we coinstructively prove that if q is a prime power greater than 4 and 1+n∈D^*,and if there ezists a pair of orthogonal Latin squares of order n,then 1+qn∈D^*.

Under certain conditions for functions α(·)β(·),and μ(·),the uniquenessm existence,regularity and compact support property of the solution to the following boundary problem

have been proved in this paper:This kind of boundary problem is related to an infiltration equation.

On the relative neighborhood graph,a similarity index which is composed of distance and point density was proposed by this paper.Also,in order to perform hierarchical clustering principles,a transformation of neighborhood rank rank matrix and a clustering method based on it was defined.Analysis and examples can demonstrate its validity.

Let{X_n,n≥1} be a stationary sequence and W₁⁽ⁿ⁾≤W₂⁽ⁿ⁾≤…≤W_n⁽ⁿ⁾ be the order statistics of X₁,X₂,…,X_n Then {W_Nn^(M_n),n≥1} is called the order statistics with random size {M_n,n≥1} and random ranks {N_n,n≥1} from {x_n,n≥1} if M_n≥N_n,a.e.N≥1 are integer-valued r.v.s.Under the same mixing conditions as Cheng's(1980),the asymptotic behavior of the normalized sequence W_Nn(M_n)-b_n,n≥1 is discussed in this paper.It is animprovement over the results in[1] and[2].

In this paper a new theorem for ensuring chat the Liénard equation has at most one limit cycle is obtained,which improves the results in^[3-8].

The definitions of up-coming and down-going waves for rnulti-dimensional wave equation are given by using pseudo-differential operators.The coupled equations for these up-coming and down-going waves are derived from the factorisation of the wave operator.It is proved that the obtained system of coupled equations and the wave equation are equivalent in the sense of high-frequency approximation (geometrical optic approximation).That means the obtained system and the wave equation have the same eikonal equation and the same transport equation.

Consider an infinite particles system chat admired to the particles randomly input a countable set I,and then they move in I according to the transition law of a known Markov chain. we show that the inno J ⊂ I;Let finite subset vations methed and Martingale theory is used to derive the filtering equations satisfied by the conditional probability distribution of the slate on J when the past of an observed set of the output stream was given,and these filtering equations are applied to obtain a necessary and sufficient condition for that observation to be independent of the value of the state of the system on J at anytime.In particular,It is discussed to the system in equilibrium behaviour.

In this paper,using special kind of atoppinga,we give the structural theorems of 2ⁿ basic β-fields in n-parameter stochastic processes,and the corresponding section theorems.As a consequence of the later,the various kinds of fortellabilities and predictabilities are respectively equivalent.

This paper surveys the solution of matrix equation AX-XB=C by means of the minimal polynomial of matrix A and B.And give a simple formula for solving the equation.The formula is a multinomial of matrix A,B and C,so that it simplifies greatly digital computation.On the other hand,if B=-A^T is stable and C is a positive definite matrix,the constructed positive definite quadratic form Liapunov function will be clear.

Generalizing the concepts of Mendelsohn triple system and large sets of Mendelsohn triple systems,we introduce the Mendelsohn system M(2,k,v)and the large sets LM(2,k,v) of such designs.We give a construction of LM(2,k,k+1) and LM(2,2k+1,2k+1).For LM(2,p,p),LM(2,p-1,p)and LM(2,p,p+1),where p is prime,we give another construction as well.

Let{X_n n≥1} be i.i.d,random variables and be a sequence of real numbers tending to infinity,and {n_k} the strictly increasing subsequence of positive integer numbers.In the present paper,we give the necessary and sufficient conditions of complete convergence for S_nk/a_nk and obtain the complete convergence for sums of random variables.

The purpose od this paper is to show the existence and the well-possesses of solutions for a class of higher order Cauchy problems in a Banach space.In particularly,we indicate how the above abstract results can be used to study some concrete partial differential equations.The integrated semigroup methods and the new results of vector-valued Laplace transforms are used to arrive at these results.

The existence of interpolation surfaces over rectangles and their concrete construction problem are studied in this paper; so is the coordinative problem of the smooth conditions when the interpolation segments are smoothly com,posed; two equivalent coordinative equations shown.

The correspoanding change-of-variance sensitivitgr is defined for the fitted-value influence of a lianear regression.Two important robust estiaeaators of a location parapneter are extended to regression case.We get so-called "redescending regression estimators" and discuss their existence and robustness.