LARGE DEVIATIONS FOR MARKOV CHAINS

Donsker-Varadhan's large deviation theory is applied to Markov chains with continuous parameter and countable state space. Since the lower estimate given by Donsker and Varadhan [5; part 4] is general enough in our context, we study only the upper estimate, and make the conditions for the estimate explicit.     

LARGE DEVIATIONS FOR SYMMETRIC DIFFUSION PROCESSES

Let a(x)=(a_(ij)(x)) be a uniformly continuous, symmetric and matrix-valued function satisfying uniformly elliptic condition, p(t, x, y) be the transition density function of the diffusion process associated with the Diriehlet space (, H_0~1 (R~d)), where(u, v)=1/2 integral from n=R~d sum from i=j to d(u(x)/x_i v(x)/x_ja_(ij)(x)dx).Then by using the sharpened Arouson's estimates established by D. W. Stroock, it is shown that2t ln p(t, x, y)=-d~2(x, y).Moreover, it is proved that P_y~6 has large deviation property with rate functionI(ω)=1/2 integral from n=0 to 1<(t), α~(-1)(ω(t)),(t)>dtas s→0 and y→x, where P_y~6 denotes the diffusion measure family associated with the Dirichlet form (ε, H_0~1(R~d)).     

LARGE DEVIATIONS AND MODERATE DEVIATIONS FOR m-NEGATIVELY ASSOCIATED RANDOM VARIABLES

M-negatively associated random variables,which generalizes the classical one of negatively associated random variables and includes m-dependent sequences as its par- ticular case,are introduced and studied.Large deviation principles and moderate devi- ation upper bounds for stationary m-negatively associated random variables are proved. Kolmogorov-type and Marcinkiewicz-type strong laws of large numbers as well as the three series theorem for m-negatively associated random variables are also given.     

LARGE DEVIATIONS FOR FIELDS WITH STATIONARY INDEPENDENT INCREMENTS

ＬＡＲＧＥＤＥＶＩＡＴＩＯＮＳＦＯＲＦＩＥＬＤＳＷＩＴＨＳＴＡＴＩＯＮＡＲＹＩＮＤＥＰＥＮＤＥＮＴＩＮＣＲＥＭＥＮＴＳＧＡＯＦＵＱＩＮＧ（高付清）（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，ＨｕｂｅｉＵｎｉｖｅｒｓｉｔｙ，Ｗｕｈａｎ４３００７２...     

LARGE DEVIATIONS FOR STATIONARY φ-MIXING SEQUENCES IN τ-TOPOLOGY

The results of Bryc on large deviations for empirical measures of stationary Φ-mixing sequences are extended. Bryc states his results in the usual weak topology on the space ofprobability measures. In this paper, under somewhat weaker assumptions than those of Bryc,the author extends Bryc's results by taking the finer topology which is generated by the integralsover bounded measurable functions.     

LARGE DEVIATIONS FOR INFINITE DIMENSIONAL AND REVERSIBLE REACTION－DIFFUSION PROCESSES

ＬＡＲＧＥＤＥＶＩＡＴＩＯＮＳＦＯＲＩＮＦＩＮＩＴＥＤＩＭＥＮＳＩＯＮＡＬＡＮＤＲＥＶＥＲＳＩＢＬＥＲＥＡＣＴＩＯＮ－ＤＩＦＦＵＳＩＯＮＰＲＯＣＥＳＳＥＳＣＨＥＮＪＩＮＷＥＮ（陈金文）（ＤｅｐｅｒｔｍｅｎｔｏｆＡｐｐｌｉｅｄＭａｔｈｅｍａｔｉｃｓ，Ｔ...     

ESTIMATES OF EIGENVALUES FOR UNIFORMLY ELLIPTIC OPERATOR OF SECOND ORDER

ＥＳＴＩＭＡＴＥＳＯＦＥＩＧＥＮＶＡＬＵＥＳＦＯＲＵＮＩＦＯＲＭＬＹＥＬＬＩＰＴＩＣＯＰＥＲＡＴＯＲＯＦＳＥＣＯＮＤＯＲＤＥＲＱＩＡＮＣＨＵＮＬＩＮ（钱椿林）ＣＨＥＮＺＵＣＨＩ（陈祖墀）（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｔｎａｔｉｃｓ，Ｕｎｉｖｅｒ...     

INEQUALITIES FOR EIGENVALUES OF THE POLYHARMONIC OPERATOR Δ~p

In this paper we consider the bounds of the eigenvalues for a class of polyharmonic operators andobtain the bounds for(n 1)th eigenvalue interm of the first n eigenvalues.Those estimates do notdepend on the domain in which the problem is considered.     

A CLASS OF COLLINEAR SCALING ALGORITHMS FOR UNCONSTRAINED OPTIMIZATON

A Class of Collinear Scaling Algorithms for Unconstrained Optimization. An appealing approach to the solution of nonlinear optimization problems based on conic models of the objective function has been in troduced by Davidon (1980). It leads to a broad class of algorithms which can be considered to generalize the existing quasi-Newton methods. One particular member of this class has been deeply discussed by Sorensen (1980), who has proved some interesting theoretical properties. In this paper, we generalize Sorensen's technique to Spedicato three-parameter family of variable-metric updates. Furthermore, we point out that the collinear scaling three- parameter family is essentially equivalent to the Spedicato three-parameter family. In addition, numerical expriments have been carried out to compare some colliner scaling algorithms with a straightforward implementation of the BFGS quasi-Newton method.     

FRANCIS QL ALGORITHM FOR FINDING THE EIGENVALUES OF ANTI-SYMMETRIC MATRICES

In this paper,we demonstrate that the double-shift QL algorithm for an irreducible anti-symmetric iridiagonal matrix with the shifts being two eigenvalues of the 2×2 matrix in the left upper corner of this matrix is convergent and the convergence rale of Ms kind of algorithm is generally cubic.     

EIGENVALUES ON THE BOUNDARY OF CERTAIN INCLUSION FOR THE SPECTRUM OF A MATRIX

We introduce four types of special eigenvalues which lie on the boundary of certain inclusion regions for the spectrum of a complex square matrix, i.e. , R_r(G_c)-,O(a)-,B_r(B_c)-. and OB(a)- eigenvalues. Then we characterize these eigenvalues and their corresponding eigenvectors for irreducible matrices, Finally we give some new sufficient conditions for an irreducible complex matrix to be nonsingular.     

ENTROPY CONSISTENCY OF LARGE TIME STEP SCHEMES FOR ISENTROPIC EQUATIONS OF GAS DYNAMICS

In this paper, We show for isentropic equations of gas dynamics with adiabatic exponent γ=3 that approximations of weak solutions generated by large time step Godunov's scheme or Glimm's scheme give entropy solution in the limit if Courant number is less than or equal to 1.     

LARGE TIME EXISTENCE AND BEHAVIOR OF SOLUTION FOR SYSTEMS OF NONLINEAR REACTION-DIFFUSION EQUATIONS

This paper deals with the existence of solution for the systems u_i-K△u=F(t, x, u, ▽u) with the initial boundary value condition, where F (t, x, y, z) grows in y, z with arbitrary power and goes to infinity as t→∞. Under suitable assumptions on the nonlinear term F and the initial value condition, we will obtain a unique global solution and an asymptotic estimate.     

EQUIVALENCE OF COMPLETE CONVERGENCE AND LAW OF LARGE NUMBERS FOR B-VALUED RANDOM ELEMENTS＇

Under some conditions on probability, this note discusses the equivalence between the complete convergence and the law of large number forB- valued independent random elements. The results of [10] become a simple corollary of the results here. At the same time, the author uses them to investigate the equivalence of strong and weak law of large numbers, and there exists an example to show that the conditions on probability are weaker. Project supported by the National Natural Science Foundation of China.     

LARGE－TIME BEHMIOR OF SOLUTIONS FOR THE SYSTEM OF COMPRESSIBLE ADIABATIC FLOW THROUGHPOROUS MEDIA

ＬＡＲＧＥ－ＴＩＭＥＢＥＨＭＩＯＲＯＦＳＯＬＵＴＩＯＮＳＦＯＲＴＨＥＳＹＳＴＥＭＯＦＣＯＭＰＲＥＳＳＩＢＬＥＡＤＩＡＢＡＴＩＣＦＬＯＷＴＨＲＯＵＧＨＰＯＲＯＵＳＭＥＤＩＡ￥ＸＩＡＯＬＩＮＧ（Ｌ．ＨＳＩＡＯ）Ｄ．ＳＥＲＲＥ（ＩｎｓｔｉｔｕｔｅｏｆＭａｔ...     

VECTOR COMPARISON PRINCIPLE FOR THE STABILITY OF MEASURE DIFFERENTIAL LARGE SCALE SYSTEMS

ＶＥＣＴＯＲＣＯＭＰＡＲＩＳＯＮＰＲＩＮＣＩＰＬＥＦＯＲＴＨＥＳＴＡＢＩＬＩＴＹＯＦＭＥＡＳＵＲＥＤＩＦＦＥＲＥＮＴＩＡＬＬＡＲＧＥＳＣＡＬＥＳＹＳＴＥＭＳ￥ＧｕａｎＺｈｉｈｏｎｇ（关治洪）（ＪｉａｎｇｈａｎＰｒｔｒｏｌｅｕｍＩｎｓｔｉｔｕｔｅ）＆Ｌ...     

THE LARGE TIME BEHAVIOR OF GLOBAL SOLUTIONS FOR A MODEL EQUATION FOR FLUID FLOW IN A PIPE

§ 1. Introduction Fluid flow in a pipe is usually modeled by the quasilinear hyperbolic system where ρ is mass density, G is momentum density, p=p(ρ) is pressure such that p' (ρ)>0 for 0<ρ<∞, f=f(|G|) is the Moody friction factor and D is pipe diameter (see [5] for detail).     

RESEARCH ANNOUNCEMENTS ON “ESTIMATES OF DIRICHLET EIGENVALUES FOR DEGENERATE △_μ-LAPLACE OPERATOR”

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LARGE TIME STEP GENERALIZATION OF RANDOM CHOICE FINITE DIFFERENCE SCHEME FOR HYPERBOLIC CONSERVATION LAWS

A natural generalization of random choice finite difference scheme of Harten and Lax for Courant number larger than 1 is obtained. We handle interactions between neighboring Riemann solvers by linear superposition of their conserved quantities. We show consistency of the scheme for arbitrarily large Courant numbers. For scalar problems the scheme is total variation diminishing.A brief discussion is given for entropy condition.     

THE LARGE TIME CONVERGENCE OF SPECTRAL METHOD FOR GENERALIZED KURAMOTO-SIVASHINSKY EQUATION (Ⅱ)

1.IntroductionInthepaper[1],westudedthegeneralizedKuramotrySivashinskyequationWeProvedtheexistenceanduniquenessofglobalsolutionforperiodicinitialproblemandgavethelargetimeerrorestimationforthesolutionofcontinuousspectralmethod.Theaimofthispaperistostudyfullydiscretespectralmethodandthelongtimebehaviorofthesolutionofthissystem.In61wegiventhelargetimeerrorestimationforfullydiscretesolutionofspectralmethod.In52weprove-theexistenceofapproximateattractorsAN,4anding3weprovetheconvergenceofapproal…