CHAOS IN TOPOLOGICAL MARKOV CHAINS

ＣＨＡＯＳＩＮＴＯＰＯＬＯＧＩＣＡＬＭＡＲＫＯＶＣＨＡＩＮＳ￥ＣＡＯＬｉａｎｇｙｕｅ；ＷＵＳｈｉｊｉｎｇ；ＺＨＡＯＨａｎｚｈａｎｇ（ＩｎｓｔｉｔｕｔｅｏｆＳｙｓｔｅｍｓＳｃｉｅｎｃｅ，ＡｃａｄｅｍｉａＳｉｎｉｃａ，Ｂｅｉｊｉｎｇ１０００８０，Ｃｈｉｎ...     

A METHOD TO APPROXIMATE DISTRIBUTIONSOF RELATED STATISTICS

1.IntroductionandResultSupposethereisand--dimensional(d21)randomsampleXi,fromsomeprobabilityspace(fi,I,P)to(R',B,),Xi4Fi,Fibeingunknown,15i5n,n21.Whatconcernsusisthedistributionalpropertyofsomep-dimensional(p21)statisticTi~Ti(XIt''IX.;FI1'',Fi)whichisus…     

ON THE ORDERING OF A CLASS OF HEXAGONAL CHAINS WITH RESPECT TO MERRIFIELD-SIMMONS INDEX

A hexagonal system is regarded as a 2-connected plane graph in which every finite region is aregular hexagon of unit side length. Hexagonal systems are of great importance for theoreticalchemistry because they are the natural graph representation of benzenoid hydrocarbonsll].Merrifield-Simmons index of a hexagonal system was extensively studied in connection withcertain topological problems of chemistry[']. A hexagonal chain is a hexagonal system with theproperties that (a) it has no vertex be…     

A CLASS OF GENERALIZED MULTIPROCESSOR SCHEDULING PROBLEMS

1. IntroductionOne of the fundamental problems in the theory of scheduling is to sChedule n independent jobs non-preemptively on m 2 2 multiprocessors. It is well-known that PllCm.. andPI I Z:=, wiCi are strongly NP-hardll'2].In this paper, we consider a class of generalized multiprocessor scheduling problem. It canbe described as follows: There are m almost identical processors M = {MI, M2,'' 5 Mm}, andn independent jobs J = {JI, J2,'' 9 Jn}. The processing time of job Ji is pi. A…     

OPTIMAL CONTROL OF A CLASS OF DISTRIBUTED PARAMETER DELAY SYSTEMS

1.IntroductionManyphysicalsystems,suchajsthemodynamics,electrodynamics,populationbiology,aregovernedbydifferentialequations,integrodifferentialequationsormoregenerallyfunctionaldifferentialevolutionequationsonBanachspace.Associatedoptimalcontrolprobl...     

Random walk search in unstructured P2P

1 .INTRODUCTIONIn the last few years , unstructured P2P applicationsare very popular ,such as Gnutella[1], Kazaa[2]. Theyare designed for sharing files among the peers in thenetworks .Thereis no precise control over the networktopology or file placement in these systems .In gener-al ,they employ flooding scheme for searching object ,and waste a lot of bandwidth[1]. Today , bandwidthconsumption attributed to these applications amountsto a considerable fraction (upto 60 %) of the total In…     

BLOW-UP SOLUTIONS FOR A CLASS OF NONLINEAR PARABOLIC EQUATIONS WITH MIXED BOUNDARY CONDITIONS

The type of problem under consideration is where D is a smooth bounded domain of RN, q = |(?)u|2. By constructing an auxiliary function and using Hopf's maximum principles on it, existence theorems of blow-up solutions, upper bound of "blow-up time" and upper estimates of "blow-up rate" are given under suitable assumptions on a, b, f, g, σand initial date U0(X). The obtained results are applied to some examples in which a, b, f, g and σare power functions or exponential functions.     

A CLASS OF REVISED BROYDEN ALGORITHMS

In this paper, we discuss the convergence of the Broyden algorithms with revised search direction. Under some inexact llne searches, we prove that the algorithms are globally convergent for continuously differentiable functions and the rate of convergence of the algorithms is one-step superlinear and n-step second-order for uniformly convex objective functions.     

SOLUTION OF A CLASS OF INVESTMENT DEVELOPMENTAL EQUATIONS

1. PerfaceIn paper [l], we have established the partial differential equation based on assets develop-mental process. In this paper we will consider the kind of distributed parameter system. Hence,we study the solution of the following problem (K):where a represents the age of productive assets, t represellts time, K(a, t) is the age--distributiondensity function of the productive assets at time t. p(a) is relative depreciation rate of assets. ris the accumulation rate of assets, A(t) means t…     

ON A CLASS OF ANISOTROPIC DIFFUSION EQUATIONS

ＯＮＡＣＬＡＳＳＯＦＡＮＩＳＯＴＲＯＰＩＣＤＩＦＦＵＳＩＯＮＥＱＵＡＴＩＯＮＳＯＮＡＣＬＡＳＳＯＦＡＮＩＳＯＴＲＯＰＩＣＤＩＦＦＵＳＩＯＮＥＱＵＡＴＩＯＮＳ￥ＧＡＯＨａｎｇ（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，ＦｕｄａｎＵｎｉｖｅｒｓｉｔ...     

VIBRATIONAL SYSTEMS OF A CLASS OF THIN CYLINDRICAL SHELLS

The vibration of thin circular cylindrical shells has been studied extensively.In this paper, the existence and uniqueness of the solution of this system are proved bymeans of semigroup theory on the Hilbert space, and the eigenvalue problem is discussed.This offers a theoretical basis for solving this kind of engineering problems.     

EXACT CONTROLLABILITY OF A CLASS OF DISTRIBUTED PARAMETER SYSTEMS

The exact controllability of a class of distributed parameter systems governedby Petrowsky equations is considered.On the basis of the Hilbert Uniqueness Methodproposed by J.L.Lions,it is found that the Petrowsky systems with Dirichlet boundarycontrol are exactly controllable.     

A CRITERION FOR DISCRETE SPECTRUM OF A CLASS OF DIFFERENTIAL OPERATORS

In this paper,a sufficient and necessary condition is obtained to ensure that the spectrum of a class of 2n-order weighted differential operators is discrete.The proof is based on the method of certain weighted Sobolev spaces to be compactly embedded in weighted L^2(R).     

计量经济中一类单指标模型的建模

本文基于对统计学中广义线性模型的分析、详细研究了计量经济中一类单指标模型的建模问题，提出了相应的参数估计与推断算法，并加以实施。实例分析说明该模型及其方法在实际应用中具有优越性。     

MATHEMATICAL PROGRAMMING WITH A CLASS OF NON-SMOOTH FUNCTIONS

1 IntroductionIn 1981, H..,.,,[1] introduced the notion of invexity aJnd showed that for inequality con-strained programs, Karush~Kuhn-Tucker(KKT) conditions are sufficient fOr optimality if thefunctions involved are invex(differentiable) functiolis. Sinc…     

THE SPECTRAL COMPLETION OF A CLASS OF OPERATOR PARTIAL MATRICES

1. IntroductionLet Hi be complex Banach spaces, i = 1, 2,'' 5 n, and B(Hi, Hi) (B(Hi) if i = j) denotethe Banach space of all bounded linear operators from Hi to Hi. Let H ~ ffi:=IHi; thenA E B(H) may .be denoted by (Ail)... with Ail e B(Hj,Hi). Given a subset J C {(i,j)li,j = 1, 2,'',n} and Ail E B(Hj,Hi) for (i,i) e J, we get a partially specified n x n matriX(Xij)... with Xij ~ Ail if (i,i) e J and Xby (Ail)J If Q = (oil) E B(H) such that oil ~ Aijwhenever (i,i) e J, the…     

A NEW CHARACTERIZATION OF NBU CLASS OF LIFE DISTRIBUTIONS WITH APPLICATION

Assume an unreliable workstation performing jobs with a random service time, namely, it occasionally breaks down because of unexpected interruptions. As an interruption really occurs, the station is instantaneously repaired and the uncompleted job is restarted again from the beginning till a job is completed without being interrupted. The total service time is shown to be NBU if and only if the total time it takes to finish each job with interruptions is stochastically larger than that without them, irrespective of when and how the breakdowns occur. As an application, a nonparametric procedure is developed to test for the strict NBU property of the service time. Finally, some numerical simulations are presented as well.     

OPTIMAL CONTROL OF GROWTH RATE FOR A CLASS OF POPULATION SYSTEMS

In this paper,we discuss the optimal control of growth rate for a class of population systems governed by nonlinear degenerate parabolic equations.Given an ap-propriate cost functional,we prove the existence of the optimal growth rate and give some necessary conditions for optimal growth rate.     

GEOMETRIC PROPERTIES OF A CLASS OF CUBIC SYSTEM WITH AN INVARIANT LINE

ＧＥＯＭＥＴＲＩＣＰＲＯＰＥＲＴＩＥＳＯＦＡＣＬＡＳＳＯＦＣＵＢＩＣＳＹＳＴＥＭＷＩＴＨＡＮＩＮＶＡＲＩＡＮＴＬＩＮＥＺＨＡＮＧＸｉｎｇａｎ；ＬＩＡＮＧＺｈａｏｊｕｎ（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，ＣｅｎｔｒａｌＣｈｉｎａＮｏｒｍａ...     

THE ASYMPTOTIC BEHAVIOR AND APPLICATIONS OF A CLASS OF PP R-STATISTICS

This paper uses R-statistics as projection indices to construct a class of projection pursuit(PP)R-statistics for multivariate two sample tests via PP techniques.Examples are presented asapplications to the location and dispersion problems.