模型选择准则的渐近性质与选择检验

模型选择分为绝对与相对两类，本文针对实用性好但理论上不甚完善的相对选择问题，归纳了其建立准则的一般性途径，证明了它的渐近统计特性，并由此提出了“选择检验”的新概念及其表达。     

PP K-MEAN CLUSTERING

In this paper, we propose a dimension-reducing, K-mean clustering procedureby Projection Pursuit (PP) technique so as to explore the clustering structure of data inhigh-dimensional space in terms of low-dimensional projective points of data, and we obtainthe a.s. consistence of the estimates of the cluster centers and projection orientations.     

ASYMPTOTIC EXPANSION AND ASYMPTOTIC BEHAVIOR OF THE SOLUTION FOR THE TIME-DEPENDENT NEUTRON TRANSPORT PROBLEM IN A SLAB WITH GENERALIZED BOUNDARY CONDITIONS

In this paper,the time-dependent neutron transport integro-differential equationin a nonuniform slab with generalized boundary conditions and initial value is considered forgeneral cases concerned with an arbitrary nonhomogeneous medium possibly with cavity,withthe anisotropic scattering and fission,and with continuous energy varying from null to any finiteconstant or from one positive constant to another positive constant.We prove that the correspon-ding neutron transport operator A has finite Spectrum points in any strip {λ|β_1≤R(?)λ≤β_2}whereβ_2>β1>-λ~*(λ~* is the essential infimum of v∑(x,v)),and obtain the asymptotic expansion ofthe time-dependent solution which exists and is unique.Furthermore,we give the existence ofthe dominant eigenvalue and indicate the asymptotic behavior of the neutron density as t→+∞.     

ASYMPTOTIC SIMILARITY OF INFINITE-DIMENSIONAL LINEAR SYSTEMS AND APPLICATIONS TO STABILITY

1.IntroductionInfinite-dimensionallinearsystemstheory,itiseasytoverifythatthespectrumandtheexponentialgroWthboundarepreservedunderasimilaritytransformation.ThispropertyisaIsosatisfiedfortheinfinite-dimensionalcaseifthesimilarityoperatorisboundedandbound-edlyinvertible.Inthisnote,weilltroduceageneralizationoftheconceptofsimilaritycalledasymptoticsimila-rityforindnite-dimensionallinearsystems.Inthefinite-dimensionalcase1similarityandasymptoticsimilarityareequivalellt.Weshowthatthisasymptoticsi…     

ASYMPTOTIC BEHAVIOR OF THE ESTIMATES OF HIGHER ORDER SPECTRA UNDER TRUNCATED WINDOW

ＡＳＹＭＰＴＯＴＩＣＢＥＨＡＶＩＯＲＯＦＴＨＥＥＳＴＩＭＡＴＥＳＯＦＨＩＧＨＥＲＯＲＤＥＲＳＰＥＣＴＲＡＵＮＤＥＲＴＲＵＮＣＡＴＥＤＷＩＮＤＯＷＹＵＤａｎ（ＩｎｓｔｉｔｕｔｅｏｆＳｙｓｔｅｍｓＳｃｉｅｎｃｅ，ＡｃａｄｅｍｉａＳｉｎｉｃａ，Ｂｅｉｊｉｎ...     

ON THE ALMOST SURELY ASYMPTOTIC BOUNDS OF A CLASS OF ORNSTEIN-UHLENBECK PROCESSES IN INFINITE DIMENSIONS*

Given a real-valued separable M-type 2 Banach space X with the p-th power of the norm of C2-class, the almost sure asymptotic upper bounds of the solutions of the Ornstein-Uhlenbeck Processes described by the following equations {dz（t）=A（t,z（t））dt＋σ（t,z（t））dW（t）,z（0）=z0∈X,are investigated. This study generalizes the corresponding well-known finite dimensional results of Lapeyre （1989） and Mao （1992）.     

THE ALGEBRAIC CRITERIA FOR THE ASYMPTOTIC BEHAVIOR OF COOPERATIVE SYSTEMS WITH CONCAVE NONLINEARITIES

For the discrete dynamical system on the nonnegative orthant generated bya cooperative and concave map T, we present an algebraic criterion of its asymptoticbehavior. The global behavior of such a system is completely determined by the sign of allprincipal minors of the matrix I-DT(0). This criterion applies to the cooperative systemwhich is concave, time-dependent and periodic in t. We give the sufficient conditions thatthe zero solution of such a system is globally asymptotically stable and that it possesses anonzero periodic solution which attracts all initial conditions in the nonnegative orthant.except at the origin. The results of Smith under weaker conditions and some applicationsare included.     

BOOTSTRAPPING PP L-STATISTICS FOR TESTS

Some bootstrap approximations of the asymptotic distributions of PP L-statistics whichwere proposed by the authors in[7]are discusse.Bootstrap statistics and their asymptotic propertiesare established.Two examples and the numerical results are given,by which one can actuallyimplement the proposed tests under the condition of normal population.     

ASYMPTOTIC BEHAVIOR OF THE SOLUTION FOR THE NEUTRON TRANSPORT EQUATION IN A SLAB WITH GENERALIZED REFLECTING BOUNDARY CONDITIONS

This paper discusses the neutron transport equation in a slab with generalized reflectingboundary conditions.By means of the positive C_0-semigroup theory,we have proved that this problemhas a unique nonnegative solution and found the spectral property of the corresponding transportoperator.Finally we give the asymptotic behavior of the solution for this equation.     

THE RANKINGS OF CONTROL SYSTEMS AND APPLICATIONS

The notion of ranking was initiated into control theory by Glad a few yearsago. In this paper we mainly discuss one kind of rankings and study its invarianceproperties. This kind of rankings is closely related to the structure algorithm. The relationsbetween invariants of this kind of rankings and the invariants given by other studies, e.g.the invertibility indices of a system and so on, are examined. As applications of rankings,we deal with some well-known problems in "ranking technique". In this paper we mainlyintroduce a new method rather than solve new problems.     

THE TAIL ESTIMATION FOR THE DISTRIBUTION OF THE SUPREMA OF A P-BRIDGE

Let X_1,X_2,…be a sequence of independent random vectors which take values in IR~2 and X_i～P.By the projection pursuit (PP) method,we canconstruct PP type Kolmogrov-Smirnov statistics:K_n=(?) 1/n~(1/2)|sum from i=1 to n(I_|a~rX_(?)(?)t|-P(a~rX_1(?)t))|,where I_([·]) is the indicator function of the set [·] and P is a probability distribution.The limit distribution of K_n is the distribution for the suprema of a P-bridgewhose index is the set of all half spaces in IR~2.Let{W_p([0,(?)])∶(?)∈[0,1]~2} be atwo parameter Brownish bridge.The main result of this paper is(?)for all λ,provided P is the uniform distribution on [0,k_1]×[0,k_2],0相似文献   

ON THE THEORY OF RESOLVENTS AND ITS APPLICATIONS

1.IntroductionSomefrequentlyusedalgebraicalgorithmssharethesamepropertythattheytransformasetofpolynomialequationstoasinglepolynomialequationsuchthatthezerosetofthepolynomialsetandthehypersurfacedefinedbythesinglepolynomialareequivalentincertainsense.FOralgorithmswiththisproperty,wemaymention'thealgorithmtofindaprimitiveelementforafinitelygeneratedalgebraicextensionfield[1],thealgorithmtofindaplanecurvewhichisbirationaltoaspacealgebraiccur.e[2]!etc.Inthispaper,wepresentageneralalgorithmwhichcan…     

ASYMPTOTIC PROPERTY OF THE TIME-DEPENDENT SOLUTION OF A RELIABILITY MODEL

We discuss a transfer line consisting of a reliable machine, an unreliable machine and a storage buffer. This transfer line can be described by a group of partial differential equations with integral boundary conditions. First we show that the operator corresponding to these equations generates a positive contraction C0-semigroup T(t), and prove that T(t) is a quasi-compact operator. Next we verify that 0 is an eigenvalue of this operator and its adjoint operator with geometric multiplicity one. Last, by using the above results we obtain that the time-dependent solution of these equations converges strongly to their steady-state solution.     

一般系统结构理论及其应用（Ⅰ）

定义若干新概念，从数学上推导一个新的一般系统模型，即一般系统结构模型。     

ON THE NUMBER OF FIXED POINTS OF NONLINEAR OPERATORS AND APPLICATIONS

In this paper, the famous Amann three-solution theorem is generalized. Multiplicity question of fixed points for nonlinear operators via two coupled parallel sub-super solutions is studied. Under suitable conditions, the existence of at least six distinct fixed points of nonlinear operators is proved. The theoretical results are then applied to nonlinear system of Hammerstein integral equations.     

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…     

THE BERRY-ESSEEN BOUND AND LIL PP CM STATISTIC TESTING UNIFORM DISTRIBUTION ON SPHERE ABOUT DIMENSION AND SAMPLE SIZE

1. IntroductionXI, Xz,'' I Xu are i.i.d. p dimension random vectors with distribution function F(x).Cuilzldefined PP Cramer-Von Mises test statistic as follows:where F:(x) ~ (Z:=, I[a'Xi 5 x])/n is the empirical distribution function of a'XI, a'X2,' ', a'X.. F"(x) ~ P(a'X, 5 x) is distribution function of a'XI, p(.) is uniform measuxeon SP--1. Under null hypothesis HO: XI has uniform distribution on SP--1, F"(x) 2 G(x) =if, g(u)du, where g(u) ~ {r(p/2)(1 -- u')(P--')/'}/{(r(1/2…     

一类多站循环服务系统的分析与建模

在多站循环服务系统中，广泛存在一类实用的非对称型、接待室容量有限、以及各站带有优先与非优先队列的模型。本文通过分析与处理，对此提出一种特殊的算法、从而可以求出平稳状态下系统与各站主要工作性能参数与曲线。     

ON THE BOUNDEDNESS OF SOLUTIONS,EXISTENCE AND UNIQUENESS OF LIMIT CYCLES FOR A CLASS OF CUBIC DIFFERENTIAL SYSTEM

In this paper, we discuss the boundedness of the solutions, the existence andthe uniqueness of the limit cycle of the following cubic differential system:x'=y, y'=-x+δy+a_2xy+a_4x+a_5x~2y. (*)We obtain the following results:(1) System (*) is bounded if and only if (i) a_5<0, a_4=0; or (ii) a_5=0, a_4<0, δ≤0,-(-8a_4)~(1/2)相似文献   

SOME THEOREMS OF THE NORDHAUS-GADDUM CLASS

Let the chromatic number of G, the edge chromatic number of G and thetotal chromatic number of G be denoted by x(G), x_1(G) and x_2(G), respectively. Forany simple graph G of order p and its complement G, the following inequalities of theNordhaus-Gaddum class are obtained:(i)|2p~(1/2)|-ε_1≤x(G)+x_1(G)≤2p-2 and 0≤x(G)·x_1(G)≤(p-1)~2 for p≥2,(ii)|2p~(1/2)|+ε_1≤x(G)+x_2(G)≤2p-1 and 0≤x(G)·x_2(G)≤p(p-1) for p≥3,(iii)p≤x_1(G)+x_2(G)≤2p-1 and 0≤x_1(G)·x_2(G)≤p(p-1) for p≥3,where ε_1=0, if p~(1/2) is an odd integer, 1, otherwise,ε_2=1, if p~(1/2) is an even integer, 0, otherwise,and [x] denotes the ceiling of x. We also show that these bounds are sharp for everypositive integer p.