复杂系统的演化过程,n(n-1)律,自聚集

研究一类复杂系统的演化过程,给出一个网络模型,由此导出f(n)=n(n-1),用以在某种程度上定性地描写演化过程中聚集与功能变化的规律。这里n表示agents的聚集数量。熟知的关系式1+1>2是n=2时的特例。当n为小数时,n的增减对系统整体功能的影响显著,此情况将称为“小n机制”。当n充分大时,系统的整体功能将有大跃升,并可用n2度量,称此为“n2效应”。一般情况下,n(n-1)描写聚集-相互作用-功能跃升的模式,用此模式可对不同领域的演化过程作某种解释。     

ANALYSIS OF BOUNDARY SHAPE OF SOLUTIONS OF NONLINEAR PERTURBATION PROBLEM

ＡＮＡＬＹＳＩＳＯＦＢＯＵＮＤＡＲＹＳＨＡＰＥＯＦＳＯＬＵＴＩＯＮＳＯＦＮＯＮＬＩＮＥＡＲＰＥＲＴＵＲＢＡＴＩＯＮＰＲＯＢＬＥＭ￥ＨＥＣｈｅｎｇ；ＺＨＡＮＧＷｅｉｔａｏ（ＩｎｓｔｉｔｕｔｅｏｆＳｙｓｔｅｍｓＳｃｉｅｎｃｅ，ＡｃａｄｅｍｉａＳｉｎｉｃａ...     

THE DISTRIBUTION OF LIMIT POINTS OFINCREMENTS OF LOCAL TIME OF THE WIENER PROCESS

ThisresearchissupportedbythePostdoctoralGrantofChina.1.IntroductionLetW(t)for05t相似文献   

对一种改进层次分析法误导的理论分析

揭示了基于最优传递矩而建立的改进层次分析法产生误导的原因，从理论上否定了该法的一些错误论断。     

CONVERGENCY OF THE MAXIMUM OF PERIODOGRAM

ＣＯＮＶＥＲＧＥＮＣＹＯＦＴＨＥＭＡＸＩＭＵＭＯＦＰＥＲＩＯＤＯＧＲＡＭ￥ＨＥＳｈｕｙｕａｎ（ＤｅｐａｒｔｍｅｎｔｏｆＰｒｏｂａｂｉｌｉｔｙａｎｄＳｔａｔｉｓｔｉｃｓ，ＰｅｋｉｎｇＵｎｉｖｅｒｓｉｔｙ，Ｂｅｉｊｉｎｇ１００８７１，Ｃｈｉｎａ）Ａｂｓｔ...     

ADMISSIBILITY OF SIMULTANEOUS ESTIMATION OF SEVERAL LOSSES

In this paper,admissibility and inadmissibility results of simultaneous estimation oflosses of multivariate normal mean estimators are given.Admissible estimators for losses ofusual estimators of multivariate gamma parameters,multivariate binomial parameters andPoisson parameters are obtained respectively.     

BLOW-UP OF SOLUTIONS OF THE IGNITION MODEL

By use of maximum principle and auxiliary function method, the paper dis-cusses the blow-up sets of the solutions of the ignition model in two cases. It is obtained that the solutions blow up in single point in nonsymmetric case and that the solutions blow up totally or at a couple of points in symmetric case.     

A PROPERTY OF PRODUCTS OF NEW GENERALIZED FUNCTIONS

ＡＰＲＯＰＥＲＴＹＯＦＰＲＯＤＵＣＴＳＯＦＮＥＷＧＥＮＥＲＡＬＩＺＥＤＦＵＮＣＴＩＯＮＳＬＩＹａｑｉｎｇ（ＩｎｓｔｉｔｕｔｅｏｆＳｙｓｔｅｍｓＳｃｉｅｎｃｅ，ＡｃａｄｅｍｉａＳｉｎｉｃａ，Ｂｅｉｊｉｎｇ１０００８０，Ｃｈｉｎａ）ＡＰＲＯＰＥＲＴＹＯＦ...     

DETERMINATION OF THE SIGN OF DIVERGENCE OF A QUADRATIC SYSTEM AT CRITICAL POINTS

Todeterminethesignofdivergenceatcriticalpointsisanimportantstepininvestigatingthestabilityofseparatrixloopsandthatoflimitcyclesgeneratedfromsuchloops(see[1--3]).JiangI4]hassolvedthisproblemforthequadraticsystemoftype(II)andaspecialboundedsystem.Thispaperwillcompletelysolvethisproblemforthegeneralcase.Themethodusedhereissimplerthanthatin[4].Considerthefollowingquadraticsystemoftype(ill):x=--y 6x lxa mad y',gi~x(l ax by),(1)whereb/0.Weconsiderthecasea/0,andwithoutlossofgenerality,wemadassumea<…     

ON A CLASS OF WEIGHT HIERARCHIES OFTERNARY LINEAR CODES OF DIMENSION 4

The possible weight hierarchies of ternary codes of dimension 4 satisfying thealmost chain condition are completely determined in this paper.     

滤波器发展的两次重大飞跃

本文以无源LCF、有源RCF和有源SCF为主线,介绍了滤波器的发展过程、概况、设计方法及特点,讨论了滤波器的演变机理,并着重阐述了无源LCF到有源RCF,和有源RCF到有源SCF的两次重大飞跃,以及无源LCF到有源SCF的直接过渡,还展望了滤波器发展的前景。     

STATISTICS OF A CLASS OF MARKOV CHAINS

In this paper we prove that the distributions of their sojourn time and hitting time at one special state for random walks which are allowed to be finite or infinite and Markov chains on star-graphs with discrete time can uniquely determine the probability distribution of the whole chains. This result also suggests a new statistical method for Markov chains.     

DECOMPOSITION OF MATRICES INTO COMMUTATORS OF REFLECTIONS

Let F be a field and let resA=rank(A-I) for any A in GLnF.We prove that every matrix in SLnF is a product of at most [resA/2] 2 commutators of reflections for n≥2 except for n=2 and F=F2.     

ON THE CONDITION FOR CONSISTENCY OF RESAMPLING ESTIMATORS OF VARIANCE OF TRIMMED L-STATISTICS

1.IntroductionLetXI,X2,''tX.beani.i.d.randomsamplewithcommondistributionfunction(c.d.f.)F(unknown),andFibetheempiricaldistributionfunction(e.d.f.)basedonthesample.ConsiderthefollowingfunctionalofFwhereF--'(t)ginf{x:F(x)2t}istheinversefunctionofF(inversef…     

层次分析积因子方法的保序性

在应用传统的层次分析方法时，不论采用相对测量还是绝对测量，都存在逆序现象。而产生逆育现象的根源是决策方案集的封闭性及反映决策者主观认识的判断方法对客观存在的决策方案集的严重依赖性。文章介绍了一种保存的层次分析方法－积因子法，证明了在一定的条件下，积因子法是唯一可选用的保序方法。     

ESTIMATION OF A KIND OF JUMP REGRESSION FUNCTION

Research on jump regression func(?)ons has not been adequate yet According to theinformation about the number of jumps,their positions and jump magnitudes,jump regressionfunctions can be classified into eight types.This paper deals especially with the secondjump regression function.First of all,a concept of trimmed spline estimate is proposed andwith it an L~2-consistent estimate of the smoothing part of the jump regression function isobtained.This along with the L~2-consistent estimate of jump magnitude constitutes an estimateof the second jump regression function.This paper discusses also the case that the jumppositions have some indeterminacy.A new criterion is suggested and its unique solutionderived.In the end,a few numerical results are given.     

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…     

STRONG CONSISTENCY OF M-ESTIMATES OF MULTIPLE REGRESSION COEFFICIENTS

ＳＴＲＯＮＧＣＯＮＳＩＳＴＥＮＣＹＯＦＭ－ＥＳＴＩＭＡＴＥＳＯＦＭＵＬＴＩＰＬＥＲＥＧＲＥＳＳＩＯＮＣＯＥＦＦＩＣＩＥＮＴＳＣＨＥＮＸｉｒｕ（ＧｒａｄｕａｔｅＳｃｈｏｏｌｏｆｔｈｅＣｈｉｎｅｓｅＡｃａｄｅｍｙｏｆＳｃｉｅｎｃｅｓ，Ｂｅｉｊｉｎｇ１００...     

ON A PROPERTY OF SOLUTIONS OF M-MATRIXEQUATIONS

1.IntroductionConsideringthefollowingsystemoflinearequationsAx~b(l.1)whereAisannxnM-matrix,bisanndimensionalvectorandbeRang(A).Theresearchonthesolutionofequation(1.1)isveryimportantinLeontiefmodelofinput-outputanalysis(see[1,2]).G.St..k.ma[Zjstudiestheabo…     

FIXED POINTS OF THE lTH POWER OF DIFFERENTIAL POLYNOMIALS GENERATED BY SOLUTIONS OF DIFFERENTIAL EQUATIONS

In this paper, we study the problem on the fixed points of the lth power of linear differential polynomials generated by second order linear differential equations. Because of the control of differential equation, we can obtain some precise estimate of their fixed points.