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…     

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.     

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.     

因素空间理论与知识表示的数学框架——概念的反馈外延与因素的重合性

本文是文献（１，２）的继续，该文及后续的论文的将系统地研究因素空间理论及其在知识表示中的应用，首先引入反馈外延这一表示概念的新工具，它为表达概念提供了直接的操作方法，然后设计了反馈外延的包络，它是对概念外延的一种逼近，最后讨论了关于概念的重合性重合性测度的公理化定义。     

CORRECTED PROOF OF A THEOREM CONCERNING A CONJECTURE OF SINGH

A theorem concerning a conjecture of Singh is formulated in[2].But the argumentin [2] contains a serious gap which is in fact the essential point of the proof.A correct proofis presented here.     

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.     

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.     

AHP理论与方法研究一致性检验与权重计算

证明判断矩阵一致性的一个充要条件，并根据此充要条件，提出一种直接进行排序权向量计算的方法     

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.     

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.     

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).     

OPTIMAL GLOBAL RATES OF CONVERGENCE OF M－ESTIMATES FOR NONPARAMETRIC REGRESSION

ＯＰＴＩＭＡＬＧＬＯＢＡＬＲＡＴＥＳＯＦＣＯＮＶＥＲＧＥＮＣＥＯＦＭ－ＥＳＴＩＭＡＴＥＳＦＯＲＮＯＮＰＡＲＡＭＥＴＲＩＣＲＥＧＲＥＳＳＩＯＮＳＨＩＰｅｉｄｅ；ＬＩＧｕｏｙｉｎｇ（ＩｎｓｔｉｔｕｔｅｏｆＳｙｓｔｅｍｓＳｃｉｅｎｃｅ，ＡｃａｄｅｍｉａＳｉ...     

NATREX AND DETERMINATION OF REAL EXCHANGE RATE OF RMB

1 IntroductionIn the past decades, a lot of 1iteratures appeared in the determination of excfiange rate, boththeoretic and empirical. One preValing paradigm is that the puxchasing power parity (PPP)holds in the long run either in weak--fOrm or in strongform. Under this hyPothesis, fluctuationsin real exchange rates are often regaJrded as temporary deviations from the long--run equllibriumexchange rate. However, these ekisting models fail to eXPlain the 1arge fluctuations in the realexchang…     

ANALYSIS OF BOUNDARY SHAPE OF SOLUTIONS OF NONLINEAR PERTURBATION PROBLEM

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

ASYMPTOTIC ANALYSIS OF THE OPTIMAL CONTROL OF AN ELASTODYNAMIC SYSTEM

Based on the idea of the reduction of optimal control systems in singularperturbations of Lions and a priori estimates in [4], we prove the convergence of theoptimal control, state and the cost function between a singular linear elastodynamic systemand a limit system. Our asymptotic analysis is applicable to the optimal control of flexiblerobotic manipulators.     

BASIC PROPERTIES OF K-SPACES

Every complete metric linear space is a K-space.A non-completenormed space can be a K-space.And non-metrizable K-spaces exist.A series ofbasic results on complete metric linear spaces Can be generalized to K-spaces.Forexample,every bounded linear operator from a K-space into a locally convex spaceis sequentially continuous;every bounded semi-norm on a K-space is sequentiallycontinuous and,therefore,piecewise separable;a.C-sequeatial K-space is both bar-relled and bornological;the family of sequentially continuous linear functionals ona K-space is weak sequentially complete.     

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。     

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.     

AN INVESTIGATION OF THE POLYNOMIAL FORFORWARD ANALYSIS OF A FLORIDA PLATFORM

1.IntroductionInthisreportwewillpresentsomecomputationalresultsforthekinematicsolutionofanin-parallelmechanismplatformdesignedattheUniversityofFlorida.Thefigureoftheplatformanalysedhereisasfollows.Figure1Theconnectingpointsjoinvenicestosidesofthepairoftriangles.Thisisaspecialcaseofwhatwehaveconsideredin[l].Sincebothofthefixedandmovingplatformsaretriangles,andsomejointcenterslieonthecorrespondingsidesofthem,wecanspecifysomeparametersin[1]foranalysis.Itturnsoutthatmorecomputationalresultscanbe…     

EXACT VALUE OF THE HARMONIOUS CHROMATIC NUMBER OF A COMPLETE TRINARY TREE

1.IntroductionLetG={VE}beafinite,undirected,simplegraPh,TheharmoniouschromaticnumberofagraPhG,denotedbyh(G),istheleastnumber0fcolorsneededtocol0rtheverticesofGinsuchawaythatanytwoadacelitverticesarec0loredbydmerelltcol0rsandanytwodistinctedgeshavedtherentcolorpairs(Here,ac0lorpairforedgee=uvisthepairofcol0rsusedt0coloruandv).Theharmoniouscol0ringshavebeenstudiedinpaPersl1-10].J.Mitchem[10]0btainedtheexactvalue0ftheharm0ni0uschr0maticnUInber0fthepath,cycleandc0mpleten-nytreewith3or4levels…