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Almost sure central limit theorems for random functions

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Science China mathematics 2006年第12期49卷 1788-1799页

作者： LU Chuanrong, QIU Jin & XU Jianjun School of mathematics and statistics, Zhejiang university of Finance and Economics, Hangzhou 310018, China department of mathematics, Zhejiang university, Hangzhou 310028, China School of mathematics and statistics Zhejiang University of Finance and Economics Hangzhou China department of mathematics Zhejiang University Hangzhou China

Let {Xn,-∞< n <∞} be a sequence of independent identically distributed random variables with EX1 = 0, EX12 = 1 and let Sn =∑k=1∞Xk, and Tn = Tn(X1,…,Xn) be a random function such that Tn = ASn + Rn, where supn E|... 详细信息

Let {Xn,-∞statistics, Von-Mises statistics, linear processes, moving average processes, error variance estimates in linear models, power sums, product-limit estimators of a continuous distribution, product-limit estimators of a quantile function, etc.

关键词： statistics,random function,almost sure central limit theorem,logarithm average.

THE PHYSICAL ENTROPY OF SINGLE CONSERVATION LAWS

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Journal of Computational mathematics 1998年第5期16卷 437-444页

作者： (department of mathematics, Peking university, Beijing 100871, China) 北京大学数学系北京

By means of the comparisons with the formulas in statistical mechanics and thermodynamics, in this paper it is demonstrated that for the single conservation law partial derivative(t)u + partial derivative(x)f(u) = 0, if the flux function f(u) is convex (or concave), then, the physical entropy is S = -f(u); Furthermore, if we assume this result can be generalized to any f(u) with two order continuous derivative, from the thermodynamical principle that the local entropy production must be non-negative, one entropy inequality is derived, by which the O.A. Olejnik's famous E- condition can be explained successfully in physics.

关键词： conservation laws entropy entropy production

On the Cayley-Bacharach property and the construction of vector bundles

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Science China mathematics 2011年第9期54卷 1891-1898页

作者： SUN Hao 1,2 1 department of mathematics and statistics,Huazhong Normal university,Wuhan 430079,China 2 department of mathematics,East China Normal university,Shanghai 200241,China department of mathematics and statistics Huazhong Normal University department of mathematics East China Normal University

We study the Cayley-Bacharach property on complex projective smooth varieties of dimension n≥2 for zero dimensional subscheme defined by the zero set of the wedge of r-n + 1 global sections of a rank r≥n vector bund... 详细信息

关键词： Cayley-Bacharach property vector bundle reflexive sheaf k-very ample

Tests for nonparametric parts on partially linear single index models

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Science China mathematics 2007年第3期50卷 439-449页

作者： Ri-quan ZHANG department of statistics, East China Normal university, Shanghai 200062, China department of mathematics, Shanxi Datong university, Datong 037009, China department of statistics East China Normal University Shanghai China department of mathematics Shanxi Datong University Datong China

Tests for nonparametric parts on partially linear single index models are considered in this paper. Based on the estimates obtained by the local linear method, the generalized likelihood ratio tests for the models are established. Under the null hypotheses the normalized tests follow asymptotically the χ2-distribution with the scale constants and the degrees of freedom being independent of the nuisance parameters, which is called the Wilks phenomenon. A simulated example is used to evaluate the performances of the testing procedures empirically.

关键词： local linear method partially linear single index models generalized likelihood ratio test Wilks phenomenon χ 2-distribution 62G10 62G20

REGULARITY　ESTIMATES　FOR　THE　OBLIQUE　DERIVATIVE　PROBLEM　ON　NON－SMOOTH　DOMAINS（I）

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Chinese Annals of mathematics,Series B 1995年第3期16卷 299-324页

作者： GUAN PENGFEI E. SAWYER(department of mathematics and statistics McMaster universityt Hamilton, Olltario LSS 4KI, canada.) MCMASTER UNIV DEPT MATH & STATHAMILTONON L8S 4K1CANADA

The authors consider the existence and regularity of the oblique derivative problem:where P is a second order elliptic differential operator on Rn,Ωis a bounded domain in Rn and is a unit vector field on the boundary of Ω(which may be tangential to the boundary).All above are assumed with limited smoothness. The authors show that solution u has an elliptic gain from f in Holder spaces(Theorem 1.1). The authors obtain LP regualrity of solution in Theorem 1.3, which generalizes the results in [7] to the limited smooth case. Some of the application nonlinear problems are also discussed.

关键词： Oblique derivative Degenerate boundary value problem Existence Regularity.

The Cauchy problem about Dirac-wave map from the 2-dimension Minkowski space to a complete Riemannian manifold

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Science China mathematics 2007年第6期50卷 859-874页

作者： Yan ZHANG School of statistics and mathematics , Zhejiang Gongshang university, Hangzhou 310018, China department of Physics, Zhejiang university, Hangzhou 310027, China School of statistics and mathematics Zhejiang Gongshang University Hangzhou China department of Physics Zhejiang University Hangzhou China

When a target manifold is complete with a bounded curvature, we prove that there exists a unique global solution which satisfies the Euler-lagrange equation of for the given Cauchy data.

关键词： Dirac-wave map nonlinear σ-model spin bundle harmonic map 53C43

Rolling Element Bearing Diagnostics by Combination of Envelope Analysis and Wavelet Transform

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Journal of university of Science and Technology Beijing 2001年第1期8卷 69-74页

作者： Ying Tang, Qiao Sun Mechanical Engineering School, university of Science and Technology Beijing, Beijing 100083, China department of Mechanical Engineering, university of calgary calgary Alberta T2N 1N4, canada Mechanical Engineering School Univ. of Sci. and Technology Beijing Beijing 100083 China

Rolling element-bearing diagnostics has been studied over the last thirty years, and envelope analysis is widely recognized as being the best approach for detection and diagnosis of rolling element bearing incipient failure. But one of the on-going difficulties with envelope technique is to determine the best frequency band to envelop. Here, wavelet transform technique is introduced into envelope analysis to solve the problem by capturing bearing defects-sensory scales (i.e. frequency bands). A modulated Gaussian function is chosen to be the analytical wavelet because it coincides well with bearing defect-induced vibration signal patterns. Vibration signals measured from railway bearing tests were studied by the proposed method. Cases of bearings with single and multiple defects on inner and outer race under different testing conditions are presented. Experimental results showed that the proposed method allowed a more accurate local description and separation of transient signal part, which were caused by impacts between defects and the mating surfaces in the bearing. The combination method provides an effective signal detection technique for rolling element-bearing diagnostics.

关键词： continuous wavelet transform envelope analysis rolling element bearing diagnostics

OVERLOAD ANALYSIS OF MARKOVIAN MODELS

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Systems Science and Mathematical Sciences 1999年第3期12卷 222-230页

作者： Yiqiang Q. ZHAO(department of mathematics mathematics and statistics university of Winnipeg,Winnipeg, Manitoba, canada R3B2E9) university of Winnipeg 加拿大

A new procedure for computing stationary probabilities for an overloadedMarkovian model is proposed in terms of the rotated Markov chain. There are two advantages to use this procedure: i) This procedure allows us to approximate an overloadedfinite model by using a stable infinite Markov chain. This will make the study easier whenthe infinite model has a simpler solution. ii) Numerically) this procedure often significantlyreduces the number of computations and the requirement of computer memory. By usingdifferent examples, we specifically demonstrate the process of implementing this rotatingprocedure.

关键词： Markov processes queues, overload.

NONOVERLAPPING DOMAIN DECOMPOSITION METHOD WITH MIXED ELEMENT FOR ELLIPTIC PROBLEMS

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Journal of Computational mathematics 1996年第4期14卷 291-300页

作者： H.X. Rui(mathematics department, Shandong university, Jinan) 山东大学数学系山东济南

In this paper we consider the nonoverlapping domain decomposition method based on mixed element approximation for elliptic problems in two dimentional space. We give a kind of discrete domain decomposition iterative algorithm using mixed finite element, the subdomain problems of which can be implemented parallelly. We also give the existence, uniqueness and convergence of the approximate solution.

关键词： Zhang NONOVERLAPPING DOMAIN DECOMPOSITION METHOD WITH MIXED ELEMENT FOR ELLIPTIC PROBLEMS EV