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Fixed Design Nonparametric Regression with Truncated and Censored Data

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Acta Mathematicae Applicatae Sinica 2003年第2期19卷 229-238页

作者： Liu-quan Sunacademy of mathematics and {2. {3., chinese academy of sciences, beijing 100080, china academy of mathematics and {2. {3. Chinese Academy of Sciences Beijing China

Abstract In this paper we consider a fixed design model in which the observations are subject to left truncation and right censoring. A generalized product-limit estimator for the conditional distribution at a given covariate value is proposed, and an almost sure asymptotic representation of this estimator is established. We also obtain the rate of uniform consistency, weak convergence and a modulus of continuity for this estimator. Applications include trimmed mean and quantile function *** applications demonstrate the usefulness of the new matrix products.

关键词： Keywords Nonparametric regression fixed design asymptotic representation truncated and censored data modulus of continuity

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ON KORN'S INEQUALITY

Journal of Computational mathematics 2003年第3期21卷 321-324页

作者： Lie-heng Wang(LSEC, ICMSEC, academy of mathematics and {2. {3., chinese academy of sciences,beijing 100080, china) 中科院数学与系统科学院 LSEC ICMSEC CAS 北京 100080

This paper is devoted to give a new proof of Korn's inequality in LT - norm (1 < γ < ∞).

关键词： Korn's inequality.

Energy Scattering for the Generalized Davey-Stewartson Equations

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Acta Mathematicae Applicatae Sinica 2003年第2期19卷 333-340页

作者： Cheng-chun Haoacademy of mathematics and {2. {3., chinese academy of sciences, beijing 100080, china academy of mathematics and {2. {3. Chinese Academy of Sciences Beijing China

Abstract Considering the generalized Davey-Stewartson equation $i\mathop u\limits^. - \Delta u + \lambda \left| u \right|^p u + \mu E\left( {\left| u \right|^q } \right)\left| u \right|^{q - 2. u = 0$ where $\lambda > 0,\mu \ge 0,E = F^{ - 1} \left( {\xi _1^2./\left| \xi \right|^2.} \right)F$ we obtain the existence of scattering operator in ^(A↑^n) := { u ] H1(A↑^n) : |x|u ] L2.A↑^n)}.

关键词： Keywords Generalized Davey-Stewartson equation pseudo conformally invariant conservation law scattering operator

A quasi-local mass for 2.spheres with negative Gauss curvature

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Science china mathematics 2008年第9期51卷 1644-1650页

作者： ZHANG Xiao Institute of mathematics, academy of mathematics and {3.s Science, chinese academy of sciences, beijing 100080, china Institute of mathematics Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing China

We extend our previous definition of quasi-local mass to 2.spheres whose Gauss curvature is negative, and prove its positivity.

关键词： general relativity quasi-local mass positivity 53.2. 53.50 83.60

A mixed method for measuring low-frequency acoustic properties of macromolecular materials

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Science china(Physics,Mechanics & Astronomy) 2006年第6期49卷 729-739页

作者： LIU Hongwei1,YAO Lei1,3.ZHAO Hong1,3.ZHANG Jichuan2.3.& XUE Zhaohong2.1. National Key Laboratory of Acoustics,Institute of Acoustics,chinese {3. of {2.,beijing 100080,china 2. Institute of Chemistry,chinese {3. of {2.,beijing 100080,china 3. Graduate University of{12.,beijing 100049,china National Key Laboratory of Acoustics Institute of Acoustics Chinese Academy of Sciences Beijing China Graduate University of chinese academy of sciences Beijing China Institute of Chemistry Chinese Academy of Sciences Beijing China

A mixed method for measuring low-frequency acoustic properties of macro-molecular materials is presented. The dynamic mechanical parameters of materials are first measured by using Dynamic Mechanical Thermal Apparatus(DMTA) at low frequen-cies,usually less than 100 Hz; then based on the Principles of Time-Temperature Super-position (TTS),these parameters are extended to the frequency range that acousticians are concerned about,usually from hundreds to thousands of hertz; finally the extended dynamic mechanical parameters are transformed into acoustic parameters with the help of acoustic measurement and inverse analysis. To test the feasibility and accuracy,we measure a kind of rubber sample in DMTA and acquire the basic acoustic parameters of the sample by using this method. While applying the basic parameters to calculating characteristics of the sample in acoustic pipe,a reasonable agreement of sound absorp-tion coefficients is obtained between the calculations and measurements in the acoustic pipe.

关键词： low-frequency acoustic properties,dynamic mechanical properties,Principles of Time-Temperature Superposition,acoustic pipe,sound absorption coefficient.

Wandering domains in the transcendental dynamics

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chinese Science Bulletin 2001年第1期46卷 34-35页

作者： WANG YuefeiInstitute of mathematics, chinese academy of sciences,{2.,{3. Institute of mathematics Chinese Academy of Sciences Beijing China

It is shown that new classes of non-critically finite entire functions do not have wandering domains.

关键词： iteration Fatou set Julia set wandering domains.

^(40)Ar/^(3.)Ar dating of shear deformation of the Xianshuihe fault zone in west Sichuan and its tectonic significance

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Science china Earth sciences 2004年第9期47卷 794-803页

作者： ZHANG Yueqiao1, CHEN Wen2. 3.& YANG Nong1 1. Institute of Geomechanics, chinese academy of Geological {2., beijing 100081, china 2. Institute of Geology, chinese academy of Geological {2., beijing 10003., china 3. Institute of Geology and Geophysics, chinese academy of sciences, beijing 10002., china Institute of Geomechanics Chinese Academy of Geological Sciences Beijing China Institute of Geology Chinese Academy of Geological Sciences Beijing China Institute of Geology and Geophysics Chinese Academy of Sciences Beijing China

Based on field geological survey, structural measurements and classical Ar/Ar dating of mica, biotite and K-feldspar, we obtain cooling ages for Miocene left-lateral shear along the Xianshuihe fault zone. The results document two thermal events during the sinistral shear. The early event (12.10 Ma) corresponds to rapid cooling of the Zheduoshan granitic massif from above 700℃ to below 3.0℃. The late event (5-3.5 Ma) corresponds to cooling of granites intruded along the eastern side of the fault zone. These dating results provide important thermochronological constraint on the timing of late Cenozoic eastward extrusion of the Chuan-Dian Block in the SE Tibetan margin.

关键词： Xianshuihe fault zone, Zheduoshan granitic massif, sinistral shear deformation, 40Ar/3.Ar dating, late Cenozoic.

Algebraically explicit analytical solu-tions for the unsteady non-Newtonian swirling flow in an annular pipe

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Science china(Physics,Mechanics & Astronomy) 2006年第4期49卷 396-400页

作者： CAI Ruixian1 & GOU Chenhua1,2.1. Institute of Engineering Thermophysics, chinese academy of sciences, beijing 100080,{2. 2. Graduate School, chinese academy of sciences, beijing 100080,{2. Institute of Engineering Thermophysics Chinese Academy of Sciences Beijing China Graduate School Chinese Academy of Sciences Beijing China

This paper presents two algebraically explicit analytical solutions for the incompressible unsteady rotational flow of Oldroyd-B type in an annular pipe. The first solution is derived with the common method of separation of variables. The second one is deduced with the method of separation of variables with addition developed in recent years. The first analytical solution is of clear physical meaning and both of them are fairly simple and valuable for the newly developing computational fluid dynamics. They can be used as the benchmark solutions to verify the applicability of the existing numerical computational methods and to inspire new differencing schemes, grid generation ways, etc. Moreover, a steady solution for the generalized second grade rheologic fluid flow is also presented. The correctness of these solutions can be easily proven by substituting them into the original governing equation.

关键词： analytical solution, Oldroyd-B type fluid, swirling flow, non-Newtonian.

Accuracy of Multivariable Refinable Functions and Two-Scale Similarity Transform

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Acta Mathematica Sinica,English Series 2000年第2期16卷 271-276页

作者： Qiuhui Sheng Silong Peng Institute of mathematics,academy of mathematics and {3.s sciences,chinese academy of sciences,beijing 100080,P.R.china Institute of mathematics Academy of Mathematics and Systems Sciences Chinese Academy of Sciences Beijing 100080 P. R. China

In this paper,we prove that if two multiresolutions satisfy a relation,then they have the same accuracy in the multivariate FSI case.

关键词： Accuracy Symbol function Two-scale similarity transform