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Fiducial inference in the pivotal family of distributions

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science china Mathematics 2006年第3期49卷 410-432页

作者： XU Xingzhong & LI Guoying Department of Mathematics, beijing institute of Technology, beijing 100081, china academy of Mathematics and systems science, chinese academy of sciences, beijing 100080, china 1. Department of Mathematics Beijing Institute of Technology Beijing 100081 China 2. academy of Mathematics and systems science Chinese Academy of Sciences Beijing 100080 China

In this paper a family, called the pivotal family, of distributions is considered.A pivotal family is determined by a generalized pivotal model. Analytical results show that a great many parametric families of distributions are pivotal. In a pivotal family of distributions a general method of deriving fiducial distributions of parameters is proposed. In the method a fiducial model plays an important role. A fiducial model is a function of a random variable with a known distribution, called the pivotal random element, when the observation of a statistic is *** method of this paper includes some other methods of deriving fiducial distributions. Specially the first fiducial distribution given by Fisher can be derived by the method. For the monotone likelihood ratio family of distributions, which is a pivotal family, the fiducial distributions have a frequentist property in the Neyman-Pearson view. Fiducial distributions of regular parametric functions also have the above frequentist property. Some advantages of the fiducial inference are exhibited in four applications of the fiducial distribution. Many examples are given, in which the fiducial distributions cannot be derived by the existing methods.

关键词： confidence bounds, fiducial distributions, fiducial model, frequentist prop-erty, generalized pivotal model, pivotal family of distributions, testing hypotheses.

CONVERGENCE OF NONLINEAR CONJUGATE GRADIENT METHODS

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Journal of Computational Mathematics 2001年第5期19卷 539-548页

作者： Yu-hong Dai (LSEC, ICMSEC, academy of Mathematics and systems sciences, chinese academy of sciences,beijing 100080, china) 中科院计算数学与科学工程计算所北京 100080

Presents a study on methods for unconstrained optimization. Assumptions of the study; Main results; Convergence properties of the methods under simplified Armijo-type line search.

关键词： unconstrained optimization conjugate gradient (generalized) line search global convergence

SYNTHESIS AND CHARACTERIZATION OF NEW STABILIZERS WITH OPTIMAL MOLECULAR WEIGHT

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chinese Journal of Polymer science 2001年第4期19卷 341-350页

作者： Jiang-qing Pan institute of Chemistry chinese academy of sciences, beijing 100080 china chinese Acad Sci Inst Chem Beijing 100080 Peoples R China

Over 2 x 10(8) tons of polymers are produced every year, and a large portion of polymers faces the degradation problem. There are many effective methods to protect polymers against degradation and the addition of stabilizers to polymer remains the most convenient and effective way of enhancing polymer life and performance. In this article, a series of effective stabilizers with optimal molecular weight (MW), including common, monomeric and polymeric stabilizers (antioxidant and light stabilizer) were synthesized using isocyanation, controlled isocyanation, hydrosilylation, epoxide addition, macroreaction of stabilizing functional compounds and polymerization of monomeric stabilizers. The structure and performance of these new stabilizers were characterized by using IR, NMR, MS, UV-spectra, XPS and elemental analysis. The current development of stabilizer synthesis was also reviewed.

关键词： preparation of stabilizer antioxidant hindered amine light stabilizer isocyanation hydrosilylation

Hyperbolic geometry with geometric algebra

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chinese science Bulletin 1997年第3期42卷 262-263页

作者： LI Hong boinstitute of systems science, chinese academy of sciences, beijing 100080, china institute of systems science Chinese Academy of Sciences Beijing China

WE use the geometric algebra in refs. [1, 2] to study hyperbolic geometry. The n-dimensional hyperbolic space Hn is taken to be the unit sphere of G1 (I-n,1) with antipodal points identified. We study typically H2: the dualities between generalized point and generalized line, between generalized triangle and imaginary triangle; convex generalized triangles; Lorentz transformations; generalized circles and double-cycles, etc. Below we list some of the results.

关键词： line Hyperbolic geometry with geometric algebra

A note on noncommutative moment problems

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science china Mathematics 2005年第8期48卷 1144-1151页

作者： MA Xiujuan School of sciences, Hebei University of Technology, Tianjin 300130, china Mathematics institute, academy of Mathematics and systems science, chinese academy of sciences, beijing 100080, china 1. School of sciences Hebei University of Technology 300130 Tianjin China 2. Mathematics institute Academy of Mathematics and Systems Science Chinese Academy of Sciences 100080 Beijing China

Noncommutative moment problems for C*-algebras are studied. We generalize a result of Hadwin on tracial states to nontracial case. Our results are applied to obtain simple solutions to moment problems on the square and the circle as well as extend the positive unital functionals from a (discrete) complex group algebra to states on the group C*-algebra.

关键词： moment, free product, state, group C*-algebra.

CONVERGENCE OF VORTEX METHODS FOR 3-D EULER EQUATIONS

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Journal of Computational Mathematics 2000年第3期18卷 239-250页

作者： Jia-fu Lin (institute of System science, academy of Mathematics and System sciences, chinese academy of sciences, beijing, 100080, china School of Mathematical sciences, Peking University, beijing 100871, china) 中科院系统科学所北京 100080

Presents a study on the convergence of vortex methods for the three-dimensional Euler equations in bounded domains. Related studies on the convergence of vortex methods; Formulation of vortex methods; Convergence for ... 详细信息

关键词： Euler equations vortex methods convergence initial-boundary value problem

Nonlinear autoregressive models with heavy-tailed innovation

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science china Mathematics 2005年第3期48卷 333-340页

作者： JIN Yang & AN Hongzhi School of Statistics, Renmin University of china, beijing 100872, china academy of Mathematics and systems science, chinese academy of sciences, beijing 100080, china Sch. of Statistics Renmin Univ. of China Beijing 100872 China Acad. of Mathematics and Syst. Sci. Chinese Acad. of Sci. Beijing 100080 China

In this paper, we discuss the relationship between the stationary marginal tail probability and the innovation's tail probability of nonlinear autoregressive models. We show that under certain conditions that ensure the stationarity and ergodicity, one dimension stationary marginal distribution has the heavy-tailed probability property with the same index as that of the innovation's tail probability.

关键词： nonlinear autoregressive model, innovation, tail probability.

Transformations and non-degenerate maps

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science china Mathematics 2005年第z1期48卷 195-205页

作者： LI Baokui & WANG Yuefei institute of Mathematics, academy of Mathematics and System sciences, chinese academy of sciences, beijing 100080, china Graduate School, chinese academy of sciences, beijing 100080, china 1. institute of Mathematics Academy of Mathematics and System Sciences Chinese Academy of Sciences 100080 Beijing China 2. Graduate School Chinese Academy of Sciences 100080 Beijing China

We shall prove the equivalences of a non-degenerate circle-preserving map and a M(o)bius transformation in ^Rn, of a non-degenerate geodesic-preserving map and an isometry in Hn of a non-degenerate line-preserving map and an affine transformation in Rn. That a map is non-degenerate means that the image of the whole space under the map is not a circle, or geodesic or line respectively. These results hold without either injective or surjective, or even continuous assumptions, which are new and of a fundamental nature in geometry.

关键词： M(o)bius transformation, circle-preserving map, non-degenerate map.

A NEW STABILIZED FINITE ELEMENT METHOD FOR SOLVING THE ADVECTION-DIFFUSION EQUATIONS

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Journal of Computational Mathematics 2002年第1期20卷 57-64页

作者： Huo-yuan Duan (institute of Mathematics, academy of Mathematics and System sciences, chinese academy of sciences, beijing 100080, china) institute of Mathematics Academy of Mathematics and System Sciences Chinese Academy of Sciences 北京 100080

Focuses on a study on the development of a stabilized finite element method for solving the advection-diffusion equations with a zero Dirichlet boundary condition. Problem formulation; Error analysis.

关键词： advection-diffusion equation stabilized finite element method