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Reducing component estimation for varying coefficient models with longitudinal data

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Science china mathematics 2008年第2期51卷 250-272页

作者： TANG QingGuo~(1,2+) WANG JinDe~2 1 Institute of Sciences,People’s Liberation Army university of Science and Technology,nanjing 210007,china 2 department of mathematics,nanjing university,nanjing 210093,china 1. Institute of Sciences People’s Liberation Army University of Science and Technology Nanjing 210007 China 2. department of mathematics Nanjing University Nanjing 210093 China

Varying-coefficient models with longitudinal observations are very useful in epidemiology and some other practical *** this paper,a reducing component procedure is proposed for es- timating the unknown functions and their derivatives in very general models,in which the unknown coefficient functions admit different or the same degrees of smoothness and the covariates can be time- *** asymptotic properties of the estimators,such as consistency,rate of convergence and asymptotic distribution,are *** asymptotic results show that the asymptotic variance of the reducing component estimators is smaller than that of the existing estimators when the coefficient functions admit different degrees of *** sample properties of our procedures are studied through Monte Carlo simulations.

关键词： varying coefficient model longitudinal data nonparametric estimation reducing component estimators asymptotic normality 62G07

Variational construction of unbounded orbits in Lagrangian systems

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Science china mathematics 2010年第3期53卷 617-624页

作者： CHENG Chong-Qing 1, & LI Xia 2 1 department of mathematics, nanjing university, nanjing 210093, china 2 department of mathematics, Suzhou university of Science and Technology, Suzhou 215001, china 1. department of mathematics Nanjing University Nanjing 210093 China2. Department of Mathematics Suzhou University of Science and Technology Suzhou 215001 China

We show the existence of unbounded orbits in perturbations of generic geodesic flow in T2 by a generic periodic potential. Different from previous work such as in Mather (1997), the initial values of the orbits obtain... 详细信息

关键词： positive definite Lagrangian variational method unbounded orbit

Diophantine vectors in analytic submanifolds of Euclidean spaces

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Science china mathematics 2007年第9期50卷 1334-1338页

作者： Rong-mei CAO~(1+) Jian-gong YOU~2 1 College of Science,nanjing university of Aeronautics and Astronautics,nanjing 210016,china 2 department of mathematics,nanjing university,nanjing 210093,china 1. College of Science Nanjing University of Aeronautics and Astronautics Nanjing 210016 China 2. department of mathematics Nanjing University Nanjing 210093 China

Let $\mathcal{M}$ be an m-dimensional analytic manifold in ? n . In this paper, we prove that almost all vectors in $\mathcal{M}$ (in the sense of Lebesgue measure) are Diophantine if there exists one Diophantine vect... 详细信息

关键词： diophantine vector analytic submanifold 32C05

Nonlinear ergodic theorem for semitopological semigroups of non-Lipschitzian mappings in Banach spaces

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Chinese Science Bulletin 1997年第1期42卷 8-11页

作者： LI Gang and MA Jipu1. department of mathematics, Yangzhou Normal College, Yangzhou 225002, china 2. department of mathematics, nanjing university, nanjing 210093, china department of mathematics Yangzhou Normal College Yangzhou China department of mathematics Nanjing University Nanjing China

LET G be a semitopological semigroup, i. e. G is a semigroup with a Hausdorff topology such that for each s∈G the mapping s|→s·t and s|→t·s from G to G are continuous. G is called right reversible if any two closed left ideals of G have non-void intersection. In this case, (G,≤) is a directed system when the binary relation '≤' on G is defined by a≤b if and only if Let E be the uniformly convex Banach space

关键词： nonlinear semigroup ergodic theorem non-Lipschitzian mapping.

A predict-correct projection method for monotone variant variational inequalities

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Chinese Science Bulletin 1998年第15期43卷 1264-1267页

作者： HAN Qiaoming 1 and HE Bingsheng 2 1. Institute of Applied mathematics, Chinese Academy of Sciences, Beijing 100080, china 2. department of mathematics, nanjing university, nanjing 210093, china Institute of Applied mathematics Chinese Academy of Sciences Beijing China department of mathematics Nanjing University Nanjing China

A predict_correct projection method is presented for solving monotone variant variational inequalities, which could exploit the advantages and overcome the difficulties of both explicit and implicit projection methods.

关键词： variant variational inequality explicit projection method implicit projection method predict_correct projection method.

Y_CΩ_(2n)are easy terms

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Chinese Science Bulletin 1998年第20期43卷 1707-1709页

作者： ZHAO Xishun 1 and WANG Ju 2 1. department of mathematics, nanjing university, nanjing 210093, china 2. Institute of Software, Chinese Academy of Sciences, Beijing 100080, china department of mathematics Nanjing University Nanjing China Institute of Software Chinese Academy of Sciences Beijing China

For any natural number n≥1, Y CΩ 2n is an easy term; that is, for any λ term M, λβ+Y\-CΩ 2n =M is consistent, where Y C is Curry fixed point combinator, Ω 2n ≡ω 2n ω 2n and ω 2n ≡λ***...x (there are 2n occurrences of x after λx ). This result is a partial solution to Jacopini’s conjecture: Y CΩ n is an easy term for any natural number n≥2.

关键词： λβ-calculus Kuper’s theorem easy term.

(1.2)INVERSES OF OPERATORS BETWEEN BANACH SPACES AND LOCAL CONJUGACY THEOREM

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Chinese Annals of mathematics,Series B 1999年第1期20卷 57-62页

作者： MA JIPU(department of mathematics,nanjing university,nanjing 210093,china) nanjing Univ Dept Math Nanjing 210093 Peoples R China

Let E and F be Banach spaces and f non-linear C1 map from E into F. The main result isTheorem 2.2, in which a connection between local conjugacy problem of f at x0E and a localfine property of f'(x) at x0(see the Definition 1.1 in this paper) are obtained. This theoremincludes as special cases the two known theorems: the finite rank theorem and Berger's Theoremfor non-linear Fredholm operators. Moreover, the thcorem gives rise the further results for somenon-linear semi-Fredholm maps and for all non-linear semi-Wedholm maps when E and F areHilbert spaces. Thus Theorem 2.2 not only just unifies the above known theorems but alsoreally generalizes them.

关键词： Nonlinear semi-Fredholm maps Conjugacy problem Banach space

Regular n-simplices in R^n with vertices in Z^(n)

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Science china mathematics 2004年第1期47卷 104-113页

作者： XIA Jianguo & QIN Hourongdepartment of mathematics, nanjing Normal university, nanjing 210097, china (email: jgxia@***) department of mathematics, nanjing university, nanjing 210093, china Dept. of Math. Nanjing Normal Univ. Nanjing 210097 China Dept. of Math. Nanjing Univ. Nanjing 210093 China

In this paper the Ⅰ and Ⅱ regular n-simplices are introduced. We prove that the sufficient and necessary conditions for existence of an Ⅰ regular n-simplex in Rn are that if n is even then n = 4m(m + 1), and if n is odd then n = 4m + 1 with that n + 1 can be expressed as a sum of two integral squares or n = 4m - 1, and that the sufficient and necessary condition for existence of a Ⅱ regular n-simplex in Rn is n = 2m2 - 1 or n = 4m(m+1)(m 6 N). The connection between regulars-simplex in Rn and combinational design is given.

关键词： regular n-simplex in Rn, quadratic form.

Measures and dimensions of fractal sets in local fields

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Progress in Natural Science:Materials International 2006年第12期16卷 1260-1268页

作者： QIU Hua** and SU Weiyi(department of mathematics, nanjing university, nanjing 210093, china) [a]department of mathematics Nanjing University Nanjing China

The study of fractal analysis over the local fields as underline spaces is very important since it can motivate new approaches and new ideas, and discover new techniques in the study of fractals. To study fractal sets in a local field K, in this paper, we define several kinds of fractal measures and dimensions of subsets in K. Some typical fractal sets in K are constructed. We also give out the Hausdorff dimensions and measures, Box-counting dimensions and Packing dimensions, and stress that there exist differences between fractal analysis on local fields and Euclidean spaces. Consequently, the theoretical foundation of fractal analysis on local fields is established.

关键词： local field p-series field Hausdorff measure and dimension Boxcounting dimension Packing measure and dimension Cantor type set.