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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 2.5002. china 2. department of Mathematics, nanjing university, nanjing 2.0093, 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.

Synthesis and Lubrication of Phosphorylcholine Derivative

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Journal of Bionic Engineering 2010年第3期7卷 254-258页

作者： Zhenliang Qiao~1, Dangsheng Xiong~1, Lude Lu~2. Pengju Jiang~2.1. department of Materials Science and Engineering, nanjing university of Science and Technology, {2. 2.0094, P.R. china 2. School of Chemical Engineering, nanjing university of Science and Technology, {2. 2.0094, P. R. china [a] department of Materials Science Engineering Nanjing University of Science Technology Nanjing 210094 P.R. China [b] School of Chemical Engineering Nanjing University of Science Technology Nanjing 210094 P. R. China

The monomer of phosphorylcholine derivative, O-(5-（2.methacryloxy）-3, 3-dimethyl-3-azapentyl)-O’-（ω-hydroxy-octyl）-phosphatequaternary ammonium salt, was designed and synthesized successfully. It was characterized by the spectra ofHNMR and Mass spectra （ESI+）, and every signal was assigned. Then the lubricating characteristics of the phosphorylcholinederivative were investigated on the tribological setup of ball-oh-flat. The Ultra-High Molecular Weight Polyethylene（UHMWPE） flat was rotated against a stainless steel ball with 6 mm diameter. The load was 2.3 N, which corresponded to amaximal Hertz contact pressure of 2. MPa. Water, phosphorylcholine derivative, and Acrylic Acid （AA） solution were used aslubricants, respectively. Compared with AA, the phosphorylcholine derivative shows significant lubrication. It can be stronglyhydrated under water due to the charged segment in chemical structure. The thick water layers within the chains serves asboundary lubricants, and this is thought to be the molecular origins of lubricating behavior.

关键词： artificial joint articular cartilage molecular lubrication mechanism phosphorylcholine synthesis UHMWPE

Study on the thermal stability and electrical properties of the high-k dielectrics (ZrO_2. _x(SiO_2._(1-x)

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Science china(Technological Sciences) 2009年第8期52卷 2222-2226页

作者： Lü ShiCheng1,2. YIN Jiang1,2. XIA YiDong2.3, GAO LiGang2.3 & LIU ZhiGuo2.3 1 department of Physics, nanjing university,{2., china 2.National Laboratory of Solid Sate Microstructures, nanjing university,{2., china 3 department of Materials Science and Engineering, nanjing university,{2., china 1. department of Physics Nanjing University Nanjing 210093 China 2. National Laboratory of Solid Sate Microstructures Nanjing University Nanjing 210093 China 3. department of Materials Science and Engineering Nanjing University Nanjing 210093 China

(ZrO2.x(SiO2.1-x (Zr-Si-O) films with different compositions were deposited on p-Si(100) substrates by using pulsed laser deposition technique. X-ray photoelectron spectra (XPS) showed that these films remained amorphous after annealing at 800℃ with RTA process in N2.for 60 s. The XPS spectra indi- cated that Zr-Si-O films with x=0.5 suffered no obvious phase separation after annealing at 800℃, and no interface layer was formed between Zr-Si-O film and Si substrate. While Zr-Si-O films with x >0.5 suffered phase separation to precipitate ZrO2.after annealing under the same condition, and SiO2.was formed at the interface. To get a good interface between Zr-Si-O films and Si substrate, Zr-Si-O films with bi-layer structure (ZrO2.0.7(SiO2.0.3/(ZrO2.0.5(SiO2.0.5/Si was deposited. The electrical properties showed that the bi-layer Zr-Si-O film is of the lowest equivalent oxide thickness and good interface with Si substrate.

关键词： high-k dielectric film pulsed laser deposition pseudo ternary alloy

Integral expressions of Lyapunov exponents for autonomous ordinary differential systems

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Science china Mathematics 2009年第1期52卷 195-216页

作者： DAI XiongPing department of Mathematics, nanjing university,{2., china 1. department of Mathematics Nanjing University Nanjing 210093 China

In the paper, the author addresses the Lyapunov characteristic spectrum of an ergodic autonomous ordinary differential system on a complete riemannian manifold of finite dimension such as the d-dimensional euclidean space ? d , not necessarily compact, by Liaowise spectral theorems that give integral expressions of Lyapunov exponents. In the context of smooth linear skew-product flows with Polish driving systems, the results are still valid. This paper seems to be an interesting contribution to the stability theory of ordinary differential systems with non-compact phase spaces.

关键词： Lyapunov spectrum of differential system multiplicative ergodic theorem C 1-vector field smooth linear skew-product flow lifting of probability 34D08 37C10 60B05 37H15 2.D10

THE SECOND EXPONENT SET OF PRIMITIVE DIGRAPHS

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Chinese Annals of Mathematics,Series B 2000年第2期21卷 233-236页

作者： MIAO ZHENGKE(department of Mathematics, nanjing university,{2., china.)(department of Mathematics, Xuzhou Normal university, Xuzhou 2.1009, china.) ZHANG KEMIN(department of Mathematics, nanjing university,{2., china.) department of Mathematics Nanjing University Nanjing 210093 China department of Mathematics Xuzhou Normal University Xuzhou 221009 China

Let D = (V, E) be a primitive digraph. The exponent of D, denoted byγ(D), is the least integer k such that for any u, v∈ V there is a directed walk of length k from u to v. The local exponent of D at a vertex u∈ V, denoted by exp_D (u), is the least integer k such that there is a directed walk of length k from u to v for each v ε V. Let V = {1,2.….,n}. Following [1], the vertices of V are ordered so that exp_D (1) ≤exp_D (2. ≤…≤exp_D(n) =λ(D). Let E_n(i):= {exp_D (i) ∈D PD_n}, where PD_n is the set of all primitive digraphs of order n. It is known that E_n(n) = {γ(D) D∈PD_n} has been completely settled by [7]. In 1998, E_n(1) was characterized by [5]. In this paper, the authors describe E_n(2. for all n≥2.

关键词： Primitive digraph Local exponent Gap

Binomial coefficients,Catalan numbers and Lucas quotients

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Science china Mathematics 2010年第9期53卷 2473-2488页

作者： SUN ZhiWei department of Mathematics,nanjing {2.,nanjing 2.0093,china 1. department of Mathematics Nanjing University Nanjing 210093 China

Let p be an odd prime and let a,m ∈ Z with a > 0 and p ︱ *** this paper we determinep ∑k=0 pa-1(2. k=d)/mk mod p2.for d=0,1;for example,where(-) is the Jacobi symbol and {un}n≥0 is the Lucas sequence given by u0 = 0,u1 = 1 and un+1 =(m-2.un-un-1(n = 1,2.3,...).As an application,we determine ∑02.for any integer r,where Ck denotes the Catalan number 2.k /(k + 1).We also pose some related conjectures.

关键词： congruences binomial coefficients Catalan numbers Lucas quotients

On contactomorphism group of contact structure overtwisted at infinity on R^3

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Science china Mathematics 2007年第8期50卷 1087-1092页

作者： Li YU department of Mathematics,nanjing {2.,nanjing 2.0093,china department of Mathematics Nanjing University Nanjing 210093 China

We compute all the homotopy groups of the compactly supported contactomorphism group of a contact structure on R^3 which is overtwisted at infinity.

关键词： contactomorphism overtwisted contact structure

A NEW CLASS OF UNIFORMLY SECOND ORDERACCURATE DIFFRENCE SCHEMES FOR 2. SCALAR CONSERVATION LAWS

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Journal of Computational Mathematics 1997年第4期15卷 311-318页

作者： Juan Cheng(department of Aerodynamics, nanjing university of Aeronautics & Astronautics,{2., china)Jia-zun Dai (department of Mathematics, Physics and Mechanics, nanjing university of Aeronautics & Astronautics, {2., china) 南京航空航天大学空气动力学系江苏南京南京航空航天大学数学系江苏南京

In this paper, concerned with the Cauchy problem for 2. nonlinear hyperbolic conservation laws,we construct a class of uniformly second order accurate finite difference schemes, which are based on the E-schemes. By applying the conver gence theorem of Coquel-Le Floch [1], the family of approximate solutions defined by the scheme is proven to converge to the unique entropy weak L∞-solution. Furthermore, some numerical experiments on the Cauchy problem for the advection equation and the Riemann problem for the 2. Burgers equation are given and the relatively satisfied result is obtained.

关键词： Math A NEW CLASS OF UNIFORMLY SECOND ORDERACCURATE DIFFRENCE SCHEMES FOR 2. SCALAR CONSERVATION LAWS high Ph

Wavelet estimation of the diffusion coefficient in time dependent diffusion models

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Science china Mathematics 2007年第11期50卷 1597-1610页

作者： Ping CHEN~(1,2.) Jin-de WANG~1 1 department of Mathematics,nanjing {2.,nanjing 2.0093,china 2.School of Science,nanjing {2. of Science and Technology,nanjing 2.0094,china department of Mathematics Nanjing University Nanjing 210093 China School of Science Nanjing University of Science Technology Nanjing 210094 China

The estimation problem for diffusion coefficients in diffusion processes has been studied in many papers,where the diffusion coefficient function is assumed to be a 1-dimensional bounded Lipschitzian function of the state or the time *** is no previous work for the nonparametric estimation of time-dependent diffusion models where the diffusion coefficient depends on both the state and the *** paper introduces and studies a wavelet estimation of the time-dependent diffusion coefficient under a more general assumption that the diffusion coefficient is a linear growth Lipschitz *** the properties of martingale,we translate the problems in diffusion into the nonparametric regression setting and give the Lr convergence rate.A strong consistency of the estimate is *** this result one can estimate the time-dependent diffusion coefficient using the same structure of the wavelet estimators under any equivalent probability *** example,in finance,the wavelet estimator is strongly consistent under the market probability measure as well as the risk neutral probability measure.

关键词： wavelet estimation time-dependent diffusion coefficient linear growth condition strong consistency