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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.

(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.

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, nanjing 210093, 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 28D10

SOLVING TRUST REGION PROBLEM IN LARGE SCALEOPTIMIZATION

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Journal of Computational mathematics 2000年第1期18卷 1-12页

作者： Bing-sheng He(department of mathematics, nanjing university, Naming 210093, china) 南京大学江苏南京 210093

Presents a study which introduced a method for solving trust region problem in scale minimization. Review of the conjugate gradient method (CG) and the projection and contraction (PC) method; Convergence behavior of t... 详细信息

关键词： trust region problem conjugate gradient method projection and contraction method

THE BLOWUP OF RADIALLY SYMMETRIC SOLUTIONS FOR 2-D QUASILINEAR WAVEEQUATIONS WITH CUBIC NONLINEARITY

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Chinese Annals of mathematics,Series B 1999年第4期20卷 455-472页

作者： YIN HUICHENG ZHENG QIN(department of mathematics, nanjing university nanjing 210093, china) nanjing Univ Dept Math Nanjing 210093 Peoples R China

For a special class of quasilinear wave equations with small initial data which satisfy the nondegenerate assumption, the authors prove that the radially symmetric solution develops singularities in the second order derivatives in finite time while the first order derivatives and the solution itself remain continuous and small. More precisely, it turns out that this solution is a "geometric blowup solution of cusp type", according to the terminology posed by S. Alinhac[2].

关键词： Lifespan Geometric blowup Nash-M■ser iteration

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, nanjing 210093, china.)(department of mathematics, Xuzhou Normal university, Xuzhou 221009, china.) ZHANG KEMIN(department of mathematics, nanjing university, nanjing 210093, 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 university,nanjing 210093,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(2k 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 =... 详细信息

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 university,nanjing 210093,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