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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 3.D08 3.C10 60B05 3.H15 28D10

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

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. {3.) 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

Magnetic fabrics in fault-related fold and its relation with finite strain: an example from Mingjiang thrust structures in Western sichuan

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Progress in Natural science:Materials International 2007年第5期17卷 551-558页

作者： Jia Dong, Chen Zhuxin, Luo Liang, Hu Qianwei and Jia Qiupeng (department of earth sciences, nanjing university,{3.) [a]department of earth sciences Nanjing University Nanjing China

The anisotropy of magnetic susceptibility (AMs) is a quick, effective and sensitive technique used to measure the weakly deformed sedimentary rocks, and also a reliable method to reveal the deforming mechanisms of fault-related folds. In Longmenshan front belt, a typical cross-section of fault-related folds is chosen to study the AMs. A total of 224 oriented specimens have been drilled at 23.different sampling sites which were distributed at the key structural positions of this structural section developed in the Xujiahe formation of the upper Triassic. six elementary types of magnetic fabrics are recognized and established through this AMs study: Da sedimentary fabric; 2) an initial deformation fabric; 3. a pencil structure fabric; 4) a weak cleavage fabric; 5) a strong cleavage fabric; 6) a stretching lineation fabric. It has been found that most of magnetic fabrics are characterized by fabrics of weak deformation which belong to the pure-shear results of a pre-folding layer parallel shortening (LPs). In the fault-bend fold, almost all magnetic fabrics are the initial deformation fabrics of weak deformation, and denote that the deformation in the forelimb is stronger than that in the backlimb and no finite strain is shown in the footwall. While in the fault-propagation fold, finite strains are concentrated in the trishear zone where magnetic fabric results are approximately consistent with the estimated consequences of the kinematic model. The tectonic stress field indicated by the magnetic fabrics is basically the same along the whole structural section and shows a NW to sE compression and shortening which is accordant with the regional compressive stress field of the Longmenshan fold-thrust belt.

关键词： magnetic fabric finite strain fault-related fold trishear zone Longmenshan.

IMPEDANCE CHARACTERIsTICs OF POLYFURAN FILMs

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Chinese Journal of Polymer science 2002年第5期20卷 419-423页

作者： Liang Li Xiao-bo Wan Gi Xue department of Polymer the state Key Laboratory of Coordination Chemistry nanjing university nanjing 210093. china nanjing Univ Dept Polymer State Key Lab Coordinat Chem Nanjing 210093 Peoples R China

Electrochemical impedance spectroscopy (EIs) was first used for the characterization of polyfuran (PFu) films that had been formed electrochemically on an Au electrode. The polyfuran was measured in high oxidation state, intermediate oxidation state and reduction state, respectively. As the oxidation level is increased, the ionic conductivity of PFu/BF4- increases. And impedance studies on PFu show that the anion BF4- appears to be mobile with a high diffusion coefficient of approximately 10(-8) cm(2).s(-1).

关键词： polyfuran electrochemical impedance spectroscopy capacitance

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 = 0,u1 = 1 and un+1 =(m-2)un-un-1(n = 1,2,3....).As an application,we determine ∑0s the Catalan number 2kk /(k + 1).We also pose some related conjectures.

关键词： congruences binomial coefficients Catalan numbers Lucas quotients

On critical values concerning the evolution of the long period families

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Chinese Journal of Astronomy and Astrophysics 2009年第4期9卷 494-500页

作者： Xi-Yun Hou1,21 Astronomy department, nanjing university, nanjing 210093. china 2 Institute of space Environment and Astronautics, nanjing university, nanjing 210093. china Astronomy department Nanjing University Nanjing 210093 China Institute of space Environment and Astronautics Nanjing University Nanjing 210093 China

In a previous paper, we proposed another special critical value concerning the evolution of the long period family around the equilateral equilibrium points, besides the two values given by Henrard. Are there any other special critical values？ After studying the stability curves of the long period family carefully, we gave a negative answer. During the study, we found an interesting family of periodic orbits which we called the homo family. We studied the evolution of this family following the increase of μ. With these findings, we were able to explain the origin of the four branches of periodic families emanating from L4 and the stability results of the equilateral equilibrium points.

关键词： celestial mechanics

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