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Shape blending of artistic brushstroke represented by disk B-spline curves

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Progress in Natural Science:Materials International 2007年第12期17卷 1501-1507页

作者： Cheng Min1,2.and Wang Guojin1(1. department of mathematics, Zhejiang{2., Hangzhou 31002., China 2. department of mathematics, Zhejiang{2. of Technology, Hangzhou 310032. China) department of mathematics Zhejiang University Hangzhou 310027 China 2. department of mathematics Zhejiang University of Technology Hangzhou 310032 China

This paper presents an algorithm for automatically generating in-between frames of two artistic brushstrokes. The basic idea of the algorithm is to represent the two key frames of artistic brushstrokes in disk B-spline curves, and then make blending of their geometric intrinsic variables. Given two key frames of artistic brushstrokes, the skeleton curves can be obtained by certain skeleton-based techniques. After disk B-spline representation of the key frames is generated, interpolation of the intrinsic variables of the initial and the target disk B-spline curves is carried out. Examples show that this method can efficiently create in-between frames of artistic brushstrokes.

关键词： computer aided calligraphy shape blending brushstroke disk B-spline curve skeleton.

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Science China Chemistry 2004年第6期47卷 466-479页

作者： SONG Huajie1,2. XIAO Heming1 & DONG Haishan2.1. department of Chemistry, nanjing university of Science and Technology,{2. 2.0094, China 2. Institute of Chemical Materials, China Academy of Engineering Physics, Mianyang 62.900, China 1. department of Chemistry Nanjing University of Science and Technology 210094 Nanjing China 2. Institute of Chemical Materials China Academy of Engineering Physics 621900 Mianyang China

The symmetry-adapted perturbation theory (SAPT) that has the ability in decompo- sition of the total interaction energy into physically meaningful components is used to provide a more fundamental understanding of intermolecular forces. This work was motivated by the diffi- culty of standard SAPT in computing the intermolecular interactions for large energetic dimer systems. SAPT based on Kohn-Sham orbitals (SAPT(DFT)) proves computationally efficient for these large systems, but has been shown to perform poorly for interaction energy components. The deficiencies of SAPT(DFT) result from wrong asymptotical behaviors of commonly used exchange-correlation potentials. To remove the deficiencies, two asymptotic corrections by means of van Leeuwen and Baerends (LB) model potential and Fermi-Amaldi (FA) type potential were applied into three small test systems comprising He2. HF2.and (N2.2.and a set of larger ni- tramide dimers at several separations. The results showed that when utilizing newly developed frequency-dependent density susceptibilities (FDDS) technique for computing dispersion energy, the FA asymptotic correction is very effective to circumvent these deficiencies in SAPT(DFT) and yields a good accuracy over the LB correction. The FA corrected SAPT(DFT) approach is capa- ble of correctly predicting all the quantitative trends in binding energies for all test cases and substantially reduces computational cost as compared with the standard SAPT calculations. The successful application of the approach to nitramide dimer demonstrates that it potentially pro- vides a good means to calculate accurately intermolecular forces in larger system such as en- ergetic systems.

关键词： intermolecular interaction, density functional theory (DFT), symmetry adapted perturbation theory (SAPT), asymptotic correction, frequency-dependent density susceptibilities (FDDS).

Maschke-type theorem and Morita context over weak Hopf algebras

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Science China mathematics 2006年第5期49卷 587-598页

作者： ZHANG Liangyun College of Science, nanjing Agricultural university, nanjing 2.0095, China department of mathematics, nanjing university, nanjing 2.0008, China 1. College of Science Nanjing Agricultural University Nanjing 210095 China 2. department of mathematics Nanjing University Nanjing 210008 China

This paper gives a Maschke-type theorem over semisimple weak Hopf algebras,extends the well-known Maschke-type theorem given by Cohen and Fishman and constructs a Morita context over weak Hopf algebras.

关键词： weak Hopf algebra, smash product, Maschke-type theorem, Morita context.

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,{2., nanjing 2.0093, 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.

Characteristics of fMRI BOLD signal and its neurophysiological mechanism

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Progress in Natural Science:Materials International 2007年第6期17卷 630-638页

作者： Zhao Xiaohu1,2. Wu Yigen3 and Guo Shengli3(1. College of Life Sciences, Zhejiang university, Hangzhou 310058, China 2. Imaging department of Tongji Hospital of Tongji university, Shanghai 2.0065, China 3. College of mathematics and Physics, nanjing university of Information Science and Technology, nanjing 2.0044, China) College of Life Sciences Zhejiang University Hangzhou 310058 China Imaging department Tongji Hospital Tongji University Shanghai 200065 China College of mathematics and Physics Nanjing University of Information Science and Technology Nanjing 210044 China

The functional magnetic resonance imaging (fMRI) based on blood oxygen level dependent (BOLD) contrast has emerged as one of the most potent noninvasive tools for mapping brain function and has been widely used to explore physiological, pathological changes and mental activity in the brain. Exploring the nature and property of BOLD signal has recently attracted more attentions. Despite that great progress has been made in investigation of the characteristics and neurophysiological basis, the exact nature of BOLD signal remains unclear. In this paper we discuss the characteristics of BOLD signals, the nonlinear BOLD response to external stimuli and the relation between BOLD signals and neural electrophysiological recordings. Furthermore, we develop our new opinions regarding nonlinear BOLD response and make some perspectives on future study.

关键词： functional magnetic resonance imaging blood oxygen level dependent nonlinear response neural electrophysiological activity.

ω-Gorenstein injective modules and dimensions

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Science China mathematics 2011年第3期54卷 421-436页

作者： ZHU HaiYan1,2.& DING NanQing3 1department of mathematics, Zhejiang{2., Zhejiang 31002., China 2.0} of mathematics, Zhejiang{2. of Technology, Zhejiang 31002., China 3department of mathematics, nanjing university, nanjing 2.0093, China 1. department of mathematics Zhejiang University Zhejiang 310027 China2. Department of Mathematics Zhejiang University of Technology Zhejiang 310023 China3. Department of Mathematics Nanjing University Nanjing 210093 China

Gorenstein injective modules and dimensions have been studied extensively by many authors. In this paper, we investigate Gorenstein injective modules and dimensions relative to a Wakamatsu tilting module.

关键词： Wakamatsu tilting module ω-Gorenstein injective module ω-Gorenstein injective dimension cotilting module

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,{2., nanjing 2.0093, China.)(department of mathematics, Xuzhou Normal university, Xuzhou 2.1009, China.) ZHANG KEMIN(department of mathematics,{2., nanjing 2.0093, 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

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,{2., nanjing 2.0093, 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 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,{2. nanjing 2.0093, 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