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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) department of Mathematics Nanjing University Nanjing 210093 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.

Polymer-assisted nanoparticulate contrast-enhancing materials

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science china Chemistry 2010年第3期53卷 479-486页

作者： DING Yin1,3.HU Yong2,WU Wei1 & JIANG XiQun1 1Laboratory of Mesoscopic Chemistry and department of Polymer science and Engineering,College of Chemistry & Chemical Engineering,nanjing {3.,nanjing 210093.china 2National Laboratory of Solid State Microstructure,department of Material science and Engineering,nanjing {3.,nanjing 210093.china 3.ey Laboratory of Analytical Chemistry for Life science,Ministry of Education,School of Chemistry and Chemical Engineering,nanjing {3.,nanjing 210093.china Laboratory of Mesoscopic Chemistry and department of Polymer science and Engineering College of Chemistry & Chemical Engineering Nanjing University Nanjing China Key Laboratory of Analytical Chemistry for Life science Ministry of Education School of Chemistry and Chemical Engineering Nanjing University Nanjing China National Laboratory of Solid State Microstructure Department of Material Science and Engineering Nanjing University Nanjing China

The application of nanotechnology in medicine research has significant potential in modern biomedical research,disease diagnosis and *** fluorophore-based detection techniques have been widely used as imaging and signal transduction tools for the detection of trace levels of *** photosensitivity of the fluorophores,however,limits their application in such complex environments as living bio-systems where degradation or photobleaching *** nanoparticles have unique and stable optical,electrical,magnetic and catalytic properties because of their various shapes,sizes and *** potential of the nanoparticles as novel imaging agents has been studied as a possible solution to this *** modification of inorganic nanoparticles could enhance their biostability in physiological conditions and ability of targeting bioactive molecules.

关键词： contrast agent cell image gold nanoparticles iron oxide nanoparticles carbon nanotubes polymeric-inorganic hybrid nanoparticles

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 3.0058, china 2. Imaging {3. of Tongji Hospital of Tongji university, Shanghai 200065, china 3. College of Mathematics and Physics, nanjing university of Information science and Technology, nanjing 210044, 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.

One-step estimation for varying coefficient models

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science china Mathematics 2005年第2期48卷 198-213页

作者： TANG Qingguo & WANG Jinde department of Mathematics, nanjing university, nanjing 210093. china Institute of {3.s, PLA university of {3. and Technology, nanjing 210007, china department of Mathematics Nanjing University Nanjing China Institute of sciences PLA University of Science and Technology Nanjing China

A one-step method is proposed to estimate the unknown functions in the varying coefficient models, in which the unknown functions admit different degrees of smoothness. In this method polynomials of different orders are used to approximate unknown functions with different degrees of smoothness. As only one minimization operation is employed, the required computation burden is much less than that required by the existing two-step estimation method. It is shown that the one-step estimators also achieve the optimal convergence rate. Moreover this property is obtained under conditions milder than that imposed in the two-step estimation method. More importantly, as only one minimization operation is employed, the full asymptotic properties, not only the asymptotic bias and variance, but also the asymptotic distributions of the estimators can be derived. The asymptotic distribution results will play a key role for making statistical inference.

关键词： varying coefficient model, one-step estimation, asymptotic distribution, optimal convergence rate.

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 department of Mathematics Nanjing University Nanjing 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) department of Mathematics Nanjing University Nanjing 210093 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

Adsorption of surfactants onto acrylic ester resins with different pore size distribution

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science china Chemistry 2006年第5期49卷 445-453页

作者： YANG Weiben1,2,3.LI Aimin1,3.CAI Jianguo1,3.MENG Guanhua1,3.& ZHANG Quanxing1,3.1. State Key Laboratory of Pollution Control and Resource Reuse,School of the Environment,nanjing university,nanjing {3.china 2. nanjing College of Chemical Technology,nanjing 210048,china 3. Jiangsu Engineering & Technology Research Center for Organic Toxicant Control and Resource Reuse,nanjing 21003.,china State Key Laboratory of Pollution Control and Resource Reuse School of the Environment Nanjing University Nanjing China nanjing College of Chemical Technology Nanjing China Jiangsu Engineering & Technology Research Center for Organic Toxicant Control and Resource Reuse Nanjing China

In this study, a series of acrylic ester resins with different pore size distribution were prepared successfully by varying the type and the amount of pore-forming agents. In order to inves-tigate the adsorption behavior and mechanism of surfactants on acrylic ester resins, three kinds of surfactants were utilized as adsorbates that were sodium 6-dodecyl benzenesulfonate (6-NaDBS), sodium 1-dodecyl benzene sulfonate (1-NaDBS) and sodium 1-dodecyl sulfonate, respectively. It was observed that the surface area was available in a particular pore size and an appropriate pore size of resins appeared to be more important for the adsorption of surfactants. As compared to commercial acrylic ester resins XAD-7 and HP2MG, 50# and 3.# resins exhibited more excellent adsorption properties toward 1-NaDBS and 6-NaDBS. The experimental equilibrium data were fitted to the Langmuir, and double-Langmuir models. Two models provided very good fittings for all resins over the temperature range studied. The investigation indicated that electrostatic attraction and hydrogen bond between resins and surfactants were the main forces and had an obvious effect on adsorption proc-ess.

关键词： acrylic ester resin, surfactant, adsorption, pore size distribution, isotherm.

Cross-linked Polyethylenimine as Potential DNA Vector for Gene Delivery with High Efficiency and Low Cytotoxicity

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Acta Biochimica et Biophysica Sinica 2006年第11期38卷 780-787页

作者： Wei DONG~(1,2) Guang-Hui JIN~1 Shu-Feng LI~(1,3. Qi-Ming SUN~1 Ding-Yuan MA~1 Zi-Chun HUA~1 1 State Key Laboratory of Pharmaceutical Biotechnology,College of Life science,nanjing university,nanjing 210093.china 2 School of Chemical Engineering nanjing university of science and Technology,nanjing 210094,china 3.College of Basic Medical science,Southeast university,nanjing 210009,china State Key Laboratory of Pharmaceutical Biotechnology College of Life Science Nanjing UniversityNanjing 210093 China School of Chemical Engineering Nanjing University of Science and TechnologyNanjing 210094 China College of Basic Medical science Southeast UniversityNanjing 210009 China

Polyethylenimine (PEI) has been known as an efficient gene carrier with the highest cationiccharge *** transfection efficiency of PEI,along with its cytotoxicity,strongly depends on itsmolecular *** enhance its gene delivery efficiency and minimize cytotoxicity,we have synthesizedsmall cross-linked PEI with biodegradable linkages and evaluated their transfection efficiencies in *** study,branched PEI with a molecular weight of 800 Da was cross-linked by small diacrylate[1,4-butanediol diacrylate or ethyleneglycol dimethacrylate (EGDMA)] for 2-6 *** efficiencies of thecross-linked PEI in in vitro transfection of plasmid DNA containing enhanced green fluorescent protein(EGFP) reporter gene were assessed in melanoma B 16F10 cell line and other cell *** cytometrywas used to quantify the cellular entry efficiency of plasmid and the transgene expression *** of the cross-linked PEI in these cells were evaluated by MTT ***-PEI 800-4h,atypical cross-linked PEI reported here,mediated a more efficient expression of reporter gene than thecommercially available 25-kDa branched PEI control,and resulted in a 9-fold increase in gene deliveryin B16F10 cells and a 16-fold increase in 293. cells,while no cytotoxicity was found at the optimizedcondition for gene ***,the transfection activity of polyplexes was preserved in thepresence of serum proteins.

关键词： polyethylenimine gene delivery cytotoxicity B16F10 293. cell line