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Characterizations of α-Bloch functions on the unit ball without use of derivative

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Science china mathematics 2008年第11期51卷 1965-1981页

作者： chen huaihui School of mathematics and Computer Science, nanjing normal university, nanjing 210097, china 1. School of mathematics and Computer Science Nanjing Normal University Nanjing 210097 China

In this paper we establish characterizations of α-Bloch functions on the unit ball without use of derivative, which are stronger, more precise and general than those obtained by Nowak and Zhao.

关键词： α-Bloch function unit ball Bergman metric 32A18 32A37

The pointwise dimension of self-similar measures

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Chinese Science Bulletin 1999年第23期44卷 2136-2140页

作者： chen Ercai and XIONG Jincheng department of mathematics , nanjing normal university , nanjing 210097, china department of mathematics , South china normal university, Guangzhou 510631 , china department of mathematics Nanjing Normal University Nanjing China department of mathematics South China Normal University Guangzhou China

The problem about the existence of pointwise dimension of self-similar measure has been discussed. The Hausdorff dimension of the set of those points for which the pointwise dimension does not exist equals the dimenti... 详细信息

关键词： self-similar measure point wise dimension Hausdorff dimension multifractal symbolic space.

Uniquely ergodic property of minimal probability measure in positive definite Lagrangian systems

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Science china mathematics 2006年第12期49卷 1864-1866页

作者： chen Jing & BAI Yuzhen department of mathematics, nanjing university, nanjing 210093, china department of mathematics, Qufu normal university, Qufu 273165, china 1. department of mathematics Nanjing University Nanjing 210093 China 2. department of mathematics Qufu Normal University Qufu 273165 China

Mane conjectured that every minimal measure in the generic Lagrangian systems is uniquely ergodic. In this paper, we will show that the answer to the Mane's conjecture is negative by analyzing the structure of the sup... 详细信息

关键词： minimal probability measure,uniquely ergodic,Mather theory,Lagrangian systems.

On the variational principle for the topological pressure for certain non-compact sets

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Science china mathematics 2010年第4期53卷 1117-1128页

作者： PEI Yu 1 & chen ErCai 1,2,1 department of mathematics,nanjing normal university,nanjing 210097,china 2 Center for Nonlinear Science,nanjing university,nanjing 210093,china 1. department of mathematics Nanjing Normal University Nanjing 210097 China2. Center for Nonlinear Science Nanjing University Nanjing 210093 China

Let (X,d,T) be a dynamical system,where (X,d) is a compact metric space and T:X → X is a continuous *** assume that the dynamical system satisfies g-almost product property and the uniform separation *** compute the topological pressure of saturated sets under these two *** the uniform separation property does not hold,we compute the topological pressure of the set of generic *** give an application of these results to multifractal analysis and finally get a conditional variational principle.

关键词： uniform separation property g-almost product property topological pressure of non-compact sets variational principle BS-dinmension

Algebraic Independence of Certain Numbers

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Acta Mathematica Sinica,English Series 1999年第4期15卷 507-514页

作者： Yonggao chen department of mathematics,nanjing normal university,nanjing 210097,P.R.chinaYaochen Zhu Institute of Applied mathematics,Academia Sinica,Beijing 100080,P.R.china department of mathematics Nanjing Normal University Nanjing P. R. China Institute of Applied mathematics Academia Sinica Beijing P. R. China

In this note the algebraic independence of values of general Mahler series with different parameters at algebraic points is established.

关键词： Algebraic independence General Mahler series Continued fraction

Studies on the Electrochemistry of Dopamine at a Pyrocatechol Sulfonephthalein Modified Glassy Carbon Electrode

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Chemical Research in Chinese Universities 2000年第1期16卷 42-48页

作者： CAI chen-xin and XUE Kuan-hong (department of Chemistry, nanjing normal university, nanjing 210097, P. R. china) nanjing normal Univ Dept Chem Nanjing 210097 Peoples R China

The electrochemical response of dopamine(DA) at a pyrocatechol sulfonephthalein modified glassy carbon(PS/GC) electrode is reported. The electrode can be used as a detector for the determination of dopamine with a high stability and a good sensitivity. The cyclic voltammetric results indicated that there was a couple of well-defined redox peaks for dopamine at the PS/GC electrode with E_(pa)= 220 mV, E_(pc)=95 mV and the formal potential E^(o')= 157. 5 mV(vs. SCE) at 100 mV/s in the buffer solution of pH 7. 0. The PS/GC electrode can also be used to separate the electrochemical responses of ascorbic acid and DA by 54 mV with the differential pulse voltammetry. Under the selected conditions, the oxidation peak currents are linear with DA concetration in the range of 5. 0 × 10^(-6) to 5. 0 × 10^(-4) mol/L, and the detection limit is 1. 0 ×10^(-6) mol/L at S/N=3. normalized with concentration, the relative sensitivity of dopamine to ascorbic acid reaches ca. 30. 8: 1.

关键词： Chemically modified electrode Neurotransmitter Dopamine Ascorbic acid Pyrocatechol sulfonephthalein

On a Function Related to Multinomial Coefficients (Ⅰ)

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Acta Mathematica Sinica,English Series 2002年第4期18卷 647-660页

作者： Yong Gao chen Chun Gang JI department of mathematics. nanjing normal university. nanjing 210097, P. R. china department of mathematics. nanjing normal university. nanjing 210097, P. R. china Institute of mathematics. Academy of mathematics and System Sciences. Chinese Academy of Sciences. Beijing 100080. P. R. china department of mathematics Nanjing Normal University Nanjing 210097 P. R. China Institute of mathematics Academy of Mathematics and System Sciences Chinese Academy of Sciences Beijing 100080 P. R. China

Let F_(p.t)(n) denote the number of the coefficients of (x_1+x_2+…+x_t)~j. 0≤j≤n-1, which are not divisible by the prime p. Define G_(p.t)(n)=F_(p.t)(n)/n~θ and β(p.t)=lim inf F_(p.t)(n)/n~θ, where θ=(log(p+t-1 t))/(logp). In this paper, we mainly prove that G_(p.t) can be extended to a continuous function on R^+, and the function G_(p.t) is nowhere monotonic. Both the set of differential points of the function G_(p.t) and the set of non-differential points of the function G_(p.t) are dense in R^+.

关键词： Prime numbers Multinomial coefficients Function

The high order Schwarz-Pick lemma on complex Hilbert balls

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Science china mathematics 2010年第10期53卷 2649-2656页

作者： DAI ShaoYu1,2,chen huaihui1 & PAN YiFei3,4 1department of mathematics,nanjing normal university,nanjing 210097,china 2department of General Study Program,Jinling Institute of Technology,nanjing 211169,china 3School of mathematics and Informatics,Jiangxi normal university,Nanchang 330022,china 4department of Mathematical Sciences,Indiana university-Purdue university Fort Wayne,Fort Wayne,IN 46805-1499,USA 1. department of mathematics Nanjing Normal University Nanjing 210097 China2. Department of General Study Program Jinling Institute of Technology Nanjing 211169 China3. School of Mathematics and Informatics Jiangxi Normal University Nanchang 330022 China4. Department of Mathematical Sciences Indiana University-Purdue University Fort Wayne Fort Wayne IN 46805-1499 USA

In this paper we prove a high order Schwarz-Pick lemma for holomorphic mappings between unit balls in complex Hilbert *** addition,a Schwarz-Pick estimate for high order Fréchet derivatives of a holomorphic function ... 详细信息

关键词： complex Hilbert ball high order Schwarz-Pick lemma

A relative local variational principle for topological pressure

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Science china mathematics 2010年第6期53卷 1491-1506页

作者： MA XianFeng1,chen ErCai2,3,& ZHANG AiHua2,4 1department of mathematics,East china university of Science and Technology,Shanghai 200237,china 2School of mathematics and Computer Science,nanjing normal university,nanjing 210097,china 3Center of Nonlinear Science,nanjing university,nanjing 210093,china 4College of mathematics and Physics,nanjing university of Posts and Telecommunications,nanjing 210046,china 1. department of mathematics East China University of Science and Technology Shanghai 200237 China2. School of Mathematics and Computer Science Nanjing Normal University Nanjing 210097 China3. Center of Nonlinear Science Nanjing University Nanjing 210093 China4. College of Mathematics and Physics Nanjing University of Posts and Telecommunications Nanjing 210046 China

We define the relative local topological pressure for any given factor map and open cover,and prove the relative local variational principle of this *** precisely,for a given factor map π:(X,T)→(Y,S) between two topological dynamical systems,an open cover U of X,a continuous,real-valued function f on X and an S-invariant measure ν on Y,we show that the corresponding relative local pressure P(T,f,U,y) satisfies sup μ∈M(X,T){ hμ(T,U|Y)+∫X f(x)dμ(x) :πμ=ν}=∫Y P(T,f,U,y)dν(y),where M(X,T) denotes the family of all T-invariant measures on ***,the supremum can be attained by a T-invariant measure.

关键词： pressure conditional entropy relative local variational principle