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Moment bounds for IID sequences under sublinear expectations

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Science china mathematics 2011年第10期54卷 2155-2160页

作者： HU Feng1,2.1department of mathematics,Qufu {2. University,Qufu 2.3165,china 2.chool of mathematics,Shandong University,Jinan 2.0100,china department of mathematics Qufu Normal University Qufu China School of mathematics Shandong University Jinan China

With the notion of independent identically distributed(IID) random variables under sublinear expectations introduced by Peng,we investigate moment bounds for IID sequences under sublinear expectations. We obtain a moment inequality for a sequence of IID random variables under sublinear expectations. As an application of this inequality,we get the following result:For any continuous functionsatisfying the growth condition |(x) | C(1 + |x|p) for some C > 0,p 1 depending on ,the central limit theorem under sublinear expectations obtained by Peng still holds.

关键词： moment bound sublinear expectation IID random variables G-normal distribution central limit theorem

On Non-Decomposable Hermitian Forms over Gaussian Domain

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Acta Mathematica Sinica,English Series 1998年第4期14卷 447-456页

作者： Zhu Fuzu, department of mathematics, {2. china normal University, shanghai 2.0062. china east china {2. University Department of Mathematics Shanghai China (GRID:grid.22069.3f) (ISNI:***)

Methods are presented for the construction of non-decomposable Hermitian forms over the ring of integers of an imaginary quadratic field.

关键词： Non-decomposable form Indecomposable form Odd form Even form Reduced form

Estimates for eigenvalues of Laplacian operator with any order

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Science china mathematics 2007年第8期50卷 1078-1086页

作者： Fa-en WU~(1+) Lin-fen CAO~2.1 department of mathematics,Beijing Jiaotong University,Beijing 100044,{2. 2.department of mathematics,Henan normal University,Xinxiang 453007,{2. department of mathematics Beijing Jiaotong University Beijing China department of mathematics Henan Normal University Xinxiang China

Let D be a bounded domain in an n-dimensional Euclidean space ? n . Assume that $$0 < \lambda _1 \leqslant \lambda _2.\leqslant \cdots \leqslant \lambda _k \leqslant \cdots $$ are the eigenvalues of the Dirichlet Lapl... 详细信息

Let D be a bounded domain in an n-dimensional Euclidean space ? n . Assume that $$0 < \lambda _1 \leqslant \lambda _2 \leqslant \cdots \leqslant \lambda _k \leqslant \cdots $$ are the eigenvalues of the Dirichlet Laplacian operator with any order l: $$\left\{ \begin{gathered} ( - \vartriangle )^l u = \lambda u, in D \hfill \\ u = \frac{{\partial u}}{{\partial \vec n}} = \cdots = \frac{{\partial ^{l - 1} u}}{{\partial \vec n^{l - 1} }} = 0, on \partial D \hfill \\ \end{gathered} \right.$$ . Then we obtain an upper bound of the (k+1)-th eigenvalue λ k+1 in terms of the first k eigenvalues. $$\sum\limits_{i = 1}^k {(\lambda _{(k + 1)} - \lambda _i )} \leqslant \frac{1}{n}[4l(n + 2l - 2)]^{\tfrac{1}{2}} \left\{ {\sum\limits_{i = 1}^k {(\lambda _{(k + 1)} - \lambda _i )^{\tfrac{1}{2}} \lambda _i^{\tfrac{{l - 1}}{l}} \sum\limits_{i = 1}^k {(\lambda _{(k + 1)} - \lambda _i )^{\tfrac{1}{2}} \lambda _i^{\tfrac{1}{l}} } } } \right\}^{\tfrac{1}{2}} $$ . This ineguality is independent of the domain D. Furthermore, for any l ? 3 the above inequality is better than all the known results. Our rusults are the natural generalization of inequalities corresponding to the case l = 2 considered by Qing-Ming Cheng and Hong-Cang Yang. When l = 1, our inequalities imply a weaker form of Yang inequalities. We aslo reprove an implication claimed by Cheng and Yang.

关键词： Dirichlet problem eigenvalue estimate Laplacian operator 35P15 58G2.

ON LOCAL STABILIZATION OF NONLINEAR CONTROL SYSTEMS

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Systems Science and Mathematical Sciences 1992年第4期5卷 289-298页

作者： ZHENG Yufan (department of mathematics,{2. china normal University,shanghai 2.0062.china)

Based on the notion of maximal absolute observability and its normalforms,a new method for studying the local stabilization for a kind of nonlinearcontrol systems is *** from the previous results given by Byrnes-Isitori and others,this new method can deal with more general systems,and hasmuch simpler way to prove the stabilization conditions and to design the feedbacklaws.

关键词： Nonlinear control absolute observability zero dynamics minimumphase

Preparation of Cyclodextrin-Based Carbonaceous Catalyst and Its Application in the Esterification

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Journal of Wuhan University of Technology(Materials Science) 2011年第3期26卷 455-458页

作者：单纯 department of Environmental and Chemical Engineering Shanghai University department of Automation Science Guangdong Polytechnic Normal University

A new carbonaceous catalyst with sulfonic acid group （-SO3H） was prepared by incomplete carbonization of β-cyclodextrin followed by *** sulfonated amorphous carbon was characterized by IR,elemental analysis,DSC-TGA and PXRD,and the catalytic activity was investigated to be an efficient catalyst for the esterification reactions with maximum yield of 87%.The sulfonated carbonaceous catalyst was readily separated from the reaction solution and keeps approximately equal catalytic *** results confirm that the active centre is the hydrophilic sulfonic acid functional group in the esterification reactions.

关键词： β-Cyclodextrin carbonization carbonaceous catalyst esterification activity

Strong law of large numbers for Markov chains indexed by an infinite tree with uniformly bounded degree

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Science china mathematics 2008年第2期51卷 195-202页

作者： HUANG HuiLin~1 YANG WeiGuo~(2.) 1 department of mathematics,{2. Jiaotong University,{2. 2.02.0,china 2.Faculty of Science,Jiangsu University,Zhenjiang 2.2.13,china department of mathematics Shanghai Jiaotong University Shanghai China Faculty of Science Jiangsu University Zhenjiang China

In this paper,we study the strong law of large numbers and Shannon-McMillan (S-M) theorem for Markov chains indexed by an infinite tree with uniformly bounded *** results generalize the analogous results on a homogene... 详细信息

关键词： Markov chains Shannon-McMillan theorem strong law of large numbers uniformly bounded tree 60F15 60J10

Differential Expression of Neutrophilic Granule Proteins between Th1 and Th2.Cells

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Acta Biochimica et Biophysica Sinica 2007年第1期39卷 67-72页

作者： De'e XIE~(1,2.) Zhiduo LIU~(1#) Zhenhu LI~1 Yongyong JI~1 Jiwu CHEN~2.and Bing SUN~(1*) ~1Institute of Biochemistry and Cell Biology,shanghai Institutes for Biological Sciences,shanghai 2.0031,{2. ~2.chool of Life Science,east east {2. normal University,shanghai 2.0062.{2. Institute of Biochemistry and Cell Biology Shanghai Institutes for Biological SciencesShanghai 200031 China School of Life Science East China Normal UniversityShanghai 200062 China

Thelper cell type 1 （Thl） and 2.（Th2. play central roles in immune *** identify thenovel genes differentially expressed between Th 1 and Th2.cells,CD4+T cells were isolated from DO 11.10transgenic mice and induced under Thl or Th2.*** showed differential expression ofneutrophilic granule proteins （NGP） between Thl and Th2.*** was first identified as a myeloid-specific granule protein with homology to the cystatin *** we confirmed greater expressionof NGP in Th2.cells by reverse transcription-polymerase chain reaction and real-time polymerase chainreaction *** also showed that the expression of NGP mRNA had a peak expression after 5 d cultureunder Th2. but not Thl-biasing conditions. Antibody against NGP was prepared,and in concert with theresults of mRNA analysis,the level of NGP protein in Th2.cells detected by Western blot analysis was alsohigher than that in Th1 ***-NGP fusion proteins overexpressed in HeLa cells were localized to *** results suggest NGP is a novel marker distinguishing Th2.from Th1 cells and maybe anovel cytokine secreted by Th2.cells.

关键词： neutrophilic granule protein cystatin Th2.cell

Extension of isometries on the unit sphere of l^p (Γ) space

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Science china mathematics 2010年第4期53卷 1085-1096页

作者： FANG XiNian 1,& WANG JianHua 2.1 School of mathematics and Statistics,Nanjing Audit University,Nanjing 2.002.,china {2.,Anhui normal University,Wuhu 2.1000,china School of mathematics and Statistics Nanjing Audit University Nanjing China department of mathematics Anhui Normal University Wuhu China

In this paper,we obtain that every isometry from the unit sphere S(l p (Γ)) of l p (Γ) (1 < p < ∞,p≠2. onto the unit sphere S(E) of a Banach space E can be extended to be a (real) linear isometry of l p (Γ) onto ... 详细信息

In this paper,we obtain that every isometry from the unit sphere S(l p (Γ)) of l p (Γ) (1 2. onto the unit sphere S(E) of a Banach space E can be extended to be a (real) linear isometry of l p (Γ) onto E,so,we give an affirmative answer to the corresponding Tingley’s problem.

关键词： isometric extension l p (Γ) space isometry 1-Lipschitz mapping

WHEN CAN THE STABLE ALGEBRA DETERMINE THE STRUCTURE OF A C-ALGEBRA ?

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Chinese Annals of mathematics,Series B 1994年第2期15卷 153-156页

作者： WU LIANGSEN (Institute of mathematics, east {2. University, shanghai 2.0062. china) 华东师范大学数学系上海 200062

Let A and B be C-algebras. Suppose that K is the algebra of all compact operators on a seperable Hilbert space, and α is an action on the stable algebra K A induced by SU(∞).It is proved that if A is α-invariant stable isomorphic to B, then there is a-isomorphism between A and B. An analogous result is obtained by considering On K A in the place of K A, where On is the Cuntz algebra (3≤ n < ∞).

关键词： C-algebra Stable algebra Cuntz algebra α-invariance.