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Summability of Fourier-Laplace Series with the Method of Lacunary Arithmetical Means at Lebesgue Points

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Acta Mathematica Sinica,English Series 2001年第3期17卷 489-496页

作者： Feng DAI Kun Yang wang department of {2..beijing normal university.beijing 100875,P.R.china E-mail:wangky@bnu,*** ***

Let ∑n-1 be the unit sphere in the n-dimensional Euclidean space Rn.For a function f ∈L(∑n-1) denote by σNδ（f） the Cesàro means of order δ of the Fourier-Laplace series of *** special value λ∶=（n-2./2.of δ is known as the critical *** the case when n is even,this paper proves the existence of the‘rare’sequence {nk} such that the summability 1/N sum from k=1 to N σnkλ（f）（x）→f（x）,N→∞ takes place at each Lebesgue point satisfying some antipole conditions.

关键词： Convergence Fourier-Laplace series Spherical harmonics Lebesgue point

A secure multi-party computation solution to intersection problems of sets and rectangles

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Progress in Natural Science:Materials International 2006年第5期16卷 538-545页

作者： LI Shundong, DAI Yiqi, wang Daoshun and LUO Ping (department of Computer Science and Technology,{2., beijing 100875, china department of Computer Science and Technology, Tsinghua university, beijing 100084, china) [a]department of computer Science and Technology Beijing Normal University Beijing China [b]department of Computer Science and Technology Tsinghua University Beijing China

Secure multi-party computation (SMC) is a research focus in international cryptographic community. At present, there is no SMC solution to the intersection problem of sets. In this paper, we first propose a SMC solution to this problem. Applying Cantor encoding method to computational geometry problems, and based on the solution to set-intersection problem, we further propose solutions to points inclusion problem and intersection problem of rectangles and further prove their privacy-preserving property with widely accepted simulation paradigm. Compared with the known solutions, these new solutions are of less computational complexity and less communication complexity, and have obvious superiority in computational and communication complexity.

关键词： Cantor encoding secure multi-party computation set-intersection rectangle-intersection computational complexity.

FLOATING QUANTIZATION EFFECTS ON MULTIRATE SAMPLED-DATA NONLINEAR CONTROL SYSTEMS

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Acta Mathematica Scientia 2007年第3期27卷 635-644页

作者：余宏旺汪志鸣 department of mathematics East China Normal University

In this article, floating quantization effects on multirate sampled-data control systems are studied. It shows that the solutions of multirate digital feedback control systems with nonlinear plant and with floating quantization in the controller are uniformly ultimately bounded if the associated linear systems consisting of linearization of the plant and controller with no quantization are Schur stable. Moreover, it also shows that the difference between the response of multirate digital controllers without quantizers and the same plant with floating quantization in the controllers can be made as small as desired by selecting proper quantization level.

关键词： Multirate sampled-data control systems quantization Schur stable uniformly ultimately bounded

Homotopy type of smooth weighted complete intersections

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Science china mathematics 2010年第6期53卷 1583-1594页

作者： wang JianBo1,& wang YuYu2.1{2. of mathematics,Tianjin university,Tianjin 300072.china 2.ollege of Mathematical Science,Tianjin normal university,Tianjin 300387,china 1. department of mathematics Tianjin University Tianjin 300072 China2. College of Mathematical Science Tianjin Normal University Tianjin 300387 China

If the total degree d has no prime divisors less than(n+3)/2.then we prove that the homotopy type of complex odd dimensional smooth weighted complete intersection Xn(d;w) is determined by the dimension n,the total degree d,the Euler characteristic and the Kervaire invariant,provided that the weights w =(ω0,...,ωn+r) is pairwise relatively prime.

关键词： weighted projective space weighted complete intersection homotopy type connected sum

Bloch constant of holomorphic mappings on the unit polydisk of C^n

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Science china mathematics 2008年第4期51卷 652-659页

作者： wang JianFei~(1+) LIU TaiShun~2.1 College of mathematics and Physics Information Engineering Zhejiang {2. university Jinhua 32.004,china 2.department of mathematics Huzhou Teachers College Huzhou 313000 china College of mathematics and Physics Information Engineering Zhejiang Normal University Jinhua China department of mathematics Huzhou Teachers College Huzhou China

In this paper,we give a definition of Bloch mappings defined in the unit polydisk D^n, which generalizes the concept of Bloch functions defined in the unit disk *** is known that Bloch theorem fails unless we have some restrictive assumption on holomorphic mappings in several complex *** shall establish the corresponding distortion theorems for subfamiliesβ(K)andβ_(loc)(K) of Bloch mappings defined in the polydisk D^n,which extend the distortion theorems of Liu and Minda to higher *** an application,we obtain lower and upper bounds of Bloch constants for various subfamilies of Bloeh mappings defined in D^*** particular,our results reduce to the classical results of Ahlfors and Landau when n=1.

关键词： Bloch constant Bloch mapping univalent ball critical point Julia lemma locally biholomorphic mapping Landau constant

JACOBI SPECTRAL METHODS FOR MULTIPLE- DIMENSIONAL SINGULAR DIFFERENTIAL EQUATIONS

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Journal of Computational mathematics 2003年第3期21卷 325-338页

作者： Li-Han wang Ben-yu Guo (department of {2., Shanghai normal university, Shanghai 2.02.4, china) department of mathematics Shanghai Normal University 上海 200234

Jacobi polynomial approximations in multiple dimensions are investigated. They are applied to numerical solutions of singular differential equations. The convergence analysis and numerical results show their advantages.

关键词： Jacobi approximations Multiple dimensions.

Weighted estimation of single index models with right censored responses

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Science china mathematics 2011年第3期54卷 479-514页

作者： wang YanHua1, LI XiaYan2. wang QiHua3 & HE ShuYuan4 1School of Sciences, {2. Institute of Technology, {2. 100081, china 2.5} of mathematics, university of Science and Technology of china, Hefei 2.002., china 3Chinese Academy of mathematics and System Science, {2. 100080, china 4School of Mathematical Sciences, Capital normal university, {2. 100048, china 1. School of Sciences Beijing Institute of Technology Beijing 100081 China2. Department of Mathematics University of Science and Technology of China Hefei 230026 China3. Chinese Academy of Mathematics and System Science Beijing 100080 China4. School of Mathematical Sciences Capital Normal University Beijing 100048 China

In this paper, the unknown link function, the direction parameter, and the heteroscedastic variance in single index models are estimated by the random weight method under the random censorship, respectively. The central limit theory and the convergence rate of the law of the iterated logarithm for the estimator of the direction parameter are derived, respectively. The optimal convergence rates for the estimators of the link function and the heteroscedastic variance are obtained. Simulation results support the theoretical results of the paper.

关键词： single index models random censorship central limit theorem law of the iterated logarithm weighted least squares unknown link function

Effects of PKCa antisense RNA on human breast cancer cell proliferation and expression of cyclinD1 and CDK4

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Chinese Science Bulletin 1999年第12期44卷 1110-1114页

作者： SANG Jianli wang YongchaoLaboratory of Cell Biology , department of Biology,{2., beijing 100875 , china Laboratory of Cell Biology Department of Biology Beijing Normal University Beijing China

The role of PKCα in human breast cancer cell proliferation and expression of cyclinD1 and CDK4 has been investigated using inhibition of PKCα expression by its antisense RNA. When PKCα expression was inhibited the rate of cell proliferation decreased apparently and the levels of cyclinD1 and CDK4 mRNA were lower than the control. The results showed that PKCα, a key member of signal transduction system, played an important role in human breast cancer cell proliferation and had a close relationship with expression of cyclinD1 and CDK4 which control start of cell cycle.

关键词： breast cancer PKCα cell proliferation cyclinD1 CDK4.

Recent progress on the structure of Ser/Thr protein phosphatases

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Science china(Life Sciences) 2008年第6期51卷 487-494页

作者： wang BaiJing1,2. ZHANG Peng1 & WEI Qun1 1 department of Biochemistry and Molecular Biology,{2., beijing Key Laboratory, beijing 100875, china 2.School of Life Science, Changchun normal university, Changchun 130032. china 1. department of Biochemistry and Molecular Biology Beijing Normal University Beijing Key Laboratory Beijing 100875 China 2. School of Life Science Changchun Normal University Changchun 130032 China

PP1, PP2. and PP2., belonging to the PPP family of Ser/Thr protein phosphatases, participate in regulating many important physiological processes, such as cell cycle control, regulation of cell growth and division regulation, etc. The sequence homology between them is relatively high, and ter- tiary structure is conserved. Because of the complexity of the structure of PP2. and the diversity of its regulatory subunits, its structure is less well known than those of PP1 and PP2.. The PP2. holoen- zyme consists of a heterodimeric core enzyme, comprising a scaffolding subunit and a catalytic sub- unit, as well as a variable regulatory subunit. In this study, the subunit compositions, similarities and differences between the Ser/Thr protein phsphatases structures are summarized.

关键词： Ser/Thr phosphatases subunit composition similarities and differences crystal structure