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The maximal super-singular integral operators on product spaces

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Science China mathematics 2011年第12期54卷 2615-2626页

作者： WANG Hui1 & CHEN JieCheng2.3. 1department of mathematics, Xidian {2., Xi’an 710071, China 2.0} of mathematics, zhejiang Normal {2., Jinhua 3.0}004, China 3.1} of mathematics, zhejiang {2., {13. 3.002., China 1. department of mathematics Xidian University Xi’an 710071 China2. Department of Mathematics Zhejiang Normal University Jinhua 321004 China3. Department of Mathematics Zhejiang University Hangzhou 310027 China

We study the maximal super-singular integral operator T＊Ω,α,β（f）（x,y）=sup ∈1〉0,∈2.0｜∫｜u｜〉ε1,｜v｜〉ε2.b1（｜u｜）b2.｜u｜）Ω（u＇,u＇）/｜u｜^n＋α｜u｜^m＋β-f（x-u,y-u）dudu｜defined on all f ∈ S（R^n ×R^m）, where 0 ≤ α,β〈∞, b1 b2.∈ L∞（R＋1 ）,Ω satisfies certain cancellation conditions and Ω∈L1（S^n-1×S^m-1）in the case α,β〉0;Ω∈L（log＋L）（S^n-1×S^m-1）in the case αβ=0 and α＋β 〉0. It is proved that, for 1〈p〈∞.T＊Ω,α,βis a bounded operator from the homogeneous Sobolev space Lα,β^p（R^n×R^m）to the Lebesgue space L^p（R^n×R^m）.

关键词： super-singular integral maximal operator product spaces

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, {2. 3.0058, China 2. Imaging {3. 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.

A SIMPLE FINITE ELEMENT METHOD FOR THE REISSNER-MINDLIN PLATE

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Journal of Computational mathematics 1994年第1期12卷 46-54页

作者： Cheng Xiao-liang (department of mathematics, {2. {3., {2., zhejiang, China) hangzhou UNIV DEPT MATHHANGZHOUPEOPLES R CHINA

A simple finite element method for the Reissner-Mindlin plate model in the primitive variables is presented and analyzed. The method uses conforming linear finite elements for both the transverse displacement and rotation. It is proved that the method converges with optimal order uniformly with respect to *** is simpler and more economical than the Arnold-Falk element[1].

关键词： Math A SIMPLE FINITE ELEMENT METHOD FOR THE REISSNER-MINDLIN PLATE IV

APPLICATION OF NEWTON'S AND CHEBYSHEV'S METHODS TO PARALLEL FACTORJZATION OF POLYNOMIALS

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Journal of Computational mathematics 2001年第4期19卷 347-356页

作者： Shi-ming Zheng (department of mathematics, Xixi Campus, {2. {3., hangzhou 3.002., China) 浙江大学浙江杭州 310028

In this paper it is shown m two different ways that one of the family of parallel iterations to determine all real quadratic factors of polynomials presented in [12. is Newton's method applied to the special equation (1.7) below. Furthermore, we apply Chebyshev's method to (1.7) and obtain a new parallel iteration for factorization of polynomials. Finally, some properties of the parallel iterations are discussed.

关键词： Newton's method Chebyshev's method Parallel iteration Factorization of polynomial.

A FAMILY OF HIGH-ODER PARALLEL ROOTFINDERS FOR POLYNOMIALS

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Journal of Computational mathematics 2000年第3期18卷 283-288页

作者： Shi-ming Zheng (department of mathematics, Xixi Campus,{2. {3., hangzhou, 3.002., China) 浙江大学浙江杭州 310028

Presents a family of parallel iterations for finding all zeros of a polynomial without evaluation of derivatives. Construction of iterations; Convergence of the iterations; Details on the numerical examples.

关键词： parallel iteration zeros of polynomial order of convergence

REMARKS ON h-TRANSFORM AND DRIFT

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Chinese Annals of mathematics,Series B 1998年第4期19卷 473-478页

作者： YING JIANGANG (department of mathematics, {2. {3., hangzhou 3.002., China.) zhejiang Univ Dept Math Hangzhou 310027 Peoples R China

The author studies the h-transforms of symmetric Markov processes and corresponding Dirichlet spaces, and also discusses the drift transformation of Fukushima and Takeda’s type[2. and improves their result by a diffe... 详细信息

关键词： Right processes Revuz measures h-transform

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, {2. {3., {2. 3.002., China 2.0} of mathematics, {2. {3. of Technology, {2. 3.002., China 3.1} of mathematics, Nanjing {3., 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

Strong uniqueness of best approximations in spaces of bounded linear operators

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Science China mathematics 2004年第3期47卷 339-351页

作者： LI Chong HE Jinsu department of mathematics, {2. {3. hangzhou 3.002., China department of mathematics, {2. Normal {3. Jinhua 3.2}004, China 1. department of mathematics Zhejiang University 310027 Hangzhou China 2. department of mathematics Zhejiang Normal University 321004 Jinhua China

The present paper is concerned with problems of the strong uniqueness of the best approximation and the characterization of a uniqueness element in operator *** results on the strong uniqueness of the best approximation operatorfrom RS-sets are proved and the uniqueness element of a sun in the compactoperator space from c0 to c0 is characterized by the strict Kolmogorov's *** recent results due to Lewicki and others are extended and improved.

关键词： best approximation operator, RS-set, sun, strong uniqueness, uniqueness element.

A note on certain square functions on product spaces

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Science China mathematics 2006年第1期49卷 98-108页

作者： WANG Meng, CHEN Jiecheng2.& FAN Dashan department of mathematics, {2. {3. (at Yuquan campus), hangzhou 3.002., China department of mathematics, {2. {3. (at Xixi campus), hangzhou 3.002., China department of mathematics, {3. of Wisconsin-Milwaukee, Milwaukee, WI53.0}1, USA department of mathematics Zhejiang University [at Yuquan campus] Hangzhou 310027 China department of mathematics Zhejiang University [at Xixi campus] Hangzhou 310028 China department of mathematics University of Wisconsin-Milwaukee Milwaukee WI53201 USA

We study certain square functions on product spaces Rn × Rm, whose integral kernels are obtained from kernels which are homogeneous in each factor Rn and Rm and locally in L(log+ L) away from Rn × {0} and {0} × Rm by means of polynomial distortions in the radial variable. As a model case, we obtain that the Marcinkiewicz integral operator is bounded on Lp(Rn × Rm)(P > 1) for Ω∈ e Llog+ L(Sn-1 × Sm-1) satisfying the cancellation condition.

关键词： square function, Marcinkiewicz integral, product space.