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Boundedness of a class of super singular integral operators and the associated commutators

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Science china mathematics 2004年第6期47卷 842-853页

作者： CHEN Qionglei & ZHANG Zhifei department of mathematics, Zhejiang university, Hangzhou 3.0028,{3. academy of mathematics and system sciences, Chinese academy of sciences, Beijing 100080,{3. 1. department of mathematics Zhejiang University 310028 Hangzhou China 2. academy of mathematics and system sciences Chinese Academy of Sciences 100080 Beijing China

In this paper we give the (L p α, L p ) boundedness of the maximal operator of a class of super singular integrals defined by $$T_{\Omega ,\alpha }^* f(x) = \mathop {\sup }\limits_{\varepsilon > 0} \left| {\int_{|x - y| > \varepsilon } {b(|y|)} \Omega (y)|y|^{ - n - \alpha } f(x - y)dy} \right|,$$ which improves and extends the known result. Moreover, by applying an off-Diagonal T1 Theorem, we also obtain the (L p , L q ) boundedness of the commutator defined by $$C_{\Omega ,\alpha } f(x) = p.v. \int_{\mathbb{R}^n } {(A(x)} - A(y))\Omega (x - y)|x - y|^{ - n - \alpha } f(y)dy.$$

关键词： singular integral operator maximal operator commutator T1 Theorem

ON THE LINEAR CONVERGENCE OF PC-METHOD FOR ACLASS OF LINEAR VARIATIONAL INEQUALITIES

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Journal of computational mathematics 1999年第2期17卷 199-208页

作者： Nai-hua Xiu(department of mathematics, Nothern Jiaotong university, Beijing 100044,{3. Instituteof Applied mathematics, Chinese academy Of sciences, Beijing 100080,{3.) 北方交通大学数学系北京

This paper studies the linear convergence properties of a class of the projection and contraction methods for the affine variational inequalities, and proposes a necessary and sufficient condition under which PC-Metho... 详细信息

关键词： affine variational inequality projection and contraction method linear convergence

The Bifurcation of the Equatorial Periodic Orbit of the Planar Polynomial Vector Fields

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Acta Mathematica Sinica,English Series 2001年第3期17卷 471-480页

作者： Xin An ZHANG department of mathematics,Central china Normal {3.,Wuhan 43.079,P.R.china Institute of mathematics,academy of mathematics and system sciences Chinese academy of sciences,Beijing 100080,P.R.china.Lan Sun CHEN Institute of mathematics,academy of mathematics and system sciences Chinese academy sciences,Beijing 100080,P.R.china.E-mail:lschen@math08.math.ac.cnZhao Jun LIANG department of mathematics,Central china Normal {3.,Wuhan 43.079,P.R.china department of mathematics Central China Normal University Wuhan 430079 P. R. China Institute of mathematics Academy of Mathematics and System Sciences Chinese Academy of Sciences Beijing 100080 P. R. China Institute of mathematics Academy of Mathematics and System Sciences Chinese Academy Sciences Beijing 100080 P. R. China

In this paper,we have obtained the necessary and sufficient condition for the set of points at infinity on the plane R^2 to be a periodic orbit which is called an equatorial periodic orbit of a planar vector field X(x),and the formulae about the multiplicity of the equatorial periodic orbit of X(x).We have also proved that the main result of [9] is erroneous with regard to the formlae.

关键词： Poincaré map Bifurcation Orthogonal projection

Limit theorem and uniqueness theorem of backward stochastic differential equations

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Science china mathematics 2006年第10期49卷 1353-1362页

作者： JIANG Long department of mathematics, china {3. of Mining and Technology, Xuzhou 221008, china Institute of mathematics, Fudan {3., Shanghai 20043., china School of mathematics and system sciences, Shandong {3., Jinan 250100, china 1. department of mathematics China University of Mining and Technology Xuzhou 221008 China 2. Institute of mathematics Fudan University Shanghai 200433 China 3. School of mathematics and system sciences Shandong University Jinan 250100 China

This paper establishes a limit theorem for solutions of backward stochastic differential equations (BSDEs). By this limit theorem, this paper proves that, under the standard assumption g(t,y,0) = 0, the generator g of a BSDE can be uniquely determined by the corresponding g-expectationεg;this paper also proves that if a filtration consistent expectation S can be represented as a g-expectationεg, then the corresponding generator g must be unique.

关键词： backward stochastic differential equation, g-expectation, generator.

Quasirational dynamic system

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Chinese Science Bulletin 2000年第14期45卷 1277-1279页

作者： SUN Daochun & YANG Lo1. department of mathematics, South china Normal {3., Guangzhou 51063., china 2. Institute of mathematics, academy of mathematics and system sciences, Chinese academy of sciences, Beijing 100080, china department of mathematics South China Normal University Guangzhou China Institute of mathematics Academy of Mathematics and System Sciences Chinese Academy of Sciences Beijing China

Using the iterations of quasirational mappings, the theorems on dynamic system are generalized to the quasirational dynamic system. Some different results are also obtained.

关键词： quasirational mapping dynamic system covering surface.

Finite element analysis for general elastic multi-structures

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Science china mathematics 2006年第1期49卷 109-129页

作者： HUANG Jianguo, SHI Zhongci & XU Yifeng department of mathematics, Shanghai Jiao long university, Shanghai 200240,{3. Division of computational Science, E-lnstitute of Shanghai Universities, Shanghai Normal university, Shanghai 20023.,{3. Institute of computational mathematics, academy of mathematics and systems Science, Chinese academy of {13., Beijing 100080,{3. department of mathematics, Chinese university of Hong Kong, Shatin, N. T., Hong Kong,{3. department of mathematics Shanghai Jiao Tong University Shanghai 200240 China Division of computational Science E-Institute of Shanghai Universities Shanghai Normal University Shanghai 200234 China Institute of computational mathematics Academy of Mathematics systems Science Chinese academy of sciences Beijing 100080 China department of mathematics Chinese University of Hong Kong Shatin N. T. Hong Kong China

A finite element method is introduced to solve the general elastic multi-structure problem, in which the displacements on bodies, the longitudinal displacements on plates and the longitudinal displacements on beams are discretized using conforming linear elements, the rotational angles on beams are discretized using conforming elements of second order, the transverse displacements on plates and beams are discretized by the Morley elements and the Hermite elements of third order, respectively. The generalized Korn's inequality is established on related nonconforming element spaces, which implies the unique solvability of the finite element method. Finally, the optimal error estimate in the energy norm is derived for the method.

关键词： elastic multi-structures, finite elements, generalized Korn's inequality, unique solvability, error estimates.

L~∞ CONVERGENCE OF QUASI-CONFORMING FINITE ELEMENTS FOR THE BIHARMONIC EQUATION

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Journal of computational mathematics 1995年第2期13卷 108-122页

作者： Wang Ming (department of mathematics, peking university, Beijing,{3.) 北京大学数学系北京

In this paper we consider the L∞ convergence for quasi-conforming finite ele-ments solving the boundary value probzlems of the biharmonic equation and give the nearly optimal order L∞ estimates.

关键词： Biharmonic equations Vertices Rectangles Interpolation Technology Polynomials Estimation methods Weighting functions Greens function Mathematical inequalities

CONVERGENCE OF (0,1,2,3. INTERPOLATION ON AN ARBITRARY system OF NODES

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Journal of computational mathematics 2001年第2期19卷 151-156页

作者： Ying-guang Shi (Institute of Computation, Hunan Normal university, Changsha 410081, china) (Institute of computational {3. and Scientific/Engineering Computing, academy of {3. and systems sciences, Chinese academy of sciences, Beijing 100 湖南师范大学湖南长沙 410081

Provides information on a study which simplified and improved convergence of (0,1,2,3. interpolation on an arbitrary system of nodes. Definitions and notations; Results; Conjectures.

关键词： Hermite interpolation Hermite-Fejer interpolation convergence

Mean Convergence of Lagrange Type Interpolation on an Arbitrary system of Nodes

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Acta Mathematicae Applicatae Sinica 2002年第2期18卷 277-288页

作者： Ying-guang Shidepartment of mathematics, Hunan Normal university, Changsha 410081,{3. & academy of mathematics and system sciences, Chinese academy of sciences, Beijing 100080,{3. department of mathematics Hunan Normal University Changsha 410081 China academy of mathematics and system {3. Chinese Academy of Sciences Beijing 100080 China

Sufficient conditions of convergence and rate of convergence for Lagrange type interpolation in the weighted Lp norm on an arbitrary system of nodes are given.

关键词： Lagrange type interpolation convergence rate of convergence