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How big are the Csorgo-Revesz increments of two-parameter Wiener processes?

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science china mathematics 2004年第6期47卷 894-907页

作者： WANG WenshengDepartment of mathematics, Hangzhou Teacher’s College, Hangzhou 310012, china Institute of Applied mathematics, chinese academy of sciences, beijing 100080, china Dept. of Math. Hangzhou Teacher's Coll. Hangzhou 310012 China Inst. of Appl. Math. Chinese Acad. of Sci. Beijing 100080 China

In this paper, we prove a theorem on the set of limit points of the increments of a two-parameter Wiener process via establishing a large deviation principle on the increments of the two-parameter Wiener process.

关键词： two-parameter Wiener process increment functional law of the iterated logarithm large deviation.

Error of One-leg Methods for Singular Perturbation Problems with Delays

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Acta Mathematicae Applicatae Sinica 2002年第4期18卷 629-640页

作者： Si-qing Gan, Geng SunDepartment of Computer science and Technology, Tsinghua University, beijing 100084, chinaacademy of mathematics and system sciences, chinese academy of sciences, beijing 100080, china Department of Computer science and Technology Tsinghua University Beijing China academy of mathematics and system sciences Chinese Academy of Sciences Beijing China

This paper is concerned with the error behaviour of one-leg methods applied to some classes of one-parameter multiple stiff singularly perturbed problems with delays. We derive the global error estimates of A-stable o... 详细信息

关键词： Singular perturbation problems delays interpolation one-leg methods convergence

MODELLING AND NUMERICAL SOLUTIONS OF A GAUGE PERIODIC TIME DEPENDENT GINZBURG-LANDAU MODEL FOR TYPE-Ⅱ SUPERCONDUCTORS

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Journal of Computational mathematics 1997年第4期15卷 365-384页

作者： Zhi-ming Chen (Institute of mathematics, chinese academy of sciences, beijing, china) 中科院数学所北京

In this paper we seek the solutions of the time dependent Ginzburg-Landau model for type-Ⅱ superconductors such that the associated physical observables are spatially periodic with respect to some lattice whose basic lattice cell is not necessarily rectangular. After appropriately foring the gange, the model can be formulated as a system of nonlinear parabolic partial differential equations with quasi-periodic boundary conditions. We first give some results concerning the existence, uniqueness and regularity of solutions and then we propose a semiimplicit finite element scheme solving the system of nonlinear partial dmerential equations and show the optimal error estimates both in the L2 and energy *** also report on some numerical results at the end of the paper.

关键词： Math QT MODELLING AND NUMERICAL SOLUTIONS OF A GAUGE PERIODIC TIME DEPENDENT GINZBURG-LANDAU MODEL FOR TYPE SUPERCONDUCTORS

NUMERICAL SOLUTION OF THE UNSTEADYINCOMPRESSIBLE NAVIER-STOKES EQUATIONS ON THECURVILINEAR HALF-STAGGERED MESHNUMERICAL SOLUTION OF THE UNSTEADYINCOMPRESSIBLE NAVIER-STOKES EQUATIONS ON THECURVILINEAR HALF-STAGGERED MESH

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Journal of Computational mathematics 2000年第5期18卷 521-540页

作者： Lan-chieh Huang (Institute of Computational mathematics and Scientific/Engineering Computing, chinese academy of sciences, beijing 100080, china) 中科院计算数学与科学工程计算所北京 100080

In this paper, the Crank-Nicholson + component-consistent pressure correction method for the numerical solution of the unsteady incompressible Navier-Stokes equation of [1] on the rectangular half-Staggered mesh has been extended to the curvilinear half-Staggered mesh. The discrete projection, both for the projection step in the solution procedure and for the related differential-algebraic equations, has been carefully studied and verified. It is proved that the proposed method is also unconditionally (in t) nonlinearly stable on the curvilinear mesh, provided the mesh is not too skewed. It is seen that for problems with an outflow boundary, the half-Staggered mesh is especially advantageous. Results of preliminary numerical experiments support these claims.

关键词： Unsteady incompressible Navier-Stokes equations Curvilinear half- staggered mesh Discrete projection.

A new trust region algorithm for image restoration

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science china mathematics 2005年第2期48卷 169-184页

作者： WEN Zaiwen & WANG Yanfei State Key Laboratory of Scientific Engineering Computing, Institute of Computational mathematics and Scientific/Engineering Computing, academy of mathematics and system sciences, chinese academy of sciences, beijing 100080, china National Key Laboratory on Remote Sensing science, Institute of Remote Sensing Applications, chinese academy of sciences, beijing 100101, china State Key Laboratory of Scientific Engineering Computing Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and System Sciences Chinese Academy of Sciences Beijing China National Key Laboratory on Remote Sensing science Institute of Remote Sensing Applications Chinese Academy of Sciences Beijing China

The image restoration problems play an important role in remote sensing and astronomical image analysis. One common method for the recovery of a true image from corrupted or blurred image is the least squares error (LSE) method. But the LSE method is unstable in practical applications. A popular way to overcome instability is the Tikhonov regularization. However, difficulties will encounter when adjusting the so-called regularization parameter a. Moreover, how to truncate the iteration at appropriate steps is also challenging. In this paper we use the trust region method to deal with the image restoration problem, meanwhile, the trust region subproblem is solved by the truncated Lanczos method and the preconditioned truncated Lanczos method. We also develop a fast algorithm for evaluating the Kronecker matrix-vector product when the matrix is banded. The trust region method is very stable and robust, and it has the nice property of updating the trust region automatically. This releases us from tedious finding the regularization parameters and truncation levels. Some numerical tests on remotely sensed images are given to show that the trust region method is promising.

关键词： trust region algorithm, image restoration, Lanczos method, Kronecker matrix-vector product, preconditioning.

Some properties on multivariate filter banks with a matrix factorization

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Progress in Natural science:Materials International 2005年第2期15卷 20-30页

作者： LIAN Qiaofang1, XIAO Hongying2* and CHEN Qiuhui3(1. Department of mathematics, beijing Jiaotong University, beijing 100044, china 2. Institute of mathematics, academy of mathematics and system sciences, chinese academy of sciences, beijing 100080, china 3. Department of Scientific Computing and Computer Applications, Zhongshan University, Guangzhou 510275, china) Dept. of mathematics Beijing Jiaotong Univ. Beijing 100044 China Inst. of mathematics Acad. of Math. and System Sci. Chinese Acad. of Sciences Beijing 100080 China Dept. of Scientific Computing Zhongshan Univ. Guangzhou 510275 China

A class of multivariate filter banks with a matrix factorization has been developed by Chen et al. The main purpose of this paper is to discuss some further properties of this kind of filter bank, such as the completeness, accuracy of the corresponding scaling functions and the relationships with Daubechies' wavelets and the multi-wavelets provided by Chui and Lian. Moreover, some examples are given to show that this kind of filter bank has a higher accuracy for the scaling functions.

关键词： filter banks completeness accuracy matrix factorization

Hyperbolic geometry with geometric algebra

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chinese science Bulletin 1997年第3期42卷 262-263页

作者： LI Hong boInstitute of systems science, chinese academy of sciences, beijing 100080, china Institute of systems science Chinese Academy of Sciences Beijing China

WE use the geometric algebra in refs. [1, 2] to study hyperbolic geometry. The n-dimensional hyperbolic space Hn is taken to be the unit sphere of G1 (I-n,1) with antipodal points identified. We study typically H2: the dualities between generalized point and generalized line, between generalized triangle and imaginary triangle; convex generalized triangles; Lorentz transformations; generalized circles and double-cycles, etc. Below we list some of the results.

关键词： line Hyperbolic geometry with geometric algebra

Local Properties of Cardinal Interpolatory Function

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Acta Mathematica Sinica,English Series 2001年第4期17卷 613-620页

作者： Han Lin CHEN Si Long PENG Institute of mathematics, academy of mathematics and system sciences chinese academy of sciences, beijing 100080, P. R. china Nadec, Institute of Automation, Academia Sinica, beijing. 100080. china Institute of mathematics Academy of Mathematics and System Sciences Chinese Academy of Sciences Beijing 100080 P. R. China

In [1], a kind of periodic cardinal interpolatory function (PCIF) is constructed, and they also use it to construct periodic wavelets. But the localizationl of PCIF is not known yet. In this paper, we studv the local property of PCIF using two different methods. The results show that PCIF has very good localization. Some new properties of Bernoulli spline are also introduced.

关键词： Periodic cardinal interpolatory function Local Spline

On Boundary Stability of Wave Equations with Variable Coefficients

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Acta Mathematicae Applicatae Sinica 2002年第4期18卷 589-598页

作者： Yu-xia Guo, Peng-fei YaoDepartment of mathematics, Tsinghua University, beijing 100084, china,Institute of system sciences. academy of mathematics and system sciences, chinese academy of sciences,beijing 100080, china Department of mathematics Tsinghua University Beijing China Institute of system sciences Academy of Mathematics and System Sciences Chinese Academy of Sciences Beijing China

In this paper, we consider the boundary stabilization of the wave equation with variable coefficients by Riemmannian geometry method subject to a different geometric condition which is motivated by the geometric multiplier identities. Several (multiplier) identities (inequalities) which have been built for constant wave equation by Kormornik and Zuazua are generalized to the variable coefficient case by some computational techniques in Riemmannian geometry, so that the precise estimates on the exponential decay rate are derived from those inequalitities. Also, the exponential decay for the solutions of semilinear wave equation with variable coefficients is obtained under natural growth and sign assumptions on the nonlinearity. Our method is rather general and can be adapted to other evolution systems with variable coefficients (e.g. elasticity plates) as well.

关键词： Wave equation exponential decay boundary stabilization the Riemannian geometry method