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CONVERGENCE OF CASCADE ALGORITHMS AND SMOOTHNESS OF REFINABLE DISTRIBUTIONS

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Chinese Annals of Mathematics,Series B 2003年第3期24卷 367-386页

作者： SUN QIYU department of Mathematics, university of Houston, Houston, TX 77204, USA. department of Mathematics, national university of singapore, 10 Kent Ridge Crescent, 119260, singapore. Univ Houston Dept Math Houston TX 77204 USA Natl Univ singapore Dept Math Singapore 119260 Singapore

In this paper, the author at first develops a method to study convergence of the cascadealgorithm in a Banach space without stable assumption on the initial (see Theorem 2.1), andthen applies the previous result on the convergence to characterizing compactly supportedrefinable distributions in fractional Sobolev spaces and Holder continuous spaces (see Theorems3.1, 3.3, and 3.4). Finally the author applies the above characterization to choosing appropriateinitial to guarantee the convergence of the cascade algorithm (see Theorem 4.2).

关键词： Cascade algorithm Cascade operator Refinable distribution Shift-invariant space Linear independent shifts Stable shifts Fractional Sobolev space

Formation, Structure and Properties of Bulk Metallic Glasses

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Journal of Materials Science & Technology 1999年第2期15卷 97-110页

作者： Y. Li(department of Materials Science, Faculty of Science, national university of singapore, Lower Kent Ridge Road,singapore 119260 E-mail:masliy@nus.edu.sg) department of Materials Science Faculty of Science National University of Singapore Lower Kent Ridge Road Singapore 119260 Singapore

Bulk metallic glasses with up to 72 mm critical section thickness have been obtained by conventional casting techniques and the properties of these materials, particularly the mechanical and magnetic properties have been studied. These materials have been demonstrated to have novel properties which are fundamentally different from their crystalline counterparts. The recent status of research and development in formation, structure and properties of bulk metallic glasses is reviewed. The techniques to produce such bulk glasses are summarized and the glass forming ability and the critical cooling rate of these materials are discussed. Further consideration of the development and application of this new class of materiaIs will be proposed.

关键词： Ni Zr Structure and Properties of Bulk Metallic Glasses Formation OK Cu Figure

Wave mechanics in quantum phase space: hydrogen atom

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Progress in Natural Science:Materials International 2007年第2期17卷 144-149页

作者： LU Jun ( department of Foundational Science, Beijing Union university, Beijing 100101, China department of Computational Science, national university of singapore, singapore 117543, singapore) [a]department of Foundational Science Beijing Union University Beijing China [b]department of Computational Science national university of singapore Singapore Singapore

The rigorous solutions of the stationary Schrodinger equation for hydrogen atom are solved with the wave-mechanics method within the framework of the quantum phase-space representation established by Torres-Vega and Frederick. The "Fourier-like" projection transformations of wave function from the phase space to position and momentum spaces are extended to three-dimensional systems. The eigenfunctions in general position and momentum spaces could be obtained through the transformations from eigenfunction in the phase space.

关键词： quantum phase space hydrogen atom projection transformation.

NUMERICAL MODEL FOR FLOW MOTION WITH VEGETATION

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Journal of Hydrodynamics 2008年第2期20卷 172-178页

作者： ZHANG Jian-tao SU Xiao-hui department of Civil and Hydraulic Engineering Dalian University of Technology Dalian 116023 China department of Civil Engineering National University of Singapore Singapore 119260 Singapore

A set of governing equations for turbulent flows in vegetated area were derived with the assumption that vegetation is of straight and rigid cylinder. The effect of vegetation on flow motion was represented by additional inertial and drag forces. The new model was validated by available experimental data for open channel flows passing through vegetated areas with different vegetation size, density and distribution. Numerical results are in good agreement with the experimental data. Finally, the flow around a supposed isolated vegetated pile was simulated and the effects of vegetation density on the wake flow were discussed. It is found that the presence of vegetation, even at a very low density, has the pronounced influence on the dissipation of flow energy, both inside the vegetation domain and outside it in the wake flow region.

关键词： numerical simulation vegetation open channel

A THIRD-ORDER BOUSSINESQ MODEL APPLIED TO NONLINEAR EVOLUTION OF SHALLOW-WATER WAVES

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Journal of Hydrodynamics 2000年第2期12卷 107-126页

作者： Zhang Ying long CCM MINDEF, department of Mech. and Prod. Eng., national university of singapore, 10 Kent Ridge Crescent, singapore 119260 Zhu Song ping department of Mathematics, the university of Wollongong, Wollongong, NSW 2522, Australia Natl Univ of singapore Singapore Singapore

The conventional Boussinesq model is extended to the third order in dispersion and nonlinearity. The new equations are shown to possess better linear dispersion characteristics. For the evolution of periodic waves over a constant depth, the computed wave envelops are spatially aperiodic and skew. The model is then applied to the study of wave focusing by a topographical lens and the results are compared with Whalin′s (1971) experimental data as well as some previous results from the conventional Boussinesq model. Encouragingly, improved agreement with Whalin′s experimental data is found. [WT5”HZ]

关键词： shallow water waves nonlinearity evolution third order Boussinesq model

Two optimization algorithms for solving robotics inverse kinematics with redundancy

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控制理论与应用（英文版） 2010年第2期8卷 166-175页

作者： Jianxin XU, Wei WANG, Yuanguang SUN (department of Electrical and Computer Engineering, national university of singapore, singapore 117576) department of Electrical and Computer Engineering National University of Singapore Singapore Singapore

The kinematic redundancy in a robot leads to an infinite number of solutions for inverse kinematics, which implies the possibility to select a 'best' solution according to an optimization criterion. In this paper, two optimization objective functions are proposed, aiming at either minimizing extra degrees of freedom (DOFs) or minimizing the total potential energy of a multilink redundant robot. Physical constraints of either equality or inequality types are taken into consideration in the objective functions. Since the closed-form solutions do not exist in general for highly nonlinear and constrained optimization problems, we adopt and develop two numerical methods, which are verified to be effective and precise in solving the two optimization problems associated with the redundant inverse kinematics. We first verify that the well established trajectory following method can precisely solve the two optimization problems, but is computation intensive. To reduce the computation time, a sequential approach that combines the sequential quadratic programming and iterative Newton-Raphson algorithm is developed. A 4-DOF Fujitsu Hoap-1 humanoid robot arm is used as a prototype to validate the effectiveness of the proposed optimization solutions.

关键词： Inverse kinematics Redundant robot Objective function Optimization Numerical approach

Decay of geometry for unimodal maps:The C^2 case

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Chinese Science Bulletin 2009年第11期54卷 1859-1862页

作者： SHEN WeiXiao1,2 1 department of Mathematics, university of Science and Technology of China, Hefei 230026, China 2 department of Mathematics, national university of singapore, singapore 117543, singapore department of Mathematics University of Science and Technology of China Hefei 230026 China department of Mathematics National University of Singapore Singapore 117543 Singapore

We prove that a C2 unimodal interval map with critical order not greater than 2 has the decay of geometry property, by showing that all the cross-ratio estimates needed in the previous proof for the C3 case remain true.

关键词：衰变几何图案件几何性质比率估计证明

Salvia miltiorrhiza and ischemic diseases

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Acta Pharmacologica Sinica 2000年第12期 34-39页

作者： Xin-Yan JI, Benny K-H TAN, Yi-Zhun ZHU (department of Pharmacology, Faculty of Medicine, national university of singapore, singapore 119260, singapore) department of Pharmacology Faculty of Medicine national university of singapore singapore 119260

The demonstration of beneficial effects of salvia miltiorrhiza (DanShen) on ischemic diseases has revolutionized the management of angina pectoris, myocardial infarction (MI) or stroke in Chinese society. Experimental studies have shown that DanShen dilated coronary arteries, increased coronary blood flow, and scavenged free radicals in ischemic diseases, so that it reduced the cellular damage from ischemia and improved heart functions. Clinical trials also indicated that DanShen was an effective medicine for angina pectoris, MI, and stroke. This review will focus on DanShen’s effects in angina pectoris, MI and stroke.

关键词： Salvia miltiorrhiza myocardial infarc-tion cardiovascular system cerebrovascular disorders antioxidants free radicls myocarodial ischemia

Efficiency Improvement of Heterojunction Polymer Photovoltaic Cells through Controlling the Morphology of the Polymer Film

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复旦学报（自然科学版） 2007年第5期46卷 655-页

作者： Jian-yong Ouyang(department of Materials Science and Engineering, national university of singapore, singapore 117576) department of Materials Science and Engineering National University of Singapore Singapore 117576

1 Results Polymer photovoltaic cells, which provide clean and renewable energy sources, have gained more and more attention. Polymer photovoltaic cells have the advantage of low fabrication cost and high mechanical flexibility. Polymers can be processed through a solution process, so that a homogeneous polymer film could be readily prepared in a large area. Recently, the light-to-electricity conversion efficiency of the polymer photovoltaic cells was improved significantly[1-2]. Polymer donor and organi...

关键词： polymer photovoltaic cell morphology temperature solvent