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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) department of Foundational Science Beijing Union University Beijing 100101 China department of Computational Science National University of Singapore Singapore 117543 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.

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. department of mathematics University of Houston TX 77204 USA department of mathematics National University of Singapore 10 Kent Ridge Crescent 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

Error Estimates for Finite-Element Navier-Stokes Solvers without Standard Inf-Sup Conditions

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Chinese Annals of mathematics,Series B 2009年第6期30卷 743-768页

作者： Robert L.PEGO department of Mathematical Sciences and Center for Nonlinear Analysis Carnegie Mellon University PittsburghPA 15213USA

The authors establish error estimates for recently developed finite-element methods for incompressible viscous flow in domains with no-slip boundary *** methods arise by discretization of a well-posed extended Navier-Stokes dynamics for which pressure is determined from current velocity and force *** methods use C1 elements for velocity and C0 elements for pressure.A stability estimate is proved for a related finite-element projection method close to classical time-splitting methods of Orszag,Israeli,DeVille and Karniadakis.

关键词： Time-dependent incompressible flow Projection method Backward facing step Driven cavity Stokes pressure Leray projection Obtuse corner Recycling

Ribosome Biogenesis Factor Bmsl-like Is Essential for Liver Development in Zebrafish

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Journal of Genetics and Genomics 2012年第9期39卷 451-462页

作者： Yong Wanga,Yue Luoa,Yunhan Hong(b,),Jinrong Peng(a,),Lijan Lo(a,b,) a College of Animal Sciences,Zhejiang university,Hangzhou 310058,China b department of Biological Sciences,national university of singapore,Science Drive 4,singapore 117543,singapore College of Animal Sciences Zhejiang University Hangzhou 310058 China department of Biological Sciences National University of Singapore Science Drive 4 Singapore 117543 Singapore

Ribosome biogenesis in the nucleolus requires numerous nucleolar proteins and small non-coding *** them is ribosome biogenesis factor Bmsl,which is highly conserved from yeast to *** yeast,Bmsl initiates ribosome biogenesis through recruiting Rcll to ***,little is known about the biological function of Bmsl in *** we report that Bmsl plays an essential role in zebrafish liver *** identified a zebrafish bms1l^（sq163） mutant which carries a T to A mutation in the gene bmsl-like（bms1l）.This mutation results in L^（152） to Q^（152） substitution in a GTPase motif in ***,bmsll^（sq163） mutation confers hypoplasia specifically in the liver,exocrine pancreas and intestine after 3 days post-fertilization（dpf）.Consistent with the bmsll^（sq163） mutant phenotypes,whole-mount in situ hybridization（WISH） on wild type embryos showed that bmsll transcripts are abundant in the entire digestive tract and its accessory *** for phospho-Histone 3（P-H3） and TUNEL assay revealed that impairment of hepatoblast proliferation rather than cell apoptosis is one of the consequences of bms1l（sq163） giving rise to an under-developed ***,our findings demonstrate that Bmsll is necessary for zebrafish liver development.

关键词： Liver development Digestive organ development Ribosome biogenesis Bmsl-like Zebrafish

Revisit of Sheppard corrections in linear regression

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Science China mathematics 2010年第6期53卷 1435-1451页

作者： LIU TianQing1,ZHANG BaoXue1,HU GuoRong1 & BAI ZhiDong1,2,1Key Laboratory for Applied Statistics of MOE and School of mathematics and Statistics,Northeast Normal university,Changchun 130024,China 2department of Statistics and Applied Probability,national university of singapore,singapore 117543,singapore Key Laboratory for Applied Statistics of MOE and School of mathematics and Statistics Northeast Normal University Changchun China department of Statistics and Applied Probability National University of Singapore Singapore Singapore

Dempster and Rubin(D&R) in their JRSSB paper considered the statistical error caused by data rounding in a linear regression model and compared the Sheppard correction,BRB correction and the ordinary LSE by *** asymptotic results when the rounding scale tends to 0 were also *** a previous research,we found that the ordinary sample variance of rounded data from normal populations is always inconsistent while the sample mean of rounded data is consistent if and only if the true mean is a multiple of the half rounding *** the light of these results,in this paper we further investigate the rounding errors in linear *** notice that these results form the basic reasons that the Sheppard corrections perform better than other methods in D&R examples and their conclusion in general cases is *** in which the Sheppard correction works worse than the BRB correction are also ***,we propose a new approach to estimate the parameters,called "two-stage estimator",and establish the consistency and asymptotic normality of the new estimators.

关键词： asymptotic normality consistency linear regression model rounded data two-stage estimates

Saddlepoint approximations for studentized compound Poisson sums with no moment conditions in audit sampling

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Science China mathematics 2010年第12期53卷 3131-3138页

作者： ZHOU GuoLiang 1 & ZHOU Wang 2, 1 Institute of Accounting and Finance, Shanghai university of Finance and Economics, Shanghai 200433, China 2 department of Statistics and Applied Probability, national university of singapore, singapore 117546, singapore Institute of Accounting and Finance Shanghai University of Finance and Economics Shanghai China department of Statistics and Applied Probability National University of Singapore Singapore Singapore

Saddlepoint approximations for the studentized compound Poisson sums with no moment conditions in audit sampling are derived. This result not only provides a very accurate approximation for studentized compound Poisson sums, but also can be applied much more widely in statistical inference of the error amount in an audit population of accounts to check the validity of financial statements of a firm. Some numerical illustrations and comparison with the normal approximation method are presented.

关键词： saddlepoint approximation Laplace approximation self-normalized compound Poisson sum stu- dentized compound Poisson sum

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

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

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