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The quantum general linear supergroup, canonical bases and Kazhdan-Lusztig polynomials

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Science china Mathematics 2009年第3期52卷 401-416页

作者： ZHANG HeChun department of Mathematical Sciences, tsinghua university,{2., china department of Mathematical Sciences Tsinghua University Beijing China

Canonical bases of the tensor powers of the natural $ U_q (\mathfrak{g}\mathfrak{l}_{m|n} ) $ -module V are constructed by adapting the work of Frenkel, Khovanov and Kirrilov to the quantum supergroup setting. This result is generalized in several directions. We first construct the canonical bases of the ?2.graded symmetric algebra of V and tensor powers of this superalgebra; then construct canonical bases for the superalgebra O q (M m|n ) of a quantum (m,n) × (m,n)-supermatrix; and finally deduce from the latter result the canonical basis of every irreducible tensor module for $ U_q (\mathfrak{g}\mathfrak{l}_{m|n} ) $ by applying a quantum analogue of the Borel-Weil construction.

关键词： canonical basis crystal basis Kazhdan-Lusztig polynomial 17B37 81R50

Simulation study and function analysis of the dynamic aortic valve

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Progress in Natural Science:Materials International 2006年第5期16卷 512-517页

作者： XIA Dongdong and BAI Jing (department of Biomedical Engineering, tsinghua university,{2., china) department of Biomedical Engineering Tsinghua University Beijing 100084 China

The dynamic aortic valve (DAV) is a new left ventricular assist device, a micro-axial blood pump implemented at the position of the aortic valve, pumping blood from the left ventricle into the aortic artery. The present dynamic aortic valve operates at 7 different rotation speeds, ranging from 3000 r/min (speed 1) to 9000 r/min (speed 7). Because in vivo experiments need a lot of live animals and take a long period of time, modeling and simulation have been widely used to simulate and analyze hydra-dynamic property of the DAV and its assisting effects. With the measurements from the mock circulatory loop, a mathematic model of the DAV is established and embedded into the previously developed canine circulatory system. Using this model, the effect of the DAV on the failing heart at each rotation speed level is investigated. The vital cardiac variables are computed and compared with in vivo experimental results, which are in good agreement with an acceptable difference mostly 15%. The establishment of the DAV model and its simulation are useful for further improvement of the DAV device.

关键词： dynamic aortic valve mathematic model computer simulation.

Computational fluid dynamics modeling and hemolysis analysis of axial blood pumps with various impeller structures

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Progress in Natural Science:Materials International 2006年第9期16卷 993-997页

作者： XIA Dongdong, ZHAO Chunzhang, ZHANG Xiwen and BAI Jing ( department of Biomedical Engineering, tsinghua university,{2., china department of Engineering Mechanics, tsinghua university,{2., china) department of Biomedical Engineering Tsinghua University Beijing 100084 China department of Engineering Mechanics Tsinghua University Beijing 100084 China

The flow fields in the blood pump were analyzed three- dimensionally using computational fluid dynamics (CFD). Hemolysis of the pump was calculated based on the changes in shear stress and related exposure times along the particle trace lines using a forward Euler approach. In this "way, how different impeller structures and rotational speeds affect the hemolysis was particularly acquired. As a result, impeller with long-short alternant vanes behaved best in hemolysis property and can be utilized to axial blood pumps development and design.

关键词： axial blood pump computational fluid dynamics hemolysis.

THE APPROXIMATIONS OF THE EXACT BOUNDARY CONDITION AT AN ARTIFICIAL BOUNDARY FOR LINEARIZED INCOMPRESSIBLE VISCOUS FLOWS

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Journal of Computational Mathematics 1998年第3期16卷 239-256页

作者： Wei-zhu Bao (department of Applied Mathematics, tsinghua university,{2., P.R. china) 清华大学应用数学系北京

We consider the linearized incompressible Navier-Stokes (Oseen) equations in a flat channel. A sequence of approximations to the exact boundary condition at an artificial boundary is derived. Then the original problem is reduced to a boundary value problem in a bounded domain, which is well-posed. A finite element approximation on the bounded domain is given, furthermore the error estimate of the finite element approximation is obtained. Numerical example shows that our artificial boundary conditions are very effective.

关键词： Oseen equations artificial boundary artificial boundary condition finite element approximation error estimate

REGULARIZATION OF SINGULAR SYSTEMS BY OUTPUTFEEDBACK

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Journal of Computational Mathematics 2000年第1期18卷 43-60页

作者： De-lin Chu Da-yong Cai(department of Mathematical Sciences, tsinghua university,{2., china) 清华大学北京 100084

Presents a study which examined problem of regularization of a singular linear time-invariant system by derivative and proportional output feedback. Reduced form for the system that can be computed using orthogonal tr... 详细信息

关键词： regularization singular systems output feedback

A new orthogonality relationship for orthotropic thin plate theory and its variational principle

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Science china(Physics,Mechanics & Astronomy) 2005年第3期48卷 371-380页

作者： LUO Jianhui 1 , LONG Yuqiu 2.& LIU Guangdong 1 1. College of Civil Engineering, Hunan university, Changsha 410082. china 2. {2. of Civil Engineering, tsinghua university, beijing 100084, china College of Civil Engineering Hunan University Changsha China department of Civil Engineering Tsinghua University Beijing China

The thought how dual vectors are constructed in a new orthogonality relationship for theory of elasticity is generalized into orthotropic thin plate bending problems by using the analogy theory between plane elasticity problems and plate bending problems. Dual differential equations are directly obtained by using a mixed variables method. A dual differential matrix to be derived possesses a peculiarity of which principal diagonal sub-matrixes are zero matrixes. Two independently and symmetrically orthogonality sub-relationships are discovered. By using the integral form for elastic bending theory of orthotropic thin plate the orthogonality relationship is demonstrated. By selecting felicitous dual vectors a new orthogonality relationship for theory of elasticity can be generalized into elastic bending theory of orthotropic thin plate. By using the integral form a variational principle which is relative to differential form and a whole function expression are proposed.

关键词： theory of elasticity, thin plate theory, dual vectors, orthogonality relationship, orthotropic, variational principle.

AR quivers,exceptional sequences and algorithms in derived Hall algebras

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Science china Mathematics 2010年第6期53卷 1609-1624页

作者： SHENG Jie department of Mathematical Sciences,tsinghua {2.,beijing 100084,china department of Mathematical Sciences Tsinghua University Beijing China

Consider the canonical isomorphism between the positive part U+ of the quantum group Uq(g) and the Hall algebra H(Λ),where the semisimple Lie algebra g and the finite-dimensional hereditary algebra Λ share a Dynkin *** and Xiao have given two algorithms to decompose the root vectors into linear combinations of monomials of Chevalley generators of U+,respectively induced by the braid group action on the exceptional sequences of Λ-modules and the structure of the Auslander-Reiten quiver of Λ.In this paper,we obtain the corresponding algorithms for the derived Hall algebra DH(Λ),which was introduced by *** show that both algorithms are applicable to the lattice algebra and Heisenberg double in the sense of *** the new recursive formulae have the same flavor with the quantum Serre relations.

关键词： derived Hall algebra exceptional sequence AR quiver

Preparation of MWNTs/Al_2._3 composites and their mechanical and electrical properties

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Science china(Technological Sciences) 2005年第6期48卷 622-631页

作者： FAN Jinpeng1,2. ZHAO Daqing1,2. XU Zening1,2.& WU Minsheng1,2.1. department of Mechanical Engineering, tsinghua university,{2., china 2. Key Laboratory for Advanced Manufacturing by Materials Processing Technology, tsinghua university,{2., china department of Mechanical Engineering Tsinghua University Beijing China Key Laboratory for Advanced Manufacturing by Materials Processing Technology Tsinghua University Beijing China

The mechanical and electrical properties of MWNTs/Al2.3 composite prepared fabricated by hot pressing are investigated. The relation between properties and microstructure of composites is also discussed. With 4wt% MWNTs as reinforcement, the fracture toughness of composite obtained reaches 5.55 MPa·m1/2. which is 80% higher than that of pure Al2.3 obtained in the same conditions. The main toughening mechanism is CNTs’ pinning alumina grain boundaries, and the pullout of CNTs takes effect also. Through adding 2.t% MWNTs and altering the mix method, the fracture toughness of the composite obtained is 3.97 MPa·m1/2. Furthermore, the electrical resistivity is as low as 8.4×10?3 ?·m, decreasing by 14 orders of magnitude compared with pure alumina ceramics. The function of CNTs in composite is related to the distribution state of CNTs in composite, and the distribution state of CNTs in matrix is dependent on preparation procedures.

关键词： MWNTs, alumina, composite, fracture toughness, electrical properties.

HIGH ACCURACY NUMERICAL METHOD OF THIN-FILM PROBLEMS IN MICROMAGNETICS

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Journal of Computational Mathematics 2003年第1期21卷 33-40页

作者： Zhongyi Huang (Deft, of Mathematical Sciences, tsinghua university, beijing, {2., china) Dept. of Mathematical Sciences Tsinghua University 北京 100084

In this paper, a new high accuracy numerical method for the thin-film problems of micron and submicron size ferromagnetic elements is proposed. For the computation of stray field, we use the finite element method(FEM) by introducing a semi-discrete artificial boundary condition [1, 2.. In our numerical experiments about the domain patterns and their movement, we can see that the results are accordant to that of experiments and other numerical methods. Our method are very convenient to deal with arbitrary shape of thin films such as a polygon with high accuracy.

关键词： Thin-film Micromagnetics stray field Semi-discrete artificial boundary condition.