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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, beijing 100084, china department of Mathematical Sciences Tsinghua University Beijing 100084 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

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, beijing 100084, china department of Engineering Mechanics, tsinghua university, beijing 100084, china) [a]department of Biomedical Engineering Tsinghua University Beijing China [b]department of Engineering Mechanics Tsinghua University Beijing 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.

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, beijing 100084, 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.

Study on the two and three-parameter working stability regions of 3Y-TZP suspension

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Science china(Technological Sciences) 2006年第5期49卷 547-568页

作者： CHEN Youqiang1, 2, ZHAng Xinni3, CHEN Sha’ou3 & QI Ping3 1. department of chemistry, Qingdao university, Qingdao 266071, china 2. department of chemistry, tsinghua university, beijing 100084, china 3. department of Physics, Qingdao university, Qingdao 266071, china 1. department of chemistry Qingdao University Qingdao 266071 China 2. department of chemistry Tsinghua University Beijing 100084 China 3. department of Physics Qingdao University Qingdao 266071 China

We determined the variation tendency of viscosity (η) at various solids load- ing (α) for 3Y-TZP suspension as a function of dispersant concentration (Cw) using vis- cosity measurement, measured the diameter of particles as a function of Cw in very dilute suspension using light scattering method, and obtained the surface features of the sedi- ment of suspension with different Cw using SEM. We also discussed the influence of the microstructure of adsorbed polymer layers on particles and their interactions in the dis- persing medium on the stability of suspension. Then two different stable states and two different unstable states for 3Y-TZP suspension were given. Accordingly, the (Cw, η), (Cw, α), and (α, η) two-parameter, and (Cw, α, η) three-parameter stability maps were con- structed. Based on the DLVO theory calculations, the dispersant concentration, particle distance (r), and interparticle potential energy (VT) maps with various solids loading for 3Y-TZP aqueous suspension were also constructed. In (Cw, r) two-parameter coordinate system, the stable motion region map for particles was established. The Cw, α, and VT,max (the highest potential energy) surface of the potential barrier map was obtained through calculation and simulation on the basis of the surfaces of Cw, r, VT maps introduced above. The (Cw, α) two-parameter stability map was then obtained from the Cw, α, VT,max map. The results showed that this theoretical map can qualitatively prove the experimentally obtained results—the existence of different dispersed states of particles in suspension system and the variation tendency of suspension stability with changing each parame- ter—were reasonable.

关键词： 3Y-TZP, suspension, stability, DLVO theory, interparticle potential energy.

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, beijing 100084, 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

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 university.beij.ng 100084,china 1. department of Mathematical Sciences Tsinghua University Beijing 100084 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

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, beijing 100084, 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

DOPIng LEVEL INCREASE OF POLY(3-METHYLTHIOPHENE)FILM DURIng ELECTROCHEMICAL POLYMERIZATION PROCESS

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Chinese Journal of Polymer Science 2002年第5期20卷 425-430页

作者： Jing-kun Xu Gao-quan Shi Feng-en Chen Xiao-yin Hong department of chemistry and Bio-organic Phosphorous chemistry Laboratory tsinghua university.beij.ng 100084, china tsinghua Univ Dept Chem Beijing 100084 Peoples R China tsinghua Univ Bioorgan Phosphorous Chem Lab Beijing 100084 Peoples R China

The Raman spectra of poly(3-methylthiophene) (PMeT) films with different thicknesses, which have been electrochemically deposited on a flat stainless steel electrode surface by direct oxidation of 3-methylthiophene in boron trifluoride diethyl etherate (BFEE) at a constant applied potential of 1.38 V (versus SCE), have been investigated by excitation with a 633-nm laser beam. The spectroscopic results demonstrated that the doping level of PMeT film was increasing during film growth. This finding was also confirmed by electrochemical examination. Moreover, the Raman bands assigned to radical cations and dications in doped PMeT films were found approximately at 1420 and 1400 cm(-1), respectively. Radical cations and dications coexist on the backbone of PMeT as conductive species and their concentrations increase with the increase of doping level. Successive cyclic voltammetry was proved to be an effective approach to improving the doping level of as-grown thin compact PMeT film.

关键词： poly(3-methylthiophene) Raman spectra doping level radical cations dications

The numbers of periodic orbits hidden at fixed points of 2-dimensional holomorphic mappings

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Science china Mathematics 2010年第3期53卷 863-886页

作者： ZHAng GuangYuan department of Mathematical Sciences, tsinghua university, beijing 100084, china 1. department of Mathematical Sciences Tsinghua University Beijing 100084 China

Let △n be the ball |x| < 1 in the complex vector space C n , let f :△n→ C n be a holomorphic mapping and let M be a positive integer. Assume that the origin 0 = (0, . . . , 0) is an isolated fixed point of both f a... 详细信息

Let △n be the ball |x| ng and let M be a positive integer. Assume that the origin 0 = (0, . . . , 0) is an isolated fixed point of both f and the M-th iteration f M of f. Then the (local) Dold index P M (f, 0) at the origin is well defined, which can be interpreted to be the number of virtual periodic points of period M of f hidden at the origin: any holomorphic mapping f 1 :△n→ C n sufficiently close to f has exactly P M (f, 0) distinct periodic points of period M near the origin, provided that all the fixed points of f M 1 near the origin are simple. Therefore, the number O M (f, 0) = P M (f, 0)/M can be understood to be the number of virtual periodic orbits of period M hidden at the fixed point. According to the works of Shub-Sullivan and Chow-Mallet-Paret-Yorke, a necessary condition so that there exists at least one virtual periodic orbit of period M hidden at the fixed point, i.e., O M (f, 0)≥1, is that the linear part of f at the origin has a periodic point of period M. It is proved by the author recently that the converse holds true. In this paper, we will study the condition for the linear part of f at 0 so that O M (f, 0)≥2. For a 2 × 2 matrix A that is arbitrarily given, the goal of this paper is to give a necessary and sufficient condition for A, such that O M (f, 0)≥2 for all holomorphic mappings f :△2 → C 2 such that f(0) = 0, Df(0) = A and that the origin 0 is an isolated fixed point of f M .

关键词： complex dynamical systems periodic points fixed point indices