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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 {2. sciences, tsinghua university, Beijing 100084, china department of mathematical {2. 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

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 {2. sciences, tsinghua university, Beijing 100084, china 1. department of mathematical {2. 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| 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 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

Upper bound and formula for class numbers of abelian function fields

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Progress in Natural Science:Materials International 2006年第3期16卷 321-323页

作者： MA Lianrong and zhang Xianke (department of {2. sciences, tsinghua university, Beijing 100084, china) department of mathematical {2. Tsinghua University Beijing 100084 China

For any abelian function field K (i.e. any subfield of a cyclotomic function field L=k (∧P) over the rational function field k ) with conductor being an irreducible polynomial over a finite field of odd characteristic, by studying the Carlitz-module structure and the character group of K, an explicit upper bound and a calculating formula of the relative divisor class number h- (K) of K are given. Our calculated results of K develop Rosen’s recent results of L .

关键词： Carlitz module cyclotomic function field class number character abelian function field.

Continuity in weak topology:higher order linear systems of ODE

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Science china Mathematics 2008年第6期51卷 1036-1058页

作者： zhang meirong {2. of mathematical sciences,Zhou Pei-Yuan Center for Applied Mathematics,tsinghua university,Beijing 100084,china department of mathematical {2. Zhou Pei-Yuan Center for Applied Mathematics Tsinghua University Beijing 100084 China

We will introduce a type of Fredholm operators which are shown to have a certain con- tinuity in weak *** this,we will prove that the fundamental matrix solutions of k-th, k≥2.order linear systems of ordinary differential equations are continuous in coefficient matrixes with weak ***,Floquet multipliers and Lyapunov exponents for periodic systems are continuous in weak ***,for the scalar Hill’s equations,Sturm-Liouville eigenvalues, periodic and anti-periodic eigenvalues,and rotation numbers are all continuous in potentials with weak *** results will lead to many interesting variational problems.

关键词： continuity weak topology Fredholm operator linear system Hill’s equation eigenvalue rotation number Lyapunov exponent 34A30 34L40 37E45 34D08 58C07 46B50

Unramified extensions of quadratic fields

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Progress in Natural Science:Materials International 2008年第3期18卷 323-324页

作者： Wei Li, Dong Yang, Xianke zhang department of {2. sciences, tsinghua university, Beijing 100084, china department of mathematical {2. Tsinghua University Beijing 100084 China

Let K be a global quadratic field, then every unramified abelian extension of Kis proved to be absolutely Galois when Kis a number field or under some natural conditions when Kis a function field. The absolute Galois ... 详细信息

关键词： Global quadratic fields Unramified extensions

Modification of POSS and their tribological properties and resistant to space atomic oxygen irradiation as lubricant additive of multialkylated cyclopentanes

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Friction 2024年第5期12卷 884-896页

作者： Xingwei WANG Chaoyang zhang Chen ZHAO Yijing LIANG Ming zhang Wufang YANG Bo YU Qiangliang YU {2. CAI Feng ZHOU Weimin LIU State Key Laboratory of Solid Lubrication Lanzhou Institute of Chemical PhysicsChinese Academy of SciencesLanzhou730000China Shandong Laboratory of Yantai Advanced Materials and Green Manufacturing Yantai264000China

Developing functional additive resistant to space atomic oxygen(AO)irradiation through simple molecular design and chemical synthesis to enhance the lubricating performance of multialkylated cyclopentanes(MACs)oil is a significant ***,sulfur-containing polyhedral oligomere silsesquioxane(POSS)were synthesize via a click-chemistry reaction of octavinyl polyhedral oligomeric with alkyl *** reduce-friction(RF),anti-wear(AW)properties and anti-AO irradiation of POSS-S-R as MACs base oil additives in atmospheric and simulated space environments were systematically investigated for the first *** demonstrate that POSS-S-R not only possesses outstanding anti-AO irradiation capacity but also effectively improves the RF and AW of MACs in atmospheric or simulated space *** improvement is due to the excellent anti-AO irradiation properties of the POSS structure itself and the high load-carrying ability of silicon-containing and sulfur-containing compounds generated by tribo-chemical reactions,which effectively separates the direct contact of the friction *** believe that this synthesized POSS-S-R is a promising additive for space lubricants.

关键词： POSS additive reduce-friction anti-wear multialkylated cyclopentanes(MACs) resistant atomic irradiation

Interfacial mechanism of hydrogel with controllable thickness for stable drag reduction

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Friction 2024年第2期12卷 231-244页

作者： Xiaotong WU Ying LIU Yunlei zhang Xingwei WANG Wufang YANG Lang JIANG Shuanhong MA meirong CAI Feng ZHOU School of Advanced Manufacturing Nanchang UniversityNanchang 330031China State Key Laboratory of Solid Lubrication Lanzhou Institute of Chemical PhysicsChinese Academy of SciencesLanzhou 730000China Yantai Zhongke Research Institute of Advanced Materials and Green Chemical Engineering Shandong Laboratory of Yantai Advanced Materials and Green ManufactureYantai 264006China

Surface wettability plays a significant role in reducing solid–liquid frictional resistance,especially the superhydrophilic/hydrophilic interface because of its excellent thermodynamic *** this work,poly(acrylic acid)-poly(acrylamide)(PAA–PAM)hydrogel coatings with different thicknesses were prepared in situ by polydopamine(PDA)-UV assisted surface catalytically initiated radical *** drag reduction performance of hydrogel surface was measured using a rotational rheometer by the plate–plate *** experimental results showed that the average drag reduction of hydrogel surface could reach up to about 56%in Couette flow,which was mainly due to the interfacial polymerization phenomenon that enhanced the ability of hydration layer to delay the momentum dissipation between fluid layers and the diffusion behavior of *** proposed drag reduction mechanism of hydrogel surface was expected to shed new light on hydrogel–liquid interface interaction and provide a new way for the development of steady-state drag reduction methods.

关键词： steady state drag reduction hydrogel interface hydration hydrophilic

Optimal variational principle for backward stochastic control systems associated with Lévy processes

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Science china Mathematics 2012年第4期55卷 745-761页

作者： TANG MaoNing 1 & zhang Qi 2.1 department of mathematical sciences,Huzhou {2.,Huzhou 313000,china 2.School of mathematical sciences,Fudan {2.,Shanghai 2.0433,china 1. department of mathematical {2. Huzhou University Huzhou 313000 China2. School of Mathematical Sciences Fudan University Shanghai 200433 China

The paper is concerned with optimal control of backward stochastic differentiM equation （BSDE） driven by Teugel＇s martingales and an independent multi-dimensional Brownian motion, where Teugel＇s martingales are a family of pairwise strongly orthonormal martingales associated with L6vy processes （see e.g., Nualart and Schoutens＇ paper in 2.00）. We derive the necessary and sufficient conditions for the existence of the optimal control by means of convex variation methods and duality techniques. As an application, the optimal control problem of linear backward stochastic differential equation with a quadratic cost criteria （or backward linear-quadratic problem, or BLQ problem for short） is discussed and characterized by a stochastic Hamilton system.

关键词： stochastic control stochastic maximum principle Ldvy processes Teugel's martingales backwardstochastic differential equations

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 {2., Qingdao 2.6071, china 2. department of Chemistry, tsinghua university, Beijing 100084, china 3. department of Physics, Qingdao {2., Qingdao 2.6071, 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.