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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

Recommendation Method for Contrastive Enhancement of Neighborhood Information

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Computers, Materials & Continua 2024年第1期78卷 453-472页

作者： Hairong Wang beijing Zhou Lisi zhang He Ma School of Computer Science and Engineering North Minzu UniversityNingxia750021China

Knowledge graph can assist in improving recommendation performance and is widely applied in various person-alized recommendation ***,existing knowledge-aware recommendation methods face challenges such as weak user-item interaction supervisory signals and noise in the knowledge *** tackle these issues,this paper proposes a neighbor information contrast-enhanced recommendation method by adding subtle noise to construct contrast views and employing contrastive learning to strengthen supervisory signals and reduce knowledge ***,first,this paper adopts heterogeneous propagation and knowledge-aware attention networks to obtain multi-order neighbor embedding of users and items,mining the high-order neighbor informa-tion of users and ***,in the neighbor information,this paper introduces weak noise following a uniform distribution to construct neighbor contrast views,effectively reducing the time overhead of view *** paper then performs contrastive learning between neighbor views to promote the uniformity of view information,adjusting the neighbor structure,and achieving the goal of reducing the knowledge noise in the knowledge ***,this paper introduces multi-task learning to mitigate the problem of weak supervisory *** validate the effectiveness of our method,experiments are conducted on theMovieLens-1M,MovieLens-2.M,Book-Crossing,and Last-FM *** results showthat compared to the best baselines,our method shows significant improvements in AUC and F1.

关键词： Contrastive learning knowledge graph recommendation method

A user-space file system for on-demand legacy desktop software

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Science China(Information sciences) 2011年第6期54卷 1142-1150页

作者： zhang YouHui 1,2., SU GeLin 1,2.& ZHENG WeiMin 1,2.1 {2. of Computer Science and Technology, {2., beijing 100084, China 2.tsinghua National Laboratory for Information Science and Technology, {2., beijing 100084, China 1. department of Computer Science and Technology Tsinghua University Beijing 100084 China2. Tsinghua National Laboratory for Information Science and Technology Tsinghua University Beijing 100084 China

Some user-level virtualization technologies have been used to convert legacy software (like the existing Windows desktop applications) into the on-demand software without any modification. To give the client a friendly and compatible method to access on-demand legacy software across the Internet, this paper presents a clientend file system for this usage case. It is a Windows user-space file system based on the cloud storage (where the on-demand software is stored), which converts the local file system accesses into remote visits. Quite a few optimizations are adopted and adjusted to suit the file-access-pattern of on-demand software, including the local cache, metadata/data/software prefetch and content-addressable storage (CAS), to decrease the number of remote visits and/or to overlap IO (input/output) operations with software execution. Detailed access-pattern analyses are also presented. This file system has been implemented and tests show that it is practical for much daily-used software-a local cache of limited size can provide up to 80% hit ratio and the corresponding overhead of running-time is about 37%. Owing to this method, on any compatible and networked computer, a user can use his/her personalized software conveniently although it does not exist on the local host.

关键词： on-demand software software as a service user-space file system cloud storage

Effects of the Biot and the squirt-flow coupling interaction on anisotropic elastic waves

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Chinese Science Bulletin 2000年第23期45卷 2130-2138页

作者： YANG Dinghui & zhang Zhongjie department of {2. sciences, tsinghua university, beijing 100084, China Institute of Geophysics, Chinese Academy of sciences, beijing 100101, China department of mathematical {2. Tsinghua University Beijing China Institute of Geophysics Chinese Academy of Sciences Beijing China

Considering the velocity anisotropy of the solid/fluid relative motion and employment of the BISQ theory based on the one-dimensional porous isotropic case, we establish a two-phase anisotropic elastic wave equation to simultaneously include the Biot and the squirt mechanisms in terms of both the basic principles of the fluid’s mass conservation and the elastic-wave dynamical equations in the two-phase anisotropic rock. Numerical results, while the Biot-flow and the squirt-flow effects are simultaneously considered in the transversely isotropic (Tl) poroelastic medium, show that the attenuation of the quasi P-wave and the quasi SV-wave strongly depend on the permeability anisotropy, and the attenuation behavior at low and high frequencies is contrary. Meanwhile, the attenuation and dispersion of the quasi P-wave are also affected seriously by the anisotropic solid/fluid coupling additional density.

关键词： two-phase anisotropy Biot flow squirt-flow elastic wave attenuation and dispersion BISQ model.

Molecular architecture and engineering of spider dragline silk protein

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Progress in Natural Science:Materials International 2005年第9期15卷 769-776页

作者： zhang Hengmu and LIU Jinyuan(department of Biological {2. and Biotechnology, tsinghua university, beijing 100084, China) department of Biological sciences and Biotechnology Tsinghua University Beijing 100084 China

Spider dragline silk, which is produced in spider major ampullate gland, is a composite proteinacious fiber with highly repetitive Ala-Gly-rich domain. The unique combination of both high tensile strength and high elasticity makes spider dragline silk superior to almost any other natural or synthetic fibers. Cloning of the genes reveals that the silk is composed of at least two major proteins. Each protein component contains multiple repeats of modular structures that alternate between Ala-rich domains and Gly-rich domains. Molecular engineering not only opens a door to the production of spidroins but also provides a valuable experimental system to test and further establish the relationship between modular structures and mechanical properties. Here, based on our own studies, we review the latest progress of the modular structure and genetic engineering and outline the future prospects.

关键词： spider dragline silk protein modular structure molecular engineering.