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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

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

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

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.

CRISPR-Cas9-based genome-editing technologies in engineering bacteria for the production of plant-derived terpenoids

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Engineering Microbiology 2024年第3期4卷 43-53页

作者： Xin Sun Haobin zhang Yuping Jia Jingyi Li meirong Jia State Key Laboratory of Bioactive Substance and Function of Natural Medicines NHC Key Laboratory of Biosynthesis of Natural ProductsCAMS Key Laboratory of Enzyme and Biocatalysis of Natural DrugsInstitute of Materia MedicaChinese Academy of Medical Sciences and Peking Union Medical CollegeBeijing 100050China Shandong Academy of Pharmaceutical sciences Jinan 250101China

Terpenoids are widely used as medicines,flavors,and ***,the use of these natural products is largely restricted by their low abundance in native ***,heterologous biosynthesis of terpenoids in microorganisms offers an alternative and sustainable approach for efficient *** genome-editing technologies have been developed for microbial strain *** regularly interspaced short palin-dromic repeats(CRISPR)-CRISPR associated protein 9(Cas9)is the most commonly used system owing to its outstanding efficiency and convenience in genome *** this review,the basic principles of CRISPR-Cas9 systems are briefly introduced and their applications in engineering bacteria for the production of plant-derived terpenoids are *** aim of this review is to provide an overview of the current developments of CRISPR-Cas9-based genome-editing technologies in bacterial engineering,concluding with perspectives on the challenges and opportunities of these technologies.

关键词： CRISPR-Cas9 Genome editing Terpenoids Metabolic engineering Bacteria

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

The regular representation and regular covariant representation of crossed products of Woronowicz C^(*)-algebras

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Science china Mathematics 2005年第9期48卷 1245-1259页

作者： zhang Xiaoxia~(1,2. & GUO Maozheng~(1,3) 1. School of mathematical {2.,Peking University,beijing 100871,china 2. department of Mathematics,Yantai University,Yantai 2.4005,china 3. LMAM,Peking University,beijing 100871,china 1. School of mathematical sciences Peking University 100871 Beijing China 2. department of Mathematics Yantai University 264005 Yantai China 3. LMAM Peking University 100871 Beijing China

In this paper,it is shown that the regular representation and regular covariant representation of the crossed products A×α G correspond to the twisted multiplicative unitary operators,where A is a Woronowicz C~*-algebra acted upon by a discrete group ***,it is also shown that the regular covariant C~*-algebra is the Woronowicz C~*-algebra which corresponds to a multiplicative ***,an explicit description of the multiplicative unitary operator for C(SU_q(2. )×α (?) is given in terms of those of the Woronowicz C~*-algebra C(SU_q(2. ) and the discrete group G.

关键词： multiplicative unitary operator, Woronowicz C*-algebra, crossed product.

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.