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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 {2., 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

Extremal eigenvalues of measure differential equations with fixed variation

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Science china Mathematics 2010年第10期53卷 2573-2588页

作者： zhang MeiRong 1,2.1 department of Mathematical {2.,tsinghua university,beijing 100084,china 2.Zhou Pei-Yuan Center for Applied Mathematics,tsinghua university,beijing 100084,china 1. department of Mathematical sciences Tsinghua University Beijing 100084 China2. Zhou Pei-Yuan Center for Applied Mathematics Tsinghua University Beijing 100084 China

In this paper we will study eigenvalues of measure differential equations which are motivated by physical problems when physical quantities are not absolutely *** taking Neumann eigenvalues of measure differential equations as an example,we will show how the extremal problems can be completely solved by exploiting the continuity results of eigenvalues in weak* topology of measures and the Lagrange multiplier rule for nonsmooth *** results can give another explanation for extremal eigenvalues of SturmLiouville operators with integrable potentials.

关键词： measure differential equation eigenvalue extremal value weak* topology Frechét derivative sub-differential

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.

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 Mathematical {2., tsinghua university, beijing 100084, china) department of Mathematical sciences 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.

A zebrafish tufm mutant model for the COXPD4 syndrome of aberrant mitochondrial function

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Journal of Genetics and Genomics 2024年第9期51卷 922-933页

作者： Ting Li Tursunjan Aziz guangyuan Li Lin zhang Jihua Yao Shunji Jia School of Life sciences Fudan UniversityShanghai 200438China State Key Laboratory of Membrane Biology Tsinghua-Peking Center for Life SciencesSchool of Life SciencesTsinghua UniversityBeijing 100084China State Key Laboratory of Molecular Developmental Biology Institute of Genetics and Developmental BiologyChinese Academy of SciencesBeijing 100101China

Mitochondrial dysfunction is a critical factor leading to a wide range of clinically heterogeneous and often severe disorders due to its central role in generating cellular *** in the TUFM gene are known to cause combined oxidative phosphorylation deficiency 4(COXPD4),a rare mitochondrial disorder characterized by a comprehensive quantitative deficiency in mitochondrial respiratory chain(MRC)*** development of a reliable animal model for COXPD4 is crucial for elucidating the roles and mechanisms of TUFM in disease pathogenesis and benefiting its medical *** this study,we construct a zebrafish tufm−/−mutant that closely resembles the COXPD4 syndrome,exhibiting compromised mitochondrial protein translation,dysfunctional mitochondria with oxidative phosphorylation defects,and significant metabolic suppression of the tricarboxylic acid *** this COXPD4 zebrafish model,we comprehensively validate the clinical relevance of TUFM mutations and identify probucol as a promising therapeutic approach for managing *** data offer valuable insights for understanding mitochondrial diseases and developing effective treatments.

关键词： Tufm Mitochondria COXPD4 Disease model Zebrafish

Covalent organic framework monolayer:Accurate syntheses and advanced application

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Nano Research 2024年第7期17卷 6603-6618页

作者： guangyuan Feng Xiaojuan Li Miao zhang Jiabi Xu Zhiping Liu Lingli Wu Shengbin Lei Key Laboratory of Organic Integrated Circuit Ministry of Education and Tianjin Key Laboratory of Molecular Optoelectronic SciencesDepartment of ChemistrySchool of Science and Collaborative Innovation Center of Chemical Science and Engineering(Tianjin)Tianjin UniversityTianjin 300072China Medical College Northwest Minzu UniversityLanzhou 730000China School of Chemistry and Chemical Engineering Lanzhou Jiaotong UniversityLanzhou 730070China

Covalent organic framework(COF)monolayers,with atomically thin,ordered networks,and rich functionality,are widely studied due to their unusual structure/property ***,synthesizing COF monolayer has remained an unmet challenge due to the difficulty of controlling reactions at the monolayer limit with large-scale *** identification and development of new reactions and polymerization conditions are critical for the further advancement of COF monolayer ***,as one-molecule-thick a freestanding films,COF monolayer offers an ideal material *** advanced applications of COF monolayer have been explored in recent *** review provides an overview of the current state of precise synthetic strategies for COF monolayer,highlighting the advantages and limitations of different synthetic approaches and key challenges related to enhancing quality,and emphasizing the unique benefits of COF monolayer as both an ideal model system and for advanced applications.

关键词： covalent organic frameworks monolayer accurate syntheses advanced application

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

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 Mathematical {2., tsinghua university, beijing 100084, china department of Mathematical sciences 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

Thermal History of Cambrian Burgess Shale-Type Deposits:New Insights from the Early Cambrian Chengjiang and Qingjiang Fossils of South china

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Journal of Earth Science 2024年第4期35卷 1215-1223页

作者： Yuheng Qiao Linhao Cui guangyuan Xing Dongjing Fu Chao Chang Robert Gaines Xingliang zhang State Key Laboratory of Continental Dynamics Shaanxi Key laboratory of Early Life and EnvironmentsDepartment of GeologyNorthwest UniversityXi’an710069China department of Geology Pomona CollegeClaremontCA91711USA

Burgess Shale-type deposits provide a wealth of information on the early evolution of *** that are central to understanding the exceptional preservation of these biotas and the paleoenvironments they inhabited may be obscured by the post-depositional alteration due to metamorphism at depth and weathering near the Earth’s *** over 50 Cambrian BST biotas,the Chengjiang and Qingjiang deposits are well known for their richness of soft-bodied taxa,fidelity of preservation,and Early Cambrian *** alteration via weathering has been well-investigated,the thermal maturity of the units bearing the two biotas has not yet been *** we investigate peak metamorphic temperatures of the two deposits using two independent *** gradient analyses demonstrate that the most fossiliferous sections of the Chengjiang were buried at a maximum depth of∼8500 m in the Early Triassic,corresponding to∼300°C,while the type area of the Qingjiang biota was buried at a maximum depth of∼8700 m in the Early Jurassic,corresponding to∼2.0°*** geothermometer analyses of fossil carbonaceous material demonstrate that peak temperatures varied across localities with different burial *** two productive sections of the Chengjiang biota were thermally altered at a peak temperature of approximately 300°C,and the main locality of the Qingjiang biota experienced a peak temperature of 2.8±2.°*** results from two independent methods are *** BST deposits for which thermal maturity has been documented,the Qingjiang biota is the least thermally mature,and therefore holds promise for enriching our understanding of BST deposits.

关键词： the Chengjiang Biota the Qingjiang Biota burial history Raman geothermometer thermal history Burgess Shale-type Lagerstätte