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A categorical interpretation of Yetter-Drinfel'd modules

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Chinese Science Bulletin 1999年第9期44卷 771-778页

作者： KAN Haibin and WANG ShuanhongInstitute of mathematics , Fudan university , Shanghai 200433 , china department of mathematics , Henan Normal university, xinxiang 453002, china Institute of mathematics Fudan Univrrsity Shanghai China Dcpartment of mathematics Henun Normal University Xinxiang China

It is known that any strict tensor category （C, I） can determine a strict braided tensor category Z （ C）, the centre of C. When A is a finite Hopf algebra, Drinfel’d has proved that Z（AM） is equivalent to D（A）M as a braided tensor category, where AM is the left A-module category, and D （A） is the Drinfel’d double of A. This is the categorical interpretation of D （A）.Z（4M） is proved to be equivalent to the Yetter-Drinfel’ d module category AY D4 as a braided tensor category for any Hopf algebra A. Furthermore, for right A-comodule category MA , Z（MA） is proved to be equivalent to the Yetter-Drinfel’ d module category AY D4 as a braided tensor category. But, in the two cases, the Yetter-Drinfel’ d module category AY DA has different braided tensor structures.

关键词： Yetter-Drinfel’d module tensor category equivalence.

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早发性结直肠癌的诊治进展

中华胃肠外科杂志 2024年第5期27卷 441-446页

作者：李雅琪李心翔复旦大学附属肿瘤医院大肠外二科、复旦大学上海医学院肿瘤学系上海200032

近年来,早发性结直肠癌(EOCRC)的发病率持续上升,但其发病机制尚不清楚。EOCRC的临床特征和分子病理学特征不同于晚发性结直肠癌,但目前两者治疗并无差别,尚缺乏关于EOCRC针对性的筛查及诊治指南。本文总结了EOCRC患者的流行病学特点、... 详细信息

近年来,早发性结直肠癌(EOCRC)的发病率持续上升,但其发病机制尚不清楚。EOCRC的临床特征和分子病理学特征不同于晚发性结直肠癌,但目前两者治疗并无差别,尚缺乏关于EOCRC针对性的筛查及诊治指南。本文总结了EOCRC患者的流行病学特点、危险因素、临床特征、分子病理特征、发生发展机制及预防筛查策略的研究进展,以期为EOCRC的诊治提供理论依据。

关键词：结直肠肿瘤,早发性流行病学危险因素临床特征分子特征

Estimates for eigenvalues of Laplacian operator with any order

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Science china mathematics 2007年第8期50卷 1078-1086页

作者： Fa-en WU~(1+) Lin-fen CAO~2 1 department of mathematics,Beijing Jiaotong university,Beijing 100044,china 2 department of mathematics,Henan Normal university,xinxiang 453007,china department of mathematics Beijing Jiaotong University Beijing 100044 China department of mathematics Henan Normal University Xinxiang 453007 China

Let D be a bounded domain in an n-dimensional Euclidean space ? n . Assume that $$0 < \lambda _1 \leqslant \lambda _2 \leqslant \cdots \leqslant \lambda _k \leqslant \cdots $$ are the eigenvalues of the Dirichlet Lapl... 详细信息

Let D be a bounded domain in an n-dimensional Euclidean space ? n . Assume that $$0 3 the above inequality is better than all the known results. Our rusults are the natural generalization of inequalities corresponding to the case l = 2 considered by Qing-Ming Cheng and Hong-Cang Yang. When l = 1, our inequalities imply a weaker form of Yang inequalities. We aslo reprove an implication claimed by Cheng and Yang.

关键词： Dirichlet problem eigenvalue estimate Laplacian operator 35P15 58G25

On the construction of multi-output Boolean functions with optimal algebraic immunity

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Science china(Information Sciences) 2012年第7期55卷 1617-1623页

作者： ZHANG Jie 1,2 ,SONG ShouChao 1 ,DU Jiao 2,3 & WEN QiaoYan 2 1 School of Science,Beijing university of Posts and Telecommunications,Beijing 100876,china 2 State Key Laboratory of Networking and Switching Technology,Beijing university of Posts and Telecommunications,Beijing 100876,china 3 department of mathematics,xinxiang university,xinxiang 4.3003,china 1. School of Science Beijing University of Posts and Telecommunications Beijing 100876 China2. State Key Laboratory of Networking and Switching Technology Beijing University of Posts and Telecommunications Beijing 100876 China3. Department of Mathematics Xinxiang University Xinxiang 453003 China

In this paper,we show a construction of multi-output Boolean functions with optimal algebraic ***,the relationship between the algebraic immunity of a multi-output Boolean function and those of its component functions is *** show that all the component functions,together with their nonzero linear combination,of the multi-output Boolean functions achieved by this construction have optimal algebraic immunity simultaneously.

关键词： algebraic immunity Boolean functions algebraic attacks annihilators

THE PHYSICAL ENTROPY OF SINGLE CONSERVATION LAWS

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Journal of Computational mathematics 1998年第5期16卷 437-444页

作者： (department of mathematics, Peking university, Beijing 100871, china) Beijing Univ Dept Math Beijing 100871 Peoples R China

By means of the comparisons with the formulas in statistical mechanics and thermodynamics, in this paper it is demonstrated that for the single conservation law partial derivative(t)u + partial derivative(x)f(u) = 0, if the flux function f(u) is convex (or concave), then, the physical entropy is S = -f(u); Furthermore, if we assume this result can be generalized to any f(u) with two order continuous derivative, from the thermodynamical principle that the local entropy production must be non-negative, one entropy inequality is derived, by which the O.A. Olejnik's famous E- condition can be explained successfully in physics.

关键词： conservation laws entropy entropy production

Genetic analysis of transcription factors in dopaminergic neuronal development in Parkinson’s disease

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Chinese Medical Journal 2024年第4期137卷 450-456页

作者： Yuwen Zhao Lixia Qin Hongxu Pan Tingwei Song Yige Wang Xiaoxia Zhou Yaqin Xiang Jinchen Li Zhenhua Liu Qiying Sun Jifeng Guo xinxiang Yan Beisha Tang Qian Xu department of Neurology Xiangya HospitalCentral South UniversityChangshaHunan 410008China department of Neurology The Second Xiangya HospitalCentral South UniversityChangshaHunan 410011China Bioinformatics Center National Clinical Research Center for Geriatric Disorders Xiangya HospitalCentral South UniversityChangshaHunan 410008China department of Geriatrics Xiangya HospitalCentral South UniversityChangshaHunan 410008China Centre for Medical Genetics and Hunan Key Laboratory of Medical Genetics School of Life SciencesCentral South UniversityChangshaHunan 410008China Key Laboratory of Hunan Province in Neurodegenerative Disorders Central South UniversityChangshaHunan 410008China

Background:Genetic variants of dopaminergic transcription factor-encoding genes are suggested to be Parkinson’s disease(PD)risk factors;however,no comprehensive analyses of these genes in patients with PD have been ***,we aimed to genetically analyze 16 dopaminergic transcription factor genes in Chinese patients with ***:Whole-exome sequencing(WES)was performed using a Chinese cohort comprising 1917 unrelated patients with familial or sporadic early-onset PD and 1652 ***,whole-genome sequencing(WGS)was performed using another Chinese cohort comprising 1962 unrelated patients with sporadic late-onset PD and 1279 ***:We detected 308 rare and 208 rare protein-altering variants in the WES and WGS cohorts,***-based association analyses of rare variants suggested that MSX1 is enriched in sporadic late-onset ***,the significance did not pass the Bonferroni ***,72 and 1730 common variants were found in the WES and WGS cohorts,***,single-variant logistic association analyses did not identify significant associations between common variants and ***:Variants of 16 typical dopaminergic transcription factors might not be major genetic risk factors for PD in Chinese ***,we highlight the complexity of PD and the need for extensive research elucidating its etiology.

关键词： Parkinson’s disease Transcription factors Dopaminergic neurons Genetic Variants

Some Uniqueness Results for a Class of Quasilinear Elliptic Eigenvalue Problems

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Acta Mathematica Sinica,English Series 1998年第2期14卷 245-260页

作者： Guo Zongming Yang Zuodong (department of mathematics,Henan Normal university,xinxiang 453002,china) department of mathematics Henan Normal University 453002 Xinxiang China

Existence and uniqueness results are obtained for positive radial solutions of a class of quasilinear elliptic equations in a N-ball or an annulus without monotone assumptions on the nonlinear term *** is also proved ... 详细信息

关键词： Quasilinear elliptic eigenvalue problems Positive radial solutions Uniqueness

Explicit Representations of Mimmal Immersions of 2-Spheres into S^(2m)

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Acta Mathematica Sinica,English Series 1997年第2期13卷 175-186页

作者： Li Xingxiao (department of mathematics,Henan Normal university,xinxiang 453002,china)Li Anmin (department of mathematics,Sichuan university,Chengdu 610064,china)

For all minimal immersions of the 2-sphere S2 into the unit 2m-sphere S2mwith area 2π[m（m+1）+2],we are able to give an explicit representation by some real *** representation is rather important in the study of minimal 2-spheres in S2mbecause the parameters concerned are independent of each *** examples are given and a classification theorem is also obtained.

关键词： Minimal immersion Holomorphic curve Directrix

AN　EXISTENCE　THEOREM　FOR　RADIAL　POSITIVE　SOLUTIONS　OF　NONLINEAR　DEGENERATE　ELLIPTIC　EQUATIONS

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Systems Science and Mathematical Sciences 1994年第4期7卷 289-292页

作者： LIU Hailiang(department of mathematics, Henan Normal university, xinxiang453002, china) 河南师范大学数学系河南新乡 453002

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关键词： Existence radial solution degenerate equation