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关键词： Noncommutative Hodge structures   Deformation quantization   Matrix factorizations  

摘要： In this paper, we present an explicit cyclic minimal A(infinity) model for the category of matrix factorizations MF(W) of an isolated hypersurface singularity. The key observation is to use Kontsevich's deformation quantization technique. Pushing this idea further, we use the Tsygan formality map to obtain a comparison theorem that the categorical Variation of Semi-infinite Hodge Structure of MF(W) is isomorphic to Saito's original geometric construction in primitive form theory. (C) 2021 Elsevier Inc. All rights reserved.

关键词： Dynamical systems   Triangulated categories   Categorical entropy   Topological entropy   Polynomial entropy   Automorphisms   Stability conditions  

摘要： For classical dynamical systems, the polynomial entropy serves as a refined invariant of the topological entropy. In the setting of categorical dynamical systems, that is, triangulated categories endowed with an endofunctor, we develop the theory of categorical polynomial entropy, refining the categorical entropy defined by Dimitrov, Haiden, Katzar-kov, and Kontsevich. We justify this notion by showing that for an automorphism of a smooth projective variety, the categorical polynomial entropy of the pullback functor on the derived category coincides with the polynomial growth rate of the induced action on cohomology. We also establish in general a Yomdin-type lower bound for the categorical polynomial entropy of an endofunctor in terms of the induced endomorphism on the numerical Grothendieck group of the category. As examples, we compute the categorical polynomial entropy for some standard functors like shifts, Serre functors, tensoring line bundles, automorphisms, spherical twists, P-twists, and so on, illustrating clearly how categorical polynomial entropy refines the study of categorical entropy and enables us to study the phenomenon of categorical trichotomy. A parallel theory of polynomial mass growth rate is developed in the presence of Bridgeland stability conditions. (c) 2021 The Authors. Published by Elsevier Inc. This is an open access article under the CC BY license (http://***/licenses/by/4.0/).

关键词： Hereditary category   (Cluster)-tilting object   (Cluster)-tilting graph   Happel-Unger's conjecture  

摘要： Let k be an algebraically closed field and H a Hom- and Ext-finite hereditary abelian k-category with tilting objects. It is proved that the cluster-tilting graph associated with His connected. As a consequence, we establish the connectedness of the tilting graph for the category coh X of coherent sheaves over a weighted projective line X of wild type. The connectedness of tilting graphs for such categories was conjectured by Happel and Unger, which has immediate applications in cluster algebras. For instance, we deduce that there is a bijection between the set of isomorphism classes of indecomposable rigid objects of the cluster category C-X of coh X and the set of cluster variables of the cluster algebra A(X) associated with coh X. (C) 2021 Elsevier Inc. All rights reserved.

关键词： 强制性规定   立法规划   劳动基准法   效力问题   强行法   私法效力   规范结构   保护劳动者权益  

摘要： 制定劳动基准法已经纳人本届人大的立法规划,但劳动基准法的效力问题依然没有得到很好的解决。我国劳动基准立法应摒弃劳动基准法是公法这一成见,从劳动基准法是强行法这一命题出发对其进行制度设计。劳动基准法的功能在于保护劳动者权益,劳动基准法是国家通过强制性规定保护劳动者的法律规范的总和。

关键词： 幂等完备范畴   函子范畴   范畴等价  

摘要： 讨论函子范畴和范畴的幂等完备化构造的相容性,证明小范畴■到任意范畴■的函子范畴■的幂等完备化范畴等价于■到幂等完备化范畴■的函子范畴■.进一步得到函子范畴■是幂等完备的,当且仅当■是幂等完备的.

关键词： 联绵词   原型范畴   双声叠韵   语义联绵   字形联绵  

摘要： 目前学界对联绵词的界定是“双音节单纯词”,根据经典范畴理论二分法原则,由义同义近语素构成的联绵词被排除在外,有些外来词却符合双音单纯词的标准。联绵词成员的取舍成为联绵词研究的困扰,有些学者质疑对联绵词是“双音节单纯词”的界定。文章通过梳理传统语言学和近现代学者对联绵词的描述,发现联绵词除了具有单纯性特征外,还具有语音、语义和记录其文字形体上的联绵性,并从认知语言学原型范畴理论的家族相似性、典型成员及范畴成员地位的不平等、边界模糊性和范畴成员的交叉性以及典型成员的变化,对联绵词概念和成员的归属问题进行解释。

关键词： 左-左BiHom-Yetter-Drinfeld模   拟三角BiHom-双代数   张量积   范畴  

摘要： 令(H,μH,ΔH,αH,βH,ψH,ωH)是BiHom-双代数.本文首先给出了H上的左-左BiHom-Yetter-Drinfeld模的定义,并证明了两个左-左BiHom-Yetter-Drinfeld模的张量积还是一个左-左BiHom-Yetter-Drinfeld模.然后研究了拟三角BiHom-双代数(H,R)上的左模范畴和左-左BiHom-Yetter-Drinfeld模构成的范畴之间的关系.

关键词： 王守仁   陆九渊   理学思想   理性认知   道德本体   知行合一   格物致知   内在矛盾  

摘要： 本书以理、性、心、知四个范畴为中心,通过对朱熹、陆九渊和王守仁三者思想的比较分析,对理学从朱学时代到王学时代的演进脉络进行了探讨和概括。本书认为,理范畴存在客观性与主观性的内在矛盾,理学的发展正是解决这一内在矛盾的过程,并最终走向主观性;性范畴逐渐被弱化(包括淡化和泛化两种方式),最终丧失了其道德本体的地位;心范畴的作用从“心具理”走向“心生理”,这是与理范畴的主观化过程相一致的;知范畴从“格物致知”的理性认知逐渐走向了“知行合一”的本能直觉。

关键词： 动态范畴化   基体/侧显   动词do  

摘要： 范畴的动态性一直以来都备受学者们关注,词义的动态发展是语言范畴动态性的最根本体现。本文基于"动态范畴化"理论,在基体/侧显理论框架下,以动词do为例,分析其词义动态范畴化的工作原理及工作方式,以期对词义的部分衍化机制做出阐释。研究发现,动词do的动态范畴化经历了范畴内的保守式渐变——相邻范畴间的互动式跨越——去范畴化的开放式嬗变,这三种类型形成了动词do动态范畴化的连续统,而突显观中的基体/侧显理论是do动态范畴化的重要工作机制之一。在do的词义范畴中,及物性的降低与缺失是其词义虚化和泛化的重要指标,对其词义范畴的动态发展有着不可忽视的意义。

关键词： BI‐   RADS   breast cancer   density   risk   screening mammography  

摘要： Breast density is strongly associated with breast cancer risk;however, studies on the association between density changes and breast cancer risk have controversial results. The aim of our study was to determine the association between breast density changes and breast cancer risk in East-Asian women. We included 3 301 279 women aged >= 40 years screened for breast cancer twice during 2009 to 2010 and 2011 to 2012. Data were obtained from the National Health Insurance Service (NHIS) database. Breast density was evaluated using the Breast Imaging-Reporting and Data System (BI-RADS). Relative risk (RR) and 5-year risk of developing breast cancer according to density category changes were calculated. Overall, 23.0% of the women had a higher breast density and 22.2% of the women had a lower breast density in second screening compared to the first. An increase in the BI-RADS density category between two subsequent mammographic screenings was associated with an increase in breast cancer risk and vice versa in terms of RR. The 5-year breast cancer risk was affected by the initial BI-RADS density category, changes in density category and patients' characteristics such as age, menopausal status and family history of breast cancer. In patients with breast cancer family history, the 5-year breast cancer risk was prominent, at a maximum of 2.39% (95% CI = 1.23-3.55) in women with breast density category of 2 to 4. Changes in the BI-RADS density category were associated with breast cancer risk. Longitudinal measures of BI-RADS density may be helpful in identifying high-risk women, especially those with a breast cancer family history.