RELATIVE ENTROPY DIMENSION FOR COUNTABLE AMENABLE GROUP ACTIONS

We study the topological complexities of relative entropy zero extensions acted upon by countable-infinite amenable groups.First,for a given Følner sequence,we define the relative entropy dimensions and the dimensions of the relative entropy generating sets to characterize the sub-exponential growth of the relative topological complexity.we also investigate the relations among these.Second,we introduce the notion of a relative dimension set.Moreover,using the method,we discuss the disjointness between the relative entropy zero extensions via the relative dimension sets of two extensions,which says that if the relative dimension sets of two extensions are different,then the extensions are disjoint.

Regional homogeneity of intrinsic brain activity related to the main alexithymia dimensions

Background Alexithymia is a multidimensional personality construct.Objective This study aims to investigate the neuronal correlates of each alexithymia dimension by examining the regional homogeneity(ReHo) of intrinsic brain activity in a resting situation.Methods From university freshmen, students with alexithymia and non-alexlthymia were recruited. Their alexithymic traits were assessed using the Toronto Alexithymia Scale-20. The ReHo was examined using a resting-state functional MRI approach.Results This study suggests significant gro叩 differences in ReHo in multiple brain regions distributed in the frontal lobe, parietal lobe, temporal lobe, occipital lobe and insular cortex. However, only the ReHo in the insula was positively associated with difficulty identifying feelings, a main dimension of alexithymia. The ReHo in the lingual gyrus,precentral gyrus and postcentral gyrus was positively associated with difficulty describing feelings in participants with alexithymia. Lastly, the ReHo in the right dorsomedial prefrontal cortex(DMPFC_R) was negatively related to the externally oriented thinking style of participants with alexithymia.Conclusion In conclusion, these results suggest that the main dimensions of alexithymia are correlated with specific brain regions' function, and the role of the insula,lingual gyrus, precentral gyrus, postcentral gyrus and DMPFC_R in the neuropathology of alexithymia should be further investigated.

Relative Ding Projective Modules over Formal Triangular Matrix Rings

Let U be a (B, A)-bimodule, A and B be rings, and be a formal triangular matrix ring. In this paper, we characterize the structure of relative Ding projective modules over T under some conditions. Furthermore, using the left global relative Ding projective dimensions of A and B, we estimate the relative Ding projective dimension of a left T-module.

我们为什么需要专业主义?

2020年年初突如其来的新冠肺炎揪动着全国人民的心。作为专业人士的医护人员、科研人员成为大家守望与依靠的对象。广大民众从未像现在这样关注专业人士,认识到他们对我们生活之如此重要。南京大学"中国企业专业化管理研究"课题团队对此领域进行了研究。本文从专业人士和专业主义的内涵讨论入手,在与关系主义和雷锋精神的比较中,凸显我们为什么需要专业主义。本文进一步运用三维平衡理论的思想,分析专业主义作为文化维度的主要力量,对社会健康运行的重要作用。特别强调,当前中国社会,政治逻辑和经济逻辑强大,文化逻辑弱小。中国社会若要完成从传统向现代的转型,经济若要跨越中等收入陷阱,就亟须加强专业人士的专业主义建设。本文呼吁,专业人士应当践行专业主义,做名副其实的专业人士,担起文化维度的社会嵌入性力量。

Resolving Subcategories of Triangulated Categories and Relative Homological Dimension

We introduce and study （pre）resolving subcategories of a triangulated category and the homological dimension relative to these subcategories. We apply the obtained properties to relative Gorenstein categories.

On Proper and Exact Relative Homological Dimensions

In Enochs'relative homological dimension theory occur the(co)resolvent and(co)proper dimensions,which are defined by proper and coproper resolutions constructed by precovers and preenvelopes,respectively.Recently,some authors have been interested in relative homological dimensions defined by just exact sequences.In this paper,we contribute to the investigation of these relative homological dimensions.First we study the relation between these two kinds of relative homological dimensions and establish some transfer results under adjoint pairs.Then relative global dimensions are studied,which lead to nice characterizations of some properties of particular cases of self-orthogonal subcategories.At the end of this paper,relative derived functors are studied and generalizations of some known results of balance for relative homology are established.

Homological Dimensions Relative to Special Subcategories

Let A be an abelian category,C an additive,full and self-orthogonal subcategory of A closed under direct summands,rG(C)the right Gorenstein subcategory of A relative to C,and⊥C the left orthogonal class of C.For an object A in A,we prove that if A is in the right 1-orthogonal class of rG(C),then the C-projective and rG(C)-projective dimensions of A are identical;if the rG(C)-projective dimension of A is finite,then the rG(C)-projective and⊥C-projective dimensions of A are identical.We also prove that the supremum of the C-projective dimensions of objects with finite C-projective dimension and that of the rG(C)-projective dimensions of objects with finite rG(C)-projective dimension coincide.Then we apply these results to the category of modules.

Relative Derived Equivalences and Relative Homological Dimensions

Let A be a small abelian category.For a closed subbifunctor F of Ext_A^1（-,-）,Buan has generalized the construction of Verdier’s quotient category to get a relative derived category,where he localized with respect to F-acyclic complexes.In this paper,the homological properties of relative derived categories are discussed,and the relation with derived categories is given.For Artin algebras,using relative derived categories,we give a relative version on derived equivalences induced by F-tilting complexes.We discuss the relationships between relative homological dimensions and relative derived equivalences.