象似性与主观化:英语存在句的“数”范畴观

英语存在句的"数"契合现象是数量象似性和标记相似性相结合的认知表征,反映了额外语符代表数量多和空间象征标志[-s]在复合结构[V+NP]中对立统一的认知经验,即在一个地点框架中占据空间和剩余空间的不对称;而"数"的嬗变是概念化者在物理空间域和品质空间域两个认知域上进行不同视角选择的结果,表达了对同一情景的不同识解。其实质上是语言的象似性和主观化相互作用的结果。象似性与主观化的不对称正是语言活力之所在,更重要的是,这种不对称性不仅仅表现在"数"范畴上,还表现在时、体等其他范畴上。以小见大,除为"数"范畴研究提供新的个案理论依据外,对"数"范畴的认知研究还可以进一步加深对语言本质的理解。

动态范畴化理论视角下英语名词“数”范畴变动情形研究

动态范畴化理论的提出与发展为英语名词“数”范畴的变动提供了合理依据。在具体语境的推动下,传统定义下的英语可数名词可向不可数名词范畴转移,不可数名词也可能进入可数名词范畴,实现再范畴化。在此过程中,转喻机制发挥着关键作用。

汉语“体”“数”语法范畴再探讨

长期以来“体、数”范畴在汉语中的表现及其标志是语言学界研究的焦点之一。本文从论证“体、数”范畴的变词语素出发,证实了汉语中存在这两个语法范畴,只是汉语由变词语素构成的语句和典型屈折语的语句在语法结构上有所不同而已。

粤方言和普通话“数”范畴体现方式的对比

"数"范畴在不同的语言中体现方式也不一样。汉语"数"范畴的体现方式有别于印欧语系的语言。缺少形态变化的粤方言和普通话,主要采用三种手段体现"数":通过添加具有复数意义的词尾体现"数";通过功能性词体现"数";通过含有数量义的限定性成分体现"数"。文章主要分析粤方言和普通话在使用这三种体现"数"的手段时所具有的共同点和不同点。

Construction of semisimple category over generalized Yetter-Drinfeld modules

Let H be a commutative, noetherian, semisimple and cosemisimple Hopf algebra with a bijective antipode over a field k. Then the semisimplicity of YD（H） is considered, where YD （H） means the disjoint union of the category of generalized Yetter-Drinfeld modules nYD^H（ α, β） for any α, β E Aut Hopf（H）. First, the fact that YD（H） is closed under Mor is proved. Secondly, based on the properties of finitely generated projective modules and semisimplicity of H, YD（H） satisfies the exact condition. Thus each object in YD（H） can be decomposed into simple ones since H is noetherian and cosemisimple. Finally, it is proved that YD （H） is a sernisimple category.

Enveloping algebras of generalized H-Hom-Lie algebras

Let H be a Hopf algebra and HYD the Yetter- Drinfeld category over H. First, the enveloping algebra of generalized H-Hom-Lie algebra L, i.e., Hom-Lie algebra L H in the category HYD, is constructed. Secondly, it is obtained that U（L） = T（ L）/L where I is the Hom-ideal of T（L） generated by {ll＇-l_（（-1））·l＇l_0-[l,l＇]｜l,l＇∈L}, and u： L,T（L）/I is the canonical map. Finally, as the applications of the result, the enveloping algebras of generalized H-Lie algebras, i.e., the Lie algebras in the category MyDn and the Hom-Lie algebras in the category of left H-comodules are presented, respectively.

Geometric Parameters of a Bocs (Ⅰ)

In this paper, the group action of a local wild Bocs'rep. category is introduced. And, it computed the parametric numbers U(n) and P(n) of the rep. category mod n(A) and ind n(t) in case n=1,2 with geometric method.

On braided Lie algebras

Let （C, C） be a braided monoidal category. The relationship between the braided Lie algebra and the left Jacobi braided Lie algebra in the category （C, C） is investigated. First, a braided C2-commutative algebra in the category （C, C） is defined and three equations on the braiding in the category （C, C） are proved. Secondly, it is verified that （A, [, ] ） is a left （strict） Jacobi braided Lie algebra if and only if （A, [, ] ） is a braided Lie algebra, where A is an associative algebra in the category （C, C）. Finally, as an application, the structures of braided Lie algebras are given in the category of Yetter-Drinfel＇d modules and the category of Hopf bimodules.

Categorification and Quasi-Hopf Algebras

We categorify the notion of coalgebras by imposing a co-associative law up to some isomorphisms on the co-multiplication map and requiring that these isomorphisms satisfy certairl law of their own, which is called the copentagon identity. We also set up a 2-category of 2-coalgebras. The purpose of this study is from the idea of reconsidering the quasi-Hopf algebras by the categorification process, so that we can study the theory of quasi-Hopf algebras and their representations in some new framework of higher category theory in natural ways.

Synchronization in Triangled Complex Networks

Using a tunable clustering coeffcient model withoutchanging the degree distribution, we investigate the effect of clustering coefficient on synchronization of networks with both unweighted and weighted couplings. For several typical categories of complex networks, the more triangles are in the networks, the worse the synchronizability of the networks is.

On the Braided Monoidal Categories of T-smash Products A ■_T H

Let A and H be Hopf algebra, T-smash product AT H generalizes twisted smash product A ＊ H. This paper shows a necessary and sufficient condition for T-smash product moduie category AT HM to be braided monoidal category.

Some Properties of Fuzzy Filter and Its Category

This paper is devoted to the study of some properties of fuzzy filters in lattice implication algebras. The structure theorem of fuzzy filters and the category of the sets of fuzzy filters were established with some basic properties of it were discussed.

Philosophy of Mathematics： Naturalism vs. Category Theory

Although E Maddy （1997） says on naturalism： ＂This is not, in itself, a philosophy of mathematics [...]＂ （161）, already by its name, or by those whose interest has called on it （Quine, Putnam et al.） ... it anyhow reveals desire to be it. Insofar as otherwise, the semantic potential of the word leaves far behind it （after all scarce） results it achieved from the relation of an exact （mathematical） expression and （overly rich） intuitive reality of Being. We plead here already from the perspective of the slogan ＂One and All＂ of the first philosopher： Tales, when by the number （which one forebodes） one could go to such an extent into areas of reality （Pythagoras）, or when （especially in the human sphere） is being over again actual final cause of Aristotle the philosophy and the mathematics to accomplish far more fruitful encounter with the Being. Alain Badiou （1988） has already pointed that： ＂Mathematics is ontology,＂ and the category theory in mathematics, having covered by itself other fields of this science, continues to find applications in a series of＂non-traditional＂ domains of reality. In that correlation the philosophy can express its （primary） needs for truth, justice, beauty, ... as well as for the overall development in the sense of purpose--also because of an undreamed power of the technological development （of hardwares and softwares） today. Namely, the naturalism in mathematics, which developed an abundant reflection on the place （importance of） the mathematical idiom in sciences--in the balance of criticism--has come rather to meager provisions, such as： ＂preestablished harmony of thinking,＂ ＂ontic commitment,＂ （Quine 1960） ＂the hygiene of mind,＂ （Maddy 1996） ＂success argument,＂ （Putnam 1975） ＂pragmatic argument,＂ （Resnik 1981） etc., which only are few places from the encounter of an exact expression such as is mathematical one and the reality of natuural sciences. Instead of philosophy of mathematics to radicalize its claims from the perspective of that （powerful） mathematical idiom and the excessive reality of Being and man＇s place in it--this time, in the spirit of biocosmology （neo-Aristotelism）.

Quantum Groups by Ore Extensions Associated withGroup Algebras

As a continuation of the work of Beattie on quantum groups constructed byOre extensions, in this paper, we characterize their centre and discuss the category ofquantum Yang-Baxter modules over them. In addition, we determine all finite dimen-sional irreducible representations over these quantum groups.

STRONGLY ALGEBRAIC LATTICES AND CONDITIONS OF MINIMAL MAPPING PRESERVING INFS

The tabor gives some characterizations of strongly algebraic lattices, and proves that thecategory of strongly algebraic lattices is complete and cocomplete. Finally, this paper gives thecomplete conditions under which the minimal mapping β: L→2L on a completely distributivelattice L preserves finite infs and arbitrary infs.

CONTINUOUS L-DOMAINS

Two characterization theorems of continuous L-domain are given. Then a problem raisedby J. D. Lawson and M. Mislove is solved.

The Change-Base Issue for Ω-Categories

Let G:Ω→Ω′be a closed unital map between commutative,unital quantales. G induces a functor G from the category of Ω-categories to that of Ω′-categories.This paper is concerned with some basic properties of G.The main results are:(1) when Ω,Ω′are integral,G:Ω→Ω′and F:Ω′→Ωare closed unital maps,F is a left adjoint of G if and only if F is a left adjoint of G;(2) G is an equivalence of categories if and only if G is an isomorphism in the category of commutative unital quantales and closed unital maps; and (3) a sufficient condition is obtained for G to preserve completeness in the sense that GA is a complete Ω′-category whenever A is a complete Ω-category.

DG Poisson algebra and its universal enveloping algebra

We introduce the notions of differential graded(DG) Poisson algebra and DG Poisson module. Let A be any DG Poisson algebra. We construct the universal enveloping algebra of A explicitly, which is denoted by A^(ue). We show that A^(ue) has a natural DG algebra structure and it satisfies certain universal property. As a consequence of the universal property, it is proved that the category of DG Poisson modules over A is isomorphic to the category of DG modules over A^(ue). Furthermore, we prove that the notion of universal enveloping algebra A^(ue) is well-behaved under opposite algebra and tensor product of DG Poisson algebras. Practical examples of DG Poisson algebras are given throughout the paper including those arising from differential geometry and homological algebra.

On two Hall algebra approaches to odd periodic triangulated categories

Given an odd-periodic algebraic triangulated category, we compare Bridgeland's Hall algebra in the sense of Bridgeland(2013) and Gorsky(2014), and the derived Hall algebra in the sense of Ten(2006), Xiao and Xu(2008) and Xu and Chen(2013), and show that the former one is the twisted form of the tensor product of the latter one and a suitable group algebra.

Grade zero part of forced graded algebras

This paper concerns a certain subcategory of the category of representations for a semisimple algebraic group G in characteristic p, which arises from the semisimple modules for the corresponding quantum group at a p-th root of unity. The subcategory, thus, records the cohomological difference between quantum groups and algebraic groups. We define translation functors in this category and use them to obtain information on the irreducible characters for G when the Lusztig character formula does not hold.