范畴Ω-Cat的函数空间及其性质

Ω-范畴具有范畴论和序理论的双重意义,可为计算机程序语言的语义提供量化的模型,本文研究了范畴Ω-Cat的Ω-值函数空间,得出了Ω-值函数空间函子与Ω-值积函子互为伴随函子,证明了范畴Ω-Cat是Cartesian闭范畴。     

拓扑空间范畴,拓扑FUZZ范畴与拓扑分子格范略畴间的反射与余反射

从整体角度出发，证明拓扑空间范畴Ｔｏｐ分别是拓扑Ｆｕｚｚ范畴ＴｏｐＦｕｚｚ与拓扑分子格范畴ＴＭＬ的反射与余反射满子范畴，ＴｏｐＦｕｚｚｙ是ＴＭＬ的反射与余反射（非满）子范畴。     

三角范畴和Abel范畴的Torsion理论

本文主要研究了三角范畴在Abel化过程中torsion理论的保持问题.利用三角范畴的coherent函子范畴是Abel范畴,证明了T的coherent函子范畴A(T)是A(D)的thick子范畴;若(X,Y)是D的torsion理论,且D=X*Y的扩张是可裂的,那么(A(X),A(Y))是A(D)的torsion理论.     

拓扑空间范畴、拓扑FUZZ范畴与拓扑分子格范畴间的反射与余反射

从整体角度出发，证明了拓扑空间范畴Ｔｏｐ分别是拓扑Ｆｕｚｚ范畴ＴｏｐＦｕｚ与拓扑分子格范畴ＴＭＬ的反射与余反射满子范畴，ＴｏｐＦｕｚ是ＴＭＬ的反射与余反射（非满）子范畴．     

FS-相容Domain的定向完备化及相关范畴性质

引入FS-相容Domain概念，研究FS-相容Domain的性质，主要结果有：（1）FS-相容Domain的收缩核与连续函数空间还是FS-相容Domain；（2）FS-相容Domain是有限生成上集，从而是Scott紧的；（3）FS-相容Domain的定向完备化是FS-Domaln；（4）有最大元的FS-Domain去掉最大元后是FS-相容Domain；（5）证明了以Scott连续映射为态射，FS-相容Domain为对象的范畴FS-CDOM是笛卡儿闭范畴并以FS-Domain范畴FS-DOM作为满的反射子范畴。     

Locale范畴的反射子范畴

本文研究ｌｏｃａｌｅ范畴的反射子范畴，给出反射子范畴的刻划定理，从一般的ｌｏｃａｌｅ出发，完全构造性地给出了ｌｏｃａｌｅ的正则反射、完全正则反射和零维反射的构造．     

态族带序结构的范畴

范畴的态族可以赋予一些结构,如Ab范畴,但在自然界中我们大量接触的是连续现象,作为现代分析的基础,连续是用序关系处理的.因此,本文赋予范畴的态族一个序结构,引进了带序范畴和正序函子,以此作为连续性的一种范畴描述.如范畴C带T_0拓扑,若(?)U_fg,(?)U_f,U_g,使得U_fg=U_f.U_g.则按开集的一种包含关系即构造出带拓扑的范畴上的序结构,从而在拓     

$D_4$型李代数包络代数旋模的范畴化

本文我们定义复数域$C$上一般线性李代数${\rm gl}_n$ BGG 范畴的若干子范畴及其上的投射函子,利用这些子范畴和投射函子范畴化了$D_4$型李代数包络代数旋模的$n$-次张量积.     

对称的满层L-Kent收敛空间范畴的子范畴

在满层的L-Kent收敛空间中引入了对称性的概念,定义了对称的满层L-Kent收敛空间范畴,对称的满层L-极限空间范畴,对称的满层L-主收敛空间范畴,对称的满层L-拓扑空间范畴.证明这四个范畴是拓扑范畴,并且后一个是前一个的反射子范畴.最后证明了对称的满层L-Kent收敛空间范畴和对称的满层L-极限空间范畴是笛卡儿闭的.     

函子范畴的等价

本文建立了函子范畴等价的Ｍｏｒｉｔａ理论．考虑的主要问题是ｍｏｄＣ何时等价于ｍｏｄＣ′及这些等价条件．同时定义了函子范畴的双模和函子张量积，并刻画了等价函子．     

Derived Functors of Graded Theories

The homotopy category of one point unions of spheres and the homotopy category of Eilenberg–MacLane spaces are examples of graded theories. Spaces yield models of these theories which can be described in terms of iterated comma categories given by functors. The associated derived functors play an important role in spectral sequences computing homotopy groups. Using cross-effect methods, the derived functors are studied and the existence of a vanishing line is proven.     

Λ-Cofibration Categories and the Homotopy Categories of Global Actions and Simplicial Complexes

We investigate the homotopy category of a -cofibration category and compare the homotopy categories of Global Actions, Simplicial Complexes and Topological Spaces.     

Independent axioms for Convexity

Join-structures or Convexity Spaces generalise the geometry of Vector Spaces by means of axioms concerning line segments. Most other generalisations of this type are just particular examples of Convexity Spaces. In the many papers on this subject the collection of axioms is too long: in this short note we exhibit an independent set of axioms for these structures.     

关于C0半群的渐近稳定性

研究Banach空间上等距C0群的性质，据此讨论了C0半群的渐近稳定性和C0半群完全轨线的存在性．在文章的最后，回答了黄发伦提出的一个关于渐近稳定性的猜测．     

Separation of semialgebraic sets

In this paper we study the problem of deciding whether two disjoint semialgebraic sets of an algebraic variety over are separable by a polynomial. For that we isolate a dense subfamily of Spaces of Orderings, named Geometric, which suffice to test separation and that reduce the problem to the study of the behaviour of the semialgebraic sets in their boundary. Then we derive several characterizations for the generic separation, among which there is a Geometric Criterion that can be tested algorithmically. Finally we show how to check recursively whether we can pass from generic separation to separation, obtaining a decision procedure for solving the problem.

     

Structure and classification of monoidal groupoids

The structure of monoidal categories in which every arrow is invertible is analyzed in this paper, where we develop a 3-dimensional Schreier-Grothendieck theory of non-abelian factor sets for their classification. In particular, we state and prove precise classification theorems for those monoidal groupoids whose isotropy groups are all abelian, as well as for their homomorphisms, by means of Leech’s cohomology groups of monoids.     

Utilizing the IP Multimedia Subsystem to create an extensible service-oriented architecture

Smart Spaces provide very promising means of creating context-aware environments. Unfortunately, a lack of information about users within Smart Spaces limits their usefulness. We propose a novel solution that involves integrating Smart Spaces with social networks through the IP Multimedia Subsystem. to create truly context-aware and adaptive spaces. By utilizing the wealth of user information present within social networks, smarter and more adaptive spaces can be created. We therefore propose the design and implementation of “SocioSpace” a Smart Spaces framework that utilizes the social context. We design and implement all components of SocioSpace, including the central server, the location management system, social network interfacing components, service delivery server and user agents. We then run various scenarios to test the reliability of the system. The results show the effectiveness of our framework in successfully creating Smart Spaces that can truly utilize social networks to deliver adaptive services that enhance the users’ experiences and make the environment more beneficial to them.     

Linear homeomorphisms of non-classical Hilbert spaces

Let K be a complete infinite rank valued field. In [4] we studied Norm Hilbert Spaces (NHS) over K i.e. K-Banach spaces for which closed subspaces admit projections of norm ≤ 1. In this paper we prove the following striking properties of continuous linear operators on NHS. Surjective endomorphisms are bijective, no NHS is linearly homeomorphic to a proper subspace (Theorem 3.7), each operator can be approximated, uniformly on bounded sets, by finite rank operators (Theorem 3.8). These properties together — in real or complex theory shared only by finite-dimensional spaces — show that NHS are more ‘rigid’ than classical Hilbert spaces.     

可拓扑生成的L-fuzzy保序算子空间的ω-分解定理及ω-可数性

讨论可拓扑生成的L-fuzzy保序算子空间的若干性质,如分解定理、可数性等。     

推广的Kantorovich算子在Ba空间中的逼近

利用Ditzian-Totik光滑模,研究了推广的Kantorovich算子在Ba空间中的逼近,得到逼近的正定理与等价定理.所得结果改进、推广和统一了一些作者的结果.