Vector equilibrium problems with elastic demands and capacity constraints

In this paper, a (weak) vector equilibrium principle for vector network problems with capacity constraints and elastic demands is introduced. A sufficient condition for a (weak) vector equilibrium flow to be a solution for a system of (weak) vector quasi-variational inequalities is obtained. By virtue of Gerstewitz’s nonconvex separation functional ξ, a (weak) ξ-equilibrium flow is introduced. Relations between a weak vector equilibrium flow and a (weak) ξ-equilibrium flow is investigated. Relations between weak vector equilibrium flows and two classes of variational inequalities are also studied.     

弱CS模的遗传性

P.F.Sm ith曾提出一个公开问题:弱CS模的直和项是否为弱CS模?论文通过一个反例证明了弱CS模的直和项不一定是弱CS模.但满足条件C3的弱CS模对其直和项具有遗传性.最后讨论了弱CS模对一般子模的遗传性.     

Weak martingale Hardy spaces and weak atomic decompositions

In this paper we define some weak martingale Hardy spaces and three kinds of weak atoms. They are the counterparts of martingale Hardy spaces and atoms in the classical martingale Hp-theory. And then three atomic decomposition theorems for martingales in weak martingale Hardy spaces are proved. With the help of the weak atomic decompositions of martingale, a sufficient condition for a sublinear operator defined on the weak martingale Hardy spaces to be bounded is given. Using the sufficient condition, we obtain a series of martingale inequalities with respect to the weak Lp-norm, the inequalities of weak (p ,p)-type and some continuous imbedding relationships between various weak martingale Hardy spaces. These inequalities are the weak versions of the basic inequalities in the classical martingale Hp-theory.     

弱Hopf群T-余代数上的弱Doi-Hopf群模

在弱Hopf群T-余代数情形下,弱量子Yetter-Drinfeld群模的概念被引入,并证明了弱量子Yetter-Drinfeld群模是特殊的弱Doi-Hopf群模.接着建立了弱量子Yetter Drinfeld群模范畴与弱Hopf群双余模代数的余不动点子代数B上模范畴之间的伴随对.最后考虑了弱量子Yetter-Drinfeld群模的积分.     

Fundamental Theorems of Weak Doi–Hopf Modules and Semisimple Weak Smash Product Hopf Algebras

Abstract

This paper, mainly gives a Fundamental Theorem of weak Doi–Hopf modules, which is not only generalizes the Fundamental Theorem of weak Hopf modules but also generalizes the Fundamental Theorem of relative Hopf modules. Moreover, it gives a sufficient and necessary condition for weak smash product algebras to be weak bialgebras, and a sufficient condition for weak smash product algebras to be semisimple weak Hopf algebras.     

Weak Hopf Algebra in Yetter-Drinfeld Categories and Weak Biproducts

The Yetter-Drinfeld category of the Hopf algebra over a field is a pre braided category. In this paper we prove this result for the weak Hopf algebra. We study the smash product and smash coproduct, weak biproducts in the weak Hopf algebra over a field k. For a weak Hopf algebra A in left Yetter-Drinfeld category HHYD. we prove that the weak biproducts of A and H is a weak Hopf algebra.     

Global and nonglobal weak solutions to a degenerate parabolic system

This paper deals with a degenerate parabolic system coupled via general reaction terms of power type. Global weak solutions are obtained by means of energy estimates and the De Giorgi's technique. In particular, the criterion for global nonexistence of weak solutions is proved by introducing suitable weak sub-solutions together with a weak comparison principle. In summary, the critical exponent for weak solutions of the degenerate parabolic system is determined.     

半拟三角弱Hopf代数

作为拟三角弱Hopf代数的推广,我们引入了半拟三角弱Hopf代数的概念.令(H,R,v)是一个半拟三角弱Hopf代数,其中,R是其半拟三角结构.我们指明R保持了拟三角弱Hopf代数中泛R-矩阵的许多基本性质.特别地,讨论了Drinfeld元的性质,证明其是可逆的并且是余作用v的余不变量.另外,证明了半拟三角弱Hopf代数的对极平方是对合的.     

Weighted weak group inverse for Hilbert space operators

We present the weighted weak group inverse, which is a new generalized inverse of operators between two Hilbert spaces, and we extend the notation of the weighted weak group inverse for rectangular matrices. Some characterizations and representations of the weighted weak group inverse are investigated. We also apply these results to define and study the weak group inverse for a Hilbert space operator. Using the weak group inverse, we define and characterize various binary relations.     

输入存贮线性有限自动机的弱可逆性

应用输入存贮线性有限自动机的结构矩阵讨论了输入存贮线性有限自动机的弱可逆性,得出输入存贮线性有限自动机延迟0步弱可逆的充要条件、延迟τ步弱可逆和严格延迟τ步弱可逆的充分条件,由此条件得出延迟τ步弱可逆和严格延迟τ步弱可逆的输入存贮线性有限自动机的构造方法并且求出延迟0步弱可逆输入存贮线性有限自动机的一个弱逆.     

多目标规划的弱镇定性、弱稳定性及其精确罚函数

本文将 Rosenberg 在文[1]中定义的单目标规划的镇定性、稳定性概念推广到多目标的情形,讨论多目标规划问题(VP)(?)f(x)s.t.g_k(x)≤0,k∈K_1,h_k(x)=0,k∈K_2的弱镇定性、弱稳定性、局部弱稳定性、一致局部弱稳定性,以及罚函数问题     

Cibils–Rosso's Theorem for Quantum Groupoids

Abstract

We generalize the Cibils–Rosso's theorem for categories of Sweedler's Hopf bimodules to the one for categories of weak entwined bimodules. We show that the weak entwined bimodules are modules over a certain algebra. Our best results are attained for categories of weak Hopf bimodules over quantum groupoids (weak Hopf algebras), as special cases of weak Doi–Hopf bimodules.     

弱Hopf代数上的Militaru-Stefan提升定理

本文研究了弱Hopf-Galois扩张的扩张模.利用忠实平坦的弱Hopf-Galois扩张理论,研究了弱Hopf代数上的Militaru-Stefan提升定理,推广了文献[10]中的相应结果.进一步地,通过诱导模的自同态环的cleft扩张刻画了弱稳定模.     

弱Hopf代数与正则幺半群

本文定义了弱Ｈｏｐｆ代数并研究了弱Ｈｏｐｆ代数的弱对极与类群元幺半群的关系．首先,本文给出弱Ｈｏｐｆ代数的一些基本性质;然后,对类群元幺半群是逆半群或纯正半群的某些弱Ｈｏｐｆ代数,描述了其弱对极的一些性质;最后,给出一类其类群元幺半群为正则半群的弱Ｈｏｐｆ代数．     

Characteristics and structures of weak efficient surfaces of production possibility sets

This paper studies the characteristics and structure of the weak surface of the production possibility set. We apply techniques and methods of transferring a polyhedral cone from its intersection form to its sum form, identify an intersection representation of the production possibility set. We give the structure theorem of weak surface of the production possibility set, which includes three complementary slackness conditions. We define the input weak efficiency and output weak efficiency for different DEA models according to the representation of the intersection form. It investigates the characteristics of the weak surfaces, and proves the structure theorems of input weak DEA efficiency and output weak DEA efficiency. The structure theorems establish weighted combination of inputs and outputs that are weak DEA efficient. Numerical examples are provided for illustration.     

弱Orlicz鞅空间的弱原子分解及其应用

对3类由凹函数生成的弱Orlicz鞅空间建立了相应的弱原子分解.作为应用,首先给出了这些弱Orlicz鞅空间上次线性算子有界的一个充分条件,并在此基础上证明了一些弱型鞅不等式,然后证明了关于这些弱Orlicz鞅空间的Marcinkiewicz型插值定理.     

Saddle points and gap functions for weak generalized Ky Fan inequalities

In this paper, we employ the image space analysis method to investigate a weak generalized Ky Fan inequality with cone constraints. Some regular weak separation functions are introduced, and generalized Lagrangian functions are constructed by using these regular weak separation functions. Under suitable convexity assumptions and Slater condition, the existence of solution for the weak generalized Ky Fan inequality with cone constraints is equivalent to a saddle point of the generalized Lagrangian functions. Moreover, we also use the regular weak separation functions to construct gap functions for the weak generalized Ky Fan inequality with cone constraints, and obtain its error bound.     

On characterizing full dimensional weak facets in DEA with variable returns to scale technology

The frontier of the Production Possibility Set (PPS) consists of two types of full dimensional facets, efficient and weak facets. Identification of all facets of the PPS can be used in sensitivity and stability analysis, to find the closet target for inefficient Decision-Making Units (DMUs), and to determine the status of returns to scale of a DMU, among others. There has been a surge of articles on determining efficient facets in recent years. There are, however, many cases where knowledge of weak facets is required for a thorough analysis. This is the case, in particular, when the frontier of the PPS is constructed only of weak facets. The existing algorithms for finding weak facets either require knowledge of all extreme directions of the PPS or applicable only under some restrictions on the position of weak efficient DMUs. We provide a complete characterization of weak facets. Using this characterization, we then devise a different algorithm to find weak facets. We illustrate our algorithm using a numerical example.     

弱Hopf代数上的ω-交叉积

在弱Hopf代数上,定义了ω-交叉积概念,并给出了ω-交叉积是弱Hopf代数的充要条件,推广了弱Hopf代数的相应结论.     

Weak and very weak Bernoulli partitions

The definitions of weak and very weak Bernoulli are reformulated to allow conditioning with respect to the entire past. For skew products which are measurable with respect to an independent generator of the base this reformulation allows one to state simple necessary and sufficient conditions for weak and very weak Bernoulli. We use these ideas to give a simple example of a partition which is very weak but not weak Bernoulli.This research was done while the author visited Stanford, supported in part by N. S. F. Grant MP 575-08324.