Lukasiewicz n值命题逻辑中命题的真度理论

利用势为 n的均匀概率空间的无穷乘积在 Lukasiewicz n值命题逻辑中引入了公式的真度概念,当3≤n≤17时证明了全体公式的真度值之集在[0,1]上是稠密的,并给出了公式真度的表达通式;利用真度定义了公式间的相似度,进而导出了全体公式集上的一种伪距离,为n值Lukasiewicz命题逻辑系统的近似推理理论提供了一种可能的框架。     

基于公式真度的公式集约简

基于经典命题逻辑的真度理论,讨论了经典命题逻辑系统当中公式集的约简问题。提出了真度约简及α-真度约简的概念,为公式集的约简提供了一种可行的操作方法。     

Fixed points of asymptotic contractions

Let be a contractive gauge function in the sense that φ is continuous, φ(s)<s for s>0, and if f:M→M satisfies d(f(x),f(y))?φ(d(x,y)) for all x,y in a complete metric space (M,d), then f always has a unique fixed point. It is proved that if T:M→M satisfies

     

Approximate colored range and point enclosure queries

In this paper, we formulate two classes of problems, the colored range query problems and the colored point enclosure query problems to model multi-dimensional range and point enclosure queries in the presence of categorical information. Many of these problems are difficult to solve using traditional data structural techniques. Based on a new framework of combining sketching techniques and traditional data structures, we obtain two sets of results in solving the problems approximately and efficiently. In addition, the framework can be employed to attack other related problems by finding the appropriate summary structures.     

A modification of a solution concept of the linear programming problem with interval coefficients in the constraints

We propose a modification of a concept of solving a linear programming problem with interval coefficients in the constraints. The original concept imposes the decision maker a way comparing intervals, our modification—which is an interactive approach, comprising the original one as its special case—gives him more freedom in the choice of the preference relation. Thanks to this flexibility he may be able to find a solution which better suits his needs and attitude towards risk. What is more, our modification corrects a serious drawback of the original method.     

Computing approximate Nash equilibria in general network revenue management games

Computing optimal capacity allocations in network revenue management is computationally hard. The problem of computing exact Nash equilibria in non-zero-sum games is computationally hard, too. We present a fast heuristic that, in case it cannot converge to an exact Nash equilibrium, computes an approximation to it in general network revenue management problems under competition. We also investigate the question whether it is worth taking competition into account when making (network) capacity allocation decisions. Computational results show that the payoffs in the approximate equilibria are very close to those in exact ones. Taking competition into account never leads to a lower revenue than ignoring competition, no matter what the competitor does. Since we apply linear continuous models, computation time is very short.     

Operator algebras with contractive approximate identities: Weak compactness and the spectrum

We continue our study of operator algebras with contractive approximate identities (cais) by presenting a couple of interesting examples of operator algebras with cais, which in particular answer questions raised in previous papers in this series, for example about whether, roughly speaking, ‘weak compactness’ of an operator algebra, or the lack of it, can be seen in the spectra of its elements.