Weighted search games

In this paper we shall deal with search games in which the strategic situation is developed on a lattice. The main characteristic of these games is that the points in each column of the lattice have a specific associated weight which directly affects the payoff function. Thus, the points in different columns represent points of different strategic value. We solve three different types of games. The first involves search, ambush and mixed situations, the second is a search and inspection game and the last is related to the accumulative games.     

Weighted heuristic search in networks

The evaluation function used in heuristic search algorithms commonly has the form , where n is any node in the network, is the cost of the best path currently known from the start node to n, and is the heuristic estimate associated with node n. A more general form of the evaluation function can be obtained by incorporating a weighting parameter α:

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, where 0≤ α ≤1. Such an evaluation function has been used in some recent experimental investigations of the 8-puzzle problem. In this paper a theoretical framework is developed for the analysis of the worst-case behavior of weighted heuristic search algorithms. A new algorithm is proposed whose worst-case performance characteristics are greatly superior to those of earlier algorithms in terms of the following two measures: how good is the solution, and how many nodes are expanded. Bounds are also obtained on some useful network parameters for both general and special types of heuristic estimate functions.     

Some common best proximity points for proximity commuting mappings

In this paper, we prove new common best proximity point theorems for a proximity commuting mapping in a complete metric space. Our results generalized a recent result of Sadiq Basha [Common best proximity points: global minimization of multi-objective functions, J. Glob. Optim., (2011)] and some results in the literature.     

Repeated proximity games

We consider repeated games with complete information and imperfect monitoring, where each player is assigned a fixed subset of players and only observes the moves chosen by the players in this subset. This structure is naturally represented by a directed graph. We prove that a generalized folk theorem holds for any payoff function if and only if the graph is 2-connected, and then extend this result to the context of finitely repeated games. Received June 1997/Revised version March 1998     

Ordered proximity spaces

We shall investigate proximities in ordered sets corresponding to ordered bicompact extensions.Translated from Matematicheskie Zametki, Vol. 4, No. 6, pp. 659–667, December, 1968.     

Fuzzy proximity spaces redefined

We use the concept ‘L-quasi-coincident’ in fuzzy set theory, to redefine L-fuzzy proximity space, and we study the following problems: proximity of L-fuzzy normal spaces, L-fuzzy filters, proximity neighborhoods and the L-fuzzy topology induced by the L-fuzzy proximity.     

Boundary proximity of SLE

This paper examines how close the chordal SLE _κ curve gets to the real line asymptotically far away from its starting point. In particular, when κ ? (0, 4), it is shown that if β > β _κ  := 1/(8/κ ? 2), then the intersection of the SLE _κ curve with the graph of the function y = x/(log x) ^β , x > e, is a.s. bounded, while it is a.s. unbounded if β = β _κ . The critical SLE₄ curve a.s. intersects the graph of $y=x^{{-({\rm log\,log\,x})}^{\alpha}}, x > e^e$ , x > e ^e , in an unbounded set if α ≤ 1, but not if α > 1. Under a very mild regularity assumption on the function y(x), we give a necessary and sufficient integrability condition for the intersection of the SLE _κ path with the graph of y to be unbounded. When the intersection is bounded a.s., we provide an estimate for the probability that the SLE _κ path hits the graph of y. We also prove that the Hausdorff dimension of the intersection set of the SLE _κ curve and the real axis is 2 ? 8/κ when 4 < κ < 8.     

Best proximity point theorems

Let us assume that A and B are non-empty subsets of a metric space. In view of the fact that a non-self mapping T:A?B does not necessarily have a fixed point, it is of considerable significance to explore the existence of an element x that is as close to Tx as possible. In other words, when the fixed point equation Tx=x has no solution, then it is attempted to determine an approximate solution x such that the error d(x,Tx) is minimum. Indeed, best proximity point theorems investigate the existence of such optimal approximate solutions, known as best proximity points, of the fixed point equation Tx=x when there is no solution. Because d(x,Tx) is at least d(A,B), a best proximity point theorem ascertains an absolute minimum of the error d(x,Tx) by stipulating an approximate solution x of the fixed point equation Tx=x to satisfy the condition that d(x,Tx)=d(A,B). This article establishes best proximity point theorems for proximal contractions, thereby extending Banach’s contraction principle to the case of non-self mappings.     

Weighted Commutator and Weighted BMO Martingales

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On Weighted L~p-Approximation by Weighted Bernstein-Durrmeyer Operators

In the present paper,we establish direct and converse theorems for weighted Bernstein-Durrmeyer operators under weighted L~p-norm with Jacobi weight w(x) = x~α(1-x)~β.All the results involved have no restriction α,β 1-1/p,which indicates that the weighted Bernstein-Durrmeyer operators have some better approximation properties than the usual Bernstein-Durrmeyer operators.     

Weighted Composition Operators on Weighted Dirichlet Spaces

We characterize the boundedness and compactness of weighted composition operators on weighted Dirichlet spaces in terms of Nevanlinna counting functions and Carleson measure.     

Valuations with preassigned proximity relations

We characterize the infinite upper triangular matrices (which we call formal proximity matrices) that can arise as proximity matrices associated with zero-dimensional valuations dominating regular noetherian local rings. In particular, for every regular noetherian local ring R of the appropriate dimension, we give a sufficient condition for such a formal proximity matrix to be the proximity matrix associated with a real rank one valuation dominating R. Furthermore, we prove that in the special case of rational function fields, each formal proximity matrix arises as the proximity matrix of a valuation whose value group is computable from the formal proximity matrix. We also give an example to show that this is false for more general fields. Finally in the case of characteristic zero, our constructions can be seen as a particular case of a structure theorem for zero-dimensional valuations dominating equicharacteristic regular noetherian local rings.     

一种邻近性的计算方法

邻近律是Gestalt定律的基本定律之一,然而迄今为止,如何在图像处理中计算元素之间的邻近性程度还没有具体方法提出．以点元素作为抽象载体提出了一种邻近性的计算方法,该方法借鉴基于最小支撑树（MST）的聚类思想,引入三角剖分和Prim算法计算元素之间的MST邻近性测度和加权MST邻近性测度用于度量元素之间的邻近性．实验结...