The scattering off a potential of finite rank (a sum of a finite number of separable potentials) is studied thoroughly in the neighborhood of infinity of potential strength; for this purpose we introduce the "strong coupling representation" by means of a canonical transformation. The same K matrix as for the infinitely strong repulsion is derived for the infinitely strong attraction. The differ...

We study a class of finite strategic games with the property that every deviation of a coalition of players that is profitable to each of its members strictly decreases the lexicographical order of a certain function defined on the set of strategy profiles. We call this property the lexicographical improvement property (LIP) and show that, in finite games, it is equivalent to the existence of a...

In this paper we establish a variety or results in ergodic theory by using techniques from probability and analysis. We discuss divergence of operators, including strong sweeping out and Bourgain's entropy method. We consider square functions, oscillation operators, and variational operators for ergodic averages. We also consider almost everywhere convergence of convo-lution powers.

We define two notions of generation between the various optimal packings Qm of m congruent disks in a subset K of R2. The first one that we call weak generation consists in getting Qn by removing m − n disks from Qm and by displacing the n remaining congruent disks which grow continuously and do not overlap. During a weak generation of Qn from Qm, we consider the contact graphs G(t) of the inte...

In many real world planning domains, some observation information is optional and useless to the execution of a plan; on the other hand, information acquisition may require some kind of cost. The problem of observation reduction for strong plans has been addressed in the literature. However, observation reduction for plans with contexts (which are more general and useful than strong plans in ro...

This paper characterizes the first cohomology group H(G,M) where M is a Banach space (with norm || ||M) that is also a left CG module such that the elements of G act onM as continuous C-linear transformations. We study this group for G an infinite, finitely generated group. Of particular interest are the implications of the vanishing of the group H(G,M). The first result is that H(G,CG) imbeds ...

Let P be a monotone increasing graph property, let G = (V,E) be a graph, and let q be a positive integer. In this paper, we study the (1 : q) Maker-Breaker game, played on the edges of G, in which Maker’s goal is to build a graph that satisfies the property P . It is clear that in order for Maker to have a chance of winning, G itself must satisfy P . We prove that if G satisfies P in some stron...

A singular masa A in a II1 factor N is defined by the property that any unitary w ∈ N for which A = wAw∗ must lie in A. A strongly singular masa A is one that satisfies the inequality ‖EA − EwAw∗‖∞,2 ≥ ‖w − EA(w)‖2 for all unitaries w ∈ N , where EA is the conditional expectation of N onto A, and ‖ · ‖∞,2 is defined for bounded maps φ : N → N by sup{‖φ(x)‖2 : x ∈ N, ‖x‖ ≤ 1}. Strong singularity...

This article presents a generic scheme for adding strong local consistencies to the set of features of constraint solvers, which is notably applicable to event-based constraint solvers. We encapsulate a subset of constraints into a global constraint. This approach allows a solver to use different levels of consistency for different subsets of constraints in the same model. Moreover, we show how...

This paper considers the cognitive interference channel (CIC) with two transmitters and two receivers, in which the cognitive transmitter non-causally knows the message and codeword of the primary transmitter. We first introduce a discrete memoryless more capable CIC, which is an extension to the more capable broadcast channel (BC). Using superposition coding, we propose an inner bound and an o...