We define a new separation property on the family of contractive similitudes that allows certain overlappings. This property is weaker than the open set condition of Hutchinson. It includes the well-known class of infinite Bernoulli convolutions associated with the P.V. numbers and the solutions of the two-scale dilation equations. Our main purpose in this paper is to prove the multifractal for...

Writing correct programs for weak memory models such as the C11 memory model is challenging because of the weak consistency guarantees these models provide. The first program logics for the verification of such programs have recently been proposed, but their usage has been limited thus far to manual proofs. Automating proofs in these logics via first-order solvers is non-trivial, due to reasoni...

A weak metric on a set is a function that satisfies the axioms of a metric except the symmetry and the separation axioms. In the present paper we introduced a weak metric, called the Apollonian weak metric, on any subset of a Euclidean space which is either bounded or whose boundary is unbounded. We then relate this weak metric to some familiar metrics such as the Poincaré metric, the Klein-Hil...

The aim of this paper is to introduce and obtain some characterizations of weakly $e$-irresolute functions by means of $e$-open sets defined by Ekici [6]. Also, we look into further properties relationships between weak $e$-irresoluteness and separation axioms and completely $e$-closed graphs.

In this paper, by virtue of a nonlinear scalarization function, two nonlinear weak separation functions, a nonlinear regular weak separation function, and a nonlinear strong separation function are first introduced, respectively. Then, by the image space analysis, a global saddle-point condition for a nonlinear function is investigated. It is shown that the existence of a saddle point is equiva...

Acknowledgments We thank T. Bell for giving us access to his image data base. Abstract We investigate the information processing of a linear mixture of independent sources of different magnitudes. In particular we consider the case where a number m of the sources can be considered as " strong " as compared to the other ones, the " weak " sources. We find that it is preferable to perform blind s...