Let K be a convex subset of Rn containing a ball of finite radius centered at c0 and contained in a ball of finite radius R. We give an oracle-polynomial-time algorithm for the weak separation problem for K given an oracle for the weak optimization problem for K. This is done by reducing the weak separation problem for K to the convex feasibility (nonemptiness) problem for a set K ′, and then b...

Weextend both theweak separation condition and the finite type condition to include finite iterated function systems (IFSs) of injective C1 conformal contractions on compact subsets of Rd . For conformal IFSs satisfying the bounded distortion property, we prove that the finite type condition implies the weak separation condition. By assuming the weak separation condition, we prove that the Haus...

It is known that, unlike the Hausdorff dimension, the Assouad dimension of a self-similar set can exceed the similarity dimension if there are overlaps in the construction. Our main result is the following precise dichotomy for self-similar sets in the line: either the weak separation property is satisfied, in which case the Hausdorff and Assouad dimensions coincide; or the weak separation prop...

We investigate two QBF resolution systems that use extension variables: weak extended Q-resolution, where the extension variables are quantified at the innermost level, and extended Q-resolution, where the extension variables can be placed inside the quantifier prefix. These systems have been considered previously by (Jussila et al. 2007), who give experimental evidence that extended Q-resoluti...

Let K be a full-dimensional convex subset of Rn. We describe a new polynomialtime Turing reduction from the weak separation problem for K to the weak optimization problem for K that is based on a geometric heuristic. We compare our reduction, which relies on analytic centers, with the standard, more general reduction.

Existence of a phase separation is proved for a classical lattice gas with finite-range pair potential under the action of a weak gravitational field.

The stochastic resonance method finds its original application on solving the issue of singlefrequency signals. In this paper, a multi-frequency stochastic resonance detection method based on wavelet transform weak signal is proposed. The first wavelet transform is carried out for detaching the negative effect of weak noisy signal in multi-frequency to realize the separation of the various freq...

Abstract The aim of this paper is to prove global in time existence weak solutions for a viscoelastic phase separation. We consider the case with singular potentials and degenerate mobilities. Our model couples diffusive interface Peterlin–Navier–Stokes equations fluids. To obtain we appropriate approximations by separation regular potential build on corresponding energy entropy estimates.