A theoretical framework is developed to describe the transformation that distributes probability density functions uniformly over space. In one dimension, the cumulative distribution can be used, but does not generalize to higher dimensions, or non-separable distributions. A potential function is shown to link probability density functions to their transformation, and to generalize the cumulati...

We study a Cauchy problem for non-convex valued evolution inclusions in non separable Banach spaces under Filippov type assumptions. We establish existence and relaxation theorems.

We prove that there is a compact separable continuum that (consistently) is not a remainder of the real line.

Previously, the use of non-separable wavelets in image processing has been hindered by the lack of a fast algorithm to perform a non-separable wavelet transform. We present two such algorithms in this paper. The rst algorithm implements a periodic wavelet transform for any valid wavelet lter sequence and dilation matrices satisfying a trace condition. We discuss some of the complicating issues ...

We study in this paper nonlinear subdivision schemes in a multivariate setting allowing arbitrary dilation matrix. We investigate the convergence of such iterative process to some limit function. Our analysis is based on some conditions on the contractivity of the associated scheme for the differences. In particular, we show the regularity of the limit function, in L and Sobolev spaces.

We study characterization of separable (classically correlated) states for composite systems of distinguishable fermions. In the computation of entanglement formation for such systems where located subsystems are coupled by the canonical anticommutation relations (not by tensor product), the state decompositions to be taken should respect the univalence superselection rule. (The usual entanglem...

Local supra-linear summation of excitatory inputs occurring in pyramidal cell dendrites, the so-called dendritic spikes, results in independent spiking dendritic sub-units, which turn pyramidal neurons into two-layer neural networks capable of computing linearly non-separable functions, such as the exclusive OR. Other neuron classes, such as interneurons, may possess only a few independent dend...

Abstract We give a direct tensor decomposition for any density matrix into Hermitian operators. Based upon the decomposition we study when the mixed states are separable and generalize the separability indicators to multi-partite states and show that a density operator is separable if and only if the separable indicator is non-negative. We then derive two bounds for the separable indicator in t...

We show that an infinite-dimensional complete linear space X has: • a dense hereditarily Baire Hamel basis if |X| ≤ c; • a dense non-meager Hamel basis if |X| = κ = 2 for some cardinal κ. According to Corollary 3.4 of [BDHMP] each infinite-dimensional separable Banach space X has a non-meager Hamel basis. This is a special case of Theorem3.3 of [BDHMP], asserting that an infinite-dimensional Ba...