Abstract We introduce a simple sufficient criterion, which allows one to tell whether subspace of bipartite or multipartite Hilbert space is entangled. The main ingredient our criterion bound on the minimal entanglement in terms vectors spanning that expressed for geometrical measures entanglement. applicable both completely and genuinely entangled subspaces. explore its usefulness several impo...

and Applied Analysis 3 x ∈ X i.e., cl Oa x Oa x for all x ∈ X . Then, ω ∈ Oa z for all z ∈ C. Since x ∈ C, then ω ∈ Oa x . On the other hand, since x ∈ x ⊂ C ⊂ Oa ω , then ω ∈ x . Hence, C x . In the following lemma, we give necessary and sufficient conditions for the equivalence classes to be S-invariant classes. Lemma 2.2. Let S,X, a be an S-flow. A class x ∈ X is an S-invariant class if and ...

We compute the skewness t3 and the corresponding hierarchical amplitude T3 of the divergence of the velocity field for arbitrary non-Gaussian initial conditions. We find that T3 qualitatively resembles the corresponding hierarchical amplitude for the density field, S3, in that it contains a term proportional to the initial skewness, which decays inversely as the linear growth factor, plus a con...

Shape from shading (SFS) has been studied for decades; nevertheless, its overly simple assumptions and its ill-conditioning have resulted in infrequent use in real applications. Price et al. recently developed an iterative scheme named shape from motion and shading (SFMS) that models both shape and reflectance of an unknown surface simultaneously. SFMS produces a fairly accurate, dense 3D recon...

We present a new approach based on Partial Differential Equations (PDEs) and shock filter theory for deblurring 2D Gaussian blurred images. The inherent problems of stability posed by the reverse heat equation and the discretization of shock filters are overcome by the use of only the initial conditions. This approach is not well suited for diffusion-oriented techniques since in this case the p...

We describe a numerical simulation of the evolution of an S3 cosmic string network which takes fully into account the non-commutative nature of the cosmic string fluxes and the topological obstructions which hinder strings from moving past each other or intercommuting. The influence of initial conditions, string tensions, and other parameters on the network’s evolution is explored. In most regi...

We study the error to the discretization in time of a parabolic evolution equation by a single-step method or by a multistep method when the initial condition is not regular. Introduction. The problem we are considering is the parabolic evolution equation ( u'(t) + Au(t) = 0, 0<t<T, (*) I (u(0) = uo. Here, A is a linear operator, unbounded on Hubert space H, of domain D(A) dense in H; the initi...