We show that, for a finite-dimensional Hilbert space, there exist observables that induce a tensor product structure such that the entanglement properties of any pure state can be tailored. In particular, we provide an explicit, finite method for constructing observables in an unstructured d-dimensional system so that an arbitrary known pure state has any Schmidt decomposition with respect to a...

This paper systematically studies finite rank dimension groups, as well as finite dimensional ordered real vector spaces with Riesz interpolation. We provide an explicit description and classification of finite rank dimension groups, in the following sense. We show that for each n, there are (up to isomorphism) finitely many ordered real vector spaces of dimension n that have Riesz interpolatio...

We examine condition numbers, preconditioners, and iterative methods for finite element discretizations of coercive PDEs in the context of the fundamental solvability result, the Lax-Milgram Lemma. Working in this Hilbert space context is justified because finite element operators are restrictions of infinite-dimensional Hilbert space operators to finite-dimensional subspaces. Moreover, useful ...

A new physics package solves radiation transport equations in one space dimension, multiple energy groups and directions. A discontinuous finite element method discretizes radiation intensity with respect to space and angle, and a continuous finite element method discretizes electron temperature in space. A splitting method solves the resulting linear equations. This is a one-dimensional analog...

in this paper, we investigate the existence of solution for a k-dimensional system of three points nabla fractional finite difference equations. also, we present an example to illustrate our result.

soil slopes are sometimes curved in plan rather than being straight. this curvature,especially when it is convex, decreases the bearing capacity of the slope. finite element methodhas been used here in this research to investigate the reducing effect of curvature on bearingcapacity of a slope. failure of soil has been assumed to be according to mohr-coulomb criteria;but the flow rule of the soi...