Search results for "Separable"
showing 10 items of 91 documents
Entanglement Theory with Continuous Variables
2016
Entanglement of distant superconducting quantum interference device rings
2005
We consider two distant mesoscopic SQUID rings, approximated with two-level systems, interacting with two-mode microwaves. The Hamiltonian of the system is used to calculate its time evolution. The cases with microwaves which at t = 0 are in separable states (classically correlated) or entangled states (quantum mechanically correlated) are studied. It is shown that the Josephson currents in the two SQUID rings are also correlated.
Set valued integrability in non separable Fréchet spaces and applications
2016
AbstractWe focus on measurability and integrability for set valued functions in non-necessarily separable Fréchet spaces. We prove some properties concerning the equivalence between different classes of measurable multifunctions. We also provide useful characterizations of Pettis set-valued integrability in the announced framework. Finally, we indicate applications to Volterra integral inclusions.
Homogeneous Suslinian Continua
2011
AbstractA continuumis said to be Suslinian if it does not contain uncountably many mutually exclusive non-degenerate subcontinua. Fitzpatrick and Lelek have shown that a metric Suslinian continuum X has the property that the set of points at which X is connected im kleinen is dense in X. We extend their result to Hausdorff Suslinian continua and obtain a number of corollaries. In particular, we prove that a homogeneous, non-degenerate, Suslinian continuum is a simple closed curve and that each separable, non-degenerate, homogenous, Suslinian continuum is metrizable.
MR2964711 Alfsen, Erik; Shultz, Fred Finding decompositions of a class of separable states. Linear Algebra Appl. 437 (2012), no. 10, 2613–2629. (Revi…
2013
New solvability conditions for the Neumann problem for ordinary singular differential equations
2000
Estimating the geometric median in Hilbert spaces with stochastic gradient algorithms: Lp and almost sure rates of convergence
2016
The geometric median, also called L 1 -median, is often used in robust statistics. Moreover, it is more and more usual to deal with large samples taking values in high dimensional spaces. In this context, a fast recursive estimator has been introduced by Cardot et?al. (2013). This work aims at studying more precisely the asymptotic behavior of the estimators of the geometric median based on such non linear stochastic gradient algorithms. The L p rates of convergence as well as almost sure rates of convergence of these estimators are derived in general separable Hilbert spaces. Moreover, the optimal rates of convergence in quadratic mean of the averaged algorithm are also given.
Mean-field games and two-point boundary value problems
2014
A large population of agents seeking to regulate their state to values characterized by a low density is considered. The problem is posed as a mean-field game, for which solutions depend on two partial differential equations, namely the Hamilton-Jacobi-Bellman equation and the Fokker-Plank-Kolmogorov equation. The case in which the distribution of agents is a sum of polynomials and the value function is quadratic is considered. It is shown that a set of ordinary differential equations, with two-point boundary value conditions, can be solved in place of the more complicated partial differential equations associated with the problem. The theory is illustrated by a numerical example.