A Generalization of Entanglement to Convex Operational Theories: Entanglement Relative to a Subspace of Observables

We define what it means for a state in a convex cone of states on a space of observables to be generalized-entangled relative to a subspace of the observables, in a general ordered linear spaces framework for operational theories. This extends the notion of ordinary entanglement in quantum information theory to a much more general framework. Some important special cases are described, in which the distinguished observables are subspaces of the observables of a quantum system, leading to results like the identification of generalized unentangled states with Lie-group-theoretic coherent states when the special observables form an irreducibly represented Lie algebra. Some open problems, including that of generalizing the semigroup of local operations with classical communication to the convex cones case, are discussed. PACS: 03.65.Ud.     

Hydrophobic dendrimers as templates for au nanoparticles

We report the synthesis, characterization, and extraction of Au dendrimer-encapsulated nanoparticles (DENs) prepared in organic solvents. DENs composed of 31 and 55 Au atoms were prepared using organic solvents and poly(amidoamine) (PAMAM) dendrimer templates modified on their periphery with dodecyl groups. The spectral and microscopic properties of the resulting materials were identical to those prepared using water-soluble PAMAM dendrimers. It was possible to extract the organic-soluble DENs into water using the water-soluble thiols tiopronin and glutathione. The properties of the resulting monolayer-protected clusters were nearly identical to those of the precursor DENs. A mechanistic model for the extraction process is discussed. The synthetic methodology reported here provides a convenient method for preparing DENs of non noble metals such as Ni and Fe.     

Highly emissive supramolecular oligo(p-phenylene vinylene) dendrimers

pi-Conjugated oligo(p-phenylene vinylene) (OPV) guest molecules for interaction with dendritic hosts were synthesized and fully characterized by NMR spectroscopy, MALDI-TOF-MS, elemental analysis and optical measurements. The binding properties of the five different OPV guests to a N,N-bis[(3-adamantyl ureido) propyl] methylamine host have been investigated. The guests that contained an aryl urea glycine spacer were bound with the highest association constant. Subsequently, an adamantyl urea modified fifth generation poly(propylene imine) dendrimer was synthesized as a multivalent host which contains 32 N,N-bis[(3-adamantyl ureido) propyl] amine binding sites. Size exclusion chromatography showed that 32 of the OPV guests strongly bind to the fifth generation adamantyl functionalized dendritic host. In the case of the supramolecular dendritic host/guest system smooth homogeneous thin films could be obtained by spin coating. The dendritic guest-host complexes showed a significantly higher emission upon binding then that of the individual molecules due to the three-dimensional orientation of the OPV guest molecules. In the solid state, this enhancement in luminescence was a factor of 10. The pi-conjugated oligomers are less aggregated in the supramolecular assemblies presumably because of a shielding effect of the bulky adamantyl units present in the hosts.     

Micelles and reverse micelles in the nickel bis(2-ethylhexyl) sulfosuccinate/water/isooctane microemulsion

The ternary system Ni(2+)(AOT)(2) (nickel 2-bis[2-ethylhexyl] sulfosuccinate)/water/isooctane presents w/o and o/w microemulsions with a Winsor progression (2Phi-3Phi-2Phi), without the addition of salt; the "fish diagram" was obtained for alpha=0.5 and gamma=0.02-0.22. Using static and dynamic light scattering the micellar size, the ratio of water to surfactant, and the density of micelles for this system were estimated. In addition, the mean interfacial curvature as a function of temperature was obtained.     

Characterization of ellipses as uniformly dense sets with respect to a family of convex bodies

Let \(K\subset \mathbb R ^N\) be a convex body containing the origin. A measurable set \(G\subset \mathbb R ^N\) with positive Lebesgue measure is said to be uniformly \(K\) -dense if, for any fixed \(r>0\) , the measure of \(G\cap (x+r K)\) is constant when \(x\) varies on the boundary of \(G\) (here, \(x+r K\) denotes a translation of a dilation of \(K\) ). We first prove that \(G\) must always be strictly convex and at least \(C^{1,1}\) -regular; also, if \(K\) is centrally symmetric, \(K\) must be strictly convex, \(C^{1,1}\) -regular and such that \(K=G-G\) up to homotheties; this implies in turn that \(G\) must be \(C^{2,1}\) -regular. Then for \(N=2\) , we prove that \(G\) is uniformly \(K\) -dense if and only if \(K\) and \(G\) are homothetic to the same ellipse. This result was already proven by Amar et al. in 2008 . However, our proof removes their regularity assumptions on \(K\) and \(G\) , and more importantly, it is susceptible to be generalized to higher dimension since, by the use of Minkowski’s inequality and an affine inequality, avoids the delicate computations of the higher-order terms in the Taylor expansion near \(r=0\) for the measure of \(G\cap (x+r\,K)\) (needed in 2008).