Facial structures for various notions of positivity and applications to the theory of entanglement

In this expository note, we explain facial structures for the convex cones consisting of positive linear maps, completely positive linear maps, decomposable positive linear maps between matrix algebras, respectively. These will be applied to study the notions of entangled edge states with positive partial transposes and optimality of entanglement witnesses.Comment: An expository note. Section 7 and Section 8 have been enlarge

Preparation of Mgo-ceo2 Mixed Oxide with Ionic Liquid as Catalyst for Dimethyl Carbonate Synthesis Via Transesterification

The synthesis and application of dimethyl carbonate (DMC) are achieving increasing importance due to its low toxicity and versatile reactivity. The phosgenation-route has been losing attraction recently due to the use of virulent phosgene. In transesterification process, DMC is co-generated with ethylene glycol (EG). In this study, various ionic liquids were used as template in coprecipitation methods to prepare mesoporous MgO-CeO2 mixed oxides particles. Among the ionic liquids, [Bmim][BF6] displayed the best performance in terms of activity, while [Omim][PF6] obtained the best selectivity for this reaction. The addition of IL's in the coprecipitation method increased the surface areaand pore volume of the catalysts. Meanwhile, the crystallite size of the catalysts was reduced many times. However, there is no effect of the surface areaand particle size as well on the catalytic activity of the catalyst in this reaction. The activity and selectivity of the catalyst depend on the base strength distribution. The moderate basic site is responsible for the catalytic activity, while the selectivity is more dependableon the strong basic site

The Normal State Resistivity of Grain Boundaries in YBa2Cu3O7-delta

Using an optimized bridge geometry we have been able to make accurate measurements of the properties of YBa2Cu3O7-delta grain boundaries above Tc. The results show a strong dependence of the change of resistance with temperature on grain boundary angle. Analysis of our results in the context of band-bending allows us to estimate the height of the potential barrier present at the grain boundary interface.Comment: 11 pages, 3 figure

Separability problem for multipartite states of rank at most four

One of the most important problems in quantum information is the separability problem, which asks whether a given quantum state is separable. We investigate multipartite states of rank at most four which are PPT (i.e., all their partial transposes are positive semidefinite). We show that any PPT state of rank two or three is separable and has length at most four. For separable states of rank four, we show that they have length at most six. It is six only for some qubit-qutrit or multiqubit states. It turns out that any PPT entangled state of rank four is necessarily supported on a 3x3 or a 2x2x2 subsystem. We obtain a very simple criterion for the separability problem of the PPT states of rank at most four: such a state is entangled if and only if its range contains no product vectors. This criterion can be easily applied since a four-dimensional subspace in the 3x3 or 2x2x2 system contains a product vector if and only if its Pluecker coordinates satisfy a homogeneous polynomial equation (the Chow form of the corresponding Segre variety). We have computed an explicit determinantal expression for the Chow form in the former case, while such expression was already known in the latter case.Comment: 19 page

High critical current densities in superconducting MgB2 thin films

Superconducting MgB2 thin films were prepared on Al2O3(0001) and MgO(100) substrates. Boron thin films were deposited by the electron-beam evaporation followed by post-annealing process with magnesium. Proper post annealing conditions were investigated to grow good superconducting MgB2 thin films. The X-ray diffraction patterns showed randomly orientated growth of MgB2 phase in our thin films. The surface morphology was examined by scanning electron microscope (SEM) and atomic force microscope (AFM). Critical current density (Jc) measured by transport method was about 10^7 A/cm^2 at 15 K, and superconducting transition temperature (Tc) was ~ 39 K in the MgB2 thin films on Al2O3.Comment: 13 pages, 4 figures, submitted on Apr. 4, 2001, only one pdf fil

Generalized Phase Synchronization in unidirectionally coupled chaotic oscillators

We investigate phase synchronization between two identical or detuned response oscillators coupled to a slightly different drive oscillator. Our result is that phase synchronization can occur between response oscillators when they are driven by correlated (but not identical) inputs from the drive oscillator. We call this phenomenon Generalized Phase Synchronization (GPS) and clarify its characteristics using Lyapunov exponents and phase difference plots.Comment: 4 pages, 5 figure

Characteristics of a Delayed System with Time-dependent Delay Time

The characteristics of a time-delayed system with time-dependent delay time is investigated. We demonstrate the nonlinearity characteristics of the time-delayed system are significantly changed depending on the properties of time-dependent delay time and especially that the reconstructed phase trajectory of the system is not collapsed into simple manifold, differently from the delayed system with fixed delay time. We discuss the possibility of a phase space reconstruction and its applications.Comment: 4 pages, 6 figures (to be published in Phys. Rev. E

Narratives of ethnic identity among practitioners in community settings in the northeast of England

The increasing ethnic diversity of the UK has been mirrored by growing public awareness of multicultural issues, alongside developments in academic and government thinking. This paper explores the contested meanings around ethnic identity/ies in community settings, drawing on semi-structured interviews with staff from Children’s Centres and allied agencies conducted for a research project that examined the relationship between identity and the participation of parents/carers in services in northeast England. The research found that respondents were unclear about, especially, white ethnic identities, and commonly referred to other social categorizations, such as age, nationality, and circumstances such as mobility, when discussing service users. While in some cases this may have reflected legitimate attempts to resist overethnicizing non-ethnic phenomena, such constructions coexisted with assumptions about ethnic difference and how it might translate into service needs. These findings raise important considerations for policy and practice

Current reversal with type-I intermittency in deterministic inertia ratchets

The intermittency is investigated when the current reversal occurs in a deterministic inertia ratchet system. To determine which type the intermittency belongs to, we obtain the return map of velocities of particle using stroboscopic recording, and numerically calculate the distribution of average laminar length ${}$. The distribution follows the scaling law of ${} \propto {\epsilon}^{-1/2}$, the characteristic relation of type-I intermittency.Comment: 4 pages, 7 figure