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

Stability of Transonic Shock Solutions for One-Dimensional Euler-Poisson Equations

In this paper, both structural and dynamical stabilities of steady transonic shock solutions for one-dimensional Euler-Poission system are investigated. First, a steady transonic shock solution with supersonic backgroumd charge is shown to be structurally stable with respect to small perturbations of the background charge, provided that the electric field is positive at the shock location. Second, any steady transonic shock solution with the supersonic background charge is proved to be dynamically and exponentially stable with respect to small perturbation of the initial data, provided the electric field is not too negative at the shock location. The proof of the first stability result relies on a monotonicity argument for the shock position and the downstream density, and a stability analysis for subsonic and supersonic solutions. The dynamical stability of the steady transonic shock for the Euler-Poisson equations can be transformed to the global well-posedness of a free boundary problem for a quasilinear second order equation with nonlinear boundary conditions. The analysis for the associated linearized problem plays an essential role

Thermodynamics for Fractional Exclusion Statistics

We discuss the thermodynamics of a gas of free particles obeying Haldane's exclusion statistics, deriving low temperature and low density expansions. For gases with a constant density of states, we derive an exact equation of state and find that temperature-dependent quantities are independent of the statistics parameter.Comment: 9 pages, Revtex, no figures. References correcte

Absence of stable collinear configurations in Ni(001)ultrathin films: canted domain structure as ground state

Brillouin light scattering (BLS) measurements were performed for (17-120) Angstrom thick Cu/Ni/Cu/Si(001) films. A monotonic dependence of the frequency of the uniform mode on an in-plane magnetic field H was observed both on increasing and on decreasing H in the range (2-14) kOe, suggesting the absence of a metastable collinear perpendicular ground state. Further investigation by magneto-optical vector magnetometry (MOKE-VM) in an unconventional canted-field geometry provided evidence for a domain structure where the magnetization is canted with respect to the perpendicular to the film. Spin wave calculations confirm the absence of stable collinear configurations.Comment: 6 pages, 3 figures (text, appendix and 1 figure added

Exact Spectrum of SU(n) Spin Chain with Inverse-Square Exchange

The spectrum and partition function of a model consisting of SU(n) spins positioned at the equilibrium positions of a classical Calogero model and interacting through inverse-square exchange are derived. The energy levels are equidistant and have a high degree of degeneracy, with several SU(n) multiplets belonging to the same energy eigenspace. The partition function takes the form of a q-deformed polynomial. This leads to a description of the system by means of an effective parafermionic hamiltonian, and to a classification of the states in terms of "modules" consisting of base-n strings of integers.Comment: 12 pages, CERN-TH-7040/9

Development and production of an oligonucleotide MuscleChip: use for validation of ambiguous ESTs

BACKGROUND: We describe the development, validation, and use of a highly redundant 120,000 oligonucleotide microarray (MuscleChip) containing 4,601 probe sets representing 1,150 known genes expressed in muscle and 2,075 EST clusters from a non-normalized subtracted muscle EST sequencing project (28,074 EST sequences). This set included 369 novel EST clusters showing no match to previously characterized proteins in any database. Each probe set was designed to contain 20–32 25 mer oligonucleotides (10–16 paired perfect match and mismatch probe pairs per gene), with each probe evaluated for hybridization kinetics (Tm) and similarity to other sequences. The 120,000 oligonucleotides were synthesized by photolithography and light-activated chemistry on each microarray. RESULTS: Hybridization of human muscle cRNAs to this MuscleChip (33 samples) showed a correlation of 0.6 between the number of ESTs sequenced in each cluster and hybridization intensity. Out of 369 novel EST clusters not showing any similarity to previously characterized proteins, we focused on 250 EST clusters that were represented by robust probe sets on the MuscleChip fulfilling all stringent rules. 102 (41%) were found to be consistently "present" by analysis of hybridization to human muscle RNA, of which 40 ESTs (39%) could be genome anchored to potential transcription units in the human genome sequence. 19 ESTs of the 40 ESTs were furthermore computer-predicted as exons by one or more than three gene identification algorithms. CONCLUSION: Our analysis found 40 transcriptionally validated, genome-anchored novel EST clusters to be expressed in human muscle. As most of these ESTs were low copy clusters (duplex and triplex) in the original 28,000 EST project, the identification of these as significantly expressed is a robust validation of the transcript units that permits subsequent focus on the novel proteins encoded by these genes

Reduction of seafood processing wastewater using technologies enhanced by swim–bed technology

The increasing growth of the seafood processing industries considerably requires more industrial process activities and water consumption. It is estimated that approximately 10–40 m3 of wastewater is generated from those industries for processing one-tonne of raw materials. Due to limitations and regulations in natural resources utilization, a suitable and systematic wastewater treatment plant is very important to meet rigorous discharge standards. As a result of food waste biodegradability, the biological treatment and some extent of swim-bed technology, including a novel acryl-fibre (biofilm) material might be used effectively to meet the effluent discharge criteria. This chapter aims to develop understanding on current problems and production of the seafood wastewater regarding treatment efficiency and methods of treatment

Building solids inside nano-space: from confined amorphous through confined solvate to confined ‘metastable’ polymorph

The nanocrystallisation of complex molecules inside mesoporous hosts and control over the resulting structure is a significant challenge. To date the largest organic molecule crystallised inside the nano-pores is a known pharmaceutical intermediate – ROY (259.3 g mol1). In this work we demonstrate smart manipulation of the phase of a larger confined pharmaceutical – indomethacin (IMC, 357.8 g mol1), a substance with known conformational flexibility and complex polymorphic behaviour. We show the detailed structural analysis and the control of solid state transformations of encapsulated molecules inside the pores of mesoscopic cellular foam (MCF, pore size ca. 29 nm) and controlled pore glass (CPG, pore size ca. 55 nm). Starting from confined amorphous IMC we drive crystallisation into a confined methanol solvate, which upon vacuum drying leads to the stabilised rare form V of IMC inside the MCF host. In contrast to the pure form, encapsulated form V does not transform into a more stable polymorph upon heating. The size of the constraining pores and the drug concentration within the pores determine whether the amorphous state of the drug is stabilised or it recrystallises into confined nanocrystals. The work presents, in a critical manner, an application of complementary techniques (DSC, PXRD, solid-state NMR, N2 adsorption) to confirm unambiguously the phase transitions under confinement and offers a comprehensive strategy towards the formation and control of nano-crystalline encapsulated organic solids