Quantum systems and representation theorem

In this paper we investigate quantum systems which are locally convex versions of abstract operator systems. Our approach is based on the duality theory for unital quantum cones. We prove the unital bipolar theorem and provide a representation theorem for a quantum system being represented as a quantum $L^{\infty }$ -system.     

Global existence and nonexistence results for a class of semilinear hyperbolic systems

In this paper, we investigate the Cauchy problem for a class of the system of semilinear hyperbolic equations with damping. With the use of the L_p → L_q type estimation for the corresponding linear problem and the method of comparison of functional, the existence and nonexistence criteria of global solutions are found. Copyright © 2012 John Wiley & Sons, Ltd.     

Optical characterization of eu-doped and undoped gd(2)o(3) nanoparticles synthesized by the hydrogen flame pyrolysis method

Rare-earth-doped nanoparticles are promising materials for fluorescent labeling, as they are characterized by a high Stokes shift, narrow emission spectra, long lifetimes, minimized photobleaching, and low toxicity. We examined the structural and optical properties of europium-doped gadolinium oxide nanoparticles synthesized by the flame pyrolysis method, with specific emphasis on full spectral characterization and fluorescence kinetics. The emission-excitation characterization revealed the presence of predominantly monoclinic but also highly luminescent cubic phases with a prominent oxygen-to-europium charge-transfer band in the 230-260 nm range. A broad emission band in the visible region, corresponding to a similar band in undoped Gd(2)O(3), related to the matrix surface defects, was observed in time-gated spectroscopy of doped nanopowders. All of the examined nanopowders showed very short decay components, on the order of 2 ns, and much longer millisecond decay times characteristic of lanthanide ions. At intermediate times, on the order of 20-100 ns, a complex behavior of the decay was observed, indicative of progressive energy transfer to the lanthanide ion, which varied with different intrashell transitions. Structural characterization data by means of XRD measurements allowed for unambiguous determination of the Eu:Gd(2)O(3) crystallographic structure and cell dimensions to be consistent with a predominantly monoclinic phase.     

Bipolar theorem for quantum cones

In this note duality properties of quantum cones are investigated. We propose a bipolar theorem for quantum cones, which provides a new proof of the operator bipolar theorem proved by Effros and Webster. In particular, a representation theorem for a quantum cone is proved.     

Cartan–Slodkowski spectra, splitting elements and noncommutative spectral mapping theorems

In this paper, we prove Slodkowski version of the infinite-dimensional spectral mapping theorem and Cartan–Slodkowski version of the finite-dimensional spectral mapping theorem for nilpotent operator Lie subalgebras with respect to the various noncommutative functional calculi.     

Exotic smooth structures on small 4-manifolds with odd signatures

Let M be (2n-1)\mathbbCP²#2n[`(\mathbbCP)]<sup>2</sup>(2n-1)\mathbb{CP}^{2}\#2n\overline{\mathbb{CP}}{}^{2} for any integer n≥1. We construct an irreducible symplectic 4-manifold homeomorphic to M and also an infinite family of pairwise non-diffeomorphic irreducible non-symplectic 4-manifolds homeomorphic to M. We also construct such exotic smooth structures when M is \mathbbCP<sup>2</sup>#4[`(\mathbbCP)]²\mathbb{CP}{}^{2}\#4\overline {\mathbb{CP}}{}^{2} or 3\mathbbCP²#k[`(\mathbbCP)]²3\mathbb{CP}{}^{2}\#k\overline{\mathbb{CP}}{}^{2} for k=6,8,10.     

Exploring the melting of a semirigid-chain polymer with temperature-resolved small-angle <Emphasis Type="Italic">X</Emphasis>-ray scattering

The thermal behavior of semirigid semicrystalline polymers differs significantly from that of flexible-chain polymers. The origin of the differences is believed to lie in the higher energy expenditure associated with the formation of adjacent re-entry folds at the crystalline surface in the case of semirigid chains. The effect of constraints imposed by the interlamellar amorphous regions on the neighboring crystals was studied with temperature-resolved synchrotron radiation small-angle X-ray scattering (SAXS). The analysis of SAXS patterns with a generalized paracrystalline lamellar stack model indicates that melting of a semirigid-chain polymer is not a random process but that the crystals grown in the smallest amorphous gaps melt first. This suggests that the hitherto largely neglected geometrical confinement effects may play an important role in determining the thermodynamic stability of semirigid-chain polymer crystals.Received: 5 March 2004, Published online: 4 May 2004PACS: 61.41. + e Polymers, elastomers, and plastics - 64.70.Dv Solid-liquid transitions - 81.10.Aj Theory and models of crystal growth; physics of crystal growth, crystal morphology and orientation     

Thermal,spectral, and thermodynamic studies for evaluation of calf thymus DNA interaction activity of some copper(II) complexes

The square-pyramidal copper(II) complexes with ciprofloxacin in the presence of bipyridine derivatives have been synthesized and characterized using elemental analysis, magnetic moment measurement, thermal analysis (TG), IR, mass and reflectance spectra. The thermal denaturation study has been used for evaluating calf thymus DNA interaction activity. Spectral and hydrodynamic measurements have been used for validating the DNA interaction study. The thermodynamic profile was established for proper understanding of DNA binding Gibbs free energy.     

Spectrophotometric determination of ciprofloxacin by ion pair formation

Various aspects of application of derivative spectrophotometry to chemical analysis and investigations of equilibria and kinetics of reactions are scrutinised. In this work the viability of a spectrophotometric technique for the determination of ciprofloxacin has been deliberated. The method is based on the formation of ion-association complexes of ciprofloxacin with nickel(II) tetra thiocyanate, which are extracted into organic solvent (40% n-butanol in methylene chloride) having absorption maxima at 623 nm. The precision and accuracy of the method was checked by UV reference methods. The validation study indicated the parameters, which are in good agreement with the data obtained from standard methods. The proposed method was fruitfully applied to determine ciprofloxacin in their tablet formulations.