The Hilbert-Space Structure of Non-Hermitian Theories with Real Spectra

We investigate the quantum-mechanical interpretation of models with non-Hermitian Hamiltonians and real spectra. After describing a general framework to reformulate such models in terms of Hermitian Hamiltonians defined on the Hilbert space L ₂(-, ), we discuss the significance of the algebra of physical observables.     

On the interpolation constant for Orlicz spaces

In this paper we deal with the interpolation from Lebesgue spaces and , into an Orlicz space , where and for some concave function , with special attention to the interpolation constant . For a bounded linear operator in and , we prove modular inequalities, which allow us to get the estimate for both the Orlicz norm and the Luxemburg norm,

where the interpolation constant depends only on and . We give estimates for , which imply . Moreover, if either or , then . If , then , and, in particular, for the case this gives the classical Orlicz interpolation theorem with the constant .

     

Barrelledness and bornological conditions on spaces of vector-valued μ-simple functions

Let S(μ, E) be the space of (classes of μ-a.e. equal) simple functions defined on a (non-trivial) measure space with values in a locally convex space E. The following results hold: S(μ,E) is quasi-barrelled (resp. bornological) if and only if E is quasi-barrelled (resp. bornological) and E′(β(E′,E)) has the property (B) of Pietsch; S(μ, E) is barrelled if and only if S(μ,K) is barrelled and E is barrelled and nuclear; S(μ, E) is never ultrabornological; and S(μ, E) is a DF-space if and only if E is a DF-space.     

Regioselective reactions of enaminones with enones—II: Intramolecular rearrangement involving carbon to oxygen acyl migrations

Intramolecular dynamic behaviour helps in predicting the regioselectivity of reactions in ambident molecules. Thus the enaminones (1) react on the C-2 carbon atom with benzoquinone. Reaction proceeds with an intramolecular acyl shift following formation of the initial reaction complex upon reaction at position C-2 of the enaminone and the quinone. Under certain conditions the reaction is regiospecific and proceeds stereospecifically.     

Solvent-induced isotope effects in NMR spectroscopy. A study of hydrogen bonding between the carbonyl group in chalcone and trifluoracetic acid (TFA-d or TFA) in chloroform solution

Splittings, δ_i, were observed for each carbon atom, C_i, of chalcone in spectra obtained from coaxial 5 and 10 mm NMR sample tubes containing solutions equimolar in the concentration of the ketone and of TFA or TFA-d as hydrogen-bond donors, respectively. It was found that a linear expression, δ_i = (K–1)x_HΔ_i+x_Dδ_i(D, H) relates these splittings, δ_i, induced by the isotopic substitution in a hydrogen bond, to the parameter Δ_i, denoting the change in chemical shift for each carbon site in complexed and free ketone, and δ_i(D, H), the solvent-induced isotope effect in a complex. The origin of the phenomenon is briefly discussed. It is also shown that the secondary deuterium isotope effect can give the same information about the form of the potential energy well in the hydrogen-bond as the primary H/D isotopte shifts.     

The limit diffusion mechanism of relaxation for spin systems

The diffusion limit theorem for stochastic differential equations is applied to analyse the dynamical evolutions of spin systems. Bloch equations are derived and the stability of asymptotic evolutions is proved. The theory is applied to nuclear magnetic relaxation of two spins.     

Mixed Semicontinuous Mappings and Their Applications to Differential Inclusions

A class of multivalued mappings, called by us mixed semicontinuous mappings, which are upper semicontinuous in some points and lower semicontinuous in remaining points is considered. A general selection theorem for mixed semicontinuous maps is proved. Then applications to differential inclusions with mixed semicontinuous right-hand sides are presented. Note that our applications generalize earlier existence results obtained both on the whole Euclidean space R ⁿ and on a compact proximate retract of R ⁿ .     

Biaxial nematic phase in model bent-core systems

We determine the bifurcation phase diagrams with isotropic (I), uniaxial (N(U)) and biaxial (N(B)) nematic phases for model bent-core mesogens using Onsager-type theory. The molecules comprise two or three Gay-Berne interacting ellipsoids of uniaxial and biaxial shape and a transverse central dipole. The Landau point is found to turn into an I-N(B) line for the three-center model with a large dipole moment. For the biaxial ellipsoids, a line of Landau points is observed even in the absence of the dipoles.     

Dynamic response of gold nanoparticle chemiresistors to organic analytes in aqueous solution

We investigate the response dynamics of 1-hexanethiol-functionalized gold nanoparticle chemiresistors exposed to the analyte octane in aqueous solution. The dynamic response is studied as a function of the analyte-water flow velocity, the thickness of the gold nanoparticle film and the analyte concentration. A theoretical model for analyte limited mass-transport is used to model the analyte diffusion into the film, the partitioning of the analyte into the 1-hexanethiol capping layers and the subsequent swelling of the film. The degree of swelling is then used to calculate the increase of the electron tunnel resistance between adjacent nanoparticles which determines the resistance change of the film. In particular, the effect of the nonlinear relationship between resistance and swelling on the dynamic response is investigated at high analyte concentration. Good agreement between experiment and the theoretical model is achieved.