Approximate reduction of non-linear discrete models with two time scales

The aim of this work is to present a general class of nonlinear discrete time models with two time scales whose dynamics is susceptible of being approached by means of a reduced system. The reduction process is included in the so-called approximate aggregation of variables methods which consist of describing the dynamics of a complex system involving many coupled variables through the dynamics of a reduced system formulated in terms of a few global variables. For the time unit of the discrete system we use that of the slow dynamics and assume that fast dynamics acts a large number of times during it. After introducing a general two-time scales nonlinear discrete model we present its reduced accompanying model and the relationships between them. The main result proves that certain asymptotic behaviours, hyperbolic asymptotically stable (A.S.) periodic solutions, to the aggregated system entail that to the original system.     

Localization of Non-Relativistic Particles

This paper is a contribution to the problem of particle localization in non-relativistic Quantum Mechanics. Our main results will be (1) to formulate the problem of localization in terms of invariant subspaces of the Hilbert space, and (2) to show that the rigged Hilbert space incorporates particle localization in a natural manner.     

Antiphytopathogenic activity of Psoralea glandulosa (Fabaceae) against Botrytis cinerea and Phytophthora cinnamomi

The resinous exudate, three meroterpenes, namely bakuchiol (1), 3-hydroxybakuchiol (2), 12-hydroxyisobakuchiol (3), and one furanocoumarin, psoralen (4), were isolated from the leaves of culen (Psoralea glandulosa). In addition to these, two semi-synthetic derivatives, bakuchiol acetate (5) and bakuchiol methyl eter (6), were obtained from 1, and were subsequently evaluated in vitro for the inhibitory effect of resin and compounds on the mycelial growth of Botrytis cinerea Pers.: Fr. and Phytophthora cinnamomi Rands. The resinous exudate inhibited the mycelial growth of both the pathogens, while bakuchiol (1) exhibited an inhibitory effect on the mycelial growth of B. cinerea up to 94% at a concentration of 150 mg/L and psoralen (4) reduced the mycelial growth of P. cinnamomi up to 80% at a concentration of 150 mg/L. These compounds have the ability of blocking the development of mycelial growth and may be used as a potential biopesticide in the agricultural sector once the in vivo test results have been validated.     

Metastable Ionic Diodes Derived from an Amine‐Based Polymer of Intrinsic Microporosity

A highly rigid amine‐based polymer of intrinsic microporosity (PIM), prepared by a polymerization reaction involving the formation of Tröger’s base, is demonstrated to act as an ionic diode with electrolyte‐dependent bistable switchable states.     

Solution structure of a peptide nucleic acid duplex from NMR data: features and limitations

This paper describes the results of a 1D and 2D NMR spectroscopy study of a palindromic 8-base pair PNA duplex GGCATGCC in H2O and H2O-D2O solutions. The (1)H NMR peaks have been assigned for most of the protons of the six central base pairs, as well as for several amide protons of the backbone. The resulting 36 interbase and base-backbone distance restraints were used together with Watson-Crick restraints to generate the PNA duplex structure in the course of 10 independent simulated annealing runs followed by restrained molecular dynamics (MD) simulations in explicit water. The resulting PNA structures correspond to a P-type helix with helical parameters close to those observed in the crystal structures of PNA. Based on the current limited number of restraints obtained from NMR spectra, alternative structures obtained by MD from starting PNA models based on DNA cannot be ruled out and are also discussed.     

Resonance expansions in quantum mechanics

The goal of this contribution is to discuss various resonance expansions that have been proposed in the literature. Presented at the 3rd International Workshop “Pseudo-Hermitian Hamiltonians in Quantum Physics”, Istanbul, Turkey, June 20–22, 2005.