Infinite horizon disturbance attenuation for discrete-time systems. A Popov-Yakubovich approach

It is proved that for the discrete-time linear systems with time-varying coefficients the existence of a controller which simultaneously stabilizes and provides prescribed disturbance attenuation for the resultant closed-loop system, implies the existence of global solutions to several Kalman-Szegö-Popov-Yakubovich systems. It is also proved that this fact is equivalent to the existence of the positive semidefinite stabilizing solutions to corresponding game-theoretic Riccati equations. The family of all controllers with the above mentioned properties is constructed in terms of the solutions to the cited Kalman-Szegö-Popov-Yakubovich systems. The main tool is the generalized Popov-Yakubovich theory which is essentially developed in an operator-theoretic framework.     

Full Nuclear Cones and a Relation Between Strong Optimization and Pareto Efficiency

In this paper we present some new and pertinent connections between the Strong Optimization and the Approximate Pareto type Efficiency, in particular, with the usual Vector Optimization, at first in the Ordered Vector Spaces by the natural Convex Cones and, afterwards, in the Ordered Hausdorff Locally Convex Spaces. The main result is obtained considering the notion of full nuclear cone. Our results, is related to an appropriate scalarization method Mathematics Subject Classification (2000). 90C29     

Mass spectra of vinyltrimethylsilane and vinyltri(methyl-d3) silane

This paper reports the mass spectrum of vinyltrimethylsilane over the range of electron-impact energy of 9 to 70 eV as determined with a quadrupole mass spectrometer. Less extensive data obtained with magnetic spectrometers are included for comparison as well as the spectrum of vinyl-tri(methyl-d₃)silane. Plots of ion intensity as a function of electron energy, nominal appearance potentials and metastable ion transitions are given. The primary ionization results in an electron deficiency on the silicon atom, followed by loss of either ·CH₃, C₂H₄ or ·C₂H₃ to give fragments of mass 85, 73 or 72, respectively. The primary fragment of mass 85 loses C₂H₂ to give the mass 59 ion. The primary fragment of mass 73 loses successively C₂H₄ and H₂ to give first the mass 45 ion and then the mass 43 ion. At 15 eV, the relative intensities of the ions are 85 > 72 > 100 > 59 > 73. At 70 eV, the relative intensities are 59 > 85 > 43 > 45 > 73 > 72 > 100.     

Raman and SERS study of metoclopramide at different pH values

Conjugate acid–base forms of the drug metoclopramide were investigated by Raman spectroscopy in aqueous solutions and by surface‐enhanced Raman scattering (SERS), when the molecules were adsorbed on colloidal silver surfaces. Raman spectra were recorded at pH values below 8, metoclopramide being poorly water soluble at higher pH values. The SERS spectra of metoclopramide were recorded in the 3–11 pH range, even in spite of its low solubility at basic pH values. The Raman and SERS spectra were assigned by means of density functional theory (DFT) calculations. By monitoring several SERS marker bands, the protonated, neutral or the coexistence of both molecular species adsorbed on the colloidal silver particles could be evidenced. The adsorbate orientation was deduced to be perpendicular to the metal surface for the protonated molecular species and tilted for the neutral metoclopramide molecular species. Copyright © 2009 John Wiley & Sons, Ltd.     

Collision and escape orbits in a generalized Hénon–Heiles model

The motion of a material point of unit mass in a field determined by a generalized Hénon–Heiles potential $U=A{q}_1^2+B{q}_2^2+C{q}_1^2{q}_2+D{q}_2^3$, with $(q_1,q_2)=$ standard Cartesian coordinates and $(A,B,C,D)\in {(0,\infty )}^2\times R^2$, is addressed for two limit situations: collision and escape. Using McGehee-type transformations, the corresponding collision and infinity boundary manifolds pasted on the phase space are determined. These are fictitious manifolds, but, due to the continuity with respect to initial data, their flow determines the near by orbit behaviour.The dynamics on the collision and infinity manifolds is fully described. The topology of the flow on the collision manifold is independent of the parameters. In the full phase space, while spiraling collision orbits are present, most of the orbits avoid collision. The topology of the flow on the infinity manifold changes as the ratio between $C$ and $D$ varies. More precisely, there are two symmetric pitchfork bifurcations along the line $2C?3D=0$, due to the reshaping of the potential along the bifurcation line. Besides rectilinear and spiraling orbits, the near-escape dynamics includes oscillatory orbits, for which angular momentum alternates sign.     

Association Phenomena of Poly(arylene ether sulfone)s in Dimethylformamide

Three poly(arylene ether sulfone)s (two polymers and one copolymer) containing diphenylfluorene, phenolphthalein and 2,4-bis[(4-chlorophenyl)sulfonyl]-1-(phenyltio) benzene)] units were synthesized by the classical Williamson polyetherification reaction. The association phenomenon in N,N-dimethylformamide (DMF) was investigated by different methods: gel permeation chromatography (GPC), viscosity, atomic force microscopy (AFM), fluorescence spectroscopy and dynamic light scattering (DLS). Both AFM and DLS measurements evidenced the formation of aggregates with spherical or ellipsoidal shape at a concentration around 0.05 wt.%. This behavior could be explained by dipole-dipole interactions between macromolecular chains, probably with the participation of solvent molecules, and by H-bonds involving hydroxyl end groups.     

DFT study and quantitative detection by surface‐enhanced Raman scattering (SERS) of ethyl carbamate

Ethyl carbamate (EC), a potentially toxic compound, is found in alcoholic beverages and fermented foodstuff. A combined experimental and theoretical study of Raman on EC is reported in this work for the first time. The Raman bands observed for EC in solid phase are characteristic for the carbonyl group, C―C, C―H and N―H stretching and deformation vibrations. These spectral features coupled with a pKa study allowed establishing the neutral species of EC present in the aqueous solutions experimentally tested at different concentrations. In addition, by performing a density functional theory study in the gas phase, the calculated geometry, the harmonic vibrational modes, and the Raman scattering activities of EC were found to be in good agreement with our experimental data and helped establish the surface‐enhanced Raman scattering (SERS) behavior and EC adsorption geometry on the silver surfaces. The Raman peak at 1006 cm⁻¹, assigned to the υ_s(CC) + ω(CH) modes, the strongest and best reproducible peak in the SERS spectra, was used for a quantitative evaluation of EC. The limit of detection, which corresponds to a signal‐to‐noise ratio equal to 3, was found to be 2 × 10⁻⁷ M (17.8 µg l⁻¹). SERS spectra obtained by using hydroxylamine hydrochloride‐reduced silver nanoparticles provide a fast and reproducible qualitative and quantitative determination of EC in aqueous solution. Copyright © 2013 John Wiley & Sons, Ltd.     

Exponential Stability in Mean Square for a General Class of Discrete-Time Linear Stochastic Systems

Abstract

The problem of the mean square exponential stability for a class of discrete-time linear stochastic systems subject to independent random perturbations and Markovian switching is investigated. The case of the linear systems whose coefficients depend both to present state and the previous state of the Markov chain is considered. Three different definitions of the concept of exponential stability in mean square are introduced and it is shown that they are not always equivalent. One definition of the concept of mean square exponential stability is done in terms of the exponential stability of the evolution defined by a sequence of linear positive operators on an ordered Hilbert space. The other two definitions are given in terms of different types of exponential behavior of the trajectories of the considered system. In our approach the Markov chain is not prefixed. The only available information about the Markov chain is the sequence of probability transition matrices and the set of its states. In this way one obtains that if the system is affected by Markovian jumping the property of exponential stability is independent of the initial distribution of the Markov chain.

The definition expressed in terms of exponential stability of the evolution generated by a sequence of linear positive operators, allows us to characterize the mean square exponential stability based on the existence of some quadratic Lyapunov functions.

The results developed in this article may be used to derive some procedures for designing stabilizing controllers for the considered class of discrete-time linear stochastic systems in the presence of a delay in the transmission of the data.     

A bivariate non-homogeneous birth and death model for predator–prey interactions

We propose a bivariate non-homogeneous birth and death process as a model for predator–prey interactions. Its expectation is periodic, as it is a solution to the classical Lotka–Volterra system. Moreover, the mean age at extinction, as defined in Kendall (1948), is infinite.     

Measurement of production date (age) of nanogram amount of uranium

JRC-Karlsruhe obtained a swipe sample from a highly enriched uranium seizure, which had taken place in 2011. Due to the very low amount of uranium (nanograms) a new method needed to be developed to determine the U production date (age). The particles on the swipe were collected on a pyrolytic graphite planchet using a vacuum impactor and they were subsequently leached with ccHNO₃. The “bulk” U isotopic composition (²³⁵U: 72.51?±?0.03 wt%) and the production date (December 1992?±?1 year) determined by MC-ICP-MS indicated that the material showed similarity with two other HEU cases seized earlier in Europe.