Stabilization of linear control systems in Hilbert space with nonlinear feedback

This paper considers the problem of stabilization of linear control systems in Hilbert space with nonlinear feedback. Extensions of known results in the linear feedback case to the nonlinear one are given.     

Nonlinear homogeneous retarded differential equations and population dynamics via translation semigroups

In this paper nonlinear homogeneous retarded differential equations and models from population dynamics and epidemiology are considered and studied by the use of translation semigroup theory. We show that the corresponding solution semigroups are equivalent to appropriate translation semigroups. Existence results for the retarded equations are established by taking the space of initial functions of the form W ^1,p ((-r,0),F) where F is a Banach space, 1≤ p<∈fty and 0<r\le∈fty . June 28, 1999     

Plasma Chemical and Electrical Modeling of a Dielectric Barrier Discharge in Kr–Cl2 Gas Mixtures

This paper reports the study of the Kr–Cl₂ plasma chemistry in terms of the homogenous model of a dielectric barrier discharge and for two kinds of the applied voltage excitation shape. The effect of Cl₂ concentration in the gas mixture, as well as gas pressure and power frequency on the discharge efficiency and the 222 nm photon generation, under typical experimental operating conditions, have been investigated and discussed. Calculations suggest that the overall conversion efficiency from electrical energy to ultraviolet emission in the lamp is in the range of 4.4–12 %, and it will be very affected at high chlorine percentage (>1 %) and high gas pressure (>200 Torr). A comparison between the sinusoidal and the burst excitation waveforms reveals that the burst excitation method provides an enhanced light source performance compared to the sinusoidal wave.     

Path Integral Solution for the Coulomb Potential in a Curved Space of Constant Positive Curvature

A new path integral treatment of a hydrogen-like atom in a uniformly curved space with a constant positive curvature is presented. By converting the radial path integral into a path integral for the modified Pöschl-Teller potential with the help of the space-time transformation technique, the radial Green’s function is expressed in closed form, from which the energy spectrum and the corresponding normalized wave functions of the bound states are extracted. In the limit of vanishing curvature, the Green’s function, the energy spectra and the correctly normalized wave functions of bound and scattering states for a standard hydrogen-like atom are found.     

Structural,elastic, electronic,optical and thermoelectric properties of the Zintl-phase Ae3AlAs3 (Ae = Sr,Ba)

First-principles calculations were performed to investigate the structural, elastic, electronic, optical and thermoelectric properties of the Zintl-phase Ae₃AlAs₃ (Ae = Sr, Ba) using two complementary approaches based on density functional theory. The pseudopotential plane-wave method was used to explore the structural and elastic properties whereas the full-potential linearised augmented plane wave approach was used to study the structural, electronic, optical and thermoelectric properties. The calculated structural parameters are in good consistency with the corresponding measured ones. The single-crystal and polycrystalline elastic constants and related properties were examined in details. The electronic properties, including energy band dispersions, density of states and charge-carrier effective masses, were computed using Tran-Blaha modified Becke-Johnson functional for the exchange-correlation potential. It is found that both studied compounds are direct band gap semiconductors. Frequency-dependence of the linear optical functions were predicted for a wide photon energy range up to 15 eV. Charge carrier concentration and temperature dependences of the basic parameters of the thermoelectric properties were explored using the semi-classical Boltzmann transport model. Our calculations unveil that the studied compounds are characterised by a high thermopower for both carriers, especially the p-type conduction is more favourable.     

Catalytic oxidation of α-pinene by transition metal using t-butyl hydroperoxide and hydrogen peroxide

The allylic oxidation of α-pinene 1 was investigated using various catalytic systems. By a proper choice of the latter, the reaction can be directed toward the selective synthesis of verbenol 2 or verbenone 3. High yield into verbenone was achieved under mild conditions with copper salts as catalysts and t-butyl hydroperoxide (TBHP) as oxidant. On the other hand, when Pd(acac)₂ was used with hydrogen peroxide, verbenol was obtained as the main product.     

Synthesis and characterization of ethylxanthato complexes of zinc(II) with P-donor ligands

Monomeric, five-coordinated bis(ethylxanthato)Zn^II(phosphine) complexes [phosphine = PPh₃, P(o-tolyl)₃, P(CH₂Ph)₃] have been synthesized by addition of the phosphine ligand (1:1 molar ratio) to CH₂Cl₂ solutions of [Zn(S₂COEt)₂]. Bidentate ligands Ph₂PCH₂CH₂PPh₂ (dppe) and Ph₂P(CH₂)₄PPh₂ (dppb) reacted in a 1:2 molar ratio to form dinuclear phosphine-bridged complexes. The Zn—P bonds are very labile and are probably broken in solution. The characterization of all the compounds has been carried out by elemental analyses and spectroscopic methods (i.r. and n.m.r.). The structure of binuclear [(S₂COEt)₂Zn(-dppb)Zn(S₂COEt)₂], determined by X-ray crystallography, shows a distorted trigonal bipyramidal environment for the Zn atoms, formed by two chelating xanthate and a bridging dppb ligand.