Classical solutions to a quadratically nonlinear gauge theory

We present some classical solutions to a gauge theory based on quadratically nonlinear Lie algebras without a central term. We observe that instanton-like and meron-like solutions force the internal fields to behave like solitons.     

Erratum: Synthesis and characterization of diorganotin(IV) complexes of Schiff bases with ONO‐type donors and crystal structure of [N‐(2‐hydroxy‐4‐nitrophenyl)‐3‐ethoxysalicylideneiminato]diphenyltin(IV)

The article referenced above was first published online on 30 August 2007 with incorrect pagination; the pagination has now been corrected online and in print. Copyright © 2007 John Wiley & Sons, Ltd.     

Application of N,N‐bis(diphenylphosphino)aniline palladium(II) complexes as pre‐catalysts in Heck coupling reactions

Palladium(II) complexes with N,N‐bis(diphenylphosphino)aniline ligands catalyse the Heck reaction between styrene and aryl bromides, affording stilbenes in good yield. The structures of two of the complexes used as pre‐catalysts have been determined by single‐crystal X‐ray diffraction. Copyright © 2007 John Wiley & Sons, Ltd.     

Portfolio optimization in stochastic markets

We consider a multiperiod mean-variance model where the model parameters change according to a stochastic market. The mean vector and covariance matrix of the random returns of risky assets all depend on the state of the market during any period where the market process is assumed to follow a Markov chain. Dynamic programming is used to solve an auxiliary problem which, in turn, gives the efficient frontier of the mean-variance formulation. An explicit expression is obtained for the efficient frontier and an illustrative example is given to demonstrate the application of the procedure.     

Mixing mechanisms of vortex ring formed by gravity slumping motion

 This paper is concerned with an experimental investigation of the mixing inside the vortex ring formed by the gravity slumping motion of a dense cloud in a less dense atmosphere. The dynamics of the spreading and instantaneous structures of the turbulent flow were examined by visualization, single and multi-point measurements of velocity and concentration for two heavy gases, carbondioxide (CO₂) and dichlorodifluoromethane (CCl₂F₂), in a configuration in that heavy gas, initially trapped in a reservoir, was released with the rise of a shutter into calm air of a sector-shaped dispersion channel. Visualization of the cloud as a whole showed a spreading motion in which an advancing frontal structure was followed by a stratified flow with a layer of dense fluid of higher velocities near the wall and, on top of it, a layer of dilute fluid whose concentration is controlled by the mixing mechanisms within the head. During the course of spreading, there was always a phase in which the head attained to a constant speed of advance, which occurred as 0.13 m/s for CO₂ and 0.48 m/s for CCl₂F₂. It was interesting to observe for CO₂ that the phase of constant speed took place in between two acceleration phases; the former was due to the initial slumping of the cloud at the exit of the reservoir, and the latter was attributed to the collapse of the head on the transition to the passive dispersion phase. Instantaneous two-dimensional velocity field, measured with particle image velocimeter (PIV), showed that the cloud overran the ambient air which caused the approaching dense fluid deflected away from the wall with significant vertical velocities and downstream-moving separation, and the air trapped under the head resulted in the density inversion which introduced further intricacy to the turbulent structure of the head. Instabilities at the upper free shear layer due to density and velocity discontinuity rolled into periodic array of vortices which engulfed a considerable amount of air as they were convected backwards over the head, but the incorporation of heavy and light fluids was completed with the appearance of microscales after the collapse on the stratified layer. Analyses of the cloud head at different downstream locations also revealed that its size remained unchanged when the speed of advance was constant, allowing the rate of change of the cloud volume being modeled with the rate of spreading. Contours of concentration obtained from digitized PIV pictures confirmed the kinematic features of the mixing revealed by the velocity field and that the concentration values within the large structures were higher than those at the upper part of the stratified layer. Motivated by the experimental observations, a semi-empirical analysis was presented to describe the results and based on local values of the Richardson and Reynolds numbers. Received: 4 October 1995 / Accepted: 4 July 1996     

Preliminary analyses of natural radionuclides in selected Turkish power plant lignites

This preliminary study presents the experimental results concerning the concentrations of selected radionuclides (²³⁸U, ²³²K, ²²⁶Ra, ²³²Th) in Af?in-Elbistan, Çan, Çay?rhan, Erzurum, Göynük, Kangal, Orhaneli, Saray, Seyitömer, Soma, Tunçbilek, Yata?an and Yeniköy lignites, which are primarily utilized as fuel for thermal power plants in Turkey. Gamma-spectrometry of 39 representative lignite samples gave results with the following concentration ranges: 8 to 296 Bq/kg for ²³⁸U, 3 to 79 Bq/kg for ²³²Th, 17 to 360 Bq/kg for 40K, and 5 to 130 Bq/kg for ²²⁶Ra. The ²³⁸U results reported here are higher than other literature values for various world coals, earth's crust and world average.     

Elimination of bremsstrahlung in activation analysis by the deflection of β-particles in a magnetic field

The structureless background at X-ray and low energy -ray region, resulting from bremsstrahlung due to the stopping of -radiations, causes serious problems in nuclear spectroscopy. In this study, in order to reduce the background and therefore to increase the sensitivity of the nuclear analytical technique and the number of elements observable, a methodology is developed to deflect the -particles by a magnetic field. The experimental setup consists of a permanent magnet /1 kG/, Ge/Li/ solid-state detector, and multichannel analyzer.     

On input/output stabilization of singular integrodifferential systems

In this paper we consider a class of systems described by singular integrodifferential equations. This type of systems appear, for example, in the modeling of certain aeroelastic control problems. We study these systems in frequency domain framework and show the existence of finite-dimensional stabilizing controllers. An algorithmic procedure is outlined for the construction of such controllers. In order to illustrate the numerical aspects of this algorithm, we present an example involving the classical Theodorsen model of an airfoil, which fits in the class of systems considered here.This work was supported in part by the National Science Foundation under Grants DMS-8907019 and MSS-9203418.     

On the interpretation of random forces derived by projection operators

We study the derivation of a Langevin equation from a microscopic basis in order to elucidate the nature of the random force. We arrive at the conclusion that the consistent interpretation of the microscopic Langevin equation in terms of a stochastic differential equation (SDE) is according to I o rules. In addition, the random force is in general not Gaussian, and it is hence not completely characterized by its second moments.     

Radiometric titration based on colloidal and slow precipitate formation

Fluoride ions and, in about 0.005M concentration, tungstate ions form gelatinous precipitates, poorly soluble in water, with calcium ions. The radiometric determinations of the above ions are based on these reactions. Accurate radiometric determination can be carried out only if the gelatinous precipitate formed during titration can be properly separated from the solution. It has been found that in the case of fluoride ions the application of crystalline, easily filtrable Ca(COO)₂·H₂O or CaCO₃, and in the case of tungstate ions the application of CaWO₄ precipitate improves the filtration properties of⁴⁵CaF₂ and⁴⁵CaWO₄, respectively, formed during titration, whereby the radiometric determinations of the above ions become possible. Titrations were carried out with 0.05M and 0.005M CaCl₂ solutions, labelled with⁴⁵Ca.