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.     

Regional elemental signatures related to combustion of lignites

In ambient air, arsenic to selenium ratio (As/Se) is generally found to be less than 1, except in areas influenced by specific point sources, such as Cu smelters. However, the annual average of this ratio is found to be much higher than unity in Turkey. This finding is rather unique and may provide a marker for air masses influenced by the coal-related emissions in Turkey. This revised version was published online in August 2006 with corrections to the Cover Date.     

High temperature stability of maghemite in partially oxidized basalt lava

Mössbauer spectroscopy of basalt lava samples, exhibiting reversible thermal magnetization (J_S-T) curves with Curie temperatures of about 580°C, has revealed considerable amounts of maghemite (γ-Fe₂O₃) in many samples. In view of the expected instability, of maghemite at temperatures above 350°C, this reversibility is rather surprising. Here we report Mössbauer studies on heated lava samples, showing high content of maghemite. The samples were kept at 600°C in oxidizing, reducing, and inactive atmospheres, respectively, for different lengths of time, and then analyzed with Mössbauer spectroscopy at room temperature. The Mössbauer spectra showed that maghemite is stable in the oxidizing atmosphere for at least several hours. In the inactive atmosphere a considerable amount of maghemite still exists after two hours heating. In the reducing atmosphere maghemite had transformed to magnetite after only 30 minutes.     

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.     

On almost-sure versions of classical limit theorems for dynamical systems

The purpose of this article is to support the idea that “whenever we can prove a limit theorem in the classical sense for a dynamical system, we can prove a suitable almost-sure version based on an empirical measure with log-average”. We follow three different approaches: martingale methods, spectral methods and induction arguments. Our results apply, among others, to Axiom A maps or flows, to systems inducing a Gibbs–Markov map, and to the stadium billiard.     

Pro-torus actions on Poincaré duality spaces

In this paper, it is shown that some of the results of torus actions on Poincaré duality spaces, Borel’s dimension formula and topological splitting principle to local weights, hold if ‘torus’ is replaced by ‘pro-torus’.     

Nonlinear dynamics of a spinor Bose-Einstein condensate in a double-well potential

We examine the nonlinear dynamical behavior of a spinor Bose-Einstein condensate in a double-well potential. Considering a condensate with large number of atoms, such that it can be described using the mean field theory, we separate the spinor dynamics from the spatial dynamics under the single-mode approximation. We limit ourselves to certain initial conditions under which the spatial mode is frozen so that we can focus on the spinor dynamics only. Identifying collective spin variables of our system, we derive the corresponding nonlinear equations of motion for them. Employing standard stability analysis, we find and characterize fixed points of the system. For a wide range of physical parameters such as tunneling strength and non-linear interactions, as well as for various initial preparations of the system, we identify qualitatively different dynamical regimes possible in the system. In particular, complete and incomplete oscillations of spin variables between quantum wells are found. We also show that by bringing some fixed points close to each other in the phase space of the system, it is possible to induce amplitude modulation to those otherwise regular tunneling oscillations.