On primitive elements of trace equal to 1 in GF(2m)

The object of this paper is to present a simple proof for the existence of primitive elements of trace equal 1, in GF(2^m).     

The NMR identification of the ring A protons of C-3 oxygenated steroids using the lanthanide paramagnetic shift technique

The lanthanide induced chemical shifts and coupling constants have been determined for ring A protons of steroids having a keto, hydroxyl, or acetate functional group at C-3. The assignments were made with the aid of suitably deuterated compounds and should prove useful in steroidal stereochemical and conformational studies.     

Chiral discrimination in lithium complexes of bis(5H-pyrroles) and bis(oxazolines)

The 1:1 and 2:1 complexes of chiral bis(5H-pyrroles) and bis(oxazolines) with the lithium cation have been studied by means of DFT methods (B3LYP/6-31G and B3LYP/6-311+G). The energetic, geometric, electronic, and orbital properties of the complexes have been analyzed. The chiral discrimination in the 2:1 complexes (homo vs heterochiral ones) indicate that in all the cases the heterochiral complexes are more stable than the homochiral ones, except for the tert-butyl derivatives. The chiral discrimination energies will be discussed on the basis of different parameters related to the lithium atom such as the N-Li distance, the orbital interaction between the lone pair of the nitrogen and an empty orbital of the lithium, and its atomic contribution to the total energy of the complexes.     

Self-trapped excitons in rare-gas dimers and solids

The excited electron states in isolated rare-gas dimers are described by a model Hamiltonian with appropriate simplifications for the short-range terms. Then the energies of self-trapped excitons are obtained by including solid state effects. The results are compared with the available transient absorption spectroscopy measurements.     

Dynamic formulation of the moment and the recursion methods

The dynamic equations at the basis of the recursion method and of the moment method are discussed using the projection techniques borrowed from statistical mechanics. A local orbital is regarded as the system of interest and the rest of the crystal takes the place of a highly non-Markovian reservoir. A rewarding aspect of the formalism is an improved relation between the chain parameters of the recursion method and the moments. It is speculated that the concepts of random forces and their dynamics could be of help in determining the asymptotic behaviour of the chain variables.     

Short-range interaction in the exciton effective-mass Hamiltonian

The integral equation for excitons is considered in the weak binding limit. The expression of the short-range electron-hole interaction is provided in terms of the Wannier functions.     

About ageing and fading of Cr-39 PADC track detectors used as air radon concentration measurement devices

PADC detectors are widely used as air radon concentration measurement devices and the typical procedure that a Radon Service Laboratory uses to manage the detectors provides a calibration phase followed by the field measurement. The calibration is performed in a reference radon concentration atmosphere, using high radon concentration values in order to achieve typical exposure values of few MBq h m^?3 with an exposure time of few days. On the other hand the field measurement is characterized by long term exposures lasting up to six months and by radon concentrations that are quite lower than the ones used in the calibration.The aim of this study is to check whether the calibration procedure is actually representative of a field measurement, or, in other words, whether and how much ageing or fading can affect the calibration factor.We found that the ageing and fading effect can produce a decrease in the detector sensitivity leading to an underestimation of the radon concentration up to 40% for exposure lasting few months. An important issue is that both ageing and fading can be ascribed to a decrease in the track etching velocity V_t.In the paper we also provide an algorithm to compensate for the sensitivity variation due to fading/ageing effect.     

Evolution of the correlation between orthogonal polarization patterns in broad-area lasers

We measure polarization-resolved instantaneous patterns in a large-aspect ratio quasi-isotropic Nd:YAG laser. High correlation between the instantaneous orthogonal polarization patterns recorded at the earlier stages of the laser pulse has been found due to the strong cross saturation between both polarization modes.     

Asymptotics of the Farey Fraction Spin Chain Free Energy at the Critical Point

We consider the Farey fraction spin chain in an external field h. Using ideas from dynamical systems and functional analysis, we show that the free energy f in the vicinity of the second-order phase transition is given, exactly, by $$f\sim\frac{t}{\log t}-\frac{1}{2}\frac{h^2}{t}\quad\mbox{for }h^2\ll t\ll1.$$ Here $t=\lambda_{G}\log(2)(1-\frac{\beta}{\beta_{c}})$ is a reduced temperature, so that the deviation from the critical point is scaled by the Lyapunov exponent of the Gauss map, λ _G . It follows that λ _G determines the amplitude of both the specific heat and susceptibility singularities. To our knowledge, there is only one other microscopically defined interacting model for which the free energy near a phase transition is known as a function of two variables. Our results confirm what was found previously with a cluster approximation, and show that a clustering mechanism is in fact responsible for the transition. However, the results disagree in part with a renormalisation group treatment.