Hypoelliptic Jacobi–Dunkl Convolution of Distributions

In this paper we give a necessary and sufficient condition in terms of the Jacobi–Dunkl transform in order that a Jacobi–Dunkl convolution of distributions is hypoelliptic.     

Kinetic resolution of sec-alcohols using a new class of readily assembled (S)-proline-derived 4-(pyrrolidino)-pyridine analogues

We report the development of a new class of readily prepared chiral 4-(pyrrolidino)-pyridine catalysts capable of exploiting both van der Waals (pi) and H-bonding interactions, thus allowing remote chiral information to stereochemically control the kinetic resolution of sec-alcohols.     

Selective Limit Theorems for Random Walks on Parabolic Biangle and Triangle Hypergroups

Let K be respectively the parabolic biangle and the triangle in and be a sequence in [0, +[ such that lim_p (p)=+. According to Koornwinder and Schwartz,⁽⁷⁾ for each there exist a convolution structure (*_(p)) such that (K, *_(p)) is a commutative hypergroup. Consider now a random walk on (K, *_(p)), assume that this random walk is stopped after j(p) steps. Then under certain conditions given below we prove that the random variables on K admit a selective limit theorems. The proofs depend on limit relations between the characters of these hypergroups and Laguerre polynomials that we give in this work.     

The Transient Behaviour of a Cyclic Queue

This paper studies a cyclic queueing problem arising in civil engineering earthmoving projects. There are m excavators and n trucks which queue to be loaded by the excavators. The problem is therefore equivalent to a machine interference problem with m operators and n machines. The size of the haul fleet must be optimized, so as to minimize the cost per unit volume of earth moved. Graphs which show regions of optimal n in the parameter space are presented for the steady-state D/D/1, M/D/1 and E _k /M/1 models. The effect of operating the M/M/m system in short work shifts, so that the initial conditions and transient behaviour are important, is then analysed and quantified as a correction to the optimal number of trucks in the haul fleet from the steady-state solution.     

Optical potential for 12C + 28Si scattering

¹²C + ²⁸Si elastic scattering angular distributions are smooth functions, relatively easily fit by optical potential predictions, at laboratory bombarding energies, E_1ab, within ≈ 10 MeV of the Coulomb barrier (i.e. up to E_1ab ≈ 27 MeV). Between E_1ab = 27 and 36 MeV the angular distributions show pronounced oscillatory structure which is not easily fit with an optical potential. No optical potential has been found to give a very good account of all the angular distributions simultaneously; the best simultaneous fit to all the data was achieved with a surface-transparent potential whose real and imaginary well depths are energy dependent.     

Crosslinking of starch xanthate. II. Reaction with polyacrolein

The reaction between polyacrolein bisulfite adduct and sodium starch xanthate in aqueous alkali gives a rapid viscosity increase and subsequent gelation. The magnitude and pattern of the viscosity development depend on the degree of substitution of the starch xanthates in the range of 0.12 to 0.45, varying from around 5000 cP centipoises (nongelling) for the lowest to more than 100 000 cP for the highest. The viscosity patterns developed with the more highly substituted xanthates show a minimum valley after a 20-30-min reaction. Analytical and spectral analyses of solid materials obtained from the ethanol precipitation of the gels indicate that the product is a monothiocarbonate stemming from the elimination of sodium hydrogen sulfide between a xanthate group of the starch and a hydroxyl group of the polyacrolein adduct. A hydrated form of polyacrolein does not react with starch xanthate under the same aqueous alkaline conditions.     

Stokes/anti-Stokes anomalies under surface enhanced Raman scattering conditions

The possibility of achieving anti-Stokes stimulation and/or pumping under surface enhanced Raman scattering conditions has been the source of intense controversies in the literature. With the aim of clarifying some of the aspects of this problem, we study theoretically and experimentally the situation in a model system which highlights some of the difficulties in the interpretation of the data. We show that many of the assumptions often presumed in the literature need to be assessed with care in each case. Through careful experiments we show, in particular, that the anti-Stokes/Stokes ratio for a specific mode in the same sample can depend on the chosen laser wavelength. This latter effect is a manifestation of the influence of the internal plasmon resonances (hot spots) in the result. Different possibilities and further research directions are highlighted and discussed.