Probabilistic analysis of the generalised assignment problem

We analyse thegeneralised assignment problem under the assumption that all coefficients are drawn uniformly and independently from [0, 1]. We show that such problems can be solved exactly with high probability, in a well-defined sense. The results are closely related to earlier work of Lueker, Goldberg and Marchetti-Spaccamela and ourselves.Supported by NATO grant RG0088/89.Supported by NSF grant CCR-8900112 and NATO grant RG0088/89.     

Application of centrifugal vacuum concentrators in residue analysis

Summary Centrifugal vacuum concentrators can be applied in residue analysis successfully: They prevent the samples from bumping and foaming. Even methanol/water- or acetonitrile/water-mixtures as extracts from food or other samples can be concentrated without separation of water prior to the evaporation process. Sulfonamides and other drugs can be concentrated with 100% recovery. Extracts with some light-sensitive substances (nitrofuranes) were evaporated without losses, as well as some hydrolysis-sensitive substances (penicillins) solved in water, whereas tetracyclines decompose in aqueous solution considerably. For more volatile substances (such as organochlorine pesticides or polychlorinated biphenyls) centrifugal vacuum concentrators can be used for preconcentration e.g. of the gelchromatographic eluate. Further, centrifugal vacuum concentrators can automate the evaporation process. In comparison to rotary evaporators, they save time for the laboratory staff when running series of 4 or more samples. It is very important to supply permanently sufficient energy for the evaporation process, especially when concentrating volumes of 10 ml or more. If the only heated part is the wall of the centrifuge, after couple of minutes the samples cool down to very low temperatures, and the evaporation process slows down. A more efficient way to supply evaporation energy is by means of IR radiation. A very modern device offers an electronically controlled IR radiation by means of temperature control on the centrifugal tubes. This in combination with vapour pressure control ensures an optimal control of the most important factors of the evaporation process.     

The mean chromatic number of paths and cycles

The mean chromatic number of a graph is defined. This is a measure of the expected performance of the greedy vertex-colouring algorithm when each ordering of the vertices is equally likely. In this note, we analyse the asymptotic behaviour of the mean chromatic number for the paths and even cycles, using generating function techniques.     

A quasiclassical trajectory study of vibrational energy transfer in collisions involving intermolecular attraction of moderate strength

Monte Carlo selected, quasiclassical trajectories have been computed on six potential energy hypersurfaces possessing potential minima or “wells” up to 50 kJ mol^?1 deep. The aim of the investigation has been to examine how vibrational energy transfer in A + BC(υ = 1) collisions is promoted by intermolecular attraction of moderate strength. Here results are reported for the mass combination m_A = 20 u, m_B = 1 u, m_C = u. The results show that even quite slight intermolecular attraction can enhance energy transfer, as long as the attraction does not just depend on the separation of A from the center-of-mass of BC. The mean loss of vibrational energy does not depend only the well depth but also on its “location” (in particular, the difference in r_BC at the minimum and in isolated BC) and on the angular anisotropy of the potential. Large transfers of energy do not occur only in complex-forming collisions; indeed, a high fraction of trajectories on all surfaces are direct but show similar transfer of energy as in the more complex trajectories on the same surface. The results of the calculations are discussed in relation to the mechanisms and rates of vibrational relaxation in collisions between radicals and between species. such as HF + HF, capable of forming hydrogen bonds.     

Spectroscopic Characterization of Open-Shell Cations: Emission and Laser Excitation spectra of Rotationally Cooled CH3(CC)2X+, X = Cl,Br

Gas phase emission and laser excitation spectra of the òE?X?²E (Σ = +½, ?½) transition of rotationally/vibrationally cooled 1-chloro- and 1-bromo-1,3-pentadiyne cations have been obtained. The emission was excited by electron impact on a seeded helium supersonic free jet and the fluorescence by laser excitation of cations produced by Penning ionization and collisional relaxation. From these two sets of data the origin bands of the spin-orbit systems are located and for the bromo species this leads to better values of the spin-orbit splitttings in the two electronic states and of the first adiabatic ionization energy. The vibrational frequencies of many of the fundamentals of these cations in the X?²E and òE states have been obtained to within ±2 cm^?1.     

Superspace formulation ofN=2 supergravity

A complete formulation ofN=2 supergravity in superspace is given including a superfield lagrangian.