A long-time tail for random walk in random scenery

Consider a simple random walk on ^d whose sites are colored black or white independently with probabilityq, resp. 1–q. Walk and coloring are independent. Letn _k be the number of steps by the walk between itskth and (k+1) th visits to a black site (i.e., the length of itskth white run), and let _k =E(n _k )–q ^–1. Our main result is a proof that (*) lim _k k ^d/2 _k = (1 –q)q ^{d/2 – 2}(d/2) ^d/2. Since it is known thatq ^{– 1} _k =E(n ₁ n _{k + 1} B) –E(n ₁ B)E(n _{k + 1} B), withB the event that the origin is black, (*) exhibits a long-time tail in the run length autocorrelation function. Numerical calculations of _k (1k100) ind=1, 2, and 3 show that there is an oscillatory behavior of _k for smallk. This damps exponentially fast, following which the power law sets in fairly rapidly. We prove that if the coloring is not independent, but is convex in the sense of FKG, then the decay of _k cannot be faster than (*).     

Influence of silica gel pretreatment and bonding technique on PAH selectivity of octadecyl bonded phases

Summary The effect of silica gel pretreatment and of different bonding techniques, on the chromatographic properties of octadecyl bonded phases is described. The experiments show that a monomeric octadecyl bonded phase, prepared from silica gel that has not been treated before bonding, has a poor selectivity towards polycyclic aromatic hydrocarbons (PAHs) and shows high adsorption of basic components. Silica gel treatment before the bonding of the monofunctional silane does not give a substantial improvement. Polymeric phases on the other hand show a much better PAH selectivity and a lower adsorptivity towards basic components. Further improvement can be achieved with the polymeric modification if silica gel treatment is carried out before bonding.     

Limit on right handed weak coupling parameters from inelastic neutrino interactions

Right handed weak quark currents coupled to the usual left handed weak lepton current would be seen in inclusive antineutrino scattering on nuclei as a contribution at largey with the quark (not antiquark) structure function. We do not see such a term, and can therefore put an upper limit on the relative strengths of such right handed currents: \(\varrho ^2 = \frac{{\sigma _R }}{{\sigma _L }}< 0.009\) , 90% confidence. This measurement puts limits on the mixing angle of left-right symmetric models. In distinction to similar limits derived from muon decay or β decay, our limits are also valid if the right handed neutrino is heavy.     

Interaction of ester functional groups with aluminum oxide surfaces studied using infrared reflection absorption spectroscopy

The bonding of two types of ester group-containing molecules with a set of different oxide layers on aluminum has been investigated using infrared reflection absorption spectroscopy. The different oxide layers were made by giving typical surface treatments to the aluminum substrate. The purpose of the investigation was to find out what type of ester-oxide bond is formed and whether this is influenced by changes in the composition and chemistry of the oxide. The extent by which these bonded ester molecules resisted disbondment in water or substitution by molecules capable of chemisorption was also investigated. The ester groups were found to show hydrogen bonding with hydroxyls on the oxide surfaces through their carbonyl oxygens. For all oxides, the ester groups showed the same nu(C = O) carbonyl stretching vibration after adsorption, indicating very similar bonding occurs. However, the oxides showed differences in the amount of molecules bonded to the oxide surface, and a clear relation was observed with the hydroxyl concentration present on the oxide surface, which was determined from XPS measurements. The two compounds showed differences in the free to bonded nu(C = O) infrared peak shift, indicating differences in bonding strength with the oxide surface between the two types of molecules. The bonding of the ester groups with the oxide surfaces was found to be not stable in the presence of water and also not in the presence of a compound capable of chemisorption with the aluminum oxide surface.