The stannylation of carbonyl-stabilised phosphorus ylids,and tin-assisted elimination reactions

The interaction of organotin halides with lithium salts of mono-substituted phosphorus ylids and also with disubstituted ylids is described.     

Combinatorial invariants for nets of conics in $$\mathrm {PG}(2,q)$$ PG ( 2 , q )

Designs, Codes and Cryptography - The problem of classifying linear systems of conics in projective planes dates back at least to Jordan, who classified pencils (one-dimensional systems) of conics...     

Functional Equations and Weierstrass Transforms

The purpose of this article is to illustrate the utility of the Weierstrass transform in the study of functional equations (and systems) of the form 1 $${\mathop \sum^N\limits_{k=0}}\alpha_{k}f(x+r_{k})=f_{0}(x)\ \ \ \, x\in\ {\rm R}.$$ One may think of α₀, α₁,…, α_N as given complex numbers, r₀, r₁,…, r_N as given real numbers, ?₀: ? → C as a given function and ? as the unknown.     

K − and\bar p Production in Au + Pb Collisions at 11.5 A GeV/cProduction in Au + Pb Collisions at 11.5 A GeV/c

I will present the first results from the E864 collaboration on the production of negative kaons and antiprotons in 10% central 11.5 A GeV/c Au+Pb nucleus collisions at the Brookhaven AGS. E864 is a high rate, open geometry spectrometer, capable of measuring particle production in a range of rapidities and transverse momenta at a single setting of the spectrometer magnets. The results are derived from the analysis of over 20 million central interactions collected in the Fall 1994 run. I will report onK ^? production in a rapidity range from 1.9<y<2.2 (y _cm=1.6) and 25<pT<150 MeV/c, and $\bar p$ production from 1.2<y<2.2 and 50<pT<400 MeV/c. A comparison with previously published results from E878 is presented and the implications for $\bar \Lambda $ production are discussed.     

Superbase-Promoted Acylation of Hindered Alcohols

The commercially available nonionic superbase P(MeNCH(2)CH(2))(3)N (1a) is very useful for the acylation of unreactive hindered alcohols as well as acid-sensitive alcohols. The reactions proceed in high yields using an acid anhydride, and 1a can be regenerated in a single step. The relative rates for benzoylation of (+/-)-menthol in C(6)D(6) using conventional acylation reagents and strong nonionic bases are compared. In general, acetylation with 1a is accelerated in the polar solvent CH(3)CN whereas benzoylation is faster in the nonpolar solvent C(6)H(6). The benzoylation intermediate RC(O)P(MeNCH(2)CH(2))(3)N(+) was found to be in equilibrium with 1a, with lower temperatures favoring the intermediate. The relative stabilities of several known acylating intermediates are compared.     

Nonresonant third-order susceptibility measurements in the nematic liquid crystal K18

We have observed a large nonresonant third-order nonlinear susceptibility, X ⁽³⁾ (-; , 0, 0) in the isotropic phase of a nematic liquid crystal 4-n-hexyl-4-cyanobiphenyl (K18). The highest value of X ⁽³⁾ obtained at 632.8 nm is 1.16274×10^-18 m²V^-2 corresponding to a temperature 29.3°C. The observed second-order pretransitional temperature T ^* from our measurements is 1.2°C below the first-order nematic to isotropic transition temperature. The dependence of the Kerr constant on (T-T ^*)^-1 is found to be in good agreement with the predictions of the Landau-de Gennes model.     

On the joint distribution of ladder variables of random walk

Summary The ladder timeN and ladder heightH of a random walk {S _n ,n1} as a pair (N, H) lie in the domain of attraction of a bivariate stable law ifS ₁ is in a domain of attraction, as was shown by Greenwood et al. (1982). In this paper we prove a converse. IfP(S _n >0) converges and (N, H) lies in a bivariate domain of attraction thenS ₁ is also in a domain of attraction.