Clumping Data in 2-Way Tables: A User-Orientated Perspective

Following a critique of existing algorithms, an algorithm is presented which will re-organize a 2-way data table to bring like rows together, and like columns together. Extensions of the method are described, and justified, to accommodate distances measured in modular arithmetic, and with bipolar columns/rows, as in repertory grid analysis. One value of the algorithms is that the user can see relationships in the tables without the data in the cells themselves ever having been transformed. Thus, users will continue to feel they own their data.     

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.     

On a functional equation of Luce

Summary In a recent communication to J. Aczél, R. Duncan Luce asked about the functional equationU(x)U(G(x)F(y)) = U(G(x))U(xy) forx, y > 0, (1) which has arisen in his research on certainty equivalents of gambles. He was particularly interested in cases in which the unknowns (U, F andG) are strictly increasing functions from (0, + ) into (0, + ). In this paper we solve (1) in the case whereU, F andG are continuously differentiable with everywhere positive first derivatives. Our solution is perhaps novel in that in certain cases (1) reduces to a functional equation in a single variable and in other cases to a functional equation in several variables; see [1] for the terminology.     

Cohomology of groups with metacyclic Sylow -subgroups

We determine the cohomology algebras for all groups with a metacyclic Sylow -subgroup. The complete -local stable decomposition of the classifying space is also determined.

     

Orientation-reversing involutions on handlebodies

The observation that the quotient orbifold of an orientation- reversing involution on a 3-dimensional handlebody has the structure of a compression body leads to a strong classification theorem, and general structure theorems. The structure theorems decompose the action along invariant discs into actions on handlebodies which preserve the -fibers of some -bundle structure. As applications, various results of R. Nelson are proved without restrictive hypotheses.

     

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.