A de bruijn-type formula for enumerating patterns of partitions

We develop a formula for enumerating the partitions of a set up to the action of a group. We give some special cases of this formula and illustrate its use with an example. Some comments are made relating the formula to an earlier formula.This work was supported in part by NSF Contract GP-43010.     

A measurement of single electrons,electron pairs,and associated phenomena,in proton-proton collisions at the CERN ISR

Measurements of single-electron production in proton-proton collisions at the CERN ISR are presented for five centre-of-mass energies √s = 23.5, 30.6, 44.8, 52.7, and 62.4 GeV. The invariant cross sections for single electrons with transverse momenta of 0.60 to 4.7 GeV/c are given. Measurements of electron-positron pairs and measurements of charged hadrons produced in association with the single electrons, are also reported.     

The effect of inclusion on the heat capacities of some simple molecules in adducts of Dianin's compound

The heat capacities of unsolvated (empty) Dianin's compound (4p-hydroxypheny]-2,2, 4-trimethylchroman) and the ethanol and carbon tetrachloride adducts of Dianin's compound have been measured in the 30–300K temperature range. The molar heat capacities of the guest species were calculated from the experimental results and compared with molar heat capacities of bulk CCl₄ and bulk C₂H₅OH The stoichiometry of the CCl₄ adduct was determined to be six host molecules per guest CCl₄, in contrast to an earlier report.Dedicated to Dr D. W. Davidson in honor of his great contributions to the sciences of inclusion phenomena.     

Rook Theory—IV. Orthogonal Sequences of Rook Polynomials

We explain combinatorially the occurrence of certain classical sequences of orthogonal polynomials as sequences of rook polynomials, and we give some new examples related to general stairstep boards.     

Electron impact studies CX—+E spectra from negative ions. Ortho effects and skeletal rearrangement reactions from sulphur compounds

+E spectra derived from the non-decomposing anion of some sulphur compounds are independent of the pressure of the collision gas. The compounds chosen for study contain peaks produced from either ortho effects or skeletal rearrangement fragments in their conventional positive ion spectra. The dissociative +E spectra are either devoid of skeletal rearangement ions or alternatiely contain such peaks in small abundance. In contrast, peaks derived from ortho reactions are present in high abundance.     

Partitions of sets of matrices

The set of all 2×2 matrices with elements from a given set Ω is partitioned into a finite number of classes. The principal object of this paper is to estimate how small a matrix is guaranteed to contain an r×s submatrix all of whose 2×2 submatrices belong to one class only. This problem includes a number of particular situations that had previously been considered in isolation. One of the tools employed is a generalization of the notion of partial order.     

Phase behavior and structure of liquid crystalline solutions of cellulose derivatives

Summary Structural and thermodynamic characteristics of liquid-crystalline solutions of four cellulose derivatives in a range of solvents were studied. Basic observations were made on these systems using polarized light microscopy, small angle light scattering, dilute solution and concentrated solution viscosities. The polymers studied include hydroxypropyl cellulose (HPC), cellulose acetate butyrate (CAB), ethyl cellulose (EC), and cellulose triacetate (CT). The formation of the liquid crystalline phase was shown to strongly depend on polymer concentration, solvent type and temperature. The critical volume fraction of polymer required to form the liquid crystal phase varied significantly as the solvent changed. The critical volume fraction decreased with increasing solvent acidity and polymer intrinsic viscosity in a given solvent. The breadth of the two phase region seems to decrease with increasing acidity. The liquid crystalline phase was in most cases determined to be cholesteric. In all cases positively birefringent cellulose derivatives form negative spherulitic domains. In one case, the negativity birefringent system (cellulose triacetate) formed positively birefringent spherulitic liquid crystalline domains. This is interpreted to mean the structure organizes itself by a tangential alignment of polymer chains within the domain. SALS measurements appear to detect domains and in some cases cholesteristic pitch.With 5 figures and 4 tables