Polynomfunktionen auf primen Restklassen

Ohne Zusammenfassung Edmund Hlawka zum fünfundsechzigsten Geburtstag     

Diameter Distribution of Spherical Primary Grains in the boolean model from small-angle scattering

A method for determining the size-distribution density of small spheres which are arranged, without any interaction between them, at random positions in space and form an isotropic twophase system is presented. In the case of higher volume fractions, frequent overlapping between the spheres is a logical consequence. This effect is an essential feature of the model itself and is well considered and observed. Stereological information, which contains all the necessary data about the unknown size distribution, is obtained from the angular intensity distribution (small-angle scattering experiment) of the particle system concerned. The resulting formula still includes, in a first representation, the volume fraction p as a free parameter. In a second step, a general analytical method for the determination of the volume fraction p from the set covariance of the considered random closed set is derived. Therefore, the unknown diameter distribution can be obtained in every detail, starting from the scattering curve of the sample, by way of two independent working steps.     

Zwei Dualräume der unendlichen,symmetrischen Gruppe

Ohne Zusammenfassung     

Über das lexikographische und das kostarke Produkt von Mengensystemen

Ohne Zusammenfassung     

Unusual and Novel C11H16 Hydrocarbons from the Southern Australian Brown Alga Dictyopteris acrostichoides (Phaeophyceae)

Unusual and novel C₁₁H₁₆ olefins with (E)- or (E,E)-configuration instead of the previously known (Z)- or (E,Z)-configuration at the double bond(s) within the longer side chain are the main products of the Australian phaeophyte Dictyopteris acrostichoides. This configuration anomaly refers to all four series of alicyclic C₁₁H₁₆ hydrocarbons, namely the disubstituted cyclopentenes and cyclopropanes, as well as the monosubstituted cycloheptadienes and cyclopentenes. Chiral compounds within the above series have the same absolute configuration. The two (cyclopent-3-enyl)hexa-1, 3-dienes 11 and 13 are found for the first time. The absolute configuration and optical purity of the hydrocarbons are determined by gas chromatography on modified cyclodextrins as chiral stationary phases. The synthesis of chiral references via lipase-catalyzed resolutions is described.