Canonical solution of the SU(3) ↓ SO(3) reduction problem from the SU(3) pattern calculus

Because of its numerous applications to physics, there have been many solutions published on the problem of reducing a given irreducible representation (irrep) of the unitary unimodular group SU(3) into irreps of the proper orthogonal subgroup SO(3). Such solutions are generally based on an arbitrary construction of a nonorthogonal basis of the highest weight space for an irrep of SO(3), followed by an equally arbitrary orthonormalization procedure. This paper presents a unique solution of this problem based on the intrinsic structure of the multiplicity function, which is a function M _L(p, q) giving the number of times irrep[L] of SO(3) is contained in irrep[pq0] of SU(3). This structure is implemented uniquely into the reduction problem through the use of the SU(3) pattern calculus.Work performed under the auspices of the U.S. Department of Energy.     

Schichtweis Abscheuern. II. Auswirkung auf die Eigenschaften von Garnen und Textilien

Ohne Zusammenfassung     

A valence bond study of three-center four-electron pi bonding: electronegativity vs electroneutrality

Three-center four-electron (3c4e) pi bonding systems analogous to that of the ozone molecule have been studied using modern valence bond theory. Molecules studied herein consist of combinations of first row atoms C, N, and O with the addition of H atoms where appropriate in order to preserve the 3c4e pi system. Breathing orbital valence bond (BOVB) calculations were preformed at the B3LYP/6-31G**-optimized geometries in order to determine structural weights, pi charge distributions, resonance energies, and pi bond energies. It is found that the most weighted VB structure depends on atomic electronegativity and charge distribution, with electronegativity as the dominant factor. By nature, these systems are delocalized, and therefore, resonance energy is the main contributor to pi bond energies. Molecules with a single dominant VB structure have low resonance energies and therefore low pi bond energies.     

Transport of metal salts by zwitterionic ligands; simple but highly efficient salicylaldoxime extractants

Attaching dialkylaminomethyl arms to commercial phenolic oxime copper extractants yields reagents which transport base metal salts very efficiently by forming neutral 1 ratio 1 or 1 ratio 2 complexes with zwitterionic forms of the ligands.     

Ordinary abelian varieties having small embedding degree

Miyaji, Nakabayashi and Takano (MNT) gave families of group orders of ordinary elliptic curves with embedding degree suitable for pairing applications. In this paper we generalise their results by giving families corresponding to non-prime group orders. We also consider the case of ordinary abelian varieties of dimension 2. We give families of group orders with embedding degrees 5, 10 and 12.     

Conceptual mis(understandings) of beginning undergraduates

In order to understand a set of mathematical skills of some importance to beginning undergraduates in engineering and mathematics, a taxonomy of three levels in increasing order of mathematical demand is proposed. The construction of a test instrument is discussed relating its purpose to the concerns of the preparation of students voiced by such as Anderson et al., to underlying theories of learning, Slavit, and to other taxonomies, Smith et al. The results of applying the questionnaire to 423 students in the period 1994–1996 is analysed and evaluated, focusing on the distributions of the distractors chosen by the students. Results suggest that the instrument is robust, that the taxonomy used is effective and raises questions that affect the teaching and learning paradigms used for mathematics pre-university and on entry to university.     

Distinguishing dose populations in sediment mixtures: a test of single-grain optical dating procedures using mixtures of laboratory-dosed quartz

Many natural deposits contain grains that have different burial histories, but reliable procedures to extract the component doses from mixed-dose samples have not been developed in optical dating. Here we present results for synthetic two- and three-component mixtures of data derived from laboratory-dosed sedimentary quartz using a single-aliquot regenerative-dose protocol and statistical models for finite mixtures. Composite sets of data were created from the doses measured for individual grains that had been bleached by sunlight and then given a beta dose of 5, 10 or 20 Gy. We found that the correct number of dose components, corresponding doses, and relative proportions of each component may be estimated if the within-component dispersion is small or is known. We also found, however, that recuperation of the OSL signal in sun-bleached quartz may produce artificially high dose estimates for some grains, an effect that should be taken into account when modelling natural mixtures.     

Energy level clusters for ν2 + ν3 type combination bands of tetrahedral molecules

Clustering of tetrahedral levels is shown to occur in ν₂ + ν₃ type combination bands of spherical top molecules due to Coriolis and vibrational anharmonic interactions. Cluster correlation diagrams are shown for cases where the vibrational splitting is both large and small compared to the Coriolis splitting, and cluster approximations are given for both cases.