Matrix elements of U(2n) generators in a multishell spin-orbit basis. I. The del-operator MEs in a two-shell composite Gelfand-Paldus basis

This is the first in a series of three articles which aimed to derive the matrix elements of the U(2n) generators in a multishell spin-orbit basis. This is a basis appropriate to many-electron systems which have a natural partitioning of the orbital space and where also spin-dependent terms are included in the Hamiltonian. The method is based on a new spin-dependent unitary group approach to the many-electron correlation problem due to Gould and Paldus [M. D. Gould and J. Paldus, J. Chem. Phys. 92, 7394, (1990)]. In this approach, the matrix elements of the U(2n) generators in the U(n) x U(2)-adapted electronic Gelfand basis are determined by the matrix elements of a single Ll(n) adjoint tensor operator called the del-operator, denoted by Delta(j)(i) (1 less than or equal to i, j less than or equal to n). Delta or del is a polynomial of degree two in the U(n) matrix E = [E-j(i)]. The approach of Gould and Paldus is based on the transformation properties of the U(2n) generators as an adjoint tensor operator of U(n) x U(2) and application of the Wigner-Eckart theorem. Hence, to generalize this approach, we need to obtain formulas for the complete set of adjoint coupling coefficients for the two-shell composite Gelfand-Paldus basis. The nonzero shift coefficients are uniquely determined and may he evaluated by the methods of Gould et al. [see the above reference]. In this article, we define zero-shift adjoint coupling coefficients for the two-shell composite Gelfand-Paldus basis which are appropriate to the many-electron problem. By definition, these are proportional to the corresponding two-shell del-operator matrix elements, and it is shown that the Racah factorization lemma applies. Formulas for these coefficients are then obtained by application of the Racah factorization lemma. The zero-shift adjoint reduced Wigner coefficients required for this procedure are evaluated first. All these coefficients are needed later for the multishell case, which leads directly to the two-shell del-operator matrix elements. Finally, we discuss an application to charge and spin densities in a two-shell molecular system. (C) 1998 John Wiley & Sons.

Membrane-bounded nucleoids in microbial symbionts of marine sponges

In thin sections of resin-embedded samples of glutaraldehyde- and osmium tetroxide-fixed tissue from five genera of marine sponges, Stromatospongia, Astrosclera, Jaspis, Pseudoceratina and Axinyssa, cells of a bacteria-like symbiont microorganism which exhibit a membrane-bounded nuclear region encompassing the fibrillar nucleoid have been observed within the sponge mesohyl. The nuclear region in these cells is bounded by a single bilayer membrane, so that the cell cytoplasm is divided into two distinct regions. The cell wall consists of subunits analogous to those in walls of some Archaea. Cells of the sponge symbionts observed here are similar to those of the archaeal sponge symbiont Cenarchaeum symbiosum. (C) 1998 Federation of European Microbiological Societies. Published by Elsevier Science B.V. All rights reserved.

Asymptotic limits of a self-dual Ginzburg-Landau functional in bounded domains

In the author's joint paper [HJS] with Jest and Struwe, we discuss asymtotic limits of a self-dual Ginzburg-Landau functional involving a section of a line bundle over a closed Riemann surface and a connection on this bundle. In this paper, the author generalizes the above results [HJS] to the case of bounded domains.

A study of the interaction between operator style and machine capability for a hydraulic mining excavator

This paper presents a case study that explores how operator digging style juxtaposes with mechanical capability for a class of hydraulic mining excavators. The relationships between actuator and digging forces are developed and these are used to identify the excavator's capability to apply forces in various directions. Two distinct modes of operation are examined to see how they relate to the mechanical capabilities of the linkage and to establish if one has merit over the other. It is found that one of these styles results in lower loading of the machine.

Pirellulosomes: A new type of membrane-bounded cell compartment in planctomycete bacteria of the genus Pirellula

A distinct type of cellular organization was found in two species of the planctomycete genus Pirellula, Pirellula marina and Pirellula staleyi. Both species possess two distinct regions within the cell which are separated by a single membrane. The major region of the cell, the pirellulosome, contains the fibrillar condensed nucleoid. The other area, the polar cap region, forms a continuous layer surrounding the entire pirellulosome and displays a cap of asymmetrically distributed material at one cell pole. Immuno- and cytochemical-labelling of P. marina demonstrated that DNA is located exclusively within the pirellulosome; cell RNA is concentrated in the pirellulosome, with some RNA also located in the polar cap region.

Renormalizing the kinetic energy operator in elementary quantum mechanics

In this paper, we consider solutions to the three-dimensional Schrodinger equation of the form psi(r) = u(r)/r, where u(0) not equal 0. The expectation value of the kinetic energy operator for such wavefunctions diverges. We show that it is possible to introduce a potential energy with an expectation value that also diverges, exactly cancelling the kinetic energy divergence. This renormalization procedure produces a self-adjoint Hamiltonian. We solve some problems with this new Hamiltonian to illustrate its usefulness.