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.

Matrix elements of U(2n) generators in a multishell spin-orbit basis. II. The two-shell nonzero shift ACCs and U(2n) generator MEs

This is the second in a series of articles whose ultimate goal is the evaluation of the matrix elements (MEs) of the U(2n) generators in a multishell spin-orbit basis. This extends the existing unitary group approach to spin-dependent configuration interaction (CI) and many-body perturbation theory calculations on molecules to systems where there is a natural partitioning of the electronic orbital space. As a necessary preliminary to obtaining the U(2n) generator MEs in a multishell spin-orbit basis, we must obtain a complete set of adjoint coupling coefficients for the two-shell composite Gelfand-Paldus basis. The zero-shift coefficients were obtained in the first article of the series. in this article, we evaluate the nonzero shift adjoint coupling coefficients for the two-shell composite Gelfand-Paldus basis. We then demonstrate that the one-shell versions of these coefficients may be obtained by taking the Gelfand-Tsetlin limit of the two-shell formulas. These coefficients,together with the zero-shift types, then enable us to write down formulas for the U(2n) generator matrix elements in a two-shell spin-orbit basis. Ultimately, the results of the series may be used to determine the many-electron density matrices for a partitioned system. (C) 1998 John Wiley & Sons, Inc.

Off-diagonal long-range order in a supersymmetric integrable model of correlated electrons

A new model for correlated electrons is presented which is integrable in one-dimension. The symmetry algebra of the model is the Lie superalgebra gl(2\1) which depends on a continuous free parameter. This symmetry algebra contains the eta pairing algebra as a subalgebra which is used to show that the model exhibits Off-Diagonal Long-Range Order in any number of dimensions.

Chaotic dynamics of cold atoms in far-off-resonant donut beams

We describe the classical two-dimensional nonlinear dynamics of cold atoms in far-off-resonant donut beams. We show that chaotic dynamics exists there for charge greater than unity, when the intensity of the beam is periodically modulated. The two-dimensional distributions of atoms in the (x,y) plant for charge 2 are simulated. We show that the atoms will accumulate on several ring regions when the system enters a regime of global chaos. [S1063-651X(99)03903-3].

New integrable model of correlated electrons with off-diagonal long-range order from so(5) symmetry

We present a new integrable model for correlated electrons which is based on so(5) symmetry. By using an eta-pairing realization we construct eigenstates of the Hamiltonian with off-diagonal long-range order. It is also shown that these states lie in the ground state sector. We exactly solve the model on a one-dimensional lattice by the Bethe ansatz.

Change in the rate of shell deposition and shell microstructure in response to shell borers in the abalone Haliotis rubra

Gastropod shells consist of two crystal types of calcium carbonate, an outer, prismatic calcite layer and an inner nacreous layer made of aragonite. In cross-section, the nacre of the nacreous layer appears to have a regular brick-like microstructure composed of thin laminae of aragonite crystals, separated by very thin sheets of protein (Lutz and Rhoads, 1980; Nakahara, 1983). In abalone (Genus, Haliotis) and other gastropods, thin layers of non-lamellar pigmented material occur within the nacre and have been termed alternatively, fine lines, growth rings or growth lines (Shepherd et al., 1995). It has been suggested that these pigmented layers are small, prismatic, calcite layers (Shepherd and Avalos-Borja, 1997; Zaremba et al., 1996) but investigations using a Raman laser in Haliotis rubra show that they contain aragonite rather than calcite (Hawkes et al, 1996). Day and Fleming (1992) suggest that the occurrence of pigmented layers is correlated with regular exogenous cues such as reproduction or temperature changes and indeed in some species, pigmented layers in the shell can be used to age abalone (review: Shepherd and Triantafillos, 1997). However, McShane and Smith (1992) suggest that pigmented layers can occur irregularly and therefore may be unreliable indicators of age.

A note on the decomposition of the health concentration index

In recent work, the concentration index has been widely used as a measure of income-related health inequality. The purpose of this note is to illustrate two different methods for decomposing the overall health concentration index using data collected from a Short Form (SF-36) survey of the general Australian population conducted in 1995. For simplicity, we focus on the physical functioning scale of the SF-36. Firstly we examine decomposition 'by component' by separating the concentration index for the physical functioning scale into the ten items on which it is based. The results show that the items contribute differently to the overall inequality measure, i.e. two of the items contributed 13% and 5%, respectively, to the overall measure. Second, to illustrate the 'by subgroup' method we decompose the concentration index by employment status. This involves separating the population into two groups: individuals currently in employment; and individuals not currently employed. We find that the inequality between these groups is about five times greater than the inequality within each group. These methods provide insights into the nature of inequality that can be used to inform policy design to reduce income related health inequalities. Copyright (C) 2002 John Wiley Sons, Ltd.

Shell utilization by the land hermit crab Coenobita scaevola (Anomura, Coenobitidae) from Wadi El-Gemal, Red Sea

We conducted a study in order to determine the shell utilization pattern of the land hermit crab Coenobita scaevola (Forskal, 1775), the only species representing the family Coenobitidae in the Red Sea. Hermit crabs were collected during July 2003 and January 2004 along the sandy shores of protected area of Wadi-Elgemal, south Red Sea. Animals were fixed in 10% formalin and transported to the laboratory where they were weighed and measured for cephalothoracic shield length (CSL) and width, left propodus length and height. Gastropod shells species were identified, weighed and measured for shell aperture width and length and shell internal volume. A total of 391 individuals were collected (219 females, 172 males) and were found occupying ten shell species, with clear significant occupation of Nerita undata. A positive relationship was obtained between the size of the shells occupied and the hermit crabs. Analysis of shell internal volume and crab dimensions demonstrated that this shell dimension constitutes mainly the determinant for C. scaevola shell utilization. With respect to the size of the animals and the occupied shell type, Nerita undata was occupied by a wide range of CSL (2.5-8.5mm). Small sized crabs (2.5-3.5mm CSL) occupied Planaxis sulcatus and Nassarius arcularius plicatus while larger specimens (8.5-9.5mm CSL) occupied Turbo radiatits, Polinices milanostomus and Monodonta canilifera. Variations in the shell occupation were also recognized among male and females. Comparisons among populational and shell use features led us to suggest the use of this land hermit crab as key-species in the preserving program of shores and protected areas, since this species is the first organism to disappear from any shore when a new tourist establishment is implemented.

TRADE-OFF BETWEEN IMMUNE STIMULATION AND EXPRESSION OF STORAGE PROTEIN GENES

Proteins stored in insect hemolymph may serve (is a source of amino acids and energy for metabolism, and development. The expression of the main storage proteins was assessed in bacterial-challenged honey bees using real-time (RT)-PCH and Western blot.. After ensuring that. the immune system had, been activated by measuring the ensuing expression (, the innate immune response genes, defensin-1 (def-1) and prophenoloxidase (pro PO), we verified the expression of four genes encoding storage proteins. The levels of vitellogenin (vg) mRNA and of the respective protein. were significantly lowered in bees injected with bacteria or water only (injury). An equivalent response was observed in orally-infected bees. The levels of apolipophorin II/I (apoLP-II/I) and hexamerin (hex 70a) mRNAs did not significantly change, but levels of Hex 70a protein subunit showed a substantial decay after bacterial challenge or injury. Infection also caused a strong reduction in the levels of apoLP-III transcripts. Our findings are consistent with a down-regulation, of the express and accumulation of storage proteins as a consequence of activation of the immune system, suggesting that this phenomenon. represents a strategy to redirect resources to combat injury or infection. (C) 2009 Wiley Periodicals, Inc.

Pt-RuO(2) electrodes prepared by thermal decomposition of polymeric precursors as catalysts for direct methanol fuel cell applications

The electrocatalytic activity of Pt and RuO(2) mixed electrodes of different compositions towards methanol oxidation was investigated. The catalysts were prepared by thermal decomposition of polymeric precursors and characterized by energy dispersive X-ray, scanning electronic microscopy, X-ray diffraction and cyclic voltammetry. This preparation method allowed obtaining uniform films with controlled stoichiometry and high surface area. Cyclic voltammetry experiments in the presence of methanol showed that mixed electrodes decreased the potential peak of methanol oxidation by approximately 100 mV (RHE) when compared to the electrode containing only Pt. In addition, voltammetric experiments indicated that the Pt(0.6)Ru(0.4)O(y) electrode led to higher oxidation current densities at lower potentials. Chronoamperometry experiments confirmed the contribution of RuO(2) to the catalytic activity as well as the better performance of the Pt(0.6)Ru(0.4)O(y) electrode composition. Formic acid and CO(2) were identified as being the reaction products formed in the electrolysis performed at 400 and 600 mV. The relative formation of CO(2) was favored in the electrolysis performed at 400 mV (RHE) with the Pt(0.6)Ru(0.4)O(y) electrode. The presence of RuO(2) in Pt-Ru-based electrodes is important for improving the catalytic activity towards methanol electrooxidation. Moreover, the thermal decomposition of polymeric precursors seems to be a promising route for the production of catalysts applicable to DMFC. (C) 2009 International Association for Hydrogen Energy. Published by Elsevier Ltd. All rights reserved.

XAS characterization of the RuO(2)-Ta(2)O(5) system local (crystal) structure

The influence of the preparation method on the structural properties of the RuO(2)-Ta(2)O(5) system was investigated. Both thin films on Ti substrates and powder samples of nominal composition Ti/RuO(2)-Ta(2)O(5) (Ru:Ta = 100:0, 90:10, 80:20, 30:70, and 0:100 at.%) were prepared through thermal decomposition of polymeric precursors (DPP). The thin films and powder samples were investigated using X-ray absorption spectroscopy (XAS). XANES analyses showed that Ru and Ta are present in the Ru(IV) and Ta(V) oxidation states. EXAFS signals of all the samples were analyzed, to obtain the average bond length (r), coordination number, and the Debye-Waller factor (sigma(2)) for each Ru-O, Ru-Ru, Ta-O nearest-neighbor. The first shell Ru-O distance was found at 1.91-1.92 angstrom with coordination number of 1.8-2.1, and at 2.01-2.02 angstrom with coordination number of 3.9-4.1. The Ta-O distance obtained for all the samples and in both modes (transmission and fluorescence) had significantly different values from the theoretical ones. The results revealed that the local structure around both the Ru and Ta sites are similar, and that they consist of distorted M-O(6) octahedra (where M = Ru or Ta). (C) 2010 Elsevier B.V. All rights reserved.