Matrix elements of U(2n) generators in a multishell spin-orbit basis. III. General formulas

This is the third and final article in a series directed toward the evaluation of the U(2n) generator matrix elements (MEs) in a multishell spin/orbit basis. Such a basis is required for many-electron systems possessing a partitioned orbital space and where spin-dependence is important. The approach taken 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. A complete set of adjoint coupling coefficients for the two-shell composite Gelfand-Paldus basis (which is appropriate to the many-electron problem) were obtained in the first and second articles of this series. Ln the first article we defined zero-shift coupling coefficients. These are proportional to the corresponding two-shell del-operator matrix elements. See P. J. Burton and and M. D. Gould, J. Chem. Phys., 104, 5112 (1996), for a discussion of the del-operator and its properties. Ln the second article of the series, the nonzero shift coupling coefficients were derived. Having obtained all the necessary coefficients, we now apply the formalism developed above to obtain the U(2n) generator MEs in a multishell spin-orbit basis. The methods used are based on the work of Gould et al. (see the above reference). (C) 1998 John Wiley & Sons, Inc.

Level-one highest weight representation of U-q[sl((N)over-cap vertical bar 1)] and Bosonization of the multicomponent Super t-J model

We study the level-one irreducible highest weight representations of the quantum affine superalgebra U-q[sl((N) over cap\1)], and calculate their characters and supercharacters. We obtain bosonized q-vertex operators acting on the irreducible U-q[sl((N) over cap\1)] modules and derive the exchange relations satisfied by the vertex operators. We give the bosonization of the multicomponent super t-J model by using the bosonized vertex operators. (C) 2000 American Institute of Physics. [S0022- 2488(00)00508-9].

Coupled experimental and thermodynamic modeling studies for metallurgical smelting and coal combustion slag systems

An extensive research program focused on the characterization of various metallurgical complex smelting and coal combustion slags is being undertaken. The research combines both experimental and thermodynamic modeling studies. The approach is illustrated by work on the PbO-ZnO-Al2O3-FeO-Fe2O3-CaO-SiO2 system. Experimental measurements of the liquidus and solidus have been undertaken under oxidizing and reducing conditions using equilibration, quenching, and electron probe X-ray microanalysis. The experimental program has been planned so as to obtain data for thermodynamic model development as well as for pseudo-ternary Liquidus diagrams that can be used directly by process operators. Thermodynamic modeling has been carried out using the computer system FACT, which contains thermodynamic databases with over 5000 compounds and evaluated solution models. The FACT package is used for the calculation of multiphase equilibria in multicomponent systems of industrial interest. A modified quasi-chemical solution model is used for the liquid slag phase. New optimizations have been carried out, which significantly improve the accuracy of the thermodynamic models for lead/zinc smelting and coal combustion processes. Examples of experimentally determined and calculated liquidus diagrams are presented. These examples provide information of direct relevance to various metallurgical smelting and coal combustion processes.

Jordan-Wigner fermionization of the one-dimensional Bariev model of three coupled XY chains

The Jordan-Wigner fermionization for the one-dimensional Bariev model of three coupled XY chains is formulated. The L-matrix in terms of fermion operators and the R-matrix are presented explicitly. Furthermore, the graded reflection equations and their solutions are discussed.

The q-deformed supersymmetric t-J model with a boundary

The q-deformed supersymmetric t-J model on a semi-infinite lattice is diagonalized by using the level-one vertex operators of the quantum affine superalgebra U-q[sl(2\1)]. We. give the bosonization of the boundary states. We give an integral expression for the correlation functions of the boundary model, and derive the difference equations which they satisfy.

Group theory and quasiprobability integrals of Wigner functions

The integral of the Wigner function of a quantum-mechanical system over a region or its boundary in the classical phase plane, is called a quasiprobability integral. Unlike a true probability integral, its value may lie outside the interval [0, 1]. It is characterized by a corresponding selfadjoint operator, to be called a region or contour operator as appropriate, which is determined by the characteristic function of that region or contour. The spectral problem is studied for commuting families of region and contour operators associated with concentric discs and circles of given radius a. Their respective eigenvalues are determined as functions of a, in terms of the Gauss-Laguerre polynomials. These polynomials provide a basis of vectors in a Hilbert space carrying the positive discrete series representation of the algebra su(1, 1) approximate to so(2, 1). The explicit relation between the spectra of operators associated with discs and circles with proportional radii, is given in terms of the discrete variable Meixner polynomials.

Characterisation of the three-dimensional structure of earthworm burrow systems using image analysis and mathematical morphology

The aim of this work was to exemplify the specific contribution of both two- and three-dimensional (31)) X-ray computed tomography to characterise earthworm burrow systems. To achieve this purpose we used 3D mathematical morphology operators to characterise burrow systems resulting from the activity of an anecic (Aporrectodea noctunia), and an endogeic species (Allolobophora chlorotica), when both species were introduced either separately or together into artificial soil cores. Images of these soil cores were obtained using a medical X-ray tomography scanner. Three-dimensional reconstructions of burrow systems were obtained using a specifically developed segmentation algorithm. To study the differences between burrow systems, a set of classical tools of mathematical morphology (granulometries) were used. So-called granulometries based on different structuring elements clearly separated the different burrow systems. They enabled us to show that burrows made by the anecic species were fatter, longer, more vertical, more continuous but less sinuous than burrows of the endogeic species. The granulometry transform of the soil matrix showed that burrows made by A. nocturna were more evenly distributed than those of A. chlorotica. Although a good discrimination was possible when only one species was introduced into the soil cores, it was not possible to separate burrows of the two species from each other in cases where species were introduced into the same soil core. This limitation, partly due to the insufficient spatial resolution of the medical scanner, precluded the use of the morphological operators to study putative interactions between the two species.

Integrability and exact solution of an electronic model with long range interactions

We present an electronic model with long range interactions. Through the quantum inverse scattering method, integrability of the model is established using a one-parameter family of typical irreducible representations of gl(211). The eigenvalues of the conserved operators are derived in terms of the Bethe ansatz, from which the energy eigenvalues of the Hamiltonian are obtained.

Drinfield twists and alegebraic Bethe ansatz of the supersymmetric t-J model

We construct the Drinfeld twists (factorizing F-matrices) for the supersymmetric t-J model. Working in the basis provided by the F-matrix (i.e. the so-called F-basis), we obtain completely symmetric representations of the monodromy matrix and the pseudo-particle creation operators of the model. These enable us to resolve the hierarchy of the nested Bethe vectors for the gl(2\1) invariant t-J model.

Drinfeld twists and symmetric Bethe vectors of supersymmetric fermion models

We construct the Drinfeld twists ( factorizing F-matrices) of the gl(m-n)-invariant fermion model. Completely symmetric representation of the pseudo-particle creation operators of the model are obtained in the basis provided by the F-matrix ( the F-basis). We resolve the hierarchy of the nested Bethe vectors in the F-basis for the gl(m-n) supersymmetric model.

Whale sharks in Ningaloo Marine Park: managing tourism in an Australian marine protected area

The whale shark is the largest fish in the ocean, A tourism industry based on interacting with whale sharks has developed recently in Ningaloo Marine Park, off the coast of Western Australia, This is the only known, accessible place in the world where whale sharks congregate in significant numbers, Results from surveys of participants in the 'whale shark experience' are reported, with the experience found to be extremely satisfying for most consumers, Yet management questions relating to diver-to-shark separation distances, the appropriate number of operators, and the use of regulation, self-regulation and economic instruments, remain, The nexus between experiential aspects of the whale shark attraction and such management concerns is examined, and the usefulness of appropriate research in resolving management questions established, It is concluded that a judicious combination of management approaches is required to ensure the sustainable development of the whale shark tourism industry. (C) 1997 Elsevier Science Ltd.

Casimir invariants and characteristic identities for gl(infinity)

A full set of (higher-order) Casimir invariants for the Lie algebra gl(infinity) is constructed and shown to be well defined in the category O-FS generated by the highest weight (unitarizable) irreducible representations with only a finite number of nonzero weight components. Moreover, the eigenvalues of these Casimir invariants are determined explicitly in terms of the highest weight. Characteristic identities satisfied by certain (infinite) matrices with entries from gl(infinity) are also determined and generalize those previously obtained for gl(n) by Bracken and Green [A. J. Bracken and H. S. Green, J. Math. Phys. 12, 2099 (1971); H. S. Green, ibid. 12, 2106 (1971)]. (C) 1997 American Institute of Physics.

Izergin-Korepin model with a boundary

The Izergin-Korepin model on a semi-infinite lattice is diagonalized by using the level-one vertex operators of the twisted quantum affine algebra U-q[((2))(2)]. We give the bosonization of the vacuum state with zero particle content. Excitation states are given by the action of the vertex operators on the vacuum state. We derive the boundary S-matrix. We give an integral expression of the correlation functions of the boundary model, and derive the difference equations which they satisfy. (C) 2001 Elsevier Science B.V. All rights reserved.

On the Hopf bifurcation in control systems with a bounded nonlinearity asymptotically homogeneous at infinity

The paper studies existence, uniqueness, and stability of large-amplitude periodic cycles arising in Hopf bifurcation at infinity of autonomous control systems with bounded nonlinear feedback. We consider systems with functional nonlinearities of Landesman-Lazer type and a class of systems with hysteresis nonlinearities. The method is based on the technique of parameter functionalization and methods of monotone concave and convex operators. (C) 2001 Academic Press.

Stability of nonlinear difference inclusions

The stability of difference inclusions x(k+1) is an element of F(x(k)) is studied, where F(x) = {F(x, gimel) : is an element of Lambda} and the selections F(., gimel) : E -->E assume values in a Banach space E, partially ordered by a cone K. It is assumed that the operators F(.,gimel) are heterotone or pseudoconcave. The main results concern asymptotically stable absorbing sets, and include the case of a single equilibrium point. The results are applied to a number of practical problems.