On the construction of correlation functions for the integrable supersymmetric fermion models

We review the recent progress on the construction of the determinant representations of the correlation functions for the integrable supersymmetric fermion models. The factorizing F-matrices (or the so-called F-basis) play an important role in the construction. In the F-basis, the creation (and the annihilation) operators and the Bethe states of the integrable models are given in completely symmetric forms. This leads to the determinant representations of the scalar products of the Bethe states for the models. Based on the scalar products, the determinant representations of the correlation functions may be obtained. As an example, in this review, we give the determinant representations of the two-point correlation function for the U-q(gl(2 vertical bar 1)) (i.e. q-deformed) supersymmetric t-J model. The determinant representations are useful for analyzing physical properties of the integrable models in the thermodynamical limit.

A Bethe ansatz solvable model for superpositions of Cooper pairs and condensed molecular bosons

We introduce a general Hamiltonian describing coherent superpositions of Cooper pairs and condensed molecular bosons. For particular choices of the coupling parameters, the model is integrable. One integrable manifold, as well as the Bethe ansatz solution, was found by Dukelsky et al. [J. Dukelsky, G.G. Dussel, C. Esebbag, S. Pittel, Phys. Rev. Lett. 93 (2004) 050403]. Here we show that there is a second integrable manifold, established using the boundary quantum inverse scattering method. In this manner we obtain the exact solution by means of the algebraic Bethe ansatz. In the case where the Cooper pair energies are degenerate we examine the relationship between the spectrum of these integrable Hamiltonians and the quasi-exactly solvable spectrum of particular Schrodinger operators. For the solution we derive here the potential of the Schrodinger operator is given in terms of hyperbolic functions. For the solution derived by Dukelsky et al., loc. cit. the potential is sextic and the wavefunctions obey PT-symmetric boundary conditions. This latter case provides a novel example of an integrable Hermitian Hamiltonian acting on a Fock space whose states map into a Hilbert space of PE-symmetric wavefunctions defined on a contour in the complex plane. (c) 2006 Elsevier B.V. All rights reserved.

Generalized Perk-Schultz models: solutions of the Yang-Baxter equation associated with quantized orthosymplectic superalgebras

The Perk-Schultz model may be expressed in terms of the solution of the Yang-Baxter equation associated with the fundamental representation of the untwisted affine extension of the general linear quantum superalgebra U-q (gl(m/n)], with a multiparametric coproduct action as given by Reshetikhin. Here, we present analogous explicit expressions for solutions of the Yang-Baxter equation associated with the fundamental representations of the twisted and untwisted affine extensions of the orthosymplectic quantum superalgebras U-q[osp(m/n)]. In this manner, we obtain generalizations of the Perk-Schultz model.

Time trials on second-order and variable-learning-rate algorithms

The performance of seven minimization algorithms are compared on five neural network problems. These include a variable-step-size algorithm, conjugate gradient, and several methods with explicit analytic or numerical approximations to the Hessian.

The role of industrial design in technological innovation

This is an exploratory study in a field which previously was virtually unexplored. The aim is to identify, for the benefit of innovators, the influence of industrial design on the commercial success of new science-based products used for professional and industrial purposes. The study is a contribution to the theory of success and failure in industrial innovation. The study begins by defining the terminology. To place the investigation in context, there is then a review of past attempts by official policy-making bodies to improve the competitiveness of British products of manufacture through good design. To elucidate the meaning of good design, attempts to establish a coherent philosophy of style in British products of manufacture during the same period are also reviewed. Following these reviews, empirical evidence is presented to identify what actually takes place in successful firms when industrial design is allocated a role in the process of technological innovation. The evidence comprises seven case studies of new science-based products used for professional or industrial purposes which have received Design Council Awards. To facilitate an objective appraisal, evidence was obtained by conducting separate semi-structured interviews, the detail of which is described, with senior personnel in innovating firms, with industrial design consultants, and with professional users. The study suggests that the likelihood of commercial success in technological innovation is greater when the form, configuration, and the overall appearance of a new product, together with the detail which delineates them, are consciously and expertly controlled. Moreover, uncertainty in innovation is likely to be reduced if the appearance of a new product is consciously designed to facilitate recognition and comprehension. Industrial design is an especially significant factor when a firm innovates against a background of international competition and comparable levels of technological competence in rival firms. The likelihood of success in innovation is enhanced if design is allocated a role closely identified with the total needs of the user and discrete from the engineering function in company organisation. Recent government measures, initiated since this study began, are corroborative of the findings.

Exponents of Subvarieties of Upper Triangular Matrices over Arbitrary Fields are Integral

Partially supported by grant RFFI 98-01-01020.

Representations and Positive Definite Functions on Hypergroups

Some relationships between representations of a hypergroup X, its algebras, and positive definite functions on X are studied. Also, various types of convergence of positive definite functions on X are discussed.