The algebraic Bethe ansatz for rational braid-monoid lattice models

In this paper we study isotropic integrable systems based on the braid-monoid algebra. These systems constitute a large family of rational multistate vertex models and are realized in terms of the B_n, C_nand D_n Lie algebra and by the superalgebra Osp(n||2m). We present a unified formulation of the quantum inverse scattering method for many of these lattice models. The appropriate fundamental commutation rules are found, allowing us to construct the eigenvectors and the eigenvaluesof the transfer matrix associated to the B_n, C_n, D_n, Osp(2nt-1||2), Osp(2||2nt-2), Osp(2nt-2||2) and Osp(1||2n) models. The corresponding Bethe ansatz equations can be formulated in terms of the root structure of the underlying algebra.     

On fundamental skew distributions

A new class of multivariate skew-normal distributions, fundamental skew-normal distributions and their canonical version, is developed. It contains the product of independent univariate skew-normal distributions as a special case. Stochastic representations and other main properties of the associated distribution theory of linear and quadratic forms are considered. A unified procedure for extending this class to other families of skew distributions such as the fundamental skew-symmetric, fundamental skew-elliptical, and fundamental skew-spherical class of distributions is also discussed.     

The synthesis of functionalised chiral bicyclic lactam and lactone N-oxides using a tandem Cope elimination/reverse Cope elimination protocol

Functionalised hydroxylamine derivatives of (S)-proline and (R)-pipecolic acid have been prepared using a Cope elimination. These undergo reverse Cope elimination onto a pendant double bond to give bicyclic lactam and lactone N-oxides containing three contiguous chiral centres, this extends the scope and applicability of the reverse Cope elimination in the synthesis of heterocyclic systems by incorporation of the lactone and lactam structural motifs.     

Differential operators in terms of Clebsch-Gordon (C-G) coefficients and the wave equation of massless tensor fields

The quantum theory of angular momentum affords a treatment of tensors and vectors in a spherical basis. By using this theory we define the tensor differential operators: divergence, curl and gradient which act on a tensor of any rank, in terms of C-G coefficients. With these definitions we obtain a matrix representation and useful properties for those operators. An interesting application of this formalism is to find the wave equation of a tensor of any rank in a linear theory. This provides a new common way to look at the wave equations associated with both Maxwell's equations and the Maxwell-like equations for the linearized Weyl curvature tensor in gravitoelectromagnetism describing gravitational radiation on a Minkowski spacetime background.     

Velocity measurements in the oscillatory boundary layer produced by acoustic waves

Simultaneous amplitude and phase velocity measurements in the oscillatory viscous boundary layer (OVBL) produced by acoustic waves are reported. The structure of the OVBL of acoustic standing waves in air with frequencies of 35, 46, and 130 Hz is determined using hot-wire anemometry. The experimental results in amplitude are close to theoretical results of linear theories; small differences are pointed out. The phase results are in good agreement for 130 Hz, the agreement decreases for 35 and 46 Hz. A discussion on the possible causes of these discrepancies is made. Received: 25 May 2001/Accepted: 31 July 2001     

Development and application of an adaptive finite element method to reaction-diffusion equations

An adaptive finite element method is developed and applied to study the ozone decomposition laminar flame. The method uses a semidiscrete, linear Galerkin approximation in which the size of the elements is controlled by an integral which minimizes the changes in mesh spacing. The sizes and locations of the elements are controlled by the location and magnitude of the largest temperature gradient. The numerical results obtained with this adaptive finite element method are compared with those obtained using fixed-node finite-difference schemes and an adaptive finite-difference method. It is shown that the adaptive finite element method developed here using 36 elements can yield as accurate flame speeds as fourth-order accurate, fixed-node, finite-difference methods when 272 collocation points are employed in the calculations.     

The biobjective absolute center problem

This paper deals with the problem of determining the absolute center of a network, taking into account two objective functions. These functions consist of minimizing the maximum of the distances from any point on the network to the vertices, using two independent lengths on each edge. We propose an algorithm in polynomial time to obtain the non-dominated location points on the network, using the Kariv and Hakimi method (1979). This work was partially supported by project number 93/108 from the Dirección General de Universidades e Investigación del Gobierno de Canarias.