Integrable Kondo impurity in one-dimensional q-deformed t-J models

Integrable Kondo impurities in two cases of one-dimensional q-deformed t-J models are studied by means of the boundary Z(2)-graded quantum inverse scattering method. The boundary K matrices depending on the local magnetic moments of the impurities are presented as nontrivial realizations of the reflection equation algebras in an impurity Hilbert space. Furthermore, these models are solved by using the algebraic Bethe ansatz method and the Bethe ansatz equations are obtained.

Structuring real-time Object-Z specifications

This paper presents a means of structuring specifications in real-time Object-Z: an integration of Object-Z with the timed refinement calculus. Incremental modification of classes using inheritance and composition of classes to form multi-component systems are examined. Two approaches to the latter are considered: using Object-Z's notion of object instantiation and introducing a parallel composition operator similar to those found in process algebras. The parallel composition operator approach is both more concise and allows more general modelling of concurrency. Its incorporation into the existing semantics of real-time Object-Z is presented.

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.

Unitary R-matrices for topological quantum computing

The main problem with current approaches to quantum computing is the difficulty of establishing and maintaining entanglement. A Topological Quantum Computer (TQC) aims to overcome this by using different physical processes that are topological in nature and which are less susceptible to disturbance by the environment. In a (2+1)-dimensional system, pseudoparticles called anyons have statistics that fall somewhere between bosons and fermions. The exchange of two anyons, an effect called braiding from knot theory, can occur in two different ways. The quantum states corresponding to the two elementary braids constitute a two-state system allowing the definition of a computational basis. Quantum gates can be built up from patterns of braids and for quantum computing it is essential that the operator describing the braiding-the R-matrix-be described by a unitary operator. The physics of anyonic systems is governed by quantum groups, in particular the quasi-triangular Hopf algebras obtained from finite groups by the application of the Drinfeld quantum double construction. Their representation theory has been described in detail by Gould and Tsohantjis, and in this review article we relate the work of Gould to TQC schemes, particularly that of Kauffman.

Twisted quantum affine superalgebra U-q[sl(2/2)((2))], U-q[osp(2/2)] invariant R-matrices and a new integrable electronic model

We describe the twisted affine superalgebra sl(2\2)((2)) and its quantized version U-q[sl(2\2)((2))]. We investigate the tensor product representation of the four-dimensional grade star representation for the fixed-point sub superalgebra U-q[osp(2\2)]. We work out the tensor product decomposition explicitly and find that the decomposition is not completely reducible. Associated with this four-dimensional grade star representation we derive two U-q[osp(2\2)] invariant R-matrices: one of them corresponds to U-q [sl(2\2)(2)] and the other to U-q [osp(2\2)((1))]. Using the R-matrix for U-q[sl(2\2)((2))], we construct a new U-q[osp(2\2)] invariant strongly correlated electronic model, which is integrable in one dimension. Interestingly this model reduces in the q = 1 limit, to the one proposed by Essler et al which has a larger sl(2\2) symmetry.

HLA-DRB1*allele-associated genetic susceptibility and protection against multiple sclerosis in Brazilian patients

Multiple sclerosis (MS) is a chronic autoimmune demyelinating disease of the central nervous system that causes neurological disorders in young adults. Previous studies in various populations highlighted an association between the HLA-DRB1*1.5 allele and MS. This study investigated the association between HLA-DRB1*15 and other HLA-DRB1 alleles and MS in a Brazilian Caucasian population sample from Londrina, Southern Brazil. HLA-DRB1 alleles were analyzed by polymerase chain reaction with specific sequence oligonucleotide primers in 119 MS patients and in 305 healthy blood donors as a control. Among the MS patients, 89 (75.0%) presented with relapsing remitting MS, 24 (20.0%) with secondary progressive MS and 6 (5.0%) with primary progressive MS. The frequency of the HLA-DRB1*15 allele observed in the MS Brazilian patients was similar to findings reported in previous studies carried out in populations worldwide. However, the results showed a higher frequency of the HLA-DRB1*15 allele in the MS patients compared to the controls, with a relative frequency of 0.1050 (10.50%) and 0.0443 (4.4%), respectively (OR=2.53; 95% CI 1.43-4.46; p=0.0009). A protector allele was also detected. The frequency of the HLA-DRB1*11 allele was reduced in the MS patients compared to the controls, with a relative frequency of 0.1345 (13.4%) and 0.1869 (18.7%), respectively (OR=0.67; 95% CI 0.44-1.03; p=0.0692). The results demonstrated that the HLA-DRB1*15 allele in heterozygosity is positively associated with MS (p=0.0079), and may be considered a genetic marker of susceptibility to the disease. A negative association between the HLA-DRB1*11 allele in homozygosity and MS was also verified (p=0.0418); this allele may be considered a genetic marker of resistance to MS in the Brazilian population.

Evaluation of the Possibility of Removing Staining by Repolishing Composite Resins Submitted to Artificial Aging

This in vitro research verified the possibility of eliminating staining caused by coffee and red wine in five composite resins, after being submitted to thermal cycling. Thirty-six specimens were prepared and immersed in water at 37 degrees C for 24 hours. After polishing, specimen color was measured in a spectrophotometer Cintra 10 UV (Visible Spectrometer, GBC, Braeside, VIC, Australia). All specimens were submitted to thermal cycling at temperatures of 5 and 55 degrees C with a dwell time of 1 minute, for 1,000 cycles in a 75% ethanol/water solution. After thermal cycling, the specimens were immersed in water at 37 degrees C until 7 days had elapsed from the time the specimens were prepared. All specimens were then taken to the spectrophotometer for color measurement. The specimens were divided into three groups (N = 12): distilled water (control), coffee, and red wine. For the staining process to occur on only one surface, all the sides, except one, of the surfaces were isolated with white wax. The specimens were immersed in one of the solutions at 37 degrees C for 14 days. The specimens were dried and taken to the spectrophotometer for color measurement. After this, the specimens were submitted to 20 mu m wear three times, and the color was measured after each one of the wear procedures. Calculation of the color difference was made using CIEDE2000 formula. According to the methodology used in this research, it was concluded that the staining caused by coffee and red wine was superficial and one wear of 20 mu m was sufficient to remove the discoloration.

Algebraic Bethe ansatz for integrable extended Hubbard models arising from supersymmetric group solutions

Integrable extended Hubbard models arising from symmetric group solutions are examined in the framework of the graded quantum inverse scattering method. The Bethe ansatz equations for all these models are derived by using the algebraic Bethe ansatz method.

Integrable extended hubbard models with boundary Kondo impurities

Three kinds of integrable Kondo impurity additions to one-dimensional q-deformed extended Hubbard models are studied by means of the boundary Z(2)-graded quantum inverse scattering method. The boundary K matrices depending on the local magnetic moments of the impurities are presented as nontrivial realisations of the reflection equation algebras in an impurity Hilbert space. The models are solved by using the algebraic Bethe ansatz method, and the Bethe ansatz equations are obtained.

Strong Grobner bases for polynomials over a principal ideal ring

Grobner bases have been generalised to polynomials over a commutative ring A in several ways. Here we focus on strong Grobner bases, also known as D-bases. Several authors have shown that strong Grobner bases can be effectively constructed over a principal ideal domain. We show that this extends to any principal ideal ring. We characterise Grobner bases and strong Grobner bases when A is a principal ideal ring. We also give algorithms for computing Grobner bases and strong Grobner bases which generalise known algorithms to principal ideal rings. In particular, we give an algorithm for computing a strong Grobner basis over a finite-chain ring, for example a Galois ring.

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.

Twisted sl(3, C)(k)((2)) current algebra: free field representation and screening currents

Motivated by application of twisted current algebra in description of the entropy of Ads(3) black hole, we investigate the simplest twisted current algebra sl(3, c)(k)((2)). Free field representation of the twisted algebra, and the corresponding twisted Sugawara energy-momentum tensor are obtained by using three (beta, gamma) pairs and two scalar fields. Primary fields and two screening currents of the first kind are presented. (C) 2001 Published by Elsevier Science B.V.