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.

Quantum Lie algebras, their existence, uniqueness and q-antisymmetry

Quantum Lie algebras are generalizations of Lie algebras which have the quantum parameter h built into their structure. They have been defined concretely as certain submodules L-h(g) of the quantized enveloping algebras U-h(g). On them the quantum Lie product is given by the quantum adjoint action. Here we define for any finite-dimensional simple complex Lie algebra g an abstract quantum Lie algebra g(h) independent of any concrete realization. Its h-dependent structure constants are given in terms of inverse quantum Clebsch-Gordan coefficients. We then show that all concrete quantum Lie algebras L-h(g) are isomorphic to an abstract quantum Lie algebra g(h). In this way we prove two important properties of quantum Lie algebras: 1) all quantum Lie algebras L-h(g) associated to the same g are isomorphic, 2) the quantum Lie product of any Ch(B) is q-antisymmetric. We also describe a construction of L-h(g) which establishes their existence.

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.

Comments on the Drinfeld realization of the quantum affine superalgebra U-q[gl(m backslash n)(1)] and its Hopf algebra structure

By generalizing the Reshetikhin and Semenov-Tian-Shansky construction to supersymmetric cases, we obtain the Drinfeld current realization for the quantum affine superalgebra U-q[gl(m\n)((1))]. We find a simple coproduct for the quantum current generators and establish the Hopf algebra structure of this super current algebra.

Reply to comment on `Integrable Kondo impurity in one-dimensional q-deformed t - J models

This is a reply to the comment by P Schlottmann and A A Zvyagin.

Automatic construction of explicit R matrices for the one-parameter families of irreducible typical highest weight (0(m)vertical bar alpha(n)) representations of U-q[gl(m vertical bar n)]

We detail the automatic construction of R matrices corresponding to (the tensor products of) the (O-m\alpha(n)) families of highest-weight representations of the quantum superalgebras Uq[gl(m\n)]. These representations are irreducible, contain a free complex parameter a, and are 2(mn)-dimensional. Our R matrices are actually (sparse) rank 4 tensors, containing a total of 2(4mn) components, each of which is in general an algebraic expression in the two complex variables q and a. Although the constructions are straightforward, we describe them in full here, to fill a perceived gap in the literature. As the algorithms are generally impracticable for manual calculation, we have implemented the entire process in MATHEMATICA; illustrating our results with U-q [gl(3\1)]. (C) 2002 Published by Elsevier Science B.V.

Exercise-induced alterations in neutrophil degranulation and respiratory burst activity: possible mechanisms of action

Neutrophils constitute 50-60% of all circulating leukocytes; they present the first line of microbicidal defense and are involved in inflammatory responses. To examine immunocompetence in athletes, numerous studies have investigated the effects of exercise on the number of circulating neutrophils and their response to stimulation by chemotactic stimuli and activating factors. Exercise causes a biphasic increase in the number of neutrophils in the blood, arising from increases in catecholamine and cortisol concentrations. Moderate intensity exercise may enhance neutrophil respiratory burst activity, possibly through increases in the concentrations of growth hormone and the inflammatory cytokine IL-6. In contrast, intense or long duration exercise may suppress neutrophil degranulation and the production of reactive oxidants via elevated circulating concentrations of epinephrine (adrenaline) and cortisol. There is evidence of neutrophil degranulation and activation of the respiratory burst following exercise-induced muscle damage. In principle, improved responsiveness of neutrophils to stimulation following exercise of moderate intensity could mean that individuals participating in moderate exercise may have improved resistance to infection. Conversely, competitive athletes undertaking regular intense exercise may be at greater risk of contracting illness. However there are limited data to support this concept. To elucidate the cellular mechanisms involved in the neutrophil responses to exercise, researchers have examined changes in the expression of cell membrane receptors, the production and release of reactive oxidants and more recently, calcium signaling. The investigation of possible modifications of other signal transduction events following exercise has not been possible because of current methodological limitations. At present, variation in exercise-induced alterations in neutrophil function appears to be due to differences in exercise protocols, training status, sampling points and laboratory assay techniques.

A Poincare-Birkhoff-Witt commutator lemma for U-q[gl(m vertical bar n)]

We present and prove in detail a Poincare-Birkhoff-Witt commutator lemma for the quantum superalgebra U-q[gl(m\n)]. (C) 2003 American Institute of Physics.

Locomotion at-1.0 degrees C: burst swimming performance of five species of Antarctic fish

We investigated the burst swimming performance of five species of Antarctic fish at -1.0degreesC. The species studied belonged to the suborder, Notothenioidei, and from the families, Nototheniidae and Bathydraconidae. Swimming performance of the fish was assessed over the initial 300 ms of a startle response using surgically attached miniature accelerometers. Escape responses in all fish consisted of a C-type fast start; consisting of an initial pronounced bending of the body into a C-shape, followed by one or more complete tail-beats and an un-powered glide. We found significant differences in the swimming performance of the five species of fish examined, with average maximum swimming velocities (U-max) ranging from 0.91 to 1.39 m s(-1) and maximum accelerations (A(max)) ranging from 10.6 to 15.6 m s(-2). The cryopelagic species, Pagothenia borchgrevinki, produced the fastest escape response, reaching a U-max and A(max) of 1.39 m s(-1) and 15.6 m s(-2), respectively. We also compared the body shapes of each fish species with their measures of maximum burst performance. The dragonfish, Gymnodraco acuticeps, from the family Bathdraconidae, did not conform to the pattern observed for the other four fish species belonging to the family Nototheniidae. However, we found a negative relationship between buoyancy of the fish species and burst swimming performance. (C) 2002 Elsevier Science Ltd. All rights reserved.

Existence and uniqueness of Q-processes with a given finite μ-invariant measure

Let Q be a stable and conservative Q-matrix over a countable state space S consisting of an irreducible class C and a single absorbing state 0 that is accessible from C. Suppose that Q admits a finite mu-subinvariant measure in on C. We derive necessary and sufficient conditions for there to exist a Q-process for which m is mu-invariant on C, as well as a necessary condition for the uniqueness of such a process.