Generalizing the soldering procedure

We start this work by revisiting the problem of the soldering of two chiral Schwinger models of opposite chiralities. We verify that, different from what one can conclude from the current literature, the usual sum of these models is, in fact, gauge invariant and corresponds to a composite model, where the component models are the vector and axial Schwinger models. As a consequence, we reinterpret this formalism as a kind of degree of freedom reduction mechanism. This result has led us to discover a second soldering possibility giving rise to the axial Schwinger model. This new result is seemingly rather general. We explore it here in the soldering of two Maxwell-Chern-Simons theories with different masses.

A Bethe ansatz solution for the closed U-q[sl(2)] Temperley-Lieb quantum spin chains

We solve the spectrum of the closed Temperley-Lieb quantum spin chains using the coordinate Bethe ansatz. These models are invariant under the quantum group U-q[sl(2)].

COMPARISON OF THE ANOMALOUS AND NONANOMALOUS GENERALIZED SCHWINGER MODELS VIA THE FUNCTIONAL FORMALISM

We calculate the Green functions of the two versions of the generalized Schwinger model, the anomalous and the nonanomalous one, in their higher order Lagrangian density form. Furthermore, it is shown through a sequence of transformations that the bosonized Lagrangian density is equivalent to the former, at least for the bosonic correlation functions. The introduction of the sources from the beginning, leading to a gauge-invariant source term, is also considered. It is verified that the two models have the same correlation functions only if the gauge-invariant sector is taken into account. Finally, there is presented a generalization of the Wess-Zumino term, and its physical consequences are studied, in particular the appearance of gauge-dependent massive excitations.

COORDINATE EXPRESSION OF CYTOKERATIN-7 AND CYTOKERATIN-20 DEFINES UNIQUE SUBSETS OF CARCINOMAS

We tested the hypothesis that the coordinate expression of cytokeratin 7 (CK 7) and cytokeratin 20 (CK 20) could distinguish among carcinomas arising from different primary sites. A total of 384 cases of carcinomas primary to various organs, as well as 16 cases of malignant mesothelioma, were evaluated using commercially available monoclonal antibodies and an avidin-biotin immunoperoxidase technique. The subset of tumors strongly expressing both CK 7 and CK 20 included virtually all bladder transitional cell carcinomas and the majority of pancreatic adenocarcinomas; the tumors negative for both CK 7 and CK 20 were largely restricted to hepatocellular, prostate, and renal cell carcinomas in addition to squamous cell and neuroendocrine carcinomas of lung. The CK 7-/CK 20+ immunophenotype, however, was highly characteristic of adenocarcinomas of colorectal origin, whereas CK 7+/CK 20- immunophenotype was typically seen in the vast majority of carcinomas arising from other sites, including ovary, endometrium, breast, and lung, as well as malignant mesothelioma. Gastric carcinomas were the most heterogeneous subgroup with respect to CK 7/CK 20 immunophenotype. In the subset of mucinous tumors, striking immunophenotypic differences were noted among those primary to the breast (CK 7+/CK 20-), gastrointestinal tract (CK 7-/CK 20+), and ovary (CK 7+/CK 20+). In all cases investigated, this CK immunophenotype was invariant in metastatic vs. primary tumors. It is concluded that, in the appropriate clinical setting, the CK 7/CK 20 immunophenotype of carcinomas is a valuable diagnostic marker in the determination of primary site of origin.

Caustics of the restricted three-body problem

Trajectories of the planar, circular, restricted three-body problem are given in the configuration space through the caustics associated to the invariant tori of quasi-periodic orbits. It is shown that the caustics of trajectories librating in any particular resonance display some features associated to that resonance. This method can be considered complementary to the Poincare surface of section method, because it provides information not accessible by the other method.

Hausdorff dimension of non-hyperbolic repellers. I: Maps with holes

This is the first paper in a two-part series devoted to studying the Hausdorff dimension of invariant sets of non-uniformly hyperbolic, non-conformal maps. Here we consider a general abstract model, that we call piecewise smooth maps with holes. We show that the Hausdorff dimension of the repeller is strictly less than the dimension of the ambient manifold. Our approach also provides information on escape rates and dynamical dimension of the repeller.

On computing discriminants of subfields of Q(zeta(pr))

The conductor-discriminant formula, namely, the Hasse Theorem, states that if a number field K is fixed by a subgroup H of Gal(Q(zeta(n))/Q), the discriminant of K can be obtained from H by computing the product of the conductors of all characters defined modulo n which are associated to K. By calculating these conductors explicitly, we derive a formula to compute the discriminant of any subfield of Q(zeta(p)r), where p is an odd prime and r is a positive integer. (C) 2002 Elsevier B.V. (USA).

CHOLESTEROL MODULATION OF LIPID PROTEIN INTERACTIONS IN LIVER MICROSOMAL MEMBRANE - A SPIN LABEL STUDY

ESR spectra of spin probes were used to monitor lipid-protein interactions in native and cholesterol-enriched microsomal membranes. In both systems composite spectra were obtained, one characteristic of bulk bilayer organization and another due to a motionally restricted population, which was ascribed to lipids in a protein microenvironment. Computer spectral subtractions revealed that cholesterol modulates the order/mobility of both populations in opposite ways, i.e., while the lipid bilayer region gives rise to more anisotropic spectra upon cholesterol enrichment, the spectra of the motionally restricted population become indicative of increased mobility and/or decreased order. These events were evidenced by measurement of both effective order parameters and correlation times. The percentages of the motionally restricted component were invariant in native and cholesterol-enriched microsomes. Variable temperature studies also indicated a lack of variation of the percentages of both spectral components, suggesting that the motionally restricted one was not due to protein aggregation. The results correlate well with the effect of cholesterol enrichment on membrane-bound enzyme kinetics and on the behavior of fluorescent probes [Castuma & Brenner (1986) Biochemistry 25, 4733-4738]. Several hypothesis are put forward to explain the molecular mechanism of the cholesterol-induced spectral changes.

A generalized Jaynes-Cummings Hamiltonian and supersymmetric shape invariance

A class of shape-invariant bound-state problems which represent two-level systems are introduced. It is shown that the coupled-channel Hamiltonians obtained correspond to the generalization of the Jaynes-Cummings Hamiltonian.

Hopf-zero bifurcations of reversible vector fields

We study the dynamics of a class of reversible vector fields having eigenvalues (0, alphai, -alphai) around their symmetric equilibria. We give a complete list of all normal forms for such vector fields, their versal unfoldings, and the corresponding bifurcation diagrams of the codimensional-one case. We also obtain some important conclusions on the existence of homoclinic and heteroclinic orbits, invariant tori and symmetric periodic orbits.

On the dynamics of the Bianchi IX system

In this paper, we study the flow on three invariant sets of dimension five for the classical Bianchi IX system. In these invariant sets, using the Darboux theory of integrability, we prove the non-existence of periodic solutions and we study their dynamics. Moreover, we find three invariant sets of dimension four where the flow is integrable.

Simple generalization of Wisdom's perturbative method

A simple generalization of Wisdom's perturbative method, as originally proposed by Wisdom (1985), is obtained. Any number of resonant cosines can be handled and the method can also accommodate more involved disturbing functions. Averaged trajectories are easily obtained by drawing level curves of the action. Here, the method is first tested for simple models of 3:1 and 2:1 resonant problems. Comparisons with numerical integration and surface-section curves show very good agreements.

Completeness of coherent states associated with self-similar potentials and Ramanujan's integral extension of the beta function

A decomposition of identity is given as a complex integral over the coherent states associated with a class of shape-invariant self-similar potentials. There is a remarkable connection between these coherent states and Ramanujan's integral extension of the beta function.

VACUUM POLARIZATION TENSOR IN 3-DIMENSIONAL QUANTUM ELECTRODYNAMICS

We evaluate the one-loop vacuum polarization tensor for three-dimensional quantum electrodynamics (QED), using an analytic regularization technique, implemented in a gauge-invariant way. We show thus that a gauge boson mass is generated at this level of radiative correction to the photon propagator. We also point out in our conclusions that the generalization for the non Abelian case is straightforward.

Non-periodic bifurcations of one-dimensional maps

We prove that a 'positive probability' subset of the boundary of '{uniformly expanding circle transformations}' consists of Kupka-Smale maps. More precisely, we construct an open class of two-parameter families of circle maps (f(alpha,theta))(alpha,theta) such that, for a positive Lebesgue measure subset of values of alpha, the family (f(alpha,theta))(theta) crosses the boundary of the uniformly expanding domain at a map for which all periodic points are hyperbolic (expanding) and no critical point is pre-periodic. Furthermore, these maps admit an absolutely continuous invariant measure. We also provide information about the geometry of the boundary of the set of hyperbolic maps.