Primary Fields and Screening Currents of gl (2/2) non-unitary conformal field theory

The non-semisimple gl(2)k current superalgebra in the standard basis and the corresponding non-unitary conformal field theory are investigated. Infinite families of primary fields corresponding to all finite-dimensional irreducible typical and atypical representations of gl(212) and three (two even and one odd) screening currents of the first kind are constructed explicitly in terms of ten free fields. (C) 2004 Elsevier B.V All rights reserved.

Eigenvalues of Casimir invariants for Uq[osp(m|n)]

For each quantum superalgebra U-q[osp(m parallel to n)] with m > 2, an infinite family of Casimir invariants is constructed. This is achieved by using an explicit form for the Lax operator. The eigenvalue of each Casimir invariant on an arbitrary irreducible highest weight module is also calculated. (c) 2005 American Institute of Physics.

On the distributed compression of quantum information

The problem of distributed compression for correlated quantum sources is considered. The classical version of this problem was solved by Slepian and Wolf, who showed that distributed compression could take full advantage of redundancy in the local sources created by the presence of correlations. Here it is shown that, in general, this is not the case for quantum sources, by proving a lower bound on the rate sum for irreducible sources of product states which is stronger than the one given by a naive application of Slepian-Wolf. Nonetheless, strategies taking advantage of correlation do exist for some special classes of quantum sources. For example, Devetak and Winter demonstrated the existence of such a strategy when one of the sources is classical. Optimal nontrivial strategies for a different extreme, sources of Bell states, are presented here. In addition, it is explained how distributed compression is connected to other problems in quantum information theory, including information-disturbance questions, entanglement distillation and quantum error correction.

Some Examples of Rigid Representations

*Research partially supported by INTAS grant 97-1644.

On Parabolic Subgroups and Hecke Algebras of some Fractal Groups

* The authors thank the “Swiss National Science Foundation” for its support.

Toward Clemens' Conjecture in Degrees between 10 and 24

1 Supported in part by the Norwegian Research Council for Science and the Humanities. It is a pleasure for this author to thank the Department of Mathematics of the University of Sofia for organizing the remarkable conference in Zlatograd during the period August 28-September 2, 1995. It is also a pleasure to thank the M.I.T. Department of Mathematics for its hospitality from January 1 to July 31, 1993, when this work was started. 2Supported in part by NSF grant 9400918-DMS.

On Li’s Coefficients for Some Classes of L-Functions

AMS Subj. Classification: 11M41, 11M26, 11S40

Kneser and Hereditarily Kneser Subgroups of a Profinite Group

2000 Mathematics Subject Classification: 20E18, 12G05, 12F10, 12F99.

A Note on the Asymptotic Behaviour of a Periodic Multitype Galton-Watson Branching Process

2000 Mathematics Subject Classification: 60J80.

On some Finite-Dimensional Representations of Artin Braid Group

Валентин В. Илиев - Авторът изучава някои хомоморфни образи G на групата на Артин на плитките върху n нишки в крайни симетрични групи. Получените пермутационни групи G са разширения на симетричната група върху n букви чрез подходяща абелева група. Разширенията G зависят от един целочислен параметър q ≥ 1 и се разцепват тогава и само тогава, когато 4 не дели q. В случая на нечетно q са намерени всички крайномерни неприводими представяния на G, а те от своя страна генерират безкрайна редица от неприводими представяния на групата на плитките.

Indice de Point Fixe pour les Morphismes de Chaînes

2000 Mathematics Subject Classification: 54H25, 55M20.

Programas de verdade, "mundos de crença": o verdadeiro segundo Paul Vayne

This study comes to reflect on the place of truth in everyday human experience. The notion of truth, expressed in different ways, in different systems of thought, cultural and historical, reveals the non-uniformity of their meaning and the arbitrary grouping under one name, truth. Given this fact, of so many beliefs taken as absolute, we ask with the historian Jean Marie Paul Veyne, if the truth is only one, or many called by a word namesake. If, through their ideas, men cannot access a definitely solid knowledge, unchanging and jaunty interference of the human condition (as their interests and affections), then in what sense it can claim a greater and exclusivist truth? Assuming the impossibility of apprehension of the reality of this type, Paul Veyne develops the notion of truth programs, referential beliefs assumed as cartographies that direct action and thought. He defends thus the idea of heterogeneity and plurality, as irreducible elements of human truths. On the one hand there is in society a plurality of truth programs, on the other there is a plurality of beliefs that is inside man. That is, in the way they believe the men also shows plural, because they believe in more than one program and counter programs. The thought of Paul Veyne is nonetheless a form of skepticism directed at all supposedly absolute and universal anthropological truths, because depending on the belief system studied and the specific moment in its history, a set of rules is established to distinguish the true from the false.

Dispersion and energy relations in periodic chains and grids

In this study wave propagation, dispersion relations, and energy relations for linear elastic periodic systems are analyzed. In particular, the dispersion relations for monoatomic chain of infinite dimension are obtained analytically by writing the Block-type wave equation for a unit cell in order to capture the dynamic behavior for chains under prescribed vibration. By comparing the discretized model (mass-spring chain) with the solid bar system, the nonlinearity of the dispersion relation for chain indicates that the periodic lattice is dispersive in contrast to the continuous rod, which is non dispersive. Further investigations have been performed considering one-dimensional diatomic linear elastic mass-spring chain. The dispersion relations, energy velocity, and group velocity have been derived. At certain range of frequencies harmonic plane waves do not propagate in contrast with monoatomic chain. Also, since the diatomic chain considered is a linear elastic chain, both of the energy velocity and the group velocity are identical. As long as the linear elastic condition is considered the results show zero flux condition without residual energy. In addition, this paper shows that the diatomic chain dispersion relations are independent on the unit cell scheme. Finally, an extension for the study covers the dispersion and energy relations for 2D- grid system. The 2x2 grid system show a periodicity of the dispersion surface in the wavenumber domain. In addition, the symmetry of the surface can be exploited to identify an Irreducible Brillouin Zone (IBZ). Compact representations of the dispersion properties of multidimensional periodic systems are obtained by plotting frequency as the wave vector’s components vary along the boundary of the IBZ, which leads to a widely accepted and effective visualization of bandgaps and overall dispersion properties.

G2-Monopoles with Singularities (Examples)

© 2016 Springer Science+Business Media DordrechtG2-Monopoles are solutions to gauge theoretical equations on G2-manifolds. If the G2-manifolds under consideration are compact, then any irreducible G2-monopole must have singularities. It is then important to understand which kind of singularities G2-monopoles can have. We give examples (in the noncompact case) of non-Abelian monopoles with Dirac type singularities, and examples of monopoles whose singularities are not of that type. We also give an existence result for Abelian monopoles with Dirac type singularities on compact manifolds. This should be one of the building blocks in a gluing construction aimed at constructing non-Abelian ones.

Renouncing the Single Image: Photography and the Realism of Abstraction

This essay addresses the issue of the relationship between abstraction and realism that it argues is at stake in the rejection of any primacy accorded to the single image, in favour of a sequencing of photographs according to certain, often novelistic and epic ideas of narrative form. Setting out from the opening text of Allan Sekula’s Fish Story, the article explores the competing tendencies towards what Georg Lukács termed ‘narration’ and ‘description’ as these are traced throughout Sekula's project (in part through a comparison with the contrasting works of Andreas Gursky). The essay concludes by suggesting the ways in which it is the irreducible actuality of abstraction within the concrete everydayness of capitalism's social world that means that all photographic ‘realism’ is intrinsically ‘haunted’ by a certain spectre of that ‘self-moving substance in the ‘shape of money’, as Marx calls it, or of the abstract form of capital itself.