Chirality and Dirac Operator on Noncommutative Sphere

We give a derivation of the Dirac operator on the noncommutative $2$-sphere within the framework of the bosonic fuzzy sphere and define Connes' triple. It turns out that there are two different types of spectra of the Dirac operator and correspondingly there are two classes of quantized algebras. As a result we obtain a new restriction on the Planck constant in Berezin's quantization. The map to the local frame in noncommutative geometry is also discussed.Comment: 24 pages, latex, no figure

Characteristic cohomology of pp-form gauge theories

The characteristic cohomology $H^k_{char}(d)$ for an arbitrary set of free $p$-form gauge fields is explicitly worked out in all form degrees $k<n-1$, where $n$ is the spacetime dimension. It is shown that this cohomology is finite-dimensional and completely generated by the forms dual to the field strengths. The gauge invariant characteristic cohomology is also computed. The results are extended to interacting $p$-form gauge theories with gauge invariant interactions. Implications for the BRST cohomology are mentioned.Comment: Latex file, no figures, 44 page

A reuse-Oriented Approach for the Construction of Scenario Bases Methods

International audienceDespite the recent interest in scenarios, the development of new methods and tools for Requirements Engineering integrating scenario based approaches has been limited. This paper reports on four different processes developed from research undertaken as part of the CREWS project which the authors believe will improve scenario use and make it more systematic. Furthermore CREWS aims to integrate these approaches into a method for scenario-based requirements engineering. To achieve this objective and be able to include existing approaches such as use case analysis we develop a component based approach which reflects a shift towards a reuse-centric approach to method engineering. The paper presents CREWS method and meta-method knowledge through the implementation of an SGML database to store, retrieve and dynamically compose chunks of CREWS processes

Ordered Weighted Average Based Fuzzy Rough Sets

Traditionally, membership to the fuzzy-rough lower, resp. upper approximation is determined by looking only at the worst, resp. best performing object. Consequently, when applied to data analysis problems, these approximations are sensitive to noisy and/or outlying samples. In this paper, we advocate a mitigated approach, in which membership to the lower and upper approximation is determined by means of an aggregation process using ordered weighted average operators. In comparison to the previously introduced vaguely quantified rough set model, which is based on a similar rationale, our proposal has the advantage that the approximations are monotonous w.r.t. the used fuzzy indiscernibility relation. Initial experiments involving a feature selection application confirm the potential of the OWA-based model

Magnetic fields in cosmic particle acceleration sources

We review here some magnetic phenomena in astrophysical particle accelerators associated with collisionless shocks in supernova remnants, radio galaxies and clusters of galaxies. A specific feature is that the accelerated particles can play an important role in magnetic field evolution in the objects. We discuss a number of CR-driven, magnetic field amplification processes that are likely to operate when diffusive shock acceleration (DSA) becomes efficient and nonlinear. The turbulent magnetic fields produced by these processes determine the maximum energies of accelerated particles and result in specific features in the observed photon radiation of the sources. Equally important, magnetic field amplification by the CR currents and pressure anisotropies may affect the shocked gas temperatures and compression, both in the shock precursor and in the downstream flow, if the shock is an efficient CR accelerator. Strong fluctuations of the magnetic field on scales above the radiation formation length in the shock vicinity result in intermittent structures observable in synchrotron emission images. Resonant and non-resonant CR streaming instabilities in the shock precursor can generate mesoscale magnetic fields with scale-sizes comparable to supernova remnants and even superbubbles. This opens the possibility that magnetic fields in the earliest galaxies were produced by the first generation Population III supernova remnants and by clustered supernovae in star forming regions.Comment: 30 pages, Space Science Review

More on quantum groups from the the quantization point of view

Star products on the classical double group of a simple Lie group and on corresponding symplectic grupoids are given so that the quantum double and the "quantized tangent bundle" are obtained in the deformation description. "Complex" quantum groups and bicovariant quantum Lie algebras are discused from this point of view. Further we discuss the quantization of the Poisson structure on symmetric algebra $S(g)$ leading to the quantized enveloping algebra $U_{h}(g)$ as an example of biquantization in the sense of Turaev. Description of $U_{h}(g)$ in terms of the generators of the bicovariant differential calculus on $F(G_q)$ is very convenient for this purpose. Finally we interpret in the deformation framework some well known properties of compact quantum groups as simple consequences of corresponding properties of classical compact Lie groups. An analogue of the classical Kirillov's universal character formula is given for the unitary irreducible representation in the compact case.Comment: 18 page

Template-stripped gold surfaces with 0.4 nm rms roughness suitable for force measurements. Application to the Casimir force in the 20-100 nm range

Using a template-stripping method, macroscopic gold surfaces with root-mean-square (rms) roughness less than 0.4 nm have been prepared, making them useful for studies of surface interactions in the nanometer range. The utility of such substrates is demonstrated by measurements of the Casimir force at surface separations between 20 and 100 nm, resulting in good agreement with theory. The significance and quantification of this agreement is addressed, as well as some methodological aspects regarding the measurement of the Casimir force with high accuracy.Comment: 7 figure

Numerical Fracture Analysis Under Temperature Variation by Energetic Method

It is known that temperature change can induce sudden crack propagation especially when the material is composed of fibers. In this fact, the crack growth process under mixed-mode coupling mechanical and thermal loads in orthotropic materials like wood is investigated in this work. The analytical formulation of A integral’s combines the real and virtual mechanical and thermal stress/strain fields under transient diet in 2D. The Mixed Mode Crack Growth specimen providing the decrease of energy release rate during crack propagation is considered in order to compute the various mixed mode ratios. By using three specific routines, the analytical formulation is implemented in finite element software Cast3m. The efficiency of the proposed model is justified by showing the evolution of energy release rate and the stress intensity factors versus crack length and versus temperature variation in time dependent materia

Polyakov soldering and second order frames : the role of the Cartan connection

The so-called "soldering" procedure performed by A.M. Polyakov in [1] for a SL(2,R)-gauge theory is geometrically explained in terms of a Cartan connection on second order frames of the projective space RP^1. The relationship between a Cartan connection and the usual (Ehresmann) connection on a principal bundle allows to gain an appropriate insight into the derivation of the genuine " diffeomorphisms out of gauge transformations" given by Polyakov himself.Comment: Accept\'e pour publication dans Lett. Math. Phy