Singular electromagnetic fields: inductive approach

In a non-convex polyhedral domain, we describe the local trace (i.e. defined on a face) of the normal derivative of an $L^2$ function, with $L^2$ Laplacian. We then provide generalized integration by parts formulae for the Laplace, divergence and curl operators. Finally, these results allow us to split electromagnetic fields into regular and singular parts, which can be characterized. To cite this article: F. Assous et al., C. R. Acad. Sci. Paris, Ser. I 341 (2005).     

Quantum groups,q oscillators,and covariant algebras

The physical interpretation of the basic concepts of the theory of covariant groups—coproducts, representations and corepresentations, action and coaction—is discussed for the examples of the simplestq deformed objects (quantum groups and algebras,q oscillators, and comodule algebras). It is shown that the reduction of the covariant algebra of quantum second-rank tensors includes the algebras of theq oscillator and quantum sphere. A special case of covariant algebra corresponds to the braid group in a space with nontrivial topology.In memory of Mikhail Konstantinovich PolivanovSt Petersburg Branch, V. A. Steklov Mathematics Institute, Russian Academy of Sciences. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 94, No. 2, pp. 193–199, February, 1993.     

Perturbation theory for particles in one-dimensional, central- or axial-symmetric fields

A perturbation theory for which all corrections to a nonperturbed state are defined by its wave function is obtained and a new applicability condition for this theory is formulated. By considering a simple example, a comparison with the Rayleigh-Schrödinger perturbation theory, giving an analytical expression for the corresponding series, is performed.     

Generalized stationary random fields with linear regressions - an operator approach

Existence, -stationarity and linearity of conditional expectations of square integrable random sequences satisfying

for a real sequence is examined. The analysis is reliant upon the use of Laurent and Toeplitz operator techniques.

     

Propagation of Electromagnetic Waves in an Open Planar Dielectric Waveguide Filled with an Nonlinear Medium I: TE Waves

Computational Mathematics and Mathematical Physics - A nonlinear Sturm–Liouville-type eigenvalue problem on an interval with the boundary conditions of the third kind and an additional...     

A combinatorial approach to jumping particles: The parallel TASEP

In this article, we continue the combinatorial study of models of particles jumping on a row of cells which we initiated with the standard totally asymmetric simple exclusion process or TASEP (Duchi and Schaeffer, Journal of Combinatorial Theory, Series A, 110(2005), 1–29). We consider here the parallel TASEP, in which particles can jump simultaneously. On the one hand, the interest in this process comes from highway traffic modeling: it is the only solvable special case of the Nagel‐Schreckenberg automaton, the most popular model in that context. On the other hand, the parallel TASEP is of some theoretical interest because the derivation of its stationary distribution, as appearing in the physics literature, is harder than that of the standard TASEP. We offer here an elementary derivation that extends the combinatorial approach we developed for the standard TASEP. In particular, we show that this stationary distribution can be expressed in terms of refinements of Catalan numbers. © 2008 Wiley Periodicals, Inc. Random Struct. Alg., 2008     

Tracking elementary particles near their primary vertex: A combinatorial approach

Colliding beams experiments in High Energy Physics rely on solid state detectors to track the flight paths of charged elementary particles near their primary point of interaction. Reconstructing tracks in this region requires, per collision, a partitioning of up to 10³ highly correlated observations into an unknown number of tracks. We report on the successful implementation of a combinatorial track finding algorithm to solve this pattern recognition problem in the context of the ALEPH experiment at CERN. Central to the implementation is a 5-dimensional axial assignment model (AP5) encompassing noise and inefficiencies of the detector, whose weights of assignments are obtained by means of an extended Kalman filter. A preprocessing step, involving the clustering and geometric partitioning of the observations, ensures reasonable bounds on the size of the problems, which are solved using a branch & bound algorithm with LP relaxation. Convergence is reached within one second of CPU time on a RISC workstation in average.     

Poisson fields and distribution functions in the statistical mechanics of charged particles

A brief survey of the Poisson analysis on the spaces of tempered distributions is given and the generalized Wick theorem for Poisson fields is formulated. For systems of charged particles, new representations in terms of integrals with respect to the Poisson measure are obtained for distribution functions and diagonal elements of a reduced density matrix; these representations are convenient for investigation of model systems of statistical mechanics by the cluster expansion method. In the quantum case, the Boltzmann, Fermi-Dirac, and Bose-Einstein statistics are studied.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 47, No. 5, pp. 710–719, May, 1995.The author expresses his deep gratitude to A. L. Rebenko for posing the problem and for his attention to the work and to G. F. Us for helpful discussions.This research was partially supported by the International Science Foundation, grant No. UB3000.     

Propagation of Electromagnetic Waves in an Open Planar Dielectric Waveguide Filled with a Nonlinear Medium II: TM Waves

Computational Mathematics and Mathematical Physics - A nonlinear eigenvalue problem on an interval is considered. The nonlinearity in the equation is specified by a nonnegative monotonically...     

On orders in number fields: Picard groups,ring class fields and applications

We focus on orders in arbitrary number fields, consider their Picard groups and finally obtain ring class fields corresponding to them. The Galois group of the ring class field is isomorphic to the Picard group.As an application, we give criteria of the integral solvability of the diophantine equation p = x2+ ny2 over a class of imaginary quadratic fields where p is a prime element.     

Spectra of radiation for spinless and spin relativistic particles in strong magnetic fields

Synchro-curvature radiation put forward by Zhang and Cheng is a new and universal radiation mechanism, it describes in detail the radiation properties of a relativistic charged particle moving in a curved magnetic field. This new radiation generalizes all the classical results of ordinary synchrotron and curvature radiations and reveals inherent linkage and unification between them. Additionly, a general, simple and unitary formula is provided for discussing the radiation problem in research of pulsars. However, the magnitude of the magnetic field of a pulsar is so strong (10⁷-10⁹T) that the quantum effects cannot be neglected. The GFWW method developed recently by Lieu and Axford is applied to generalize the results of Zhang and Cheng. The quantum limited synchro-curvature radiation spectra for spinless K-G particles and spin-1/2 Dirac particles are presented, respectively. Their radiation properties are also discussed. Project supported by the National Natural Science Foundation of China and the National “Climbing Project”.     

Matrix multiplication and transformations: an APOS approach

This study presents a contribution to research in undergraduate teaching and learning of linear algebra, in particular, the learning of matrix multiplication. A didactical experience consisting on a modeling situation and a didactical sequence to guide students’ work on the situation were designed and tested using APOS theory. We show results of research on students’ activity and learning while using the sequence and through analysis of student’s work and assessment questions. The didactic sequence proved to have potential to foster students’ learning of function, matrix transformations and matrix multiplication. A detailed analysis of those constructions that seem to be essential for students understanding of this topic including linear transformations is presented. These results are contributions of this study to the literature.     

Class fields,Dirichlet characters, and extended genus fields of global function fields

We study the extended genus field of an abelian extension of a rational function field. We follow the definition of Anglès and Jaulent, which uses the class field theory. First, we show that the natural definition of extended genus field of a cyclotomic function field obtained by means of Dirichlet characters is the same as the one given by Anglès and Jaulent. Next, we study the extended genus field of a finite abelian extension of a rational function field along the lines of the study of genus fields of abelian extensions of rational function fields. In the absolute abelian case, we compare this approach with the one given by Anglès and Jaulent.     

SL(m,C)-equivariant and translation covariant continuous tensor valuations

The space of continuous, $\mathrm{SL}(m,\mathbb{C})$-equivariant, $m\ge 2$, and translation covariant valuations taking values in the space of real symmetric tensors on ${\mathbb{C}}^m?{\mathbb{R}}^{2m}$ of rank $r\ge 0$ is completely described. The classification involves the moment tensor valuation for $r\ge 1$ and is analogous to the known classification of the corresponding tensor valuations that are $\mathrm{SL}(2m,\mathbb{R})$-equivariant, although the method of proof cannot be adapted.     

Generic substitution policy,an incentive approach

Generic substitution policy has been adopted in several countries in order to control health expenditures. Using a model based on incentives, this work aims to analyze the response of doctors and pharmaceutical companies to the implementation of this policy. It is shown that after the implementation of GSP, the effort of doctor’s convincing the patient to take generics increase or decrease depending on his level of concern for patient well-being; pharmaceutical companies decrease the amount of detailing and the market share of generics tends to increase.     

Waves analysis and spatiotemporal pattern formation of an ecosystem model

In this paper, we consider a predator–prey model given by a reaction–diffusion system. This model incorporates Holling-type-II (Michaelis–Menten) and modified Leslie-Gower functional responses. We show the existence of qualitatively different types of system behaviors realized for various parameter values. Our model is investigated with methods of the qualitative theory and the theory of bifurcations. We generalize the traveling waves existence method for populations dynamics with positive derivative densities, to the predator–prey system in which growth densities may change sign. Parallel to this is a discussion and an analysis of alternative model outcomes such as complex pattern formation and spatio-temporal chaos behavior.