Hysteresis and Eddy-current Relaxation in SiFe Materials

The rate-dependent effects in metallic ferromagnetic materials with magnetization processes attributed to domain-walls motion were studied. The experimental method for eddy-current relaxation time determination was proposed. Some discrepancies between the data and theoretical predictions were observed and discussed. The origin of these discrepancies is accounted for by the decrease of viscous-type relaxation process as the rate of change of averaged magnetization is approaching zero.     

Tensor Products of Quantum Structures and Their Applications in Quantum Measurements

Tensor products of quantum logics and effect algebras with some known problems are reviewed. It is noticed that although tensor products of effect algebras having at least one state exist, in the category of complex Hilbert space effect algebras similar problems as with tensor products of projection lattices occur. Nevertheless, if one of the two coupled physical systems is classical, tensor product exists and can be considered as a Boolean power. Some applications of tensor products (in the form of Boolean powers) to quantum measurements are reviewed.     

Generalized Mukai conjecture for special Fano varieties

Let X be a Fano variety of dimension n, pseudoindex i _X and Picard number ρ_X. A generalization of a conjecture of Mukai says that ρ_X(i _X −1)≤n. We prove that the conjecture holds for a variety X of pseudoindex i _X ≥n+3/3 if X admits an unsplit covering family of rational curves; we also prove that this condition is satisfied if ρ_X> and either X has a fiber type extremal contraction or has not small extremal contractions. Finally we prove that the conjecture holds if X has dimension five.     

A preconditioned domain decomposition algorithm for the solution of the elliptic Neumann problem

A new preconditioned conjugate gradient (PCG)-based domain decomposition method is given for the solution of linear equations arising in the finite element method applied to the elliptic Neumann problem. The novelty of the proposed method is in the recommended preconditioner which is constructed by using cyclic matrix. The resulting preconditioned algorithms are well suited to parallel computation.     

Asymptotic conditions for the electromagnetic form factors of hadrons represented by the VMD model

A system of linear homogeneous algebraic equations for the coupling constant ratios of vector mesons to hadrons is derived by imposing the assumed asymptotic behavior upon the VMD pole parameterization of an hadron electromagnetic form factor. A similar system of equations with a simpler structure of the coefficients, taken as even powers of the vector-meson masses, is derived by means of integral superconvergent sum rules for the imaginary part of the considered form factor using its appropriate -function approximation. Although both systems have been derived starting from different properties of the electromagnetic form factor and they each have their own appearances, it is shown explicitly that they are fully equivalent. Received: 20 March 2002 / Revised version: 3 December 2002 / Published online: 7 March 2003     

Addendum and Corrigendum to "Local Saturation of Conservative Operators'

In this note we make a correction in the paper [1] by two of the authors. Specifically we modify an auxiliary localization result and prove that the applications to the saturation theory of some outstanding conservative operators remain valid. Moreover, we enrich a corollary dealing with the well-known Szász-Mirakjan operators. This revised version was published online in June 2006 with corrections to the Cover Date.     

On the Hahn--Mazurkiewicz theorem

The following generalization of the Hahn-Mazurkiewicz theorem is proved: Let (E,e) be a locally compact locally connected metric space. Let M be a continuum in this space and let d,e∈ M. Then there is a continuous mapping f: [0,1]→E such that f(0) = d, f(1)= e and M⊂f([0,1]). Also some corollaries of this theorem are proved.     

Semi-implicit complementary volume scheme for solving level set like equations in image processing and curve evolution

Summary. We introduce linear semi-implicit complementary volume numerical scheme for solving level set like nonlinear degenerate diffusion equations arising in image processing and curve evolution problems. We study discretization of image selective smoothing equation of mean curvature flow type given by Alvarez, Lions and Morel ([3]). Solution of the level set equation of Osher and Sethian ([26], \[30]) is also included in the study. We prove and estimates for the proposed scheme and give existence of its (generalized) solution in every discrete time-scale step. Efficiency of the scheme is given by its linearity and stability. Preconditioned iterative solvers are used for computing arising linear systems. We present computational results related to image processing and plane curve evolution. Received April 25, 2000 / Revised version received June 11, 2001 / Published online November 15, 2001     

Derivation of the k–ε model for locally homogeneous turbulence by homogenization techniques

We derive the incompressible and compressible k–ε model for locally homogeneous turbulence. The model is rigorously derived on formal mathematical grounds using the MPP modelling technique. This lets us calculate by either analytical or numerical means the closure constants of the model. To cite this article: T. Chacón Rebollo, D. Franco Coronil, C. R. Acad. Sci. Paris, Ser. I 337 (2003).