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Conical diffraction by multilayer gratings: A recursive integral equation approach

Gunther Schmidt (2013)

Applications of Mathematics

The paper is devoted to an integral equation algorithm for studying the scattering of plane waves by multilayer diffraction gratings under oblique incidence. The scattering problem is described by a system of Helmholtz equations with piecewise constant coefficients in ℝ 2 coupled by special transmission conditions at the interfaces between different layers. Boundary integral methods lead to a system of singular integral equations, containing at least two equations for each interface. To deal with...

Conjetura de Kato sobre los abiertos de R.

Pascal Auscher, Philippe Tchamitchian (1992)

Revista Matemática Iberoamericana

We prove Kato's conjecture for second order elliptic differential operators on an open set in dimension 1 with arbitrary boundary conditions. The general case reduces to studying the operator T = - d/dx a(x) d/dx on an interval, when a(x) is a bounded and accretive function. We show for the latter situation that the domain of T is spanned by an unconditional basis of wavelets with cancellation properties that compensate the action of the non-regular function a(x).

Connecting orbits of time dependent Lagrangian systems

Patrick Bernard (2002)

Annales de l’institut Fourier

We generalize to higher dimension results of Birkhoff and Mather on the existence of orbits wandering in regions of instability of twist maps. This generalization is strongly inspired by the one proposed by Mather. However, its advantage is that it contains most of the results of Birkhoff and Mather on twist maps.

Connections between real polynomial solutions of hypergeometric-type differential equations with Rodrigues formula

Hans Weber (2007)

Open Mathematics

Starting from the Rodrigues representation of polynomial solutions of the general hypergeometric-type differential equation complementary polynomials are constructed using a natural method. Among the key results is a generating function in closed form leading to short and transparent derivations of recursion relations and addition theorem. The complementary polynomials satisfy a hypergeometric-type differential equation themselves, have a three-term recursion among others and obey Rodrigues formulas....

Conservation law constrained optimization based upon front-tracking

Martin Gugat, Michaël Herty, Axel Klar, Gunter Leugering (2006)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

We consider models based on conservation laws. For the optimization of such systems, a sensitivity analysis is essential to determine how changes in the decision variables influence the objective function. Here we study the sensitivity with respect to the initial data of objective functions that depend upon the solution of Riemann problems with piecewise linear flux functions. We present representations for the one–sided directional derivatives of the objective functions. The results can be used...

Conservation law constrained optimization based upon Front-Tracking

Martin Gugat, Michaël Herty, Axel Klar, Gunter Leugering (2007)

ESAIM: Mathematical Modelling and Numerical Analysis

We consider models based on conservation laws. For the optimization of such systems, a sensitivity analysis is essential to determine how changes in the decision variables influence the objective function. Here we study the sensitivity with respect to the initial data of objective functions that depend upon the solution of Riemann problems with piecewise linear flux functions. We present representations for the one–sided directional derivatives of the objective functions. The results can be used...

Currently displaying 421 – 440 of 875