Potential theory for quasiliniear elliptic equations

We discuss the potential theory associated with the quasilinear elliptic equation $$-{ m div}(A(x,abla u))+B(x,u)=0.$$ We study the validity of Bauer convergence property, the Brelot convergence property. We discuss the validity of the Keller-Osserman property and the existence of Evans functions

Strong nonmontonicity of the picard dimension

Boukricha A, Hansen W. Strong nonmontonicity of the picard dimension. Communications in Partial Differential Equations . 1995;20(3-4):567-590

Martin boundary for Schrödinger operators with singularity

Boukricha A, Hansen W. Martin boundary for Schrödinger operators with singularity. Mathematische Annalen. 1994;300(1):573-587

Mathematical Modeling for scalar sscalar interface problems between dielectric and metamaterial

International audienceSome electromagnetic materials have, in a given frequency range, an e ective dielectric permittivity and/or a magnetic permeability which are real-valued negative coe cients when dissipa- tion is neglected. They are usually called metamaterials. We study a scalar transmission problem between a classical dielectric material and a metamaterial, set in an open, bounded subset of R

Mathematical Modeling for scalar sscalar interface problems between dielectric and metamaterial

International audienceSome electromagnetic materials have, in a given frequency range, an e ective dielectric permittivity and/or a magnetic permeability which are real-valued negative coe cients when dissipa- tion is neglected. They are usually called metamaterials. We study a scalar transmission problem between a classical dielectric material and a metamaterial, set in an open, bounded subset of R

Finite elements method for solving a cloaked problem

International audienceThe main objective of this paper is to design a novel finite element discretization for simulating two-dimensional acoustic cloaking devices. A simple numerical experiment can illustrate that a direct application of Lagrange finite elements to study cloaking devices can lead to inaccurate solutions

On Mathematical Modeling of Cloaking

International audienceIn this paper we present a rigorous derivation of the material parameters for both the cylinder and rectangle cloaking structures. Numerical results using these material parameters are presented to demonstrate the cloaking e ffect.

Empathy and its modulation in a virtual human

Boukricha H, Wachsmuth I, Carminati MN, Knoeferle P. Empathy and its modulation in a virtual human. In: Timm IJ, Thimm M, eds. KI 2013: Advances in Artificial Intelligence. LNAI. Vol 8077. Berlin, Heidelberg: Springer; 2013: 25-36.Endowing artificial agents with the ability to empathize is believed to enhance their social behavior and to make them more likable, trustworthy, and caring. Neuropsychological findings substantiate that empathy occurs to different degrees depending on several factors including, among others, a person’s mood, personality, and social relationships with others. Although there is increasing interest in endowing artificial agents with affect, personality, and the ability to build social relationships, little attention has been devoted to the role of such factors in influencing their empathic behavior. In this paper, we present a computational model of empathy which allows a virtual human to exhibit different degrees of empathy. The presented model is based on psychological models of empathy and is applied and evaluated in the context of a conversational agent scenario

The picard principle and the behaviour of continuous solutions of the Schroedinger equation at an isolated singularity

Supported by Stiftung VolkswagenwerkSIGLECopy held by FIZ Karlsruhe; available from UB/TIB Hannover / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekDEGerman