Polar Varieties and Efficient Real Equation Solving: The Hypersurface Case

The objective of this paper is to show how the recently proposed method by Giusti, Heintz, Morais, Morgenstern, Pardo \cite{gihemorpar} can be applied to a case of real polynomial equation solving. Our main result concerns the problem of finding one representative point for each connected component of a real bounded smooth hypersurface. The algorithm in \cite{gihemorpar} yields a method for symbolically solving a zero-dimensional polynomial equation system in the affine (and toric) case. Its main feature is the use of adapted data structure: Arithmetical networks and straight-line programs. The algorithm solves any affine zero-dimensional equation system in non-uniform sequential time that is polynomial in the length of the input description and an adequately defined {\em affine degree} of the equation system. Replacing the affine degree of the equation system by a suitably defined {\em real degree} of certain polar varieties associated to the input equation, which describes the hypersurface under consideration, and using straight-line program codification of the input and intermediate results, we obtain a method for the problem introduced above that is polynomial in the input length and the real degree.Comment: Late

Convergence of simple adaptive Galerkin schemes based on h − h/2 error estimators

We discuss several adaptive mesh-refinement strategies based on (h − h/2)-error estimation. This class of adaptivemethods is particularly popular in practise since it is problem independent and requires virtually no implementational overhead. We prove that, under the saturation assumption, these adaptive algorithms are convergent. Our framework applies not only to finite element methods, but also yields a first convergence proof for adaptive boundary element schemes. For a finite element model problem, we extend the proposed adaptive scheme and prove convergence even if the saturation assumption fails to hold in general

Temperature Dependence Of The Electrical Resistivity Of LaxLu1-xAs

We investigate the temperature-dependent resistivity of single-crystalline films of LaxLu1-xAs over the 5-300 K range. The resistivity was separated into lattice, carrier and impurity scattering regions. The effect of impurity scattering is significant below 20 K, while carrier scattering dominates at 20-80 K and lattice scattering dominates above 80 K. All scattering regions show strong dependence on the La content of the films. While the resistivity of 600 nm LuAs films agree well with the reported bulk resistivity values, 3 nm films possessed significantly higher resistivity, suggesting that interfacial roughness significantly impacts the scattering of carriers at the nanoscale limit. (C) 2013 Author(s). All article content, except where otherwise noted, is licensed under a Creative Commons Attribution 3.0 Unported License.Microelectronics Research Cente