Resultant

Summary

In mathematics, the resultant of two polynomials is a polynomial expression of their coefficients that is equal to zero if and only if the polynomials have a common root (possibly in a field extension), or, equivalently, a common factor (over their field of coefficients). In some older texts, the resultant is also called the eliminant. The resultant is widely used in number theory, either directly or through the discriminant, which is essentially the resultant of a polynomial and its derivative. The resultant of two polynomials with rational or polynomial coefficients may be computed efficiently on a computer. It is a basic tool of computer algebra, and is a built-in function of most computer algebra systems. It is used, among others, for cylindrical algebraic decomposition, integration of rational functions and drawing of curves defined by a bivariate polynomial equation. The resultant of n homogeneous polynomials in n variables (also called multivariate resultant, or Macaulay's r

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Voyage au centre de la mer, vers un archipel industriel

Muriz Djurdjevic

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Comparison of In Situ Micromechanical Strain-Rate Sensitivity Measurement Techniques

Xavier Maeder, Johann Michler, Stefano Mischler

Strain-rate sensitivity (SRS) measurements using transient small-scale techniques are becoming increasingly popular for investigating nanostructured films and microcomponents since they can provide fundamental insights into the plastic deformation mechanisms within small volumes of material. Previously, researchers have typically used either nanoindentation or microcompression strain-rate jump tests on a variety of nanostructured materials and compared the resultant values with bulk compression data as a reference. However, no systematic comparison of the different transient micromechanical techniques has been performed on the same material to establish their relative merits or the consistency of their results. In this study, the SRS of nanocrystalline nickel is investigated using three independent, in situ, transient experimental techniques: miniature tension, nanoindentation, and micropillar compression. The obtained SRS exponents m measured by all techniques were found to be in good agreement, and the resulting apparent activation volume V-app of approximately 10 b(3) is consistent with grain boundary diffusion processes and dislocation glide-based plasticity.

Springer Verlag2015

Multi-stream approaches have proven to be very successful in speech recognition tasks and to a certain extent in speaker authentication tasks. In this study we propose a noise-robust multi-stream text-independent speaker authentication system. This system has two steps: first train the stream experts under clean conditions and then train the combination mechanism to merge the scores of the stream experts under both clean and noisy conditions. The idea here is to take advantage of the rather predictable reliability and diversity of streams under different conditions. Hence, noise-robustness is mainly due to the combination mechanism. This two-step approach offers several practical advantages: the stream experts can be trained in parallel (e.g., by using several machines); heterogeneous types of features can be used and the resultant system can be robust to different noise types (wide bands or narrow bands) as compared to sub-streams. An important finding is that a trade-off is often necessary between the overall good performance under all conditions (clean and noisy) and good performance under clean conditions. To reconcile this trade-off, we propose to give more emphasis or prior to clean conditions, thus, resulting in a combination mechanism that does not deteriorate under clean conditions (as compared to the best stream) yet is robust to noisy conditions.

IDIAP2004