MS FT-2-2 7 Orthogonal polynomials and quadrature: Theory, computation, and applications

Quadrature rules find many applications in science and engineering. Their analysis is a classical area of applied mathematics and continues to attract considerable attention. This seminar brings together speakers with expertise in a large variety of quadrature rules. It is the aim of the seminar to provide an overview of recent developments in the analysis of quadrature rules. The computation of error estimates and novel applications also are described

Generalized averaged Gaussian quadrature and applications

A simple numerical method for constructing the optimal generalized averaged Gaussian quadrature formulas will be presented. These formulas exist in many cases in which real positive GaussKronrod formulas do not exist, and can be used as an adequate alternative in order to estimate the error of a Gaussian rule. We also investigate the conditions under which the optimal averaged Gaussian quadrature formulas and their truncated variants are internal

UVR8 mediated spatial differences as a prerequisite for UV-B induced inflorescence phototropism

In Arabidopsis hypocotyls, phototropins are the dominant photoreceptors for the positive phototropism response towards unilateral ultraviolet-B (UV-B) radiation. We report a stark contrast of response mechanism with inflorescence stems with a central role for UV RESISTANCE LOCUS 8 (UVR8). The perception of UV-B occurs mainly in the epidermis and cortex with a lesser contribution of the endodermis. Unilateral UV-B exposure does not lead to a spatial difference in UVR8 protein levels but does cause differential UVR8 signal throughout the stem with at the irradiated side 1) increase of the transcription factor ELONGATED HYPOCOTYL 5 (HY5), 2) an associated strong activation of flavonoid biosynthesis genes and flavonoid accumulation, 3) increased GA2oxidase expression, diminished gibberellin1 levels and accumulation of DELLA protein REPRESSOR OF GA1 (RGA) and, 4) increased expression of the auxin transport regulator, PINOID, contributing to local diminished auxin signalling. Our molecular findings are in support of the Blaauw theory (1919), suggesting that differential growth occurs trough unilateral photomorphogenic growth inhibition. Together the data indicate phototropin independent inflorescence phototropism through multiple locally UVR8-regulated hormone pathways