Über algebraische Gleichungen,die nur Wurzeln mit negativen Realteilen besitzen

Ohne Zusammenfassung     

Über das Riemannsche Summierungsverfahren

Ohne Zusammenfassung     

Über die Nullstellen einiger Klassen von Polynomen

Ohne Zusammenfassung     

Sur les fonctions méromorphes limites de fonctions rationnelles

Sans résumé     

Über die absolute Summierung der Dirichletschen Reihen

Ohne Zusammenfassung     

Mutual influence of LDPE and PP in their blends during crystallization

An indication for the mutual influence of LDPE and PP was the change of the morphology parameters of PE and PP at different ratios of the polymers in blends. That influence depends on the blend composition and is different for PE and PP. It is especially interesting in the blend PE75/PP25 where the influence between PE and PP shows dependence also on the sample geometry. Melting parameters, non-isothermal crystallization parameters - crystallization peak temperature T_c, crystallization begin temperature T_onset, half-width w_1/2 of the crystallization peak, degree of crystallinity α and crystallization rate coefficient CRC, as well as the isothermal kinetics parameters showed dependence on the blend composition. It was established that PE is more stable then PP concerning the mutual influence of both polymers on their crystallization. It was established that PE affects the crystal nucleation of PP and causes a decreasing of PP spherulite size.     

Large ∣k∣ Behavior of Complex Geometric Optics Solutions to d-bar Problems

Complex geometric optics solutions to a system of d-bar equations appearing in the context of electrical impedance tomography and the scattering theory of the integrable Davey-Stewartson II equations are studied for large values of the spectral parameter k. For potentials $q\in {⟨\cdot ⟩}^{-2}{H}^s\left(ℂ\right)$ for some $s\in \left]1,2\right]$, it is shown that the solution converges as the geometric series in $1/{\left|k\right|}^{s-1}$. For potentials q being the characteristic function of a strictly convex open set with smooth boundary, this still holds with s = 3/2, i.e., with $1/\sqrt{\mid k\mid }$ instead of $1/{\left|k\right|}^{s-1}$. The leading-order contributions are computed explicitly. Numerical simulations show the applicability of the asymptotic formulae for the example of the characteristic function of the disk. © 2022 Courant Institute of Mathematics and Wiley Periodicals LLC.