Localized Induction Equation for Stretched Vortex Filament

We study numerically the motion of the stretched vortex filaments by using the localized induction equation with the stretch and that without the stretch.Comment: Published in SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) at http://www.emis.de/journals/SIGMA

Calculations of Cotton Effects in the Vacuum UV Region for Aldonic Acid 1,4-Lactones and Interpretations of Hudson\u27s Lactone Rule

A graphic method of Drude equation was applied to a series of aldonic acid 1,4-lactones 1-7 to investigate possible Cotton effects below 200nm. The calculation shows three bands at 220nm, 170 nm and 130 nm to reflect the stereochemistries at C-2, C-4 and rtng conformations and vicinal OH at C-3 and C-4, respectively. The sum of the rotational contributions at 589 nm of these bands explained the applicability of Hudson\u27s lactone rule in sugar lactones

Calculations of Cotton Effects in the Vacuum UV Region for Chilar v-Lactones. Correlation with the Absolute Stereochemistry

A graphic method of Drude equations was applied to calculate the Cotton effects below 180 nm region for various types of aand/ er y-substituted-y-lactones 1-10. The Cotton effects at ca. 170 nm were found to reflect the stereochemistry at C-2 (negative for f3 and positive for a) and C-4 (positive for f3 and negative for a) as well as the ring conformation (positive for E3 and negative for 3E) of which rotational contributions at 589 nm were suggested as the origin of Hudson\u27s lactone rule