Dyadic exercises for octahedral extensions II

Rédei fields and dyadic extensions

For an arbitrary non-square discriminant D, the Rédei field Γ0(D) is introduced as an extension of K = Q( √ D) analogous to the genus field and connected with the Rédei-Reichardt Theorem. It is shown how to compute Rédei fields, and this is used to find socles of dyadic extensions of K for negative D. Finally, a theorem and two conjectures are presented relating the fields Q( √ −p) and Q( √ −2p...

Octahedral Crystals in Phycomyces. Ii

"Phycomyces blakesleeanus" sporangiophores contain octahedral crystals throughout their cytoplasm and vacuole. More octahedral crystals were found in the wild-type strain G5 (+) than in the beta-carotene-deficient mutant C5 (-), and much more than in the mutant C141 (-), which is sensitive to only high light intensity. In the wild type, the number of crystals per sporangiophore increased until ...

Exercises for Asset Pricing II Spring 2005

Octahedral ruthenium (II) polypyridyl complexes as antimicrobial agents against mycobacterium

Tuberculosis is one of the world's deadliest infectious disease with 1.5 millions deaths annually. It is imperative to discover novel compounds with potent activity against M. tuberculosis. In this study, susceptibilities of M. smegmatis to the octahedral ruthenium(II) polypyridyl complexes, 1 {[(bpy)3Ru] (PF6)2 (bpy = 2,2'-bipyridine)}, 2 {[(phen)2Ru(dppz)](PF6)2 (phen = 1,10-phenanthroline, d...

Induced Modules and Extensions of Representations, Ii

Grothendieck [7] showed that finite dimensional vector bundles over the projective line split into direct sums of line bundles (see also Andersen [1]). We begin this paper, after two preliminary sections, by proving this result (Theorem (3.5)) for induced bundles using representation theoretic techniques. The proof yields partial results in the infinite dimensional case and leads to the definit...