Generalized symmetric planes

In this paper we relate the theory of stable planes to the theory of generalized symmetric spaces in the sense of differential geometry where the symmetries may be of arbitrary order. This leads to the notion of a generalized symmetric plane. We assign to every generalized symmetric plane an associated infinitesimal model and show that the associated infinitesimal model essentially determines a generalized symmetric plane up to global isomorphism. In particular, every generalized symmetric plane with an abelian group of transvections is a topological translation plane.     

A topological representation of lattices

Presented by R. S. Pierce.     

The shadowgraph method in convection experiments

The shadowgraph method is applied to thermal convection experiments and electro-hydrodynamic convection (EHC) in nematic liquid crystals. In both cases convection leads to a spatially periodic field of the refractive index causing a spatially periodic intensity modulation of parallel light passing the cell. Close to the onset of convection the temperature or director field is given by linear stability analysis. Knowing these functions the determination of their amplitudes becomes possible by means of the shadowgraph method. The method is demostrated using various examples of thermal and EHC convection experiments.     

Parameters for bromination of pyrroles in bromoperoxidase-catalyzed oxidations

Ester-, cyano-, and carboxamide-substituted 1H-pyrroles undergo electrophilic aromatic bromination, if treated with hydrogen peroxide and sodium bromide at pH 6.2 and 20 °C. Oxidation of bromide under such conditions is catalyzed by a vanadate(V)-dependent bromoperoxidase, in a substrate/enzyme ratio of 32-63 μmol %. To obtain maximum yields of bromopyrroles (up to 91%) by spending least amount of substrates and catalyst, hydrogen peroxide and sodium bromide have to be added continuously to the enzyme and the 2-acceptor-substituted pyrrole (1.5 mmol) in a solution of morpholine-4-ethanesulfonic acid buffer. This technique was applied to prepare two marine natural products under biomimetic conditions, that is, methyl 4,5-dibromopyrrole-2-carboxylate (from Agelas oroides) and 4,5-dibromopyrrole-2-carboxamide (from Acanthella carteri).     

Parallel solution-phase synthesis of a 2-aminothiazole library including fully automated work-up

A straightforward and effective procedure for the solution phase preparation of a 2-aminothiazole combinatorial library is described. Reaction, work-up and isolation of the title compounds as free bases was accomplished in a fully automated fashion using the Chemspeed ASW 2000 automated synthesizer. The compounds were obtained in good yields and excellent purities without any further purification procedure.     

Operator geometric stable laws

Operator geometric stable laws are the weak limits of operator normed and centered geometric random sums of independent, identically distributed random vectors. They generalize operator stable laws and geometric stable laws. In this work we characterize operator geometric stable distributions, their divisibility and domains of attraction, and present their application to finance. Operator geometric stable laws are useful for modeling financial portfolios where the cumulative price change vectors are sums of a random number of small random shocks with heavy tails, and each component has a different tail index.