Entropy of a fibered dynamical system

The entropy of the geodesic flow associated to a fibered dynamical system is shown to be zero; in particular the entropy of a quantizable dynamical system is zero. An ergodic dynamical system which defines a quantizable dynamical system is outlined.This research was supported in part by NSF GP-20856 A 1     

Alkylidenebis-1-methyl-2-alkylidenehydrazines as intermediates in the reaction of methylhydrazine with aliphatic aldehydes

It has been shown that heptylidenebis-1-methyl-2-heptylidenehydrazine (Va) is an intermediate in the reaction of methylhydrazine with heptanal. The bis-compound (Va) reacts with methylhydrazine to give heptanal methylhydrazone (IIa), or with heptanal, in the presence of acid, to afford 5-hexyl-1-methyl-4-pentyl-2-pyrazoline (Ia). The latter also results from the treatment of IIa with acid.     

Optimal Claiming on Vehicle Insurance Revisited

Most motorists involved in an accident will claim from their insurance company only if the cost of repair exceeds a certain amount. In this paper, optimal no-claim limits are determined for a common type of insurance policy, and a simple decision rule which might be used by a motorist is shown to have an expected cost very close to the optimal decision rule.     

Free convection from a horizontal line source of heat

Summary In this paper a study is made of finite Grashof number effects upon the flow, in an unbounded domain, in the buoyant plume which forms over a horizontal line source of heat. The consequences of introducing a plane boundary into the domain are also assessed for two particular configurations.

---

Zusammenfassung In dieser Arbeit wird der Effekt der endlichen Grashof-Zahl auf die Strömung untersucht, in einem unbegrenzten Medium mit natürlicher Konvektion, die durch eine horizontale linienförmige Quelle erzeugt wird. Die Folgen einer ebenen Begrenzungsfläche werden für zwei besondere Konfigurationen untersucht.

     

Determination of deuterium in organic compounds by infrared spectrophotometry

The Trenner-Arison-Walker method for the micro-analysis of deuterium in organic compounds involves oxidation of the compound with copper oxide in a sealed tube, collection of the water by vacuum distillation, and analysis of the water by infrared spectrophotometry. Experience in applying this technique to a variety of organic compounds in our laboratory has suggested a number of procedural modifications. These principally affect the methods of sample handling and water collection. Difficulties associated with temperature changes on the spectrophotometry of the deuterium-enriched water are overcome by differential analysis against natural-abundance water using a double-beam spectrophotometer.     

He(I)/He(II) photoelectron band intensity ratios for simple organic molecules

Band intensifies in the He(I) and HE(II) photoelectron spectra of some simple organic molecules (methanol, methylamine, formaldehyde, acetaldehyde, formic acid, acetic acid, methyl formate, ethylene, butadiene and methyl isothiocyanate) have been measured. The relative band intensity ratios for a number of ionizations from n and π orbitals are presented.