Noncommutative Dynamics of Random Operators

We continue our program of unifying general relativity and quantum mechanics in terms of a noncommutative algebra ${\cal A}$ on a transformation groupoid $\Gamma = E \times G$ where $E$ is the total space of a principal fibre bundle over spacetime, and $G$ a suitable group acting on $\Gamma$. We show that every $a \in {\cal A}$ defines a random operator, and we study the dynamics of such operators. In the noncommutative regime, there is no usual time but, on the strength of the Tomita-Takesaki theorem, there exists a one-parameter group of automorphisms of the algebra ${\cal A}$ which can be used to define a state dependent dynamics; i.e., the pair $({\cal A}, \phi)$, where $\phi$ is a state on ${\cal A}$, is a ``dynamic object''. Only if certain additional conditions are satisfied, the Connes-Nikodym-Radon theorem can be applied and the dependence on $\phi$ disappears. In these cases, the usual unitary quantum mechanical evolution is recovered. We also notice that the same pair $({\cal A}, \phi)$ defines the so-called free probability calculus, as developed by Voiculescu and others, with the state $\phi$ playing the role of the noncommutative probability measure. This shows that in the noncommutative regime dynamics and probability are unified. This also explains probabilistic properties of the usual quantum mechanics.Comment: 13 pages, LaTe

The Nature and Development of Giftedness

Following a short discussion of conceptual and theoretical problems of giftedness, the methodological foundations and selected results of a (presently) four year longitudinal study are presented. This study is based on a multidimensional concept of giftedness: intelligence, creativity, social competence, musical ability, psychomotor ability (or practical intelligence). Both academic achievements and leisure activities, as well as cognitive and motivational personality factors and school and family socialisation conditions relevant to giftedness, were studied. During the second project phase developmental aspects and achievement analyses of gifted and normal students aged 6 to 18 years were the central aspects of the study. Finally, methodological problems in the identification of gifted children and adolescents as well as consequences for the nurturing of giftedness are discussed

Apparatus and method for reducing thermal stress in a turbine rotor

A gas turbine is described wherein the thermal stresses in the turbine rotor are reduced. The rotor includes a central disc with a peripheral rim, and a plurality of blades extending radially outward from the rim. To reduce thermal stresses, a duct arrangement is provided which selectively directs hot gases from the turbine combustor to the rim during the turbine start up. The hot gases from the combustor serve to heat the rim, and decrease the start up period necessary to bring the temperature profile of the rotor into the operating temperature range. After the start up period, the duct arrangement is then used to direct cool gases from the turbine compressor to the rim of the rotor in order to maintain a lower rotor equilibrium temperature

The 300 H.P. Benz Aircraft Engine

A description is given of the Benz 12-cylinder aircraft engine. The 300 H.P. engine, with the cylinders placed at an angle of 60 degrees not only realizes a long-cherished conception, but has received refinement in detail. It may be described as a perfect example of modern German aircraft engine construction. Here, a detailed description is given of the construction of this engine. Emphasis is placed on the design and construction of the cylinders, pistons, and connecting rods. Also discussed are engine fitting, lubrication, oil pumps, bearings, the oil tank, fuel pump, carburetors, and cooling system