Star product and contact Weyl manifold

Contact algebra is introduced, which is a Lie algebra given as a one-dimesional exrention of a Weyl algebra. A contact Lie algebra bundle called a contact Weyl manifold is considered over a symplectic manifold which contains a Weyl manifold as a subbundle. A relationship is discussed between deformation quantization on s symplectic manifold and a Weyl manifold over the symplectic manifold. The contact Weyl manifold has a canonical connection which gives rise the relation, and is regarded as an extension of Fedosov connection

Effect of Heat Treatment on the Serration of Low-Concentrated Al-Zn Alloys

The effect of heat-treatment conditions on occurrence of serration in Al-Zn alloys was investigated. Specimens were aged for various times up to 2.6Ms at 293K or 273K after quenching from various temperatures (T(Q)), 473K to 853K, and tensile-tested at room temperature. Serration occurred more easily according as T(Q) became lower and the aging time became shorter: in the case that T(Q)=473K serration was observed even after aging for 2.6Ms, while in the case that T(Q)=773K serration did not occur irrespective of aging conditions. Serration was also recognized when the specimens were furnace-cooled from 773K to room temperature. These results together with those obtained by the electrical resistometry suggest that the serration in the low'concentrated Al-Zn alloy is caused by the formation of small GP zones whose Guinier radius is less than 1nm or some sort of solute clusters

Expressions of algebra elements and transcendental noncommutative calculus

Ideas from deformation quantization are applied to deform the expression of elements of an algebra. Extending these ideas to certain transcendental elements implies that \frac{1}{i\h}uv in the Weyl algebra is naturally viewed as an indeterminate living in a discrete set $\mathbb{N}{+}{1/2}$ {\it or} ${-}(\mathbb{N}{+}{1/2})$ . This may yield a more mathematical understanding of Dirac's positron theory