Measurement and self-adjoint operators

The approximations of classical mechanics resulting from quantum mechanics are richer than a correspondence of classical dynamical variables with self-adjoint Hilbert space operators. Assertion that classical dynamic variables correspond to self-adjoint Hilbert space operators is disputable and sets unnatural limits on quantum mechanics. Well known examples of classical dynamical variables not associated with self-adjoint Hilbert space operators are discussed as a motivation for the realizations of quantum field theory that lack Hermitian field operators but exhibit interaction.Comment: 17 page

AGRO-ETHICS: EXTENSION, RESEARCH, AND TEACHING

Teaching/Communication/Extension/Profession,

On Universal Cycles for Multisets

A Universal Cycle for t-multisets of [n]={1,...,n} is a cyclic sequence of $\binom{n+t-1}{t}$ integers from [n] with the property that each t-multiset of [n] appears exactly once consecutively in the sequence. For such a sequence to exist it is necessary that n divides $\binom{n+t-1}{t}$, and it is reasonable to conjecture that this condition is sufficient for large enough n in terms of t. We prove the conjecture completely for t in {2,3} and partially for t in {4,6}. These results also support a positive answer to a question of Knuth.Comment: 14 pages, two figures, will appear in Discrete Mathematics' special issue on de Bruijn Cycles, Gray Codes and their generalizations; paper revised according to journal referees' suggestion

Abandon Ship

The clear notes of the bugle sounding chow call came over the loudspeakers throughout the ship. I stood waiting in the mess line, formed topside on the main deck aft. The last rays of the sun caught the signal flags flying - gave them a brilliant cast of red, green and yellow. The new cruiser rolled in the huge swells, leaving a foaming white trail behind her. The men stood silently gazing at the horizon. The ship gave a slight shudder each time one of the swells crashed into her. The sharp clanging of the ship\u27s general-alarm bell, followed by the shrill call of the bugle, broke the silence. All hands, man your battle stations! blared from the loud speaker

Managed Haying and Grazing of CRP

Agricultural and Food Policy,