Heisenberg revisited

Heisenberg–Weyl algebra revisited: Combinatorics of words and paths

The Heisenberg–Weyl algebra, which underlies virtually all physical representations of Quantum Theory, is considered from the combinatorial point of view. We provide a concrete model of the algebra in terms of paths on a lattice with some decomposition rules. We also discuss the rook problem on the associated Ferrers board; this is related to the calculus in the normally ordered basis. From thi...

QUICKSELECT Revisited

We give an overview of the running time analysis of the random divide-and-conquer algorithm FIND or QUICKSELECT. The results concern moments, distribution of FIND’s running time, the limiting distribution, a stochastic bound and the key: a stochastic fixed point equation.

PENDRED\'S SYNDROME REVISITED

Pendred's syndrome is defined as a triad of congenital perceptive hearing loss, goiter, and abnormal perchlorate test. Three brothers with Pendred's syndrome [P.S.] are reported. The oldest brother has hearing loss (he has been deaf and mute since childhood) and has a large goiter. A thyroid scan revealed euthyroid multinodular goiter and a perchlorate test was performed, and reported abno...

A Necessary Condition for Weyl-Heisenberg Frames

USHER\'S SYNDROME REVISITED

Usher's syndrome is a genetically inherited autosomal recessive disorder resulting in the double handicap of deafness and progressive blindness, known as retinitis pigmentosa. The disease is also associated with psychoses, mental retardation, and other major neurophysiological changes. It appears to be more common among Jewish individuals and consanguinous marriages. While it is rare in th...