Occupational Redemption

In Occupational Hazards in the February 1981 Word Ways, Richard E. Douglass suggests that various jobholders can be gotten rid of in ways more euphemistically ambiguous than simply being fired, canned, or sacked. For the most part, he plays upon the semantic properties of absorbed roots conjoined with the negative prefixes de- and dis- and shows how a nobleman would be discounted, distributed or subject to delivery and a tennis player disadvantaged or defaulted (or, we add, deserved or deduced). In a more optimistic vein, let us ask ourselves how, using the prefix re- and the suffix -ed, we can describe the reinstatement to their jobs of the following people

Components of Gr\"obner strata in the Hilbert scheme of points

We fix the lexicographic order $\prec$ on the polynomial ring $S=k[x_{1},...,x_{n}]$ over a ring $k$. We define \Hi^{\prec\Delta}_{S/k}, the moduli space of reduced Gr\"obner bases with a given finite standard set $\Delta$, and its open subscheme \Hi^{\prec\Delta,\et}_{S/k}, the moduli space of families of #\Delta points whose attached ideal has the standard set $\Delta$. We determine the number of irreducible and connected components of the latter scheme; we show that it is equidimensional over ${\rm Spec}\,k$; and we determine its relative dimension over ${\rm Spec} k$. We show that analogous statements do not hold for the scheme \Hi^{\prec\Delta}_{S/k}. Our results prove a version of a conjecture by Bernd Sturmfels.Comment: 49 page

The States We\u27re In

Celebrated June 14, Flag Day commemorates the adoption by the Continental Congress of the Stars and Stripes in 1777 as the official flag of America. The thirteen stripes on the flag represent the original colonies and the fifty stars the united states of the United States

What do You Call a Naked Grizzly?

Homophones are words that sound alike but are spelled differently and have different meanings. Examples of sound-alike words are flair and flare, colonel and kernel, and poor, pore and pour. Here is a puzzle designed to test your ear for homophones

The Quantum Hall Effect of Field Induced Spin Density Wave Phases: the Physics of the Ultra Quantum Crystal

The Quantum Hall Effect of Field Induced Spin Density Wave Phases is accounted for within a weak coupling theory which assumes that in the relevant low temperature part of the phase diagram the quasi one dimensional conductor is well described by Fermi liquid theory. Recent experimental results show that sign inversion of the Hall Plateaux takes place all the way down from the instability line of the normal state. The Quantum Nesting model, when it takes into account small perturbations away from perfect nesting, describes well not only the usual sequence of Hall plateaux, but also the anomalies connected with sign inversion of the Hall Effect. Experimental observation of de-doubling of sub-phase to sub-phase transition lines suggests that superposition of SDW order parameters occurs in some parts of the phase diagram. The collective excitations of the Ultra Quantum Crystal have a specific magneto-roton structure. The SDW case exhibits,apart from the usual spin waves, topological excitations which are either skyrmions or half skyrmions. It is suggested that magneto-rotons may have been observed some years ago in specific heat experiments.Comment: 17 pages, latex, 6 figures, available on request at [email protected]