Grasshoppers Feeding on Red Pine Trees in Michigan (Orthoptera: Acrididae)

Very few North American grasshoppers are true feeders on conifers. The several species of the punctulatus species-group of the genus Melanoplus, as summarized and revised by Rehn (1946), have been reported as occurring on pine, juniper, and cedar, but few reports of actual feeding on conifers have appeared in the literature. Because of this paucity of information regarding the use of conifers as food for grasshoppers, we summarize here observations of several kinds of grasshoppers feeding on red pine (Pinus resinosa Aiton) in 1966 in Michigan

Single-photon exchange interaction in a semiconductor microcavity

We consider the effective coupling of localized spins in a semiconductor quantum dot embedded in a microcavity. The lowest cavity mode and the quantum dot exciton are coupled and close in energy, forming a polariton. The fermions forming the exciton interact with localized spins via exchange. Exact diagonalization of a Hamiltonian in which photons, spins and excitons are treated quantum mechanically shows that {\it a single polariton} induces a sizable indirect exchange interaction between otherwise independent spins. The origin, symmetry properties and the intensity of that interaction depend both on the dot-cavity coupling and detuning. In the case of a (Cd,Mn)Te quantum dot, Mn-Mn ferromagnetic coupling mediated by a single photon survives above 1 K whereas the exciton mediated coupling survives at 15 K.Comment: 4 pages, 3 figure

Projective equivalence of ideals in Noetherian integral domains

Let I be a nonzero proper ideal in a Noetherian integral domain R. In this paper we establish the existence of a finite separable integral extension domain A of R and a positive integer m such that all the Rees integers of IA are equal to m. Moreover, if R has altitude one, then all the Rees integers of J = Rad(IA) are equal to one and the ideals J^m and IA have the same integral closure. Thus Rad(IA) = J is a projectively full radical ideal that is projectively equivalent to IA. In particular, if R is Dedekind, then there exists a Dedekind domain A having the following properties: (i) A is a finite separable integral extension of R; and (ii) there exists a radical ideal J of A and a positive integer m such that IA = J^m.Comment: 20 page