Note on the nature of cosmic rays

The recent experiments of Bothe and Kolhoerster(1) have led to an important and interesting conclusion. The ionization phenomena, by means of which cosmic rays are measured, are produced by highly penetrating corpuscular rays. It remains, however, an open question whether this corpuscular radiation is identical with the cosmic rays themselves, or is secondary in its nature, produced by primary rays of an electromagnetic character. Bothe and Kolhoerster admit both possibilities, but they seem to lean toward the first, owing to the fact that their corpuscular rays show a penetration of the same order of magnitude as that of the cosmic rays themselves

Category equivalences involving graded modules over path algebras of quivers

Let kQ be the path algebra of a quiver Q with its standard grading. We show that the category of graded kQ-modules modulo those that are the sum of their finite dimensional submodules, QGr(kQ), is equivalent to several other categories: the graded modules over a suitable Leavitt path algebra, the modules over a certain direct limit of finite dimensional multi-matrix algebras, QGr(kQ') where Q' is the quiver whose incidence matrix is the n^{th} power of that for Q, and others. A relation with a suitable Cuntz-Krieger algebra is established. All short exact sequences in the full subcategory of finitely presented objects in QGr(kQ), split so that subcategory can be given the structure of a triangulated category with suspension functor the Serre degree twist (-1); it is shown that this triangulated category is equivalent to the "singularity category" for the radical square zero algebra kQ/kQ_{\ge 2}.Comment: Several changes made as a result of the referee's report. Added Lemma 3.5 and Prop. 3.6 showing that O is a generato

Aspects of the Hypermultiplet Moduli Space in String Duality

A type IIA string (or F-theory) compactified on a Calabi-Yau threefold is believed to be dual to a heterotic string on a K3 surface times a 2-torus (or on a K3 surface). We consider how the resulting moduli space of hypermultiplets is identified between these two pictures in the case of the E8xE8 heterotic string. As examples we discuss SU(2)-bundles and G2-bundles on the K3 surface and the case of point-like instantons. We are lead to a rather beautiful identification between the integral cohomology of the Calabi-Yau threefold and some integral structures on the heterotic side somewhat reminiscent of mirror symmetry. We discuss the consequences for probing nonperturbative effects in the both the type IIA string and the heterotic string.Comment: 27 Pages, LaTeX 2e, 2 separate figure