Under two boundary conditions: the generalized Atiyah-Patodi-Singer boundary condition and the modified generalized Atiyah-Patodi-Singer boundary condition, we get the lower bounds for the eigenvalues of the fundamental Dirac operator on compact spin manifolds with nonempty boundary.

This paper studies a partial order on the general linear group GL(V ) called the absolute order, derived from viewing GL(V ) as a group generated by reflections, that is, elements whose fixed space has codimension one. The absolute order on GL(V ) is shown to have two equivalent descriptions: one via additivity of length for factorizations into reflections and the other via additivity of fixed ...

The discovery of the therapeutic properties of certain steroids has recently given rise to interesting chemical and pharmacological problems. The remarkable antiphlogistic activities of halogenated derivatives of hydrocortisone, and the disappearance of secondary effects obtained by the A1-diene derivatives of cortisone, have suggested the synthesis of a steroid which joins the two chemical cha...