D E C E M B E R 2 0 0 5 C R E D IT When J. Langdon Down first described savant syndrome in 1887, coining its name and noting its association with astounding powers of memory, he cited a patient who could recite Edward Gibbon’s The Decline and Fall of the Roman Empire verbatim. Since then, in almost all cases, savant memory has been linked to a specific domain, such as music, art or mathematics....

We consider Schrödinger operators in R with complex potentials supported on a hyperplane and show that all eigenvalues lie in a disk in the complex plane with radius bounded in terms of the L norm of the potential with d − 1 < p ≤ d. We also prove bounds on sums of powers of eigenvalues. Introduction and main results. Recently there has been great interest in bounds on eigenvalues of Schrödinge...

We prove that each ideal of a locally formally equidimensional analytically un-ramiied Noetherian integral domain is the contraction of an ideal of a one-dimensional semilo-cal birational extension domain. We give an application to a problem concerning the primary decomposition of powers of ideals in Noetherian rings. It is shown in S2] that for each ideal I in a Noetherian commutative ring R t...