A Few Remarks on the Mohan Kumar Theorem

On a Theorem of Mohan Kumar and Nori

A celebrated theorem of Suslin asserts that a unimodular row x1 1 , . . . , x mn n is completable if m1 · · ·mn is divisible by (n − 1)!. Examples due to Suslin and to Mohan Kumar and Nori show that this result is the best possible in all characteristics. We give a new version of the proof of Mohan Kumar and Nori which avoids the need to use Grothendieck’s Riemann– Roch theorem or other deep re...

A Few Remarks on Algorithmic Composition

Remarks on a Theorem Of

In a recent paper E. J. McShane [3]2 has given a theorem which is the common core of a variety of results about Baire sets, Baire functions, and convex sets in topological spaces including groups and linear spaces. In general terms his theorem states that if J is a family of open maps defined in one topological space Xi into another, X2, the total image JiS) of a second category Baire set S in ...

A Few Remarks On Topological Field Theory

Physics 695, Fall 2015. September 9, 2015. Version December 10, 2015

Remarks on Pickands theorem

In this article we present Pickands theorem and his double sum method. We follow Piterbarg’s proof of this theorem. Since his proof relies on general lemmas we present a complete proof of Pickands theorem using Borell inequality and Slepian lemma. The original Pickands proof is rather complicated and is mixed with upcrossing probabilities for stationary Gaussian processes. We give a lower bound...