Notes on Simple Modules over Leavitt Path Algebras

Given an arbitrary graph E and any field K, a new class of simple left modules over the Leavitt path algebra L of the graph E over K is constructed by using vertices that emit infinitely many edges. The corresponding annihilating primitive ideals are described and is used to show that these new class of simple L-modules are different from(that is non-isomorphic to) any of the previously known simple modules. Using a Boolean subring of idempotents induced by paths in E, bounds for the cardinality of the set of distinct isomorphism classes of simple L-modules are given. We also append other information about the Leavitt path algebra L(E) of a finite graph E over which every simple left module is finitely presented.Comment: 17 page

Fast estimation of false alarm probabilities of STAP detectors - the AMF

This paper describes an attempt to harness the power of adaptive importance sampling techniques for estimating false alarm probabilities of detectors that use space-time adaptive processing. Fast simulation using these techniques have been notably successful in the study of conventional constant false alarm rate radar detectors, and in several other applications. The principal task here is to examine the viability of using importance sampling methods for STAP detection. Though a modest beginning, the adaptive matched filter detection algorithm is analysed successfully using fast simulation. Of the two biasing methods considered, one is implemented and shown to yield excellent results. The important problem of detector threshold determination is also addressed, with matching outcome. The work reported here serves to pave the way to development of more advanced estimation techniques that can facilitate design of powerful and robust detection algorithms designed to counter hostile and heterogeneous clutter environments