Stratification of Unfoldings of Corank 1 Singularities

In the study of equisingularity of families of mappings Gaffney introduced the crucial notion of excellent unfoldings. This definition essentially says that the family can be stratified so that there are no strata of dimension 1 other than the parameter axis for the family. Consider a family of corank 1 multi-germs with source dimension less than target. In this paper it is shown how image Milnor numbers can ensure some of the conditions involved in being excellent. The methods used can also be successfully applied to cases where the double point set is a curve. In order to prove the results the rational cohomology description of the disentanglement of a corank 1 multi-germ is given for the first time. Then, using a simple generalization of the Marar-Mond Theorem on the multiple point space of such maps, this description is applied to give conditions which imply the upper semi-continuity of the image Milnor number. From this the main results follow.Comment: 21 Page

Junior

This recital is presented in partial fulfillment of requirements for the degree Bachelor of Music in Performance. Mr. Lora studies double bass with Marc Miller.https://digitalcommons.kennesaw.edu/musicprograms/2007/thumbnail.jp

New Structures and their Applications to Variants of Zero Forcing and Propagation Time

We introduce a generalization of the concept of a chronological list of forces, called a relaxed chronology. This concept is used to introduce a new way of formulating the standard zero forcing process, which we refer to as parallel increasing path covers, or PIPs. The combinatorial properties of PIPs are utilized to identify bounds comparing standard zero forcing propagation time to positive semidefinite propagation time. A collection of paths within a set of PSD forcing trees, called a path bundle, is used to identify the PSD forcing analog of the reversal of a standard zero forcing process, as well as to draw a connection between PSD forcing and rigid-linkage forcing