Research

Projects

Notes on Injective, Commutative C*-algebras These are notes on the conditions for injectivity in the category of commutative, unital C*-algebras with *-homomorphisms. Also, this has the construction and verification of the injective hull for such objects.

A Review of Projective C*-Algebras and Boundary Maps Presenting the work of Loring, this talk and paper will concern with expressing the K-theoretic index and exponential maps by means of projective and semi-projective C*-algebras. PDE Solution Animations #3 These are GIF animations based on the solutions derived in the Applied 2 homework problems dealing with solving PDEs using the characteristic method. Note that each becomes multi-valued after a specific time. Problem 7.2.1.1 Problem 7.2.1.2 Problem 7.2.1.3 Problem 7.2.1.5 Problem 7.2.2.5, a wavefront solution to a PDE PDE Solution Animations #2 These are GIF animations based on the solutions derived in the Applied 2 homework problems dealing with solving PDEs using the characteristic method. Problem 7.1.3a Problem 7.1.3b Problem 7.1.3c Problem 7.1.4 Problem 7.1.5 Problem 7.1.6, solution to a PDE using the Airy Ai(x) function PDE Solution Animations #1 This GIF animation is based on the solution to a PDE describing a string of infinite length falling from rest. Osculating Circle Animation This is an animated GIF of the an approximating circle wandering around a curve, a(t) = &lsaquo cos(t), sin(t)cos(t) &rsaquo. Frenet Frame Animation This is an animated GIF of the unit tangent, normal, and binormal wandering around a curve, a(t) = &lsaquo 2cos(t)cos(t), 2sin(t)cos(t), 2sin(t) &rsaquo.