This dissertation introduces two new results for cubical complexes. The first is a simple statistic on noncrossing partitions that expresses each coordinate of the toric[...]

This dissertation is mainly a study of the center problem in the context of a family of three dimensional systems of ordinary differential equations of the form· {u} = &a[...]

Bulk boron carbide has been widely used in ballistic armored vest and the property characterization has been heavily focused on mechanical properties. Even though boron c[...]

For the last several decades, the Finite Element Method (FEM) has been a powerful tool in solving challenging science and engineering problems, especially when solution d[...]

Coordinate Measuring Machines (CMMs) can be used to measure a great variety of parts. Essentially, any three-dimensional surface can be evaluated. Characterizing the mea[...]

This dissertation presents work done in investigation of a novel polishing process called Vortex Machining. Vortex Machining uses an oscillating probe to induce vortices [...]

We study of the notion of selective separability(SS), which was introduced by Marion Scheepers, and its connection with the game-theoretic strengthening, strategically se[...]

For approximating the solution of partial differential equations (PDE), meshless methods have been introduced to alleviate the difficulties arising in mesh generation usi[...]

Edwards curves are a new normal form for elliptic curves that exhibit some cryptographically desirable properties and advantages over the typical Weierstrass form. Becaus[...]