Mathematics Commons^™

A New Undergraduate Curriculum On Mathematical Biology At University Of Dayton, Muhammad Usman, Amit Singh

Muhammad Usman

The beginning of modern science is marked by efforts of pioneers to understand the natural world using a quantitative approach. As Galileo wrote, "the book of nature is written in the language of mathematics". The traditional undergraduate course curriculum is heavily focused on individual disciplines like biology, physics, chemistry, mathematics rather than interdisciplinary courses. This fragmented teaching of sciences in majority of universities leave biology outside the quantitative and mathematical approaches. The landscape of biomedical science has transformed dramatically with advances in high throughput experimental approaches, which led to the huge amount of data. The best possible approach to generate …

Besov-Spaces On Domains In Rd, Ronald Devore, Robert Sharpley

Robert Sharpley

No abstract provided.

On The Differentiability Of Functions In Rn, Ronald Devore, Robert Sharpley

Robert Sharpley

No abstract provided.

Circular Units Of Function Fields, Frederick Harrop

Frederick F Harrop

A unit index-class number formula is proved for subfields of cyclotomic function fields in analogy with similar results for subfields of cyclotomic number fields.

The Road Trip Property: An Aid In Classifying Groups With Quadratic Isopermietric Inequalities, Rachel Bishop-Ross

Rachel E. Bishop-Ross

A property of geodesic metric spaces, called the road trip property, that generalizes hyperbolic and convex metric spaces is introduced. This property is shown to be invariant under quasi-isometry.

Pulse Dynamics In An Actively Mode-Locked Laser, John Geddes, Willie Firth, Kelly Black

John B. Geddes

We consider pulse formation dynamics in an actively mode-locked laser. We show that an amplitude-modulated laser is subject to large transient growth and we demonstrate that at threshold the transient growth is precisely the Petermann excess noise factor for a laser governed by a nonnormal operator. We also demonstrate an exact reduction from the governing PDEs to a low-dimensional system of ODEs for the parameters of an evolving pulse. A linearized version of these equations allows us to find analytical expressions for the transient growth below threshold. We also show that the nonlinear system collapses onto an appropriate fixed point, …

Reductions Of Graphs And Spanning Eulerian Subgraphs, Zhi-Hong Chen

Zhi-Hong Chen