Physical Sciences and Mathematics Commons^™

Optimal Summer Camp Layout, Anthony Bonifonte

Honors Papers

Convex optimization is an important branch of operations research. It generalizes linear programming and offers powerful tools for modelling problems and discovering optimal solutions to real world problems. Mathematically it is an interesting topic because it ties together many branches: linear algebra, multivariable calculus, and numerical analysis, to name a few. Modelling a problem as a convex optimization problem can be challenging but offers many benefits. Algorithm design is critically important to ensure precision of solutions that solve with minimal computation power. From an engineering perspective it is also incredibly useful, since many more situations can be modeled than with …

Simple Games On Networks, Jason Kimmel

Honors Papers

In the same way that traditional game theory captured the minds of economists and allowed complex problems to be studied using simple models, so have games on networks come to be used in computer science. In particular, previous work has focused on extending a two-player base game M over a network G by having each vertex in G chose a strategy from the base game and play it simultaneously against all adjacent nodes. Similarly, the utility for each vertex becomes the sum of the utility of that node in each of the games it plays against its neighbors. The resulting …

Normal And Δ-Normal Configurations In Toric Algebra, Liam Solus

Honors Papers

Toric algebra is a field of study that lies at the intersection of algebra, geometry, and combinatorics. Thus, the algebraic properties of the toric ideal IA defined by the vector configuration A are often characterizable via the geometric and combinatorial properties of its corresponding toric variety and A, respectively. Here, we focus on the property of normality of A. A normal vector configuration defines the toric ideal of a normal toric variety. However, the definition of normality of A is based entirely on the algebraic structures associated with A without regard to any of its combinatorial properties. In this paper, …

Infrared Spectroscopy Of Trapped Gases In Metal-Organic Frameworks, Jennifer M. Schloss

Honors Papers

There are a range of environmental and industrial applications to capturing carbon dioxide from gas mixtures. Currently, materials being used in these applications bind carbon dioxide too strongly for practical purposes, such that they require large amounts of energy to be regenerated for reuse.

Highly porous materials called metal-organic frameworks (MOFs) could serve much more effectively as carbon-capturing materials, as they suck up large amounts of carbon dioxide gas at pressures and temperatures that are nearly ideal for carbon-capture applications. Moreover, they require much less energy than current materials to release the carbon dioxide and be regenerated. Additionally, many different …

Magnetic Properties Of The Bishop Ash In The San Andreas Fault Borderlands, Becky Strauss

Honors Papers

The San Andreas Fault marks one of the most tectonically active regions of the United States, producing frequent earthquakes that have decimated major population centers throughout central and southern California. Its northern regions have been thoroughly studied, but the complex behavior of the southeast portion of the fault is often neglected, in spite of its potential to nucleate a major earthquake within the next few centuries. In this study, I examined the magnetic traits of the Bishop Ash, a well-dated marker horizon of volcanic ash, to assess deformation adjacent to this part of the fault at hand-sample scale. To this …