Honors Theses Open Access
 
Filters: Department: "Mathematics" Format: "application/pdf" Collection: "ir_htoa" Year End: 2016
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1 Sullivan, Steven M.A trace formula for G2An n-dimensional matrix representation of a group G on a vector space V is a homomorphism from G to GL(V). For our purposes, we consider an irreducible representation to be a representation which cannot be decomposed into the direct sum of smaller-dimensional representations. Let H be a subgroup of ...Trace formulas2013-05
2 Ellingson, DrewBitangent lines to planar quartic curves in algebraic and tropical geometryBitangents are lines which are tangent to a curve at two points. The bitangents of a classical quartic are well understood, and a result originally due to Cayley tells us that there are always precisely 28 bitangents to a generic quartic plane curve. When looking at Tropical Geometry, the situation ...Tropical geometry; Curves, Quartic; Curves, Algebraic; Bitangents2015-04
3 Gondolo, AlessandroCharacterization and Synthesis of Rayleigh Damped Elastodynamic NetworksWe consider damped elastodynamic networks where the damping matrix is assumed to be a non-negative linear combination of the stiffness and mass matrices (Rayleigh damping). We give here a characterization of the frequency response of such networks. We also answer the synthesis question for such netw...Damping (Mechanics) - Mathematics2013-05
4 Bowen, BradyFractal geometry of melt ponds: Modeling the fractal geometry of arctic melt ponds using the level sets of random surfacesDuring the late spring, most of the Arctic Ocean is covered by sea ice with a layer of snow on top. As the snow and sea ice begin to melt, water collects on the surface to form melt ponds. As melting progresses, sparse, disconnected ponds coalesce to form complex, self-similar structures which are c...Melt pond geometry2016-04
5 Wang, WenyiImaging in a homogeneous aluminum plate by using ultrasonic wavesThis project is about detecting and imaging damage (such as cracks) in a plate by using ultrasonic waves. The waves are generated by a source (an ultrasonic transducer) that is part of a robot that can move on the plate. The waves traveling in the plate are recorded at a receiver (another ultrasonic...Ultrasonic transducer - Mathematics; Kirchoff migration - Research2014-12
6 Beams, AlexanderImplications of antibiotic use for co-infections when a fitness trade-off for resistance is presentHow much does indiscriminate antibiotic use promote the spread of antibiotic-resistant infections in a population? Assuming a fitness trade-off for resistance exists, it is possible for an antibiotic-vulnerable strain to outlast a resistant type within an untreated host carrying both. That means pru...Drug resistance in microorganisms -- Mathematical models Co-infections2015
7 Allam, JeremyLow-energy satellite transfer from Earth to MarsA new type of satellite transfer that uses half the amount of fuel as conventional transfers has been discovered. This transfer, called a low-energy transfer, proved to work in 1991 when a Japanese satellite successfully went in orbit around the moon using this technique. Since then, more research h...Space vehicles -- Dynamics -- Mathematics Space flight to Mars -- Mathematics2015-04
8 Tuft, MarieQuantitative analysis of virus trafficking in a biological cellVirus replication is a complex process that is important to understand. If a virus is to successfully infect a host cell it must travel from the cell wall to the nucleus by hijacking that cell's existing transport system of microtubules. This motion occurs as two iterated steps: passive diffusion th...Viruses -- Reproduction -- Mathematical models; Virus trafficking2015-05
9 Bingham, KouverReflection groups and coxeter groupsIn this paper we give a survey of the theory of Coxeter Groups and Reflection groups. This survey will give an undergraduate reader a full picture of Coxeter Group theory, and will lean slightly heavily on the side of showing examples, although the course of discussion will be based on theory. We'll...Finite groups2014-07
10 Du, WantongThe role of mRNA decay in a genetic switchGenes can be switched on or off by regulatory proteins. For example, two genes may each synthesize a protein that downregulates the other gene, creating a repressor- repressor switch that has two stable steady states: one being when the first gene is "on" and the second gene is repressed, and the ot...Messenger RNA - Research; Genetic regulation - Research; Genetic switch; Gene repression; Neural circuitry2016-04
11 Scott, IsabelleTropical analog to the log canonical thresholdIn algebraic geometry, the log canonical threshold is a property of singularities of planar curves. While singularities have multiplicities, the log canonical threshold can be a more telling invariant. It helps to classify curves beyond what the multiplicity indicates by examining how quickly the in...Geometry, Algebraic2013-04
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