Physical Sciences and Mathematics Commons^™

Spatial Isomorphisms Of Algebras Of Truncated Toeplitz Operators, Stephan Ramon Garcia, William T. Ross, Warren R. Wogen

Pomona Faculty Publications and Research

We examine when two maximal abelian algebras in the truncated Toeplitz operators are spatially isomorphic. This builds upon recent work of N. Sedlock, who obtained a complete description of the maximal algebras of truncated Toeplitz operators.

Topological Symmetry Groups Of K4r+3, Dwayne Chambers '12, Erica Flapan, John D. O'Brien

Pomona Faculty Publications and Research

We present the concept of the topological symmetry group as a way to analyze the symmetries of non-rigid molecules. Then we characterize all of the groups which can occur as the topological symmetry group of an embedding of a complete graph of the form K4r+3^in S³.

Inter-Colony Comparison Of Diving Behavior Of An Arctic Top Predator: Implications For Warming In The Greenland Sea, Nina J. Karnovsky, Zachary W. Brown '07, Jorg Welcker, Ann M.A. Harding, Wojciech Walkusz, André Cavalcanti, Johanna S. Hardin, Alexander Kitaysky, Geir Gabrielsen, David Grémillet

Pomona Faculty Publications and Research

The goal of this study was to assess how diverse oceanographic conditions and prey communities affect the foraging behavior of little auks Alle alle. The Greenland Sea is characterized by 3 distinct water masses: (1) the East Greenland Current (EGC), which carries Arctic waters southward; (2) the Sørkapp Current (SC), which originates in the Arctic Ocean but flows north along the west coast of Spitsbergen; and (3) the West Spitsbergen Current (WSC), which carries warm Atlantic-derived water north. Each of these 3 water masses is characterized by a distinct mesozooplankton community. Little auks breeding adjacent to the EGC have …

Geologic Map Of The Ganiki Planitia Quadrangle (V–14), Venus, Eric B. Grosfils, Sylvan M. Long, Elizabeth M. Venechuk, Debra M. Hurwitz, Joseph W. Richards, Brian Kastl, Dorothy E. Drury, Johanna S. Hardin

Pomona Faculty Publications and Research

Our current research focuses on addressing four specific questions. Has the dominant style of volcanic expression within the quadrangle varied in a systematic fashion over time? Does the tectonic deformation within the quadrangle record significant regional patterns that vary spatially or temporally, and if so what are the scales, orientations and sources of the stress fields driving this deformation? If mantle upwelling and downwelling have played a significant role in the formation of Atla Regio and Atalanta Planitia as has been proposed, does the geology of Ganiki Planitia record evidence of northwest-directed lateral mantle flow connecting the two sites? Finally, …

Unitary Equivalence To A Complex Symmetric Matrix: A Modulus Criterion, Stephan Ramon Garcia, Daniel E. Poore '11, Madeline K. Wyse '11

Pomona Faculty Publications and Research

We develop a procedure for determining whether a square complex matrix is unitarily equivalent to a complex symmetric (i.e., self-transpose) matrix. We compare our approach to several existing methods [1, 19, 20] and present a number of examples.

Classical Kloosterman Sums: Representation Theory, Magic Squares, And Ramanujan Multigraphs, Patrick S. Fleming, Stephan Ramon Garcia, Gizem Karaali

Pomona Faculty Publications and Research

We consider a certain finite group for which Kloosterman sums appear as character values. This leads us to consider a concrete family of commuting hermitian matrices which have Kloosterman sums as eigenvalues. These matrices satisfy a number of “magical” combinatorial properties and they encode various arithmetic properties of Kloosterman sums. These matrices can also be regarded as adjacency matrices for multigraphs which display Ramanujan-like behavior.

Trash Talk: A Case Study Of Waste Analysis At Pomona College, Char Miller, Bowen Close

Pomona Faculty Publications and Research

Purpose: This paper presents the pedagogical initiatives associated with and the practical outcomes of a multi-student independent study that analyzed the campus waste stream and developed real-world solutions in accord with the college’s sustainability commitments and goals.

Design/methodology: The paper reviews the course structure, presents research findings and the individual student-developed solutions, and assesses their ability to reduce the campus’s waste stream.

Findings: Developing a class to audit the campus waste stream offers students an unusual educational opportunity to apply theoretical insights to and test these against a real-world problem; their analyses and projects also has helped …

Overcoming The Obstacles To Sustainability In Ghana, Ashley M. Scott

CMC Senior Theses

For several decades following its independence from Great Britain, Ghana’s policies continued to promote over-extraction of natural resources to the detriment of its economy and rural communities. Agricultural and forestry policy has gradually evolved to foster more sustainable and equitable practices, as in building partnerships with the private sector to fund infrastructure improvements. Policy has recently recognized the dire need to adopt agricultural practices and means of forest resource extraction that are compatible with ecological stewardship. However, many shortcomings are still apparent. Large logging operations completely disregard forestry regulations with impunity, whereas rural sustenance extractors are severely punished in the …

Energy Storage: Technology For A More Efficient Grid, Noah Proser

CMC Senior Theses

Energy storage technologies have the potential to revolutionize the electric grid by allowing for the integration of renewable generation while increasing the utilization and efficiency of current grid assets. These technologies include pumped hydroelectric storage, compressed air energy storage (CAES), flywheels, batteries, thermal energy storage (TES), super capacitors, and superconducting magnetic energy storage (SMES). While energy storage has been implemented in some areas, its benefits are greatly undervalued by current regulatory frameworks leading to suboptimal outcomes for grid operators, utilities, and ratepayers. Large-scale adoption of storage technologies will require regulatory frameworks that recognize the benefits of grid-scale storage across generation, …

The Mathematical Landscape, Antonio Collazo

CMC Senior Theses

The intent of this paper is to present the reader will enough information to spark a curiosity in to the subject. By no means is the following a complete formulation of any of the topics covered. I want to give the reader a tour of the mathematical landscape. There are plenty of further details to explore in each section, I have just touched the tip the iceberg. The work is basically in four sections: Numbers, Geometry, Functions, Sets and Logic, which are the basic building blocks of Math. The first sections are a exposition into the mathematical objects and their …

How Other Drivers’ Vehicle Characteristics Influence Your Driving Speed, Russell Brockett

CMC Senior Theses

An analysis of the effect of passing vehicles’ characteristics and their impact on other drivers’ velocities was investigated. Three experimental studies were proposed and likely outcomes were discussed. Experiment 1 focused on the effect of passing vehicle type (SUV, sedan or truck) on driver speed. Drivers were hypothesized as going faster when the same vehicle type as they were driving passed them versus when no vehicle or a different vehicle passed them. Experiment 2 focused on the effect of passing SUV age on driver’s speed. Evidence suggests passing older SUVs will increase the driver’s speed more than new SUVs. Experiment …

Women In Mathematics: An Historical Account Of Women's Experiences And Achievement, Kendra D. Huff

CMC Senior Theses

For a long time, women have struggled to gain complete acceptance in the mathematics field. The purpose of this paper is to explore the history of women in the field of mathematics, the impact and experiences of current female mathematicians, and the common trends for women in the mathematics field, through literature review and personal interviews. This paper looks at the lives of four famous female mathematicians, as well as female mathematicians in the Claremont Colleges who were interviewed for this paper. Specifically this paper examines the discrimination they faced and how they overcame this discrimination, as well as the …

Twisted Virtual Biracks, Jessica Ceniceros

CMC Senior Theses

This thesis will take a look at a branch of topology called knot theory. We will first look at what started the study of this field, classical knot theory. Knot invariants such as the Bracket polynomial and the Jones polynomial will be introduced and studied. We will then explore racks and biracks along with the axioms obtained from the Reidemeister moves. We will then move on to generalize classical knot theory to what is now known as virtual knot theory which was first introduced by Louis Kauffman. Finally, we take a look at a newer aspect of knot theory, twisted …

Fabrication And Preliminary Characterization Of Hydrophobic Silica Aerogel Films For Oil Remediation Studies, Ellen Yang

Pomona Senior Theses

Due to the potential of oil sorbents for oil spill clean-up, hydrophobic silica-based aerogel thin films have been synthesized and characterized by various methods. Aerogels were prepared using a two-step acid/base sol-gel process and functionalized with trimethylchlorosilane in hexane, followed by drying in ambient conditions. After film deposition by spin-coating, samples were characterized by scanning electron microscopy, nitrogen adsorption analysis (BET surface area = 377.66 m2 /g), and variable-angle spectroscopic ellipsometry (thickness of 287.00 ± 0.85 nm, refractive index of 1.08, porosity of 80.9%). Unlike previous studies with aerogel films, quartz crystal microbalance with dissipation monitoring (QCM-D) was applied to …

Problems In Gps Accuracy, Michael Thomas Vodhanel

CGU Theses & Dissertations

Improving and predicting the accuracy of positioning estimates derived from the global positioning system (GPS) continues to be a problem of great interest. Dependable and accurate positioning is especially important for navigation applications such as the landing of commercial aircraft. This subject gives rise to many interesting and challenging mathematical problems. This dissertation investigates two such problems. The first problem involves the study of the relationship between positioning accuracy and satellite geometry configurations relative to a user's position. In this work, accuracy is measured by so-called dilution of precision (DOP) terms. The DOP terms arise from the linear regression model …

A Secure Behavior Modification Sensor System For Physical Activity Improvement, Alan Price

CGU Theses & Dissertations

Today, advances in wireless sensor networks are making it possible to capture large amounts of information about a person and their interaction within their home environment. However, what is missing is how to ensure the security of the collected data and its use to alter human behavior for positive benefit.

In this research, exploration was conducted involving the "infrastructure" and "intelligence" aspects of a wireless sensor network through a Behavior Modification Sensor System. First was to understand how a secure wireless sensor network could be established through the symmetric distribution of keys (the securing of the infrastructure), and it involves …

Do Facework Behaviors Matter During Conflicts Among Online Discussion Team Members?, Jesus Herman Canelon

CGU Theses & Dissertations

According to researchers, face is an important possession carried by individuals into interactions with others. Face has been studied in diverse areas such as: politeness, compliance gaining, emotional discourse, negotiations, face-negotiation theory, and conflict. Perhaps because of its value, face can be vulnerable during conflict situations. Facework behaviors are the communicative strategies that people use during conflicts to protect face (theirs or others), threaten others' face, and to avoid or resolve conflicts. So far, studies about facework behaviors have focused on face-to-face interactions. Preliminary studies have shown: a. facework behaviors may affect the outcomes of online discussion teams, b. sex …

Is Leed A True Leader? Studying The Effectiveness Of Leed Certification In Encouraging Green Building, Megan M. Turner

Pomona Senior Theses

Leadership in Energy and Environmental Design (or LEED) is the most commonly used green building rating system in the United States, bestowing upon LEED certified buildings the prestige of being considered more sustainable than their non-certified neighbors. The public often assumes that LEED certified buildings are completely sustainable or even net-zero with regards to greenhouse gas emissions, but in actuality buildings certified under the most popular version of LEED are only required to be 15% more energy efficient than required by most state building codes – a far cry from the energy usage cuts needed to stave off global warming. …

When Curiosity Kills More Than The Cat: The Perils Of Unchecked Scientific Inquiry, Jamie Shannon

Pomona Senior Theses

This work analyzes the ecological, physical, emotional and health impacts of the US nuclear testing done in the Marshall Islands in the mid-20th century.

Sums Of Evenly Spaced Binomial Coefficients, Arthur T. Benjamin, Bob Chen '10, Kimberly Kindred

All HMC Faculty Publications and Research

We provide a combinatorial proof of a formula for the sum of evenly spaced binomial coefficients. This identity, along with a generalization, are proved by counting weighted walks on a graph.

Teaching Research: Encouraging Discoveries, Francis E. Su

All HMC Faculty Publications and Research

What does it take to turn a learner into a discoverer? Or to turn a teacher into a co-adventurer? A handful of experiences—from teaching a middle-school math class to doing research with undergraduates—have changed the way that I would answer these questions. Some of the lessons I’ve learned have surprised me.

Engineering Flow States With Localized Forcing In A Thin, Marangoni-Driven Inclined Film, Rachel Levy, Stephen Rosenthal '09, Jeffrey Wong '11

All HMC Faculty Publications and Research

Numerical simulations of lubrication models provide clues for experimentalists about the development of wave structures in thin liquid films. We analyze numerical simulations of a lubrication model for an inclined thin liquid film modified by Marangoni forces due to a thermal gradient and additional localized forcing heating the substrate. Numerical results can be explained through connections to theory for hyperbolic conservation laws predicting wave fronts from Marangoni-driven thin films without forcing. We demonstrate how a variety of forcing profiles, such as Gaussian, rectangular, and triangular, affect the formation of downstream transient structures, including an N wave not commonly discussed in …

Compressed Sensing With Coherent And Redundant Dictionaries, Emmanuel J. Candès, Yonina C. Eldar, Deanna Needell, Paige Randall

CMC Faculty Publications and Research

This article presents novel results concerning the recovery of signals from undersampled data in the common situation where such signals are not sparse in an orthonormal basis or incoherent dictionary, but in a truly redundant dictionary. This work thus bridges a gap in the literature and shows not only that compressed sensing is viable in this context, but also that accurate recovery is possible via an ℓ₁-analysis optimization problem. We introduce a condition on the measurement/sensing matrix, which is a natural generalization of the now well-known restricted isometry property, and which guarantees accurate recovery of signals that are …

"Toward Integration: From Quantitative Biology To Mathbio-Biomath?", Pat Marsteller, Lisette G. De Pillis, Ann Findley, Karl Joplin, John Pelesko, Karen Nelson, Katerina Thompson, David Usher, Joseph Watkins

All HMC Faculty Publications and Research

In response to the call of BIO2010 for integrating quantitative skills into undergraduate biology education, 30 Howard Hughes Medical Institute (HHMI) Program Directors at the 2006 HHMI Program Directors Meeting established a consortium to investigate, implement, develop, and disseminate best practices resulting from the integration of math and biology. With the assistance of an HHMI-funded mini-grant, led by Karl Joplin of East Tennessee State University, and support in institutional HHMI grants at Emory and University of Delaware, these institutions held a series of summer institutes and workshops to document progress toward and address the challenges of implementing a more quantitative …

Dislocations And Vacancies In Two-Dimensional Mixed Crystals Of Spheres And Dimers, Sharon J. Gerbode, Desmond C. Ong, Chekesha M. Liddell, Itai Cohen

All HMC Faculty Publications and Research

In colloidal crystals of spheres, dislocation motion is unrestricted. On the other hand, recent studies of relaxation in crystals of colloidal dimer particles have demonstrated that the dislocation dynamics in such crystals are reminiscent of glassy systems. The observed glassy dynamics arise as a result of dislocation cages formed by certain dimer orientations. In the current study, we use experiments and simulations to investigate the transition that arises when a pure sphere crystal is doped with an increasing concentration of dimers. Specifically, we focus on both dislocation caging and vacancy motion. Interestingly, we find that any nonzero fraction of dimers …

Existence Of Solutions For A Semilinear Wave Equation With Non-Monotone Nonlinearity, Alfonso Castro, Benjamin Preskill '09

All HMC Faculty Publications and Research

For double-periodic and Dirichlet-periodic boundary conditions, we prove the existence of solutions to a forced semilinear wave equation with asymptotically linear nonlinearity, no resonance, and non-monotone nonlinearity when the forcing term is not flat on characteristics. The solutions are in L^∞ when the forcing term is in L^∞ and continous when the forcing term is continuous. This is in contrast with the results in [4], where the non-enxistence of continuous solutions is established even when forcing term is of class C^∞ but is flat on a characteristic.

Algebraic Points Of Small Height Missing A Union Of Varieties, Lenny Fukshansky

CMC Faculty Publications and Research

Let K be a number field, Q, or the field of rational functions on a smooth projective curve over a perfect field, and let V be a subspace of K^N where N≥ 2. Let Z_K be a union of varieties defined over K such that V ⊈ Z_K. We prove the existence of a point of small height in V \ Z_K, providing an explicit upper bound on the height of such a point in terms of the height of V and the degree of hypersurface containing Z_K, where dependence on …

Glassy Dislocation Dynamics In 2d Colloidal Dimer Crystals, Sharon J. Gerbode, Ugmang Agarwal, Desmond C. Ong, Chekesha M. Liddell, Fernando Escobedo, Itai Cohen

All HMC Faculty Publications and Research

Although glassy relaxation is typically associated with disorder, here we report on a new type of glassy dynamics relating to dislocations within 2D crystals of colloidal dimers. Previous studies have demonstrated that dislocation motion in dimer crystals is restricted by certain particle orientations. Here, we drag an optically trapped particle through such dimer crystals, creating dislocations. We find a two-stage relaxation response where initially dislocations glide until encountering particles that cage their motion. Subsequent relaxation occurs logarithmically slowly through a second process where dislocations hop between caged configurations. Finally, in simulations of sheared dimer crystals, the dislocation mean squared displacement …

Combinatorial Trigonometry With Chebyshev Polynomials, Arthur T. Benjamin, Larry Ericksen, Pallavi Jayawant, Mark Shattuck

All HMC Faculty Publications and Research

We provide a combinatorial proof of the trigonometric identity cos(n_{θ) =} T_ncos(θ),
where T_n is the Chebyshev polynomial of the first kind. We also provide combinatorial proofs of other trigonometric identities, including those involving Chebyshev polynomials of the second kind.

Combinatorially Composing Chebyshev Polynomials, Arthur T. Benjamin, Daniel Walton '07

All HMC Faculty Publications and Research

We present a combinatorial proof of two fundamental composition identities associated with Chebyshev polynomials. Namely, for all m, n ≥ 0, T_m(T_n(x)) = T_mn(x) and U_m-1 (T_n(x))U_n-1(x) = U_mn-1(x).