Another Proof Of The Existence A Dedekind Complete Totally Ordered Field,
2011
California Polytechnic State University - San Luis Obispo
Another Proof Of The Existence A Dedekind Complete Totally Ordered Field, James F. Hall, Todor D. Todorov
Mathematics
We describe the Dedekind cuts explicitly in terms of non-standard rational numbers. This leads to another construction of a Dedekind complete totally ordered field or, equivalently, to another proof of the consistency of the axioms of the real numbers. We believe that our construction is simpler and shorter than the classical Dedekind construction and Cantor construction of such fields assuming some basic familiarity with non-standard analysis.
Tilings, Patterns And Technology,
2011
Ateneo de Manila University
Tilings, Patterns And Technology, Ma. Louise Antonette N. De Las Peñas, Angela Fatima H. Guzon
Mathematics Faculty Publications
In this paper we discuss various situations where tilings and patterns, with the aid of technology, facilitate the teaching of mathematics and serve as tools in understanding and developing new mathematical ideas. We also illustrate how technology makes possible cultural connections in the study of mathematics using Islamic tilings and patterns.
Coalitions And Cliques In The School Choice Problem,
2011
University of California - San Diego
Coalitions And Cliques In The School Choice Problem, Sinan Aksoy, Alexander Adam Azzam, Chaya Coppersmith, Julie Glass, Gizem Karaali, Xueying Zhao, Xinjing Zhu
Pomona Faculty Publications and Research
The school choice mechanism design problem focuses on assignment mechanisms matching students to public schools in a given school district. The well-known Gale Shapley Student Optimal Stable Matching Mechanism (SOSM) is the most efficient stable mechanism proposed so far as a solution to this problem. However its inefficiency is well-documented, and recently the Efficiency Adjusted Deferred Acceptance Mechanism (EADAM) was proposed as a remedy for this weakness. In this note we describe two related adjustments to SOSM with the intention to address the same inefficiency issue. In one we create possibly artificial coalitions among students where some students modify their …
Review: Nearly Invariant Subspaces For Backwards Shifts On Vector-Valued Hardy Spaces,
2011
Pomona College
Review: Nearly Invariant Subspaces For Backwards Shifts On Vector-Valued Hardy Spaces, Stephan Ramon Garcia
Pomona Faculty Publications and Research
No abstract provided.
Review: Massey Products On Cycles Of Projective Lines And Trigonometric Solutions Of The Yang-Baxter Equations,
2011
Pomona College
Review: Massey Products On Cycles Of Projective Lines And Trigonometric Solutions Of The Yang-Baxter Equations, Gizem Karaali
Pomona Faculty Publications and Research
No abstract provided.
Unitary Equivalence To A Complex Symmetric Matrix: A Modulus Criterion,
2011
Pomona College
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.
Nilpotent Elements And Reduced Rings,
2011
TÜBİTAK
Nilpotent Elements And Reduced Rings, Junchao Wei, Libin Li
Turkish Journal of Mathematics
In this paper, we show the following results: (1) R is a min-leftsemicentral ring if and only if eR(1-e)Re=0 for all e \in ME_l(R); (2) Quasi-normal rings, NI rings and weakly reversible rings are all min-leftsemicentral ring; (3) R is left MC2 ring if and only if aRe=0 implies eRa=0 for all e \in ME_l(R) and a \in R if and only if every projective simple left R-module is MUP-injective; (4) R is reduced if and only if R is n-regular and quasi-normal if and only if R is n-regular and weakly reversible; (5) R is strongly regular if and …
The Cyclicity Of The Period Annulus Of A Quadratic Reversible System With One Center Of Genus One,
2011
TÜBİTAK
The Cyclicity Of The Period Annulus Of A Quadratic Reversible System With One Center Of Genus One, Linping Peng, Yannan Sun
Turkish Journal of Mathematics
This paper is concerned with a quadratic reversible and non-Hamiltonian system with one center of genus one. By using the properties of related elliptic integrals and the geometry of some planar curves defined by them, we prove that the cyclicity of the period annulus of the considered system under small quadratic perturbations is two. This verifies Gautier's conjecture about the cyclicity of the related period annulus.
2011 Undergraduate Mathematics Day Poster,
2011
University of Dayton
2011 Undergraduate Mathematics Day Poster, University Of Dayton. Department Of Mathematics
Undergraduate Mathematics Day: Programs, Lectures, Promotional Materials
No abstract provided.
Geologic Map Of The Ganiki Planitia Quadrangle (V–14), Venus,
2011
Pomona College
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, …
Operation Comics: The Story Continues,
2011
Western Kentucky University
Operation Comics: The Story Continues, Bruce Kessler, Janet Tassell, Tressa Tullis
Mathematics Faculty Publications
During the 2008-2009 academic year, the author K. wrote three issues of Operation Comics, a comic book with embedded mathematics content appropriate for 4th through 6th grade students. Several printed comics were placed in Cumberland Trace Elementary in the Warren County School System in Bowling Green, Kentucky, US. The author Ta. was enlisted to measure the impact of the comics on the attitudes and motivation of the students using the comics. A preliminary report was given by K. at the 2009 Bridges Banff Conference, and the written report appeared in the proceedings. Since then, data has been collected on the …
Morse Theory,
2011
California State University, San Bernardino
Morse Theory, Rozaena Naim
Theses Digitization Project
This study will mainly concentrate on Morse Theory. Morse Theory is the study of the relations between functions on a space and the shape of the space. The main part of Morse Theory is to look at the critical points of a function, and to find information on the shape of the space using the information about the critical points.
Ore's Theorem,
2011
California State University, San Bernardino
Ore's Theorem, Jarom Viehweg
Theses Digitization Project
The purpose of this project was to study the classical result in this direction discovered by O. Ore in 1938, as well as related theorems and corollaries. Ore's Theorem and its corollaries provide us with several results relating distributive lattices with cyclic groups.
Analysis Of The “Travelling Salesman Problem” And An Application Of Heuristic Techniques For Finding A New Solution,
2011
Bridgewater State University
Analysis Of The “Travelling Salesman Problem” And An Application Of Heuristic Techniques For Finding A New Solution, Mateusz Pacha-Sucharzewski
Undergraduate Review
In 1832, a German travelling salesman published a handbook describing his profession. Sadly, his name is unknown; he only stated that the book was written by “one old travelling salesman.” However, he has come down in history thanks to a rather simple and quite obvious observation. He pointed out that when one goes on a business trip, one should plan it carefully; by doing so, one can “win” a great deal of time and increase the trip’s “economy.” Two centuries later, mathematicians and scientists are still struggling with what is now known as the “Travelling Salesman Problem” (TSP).
Diffusion Of Tin From Tec-8 Conductive Glass Into Mesoporous Titanium Dioxide In Dye Sensitized Solar Cells,
2011
Chicago State University
Diffusion Of Tin From Tec-8 Conductive Glass Into Mesoporous Titanium Dioxide In Dye Sensitized Solar Cells, Julienne Cabell, Robert J. Lesuer
Mathematics Faculty Proceedings, Presentations, Speeches, Lectures
The photoanode of a dye sensitized solar cell is typically a mesoporous titanium dioxide thin film adhered to a conductive glass plate. In the case of TEC-8 glass, an approximately 500 nm film of tin oxide provides the conductivity of this substrate. During the calcining step of photoanode fabrication, tin diffuses into the titanium dioxide layer. Scanning Electron Microscopy and Electron Dispersion Microscopy are used to analyze quantitatively the diffusion of tin through the photoanode. At temperatures (400 to 600 °C) and times (30 to 90 min) typically employed in the calcinations of titanium dioxide layers for dye sensitized solar …
Classical Kloosterman Sums: Representation Theory, Magic Squares, And Ramanujan Multigraphs,
2011
South Dakota School of Mines and Technology
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.
Quotient Sets And Diophantine Equations,
2011
Pomona College
Quotient Sets And Diophantine Equations, Stephan Ramon Garcia, Vincent Selhorst-Jones '09, Daniel E. Poore '11, Noah Simon '08
Pomona Faculty Publications and Research
Quotient sets U / U = {u / u¹: u, u¹ ϵ U} have been considered several times before in the MONTHLY. We consider more general quotient sets U / V and we apply our results to certain simultaneous Diophantine equations with side constraints.
Spatial Isomorphisms Of Algebras Of Truncated Toeplitz Operators,
2011
Pomona College
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.
A Topological Approach To Molecular Chirality,
2011
Pomona College
A Topological Approach To Molecular Chirality, Erica Flapan
Pomona Faculty Publications and Research
Topology is the study of deformations of geometric figures. Chemistry is the study of molecular structures. At first glance these fields seem to have nothing in common. But let’s take a closer look to see how these fields come together in the study of molecular symmetries.
Exploring Confidence Intervals In The Case Of Binomial And Hypergeometric Distributions,
2011
University of Central Florida
Exploring Confidence Intervals In The Case Of Binomial And Hypergeometric Distributions, Irene Mojica
Electronic Theses and Dissertations
The objective of this thesis is to examine one of the most fundamental and yet important methodologies used in statistical practice, interval estimation of the probability of success in a binomial distribution. The textbook confidence interval for this problem is known as the Wald interval as it comes from the Wald large sample test for the binomial case. It is generally acknowledged that the actual coverage probability of the standard interval is poor for values of p near 0 or 1. Moreover, recently it has been documented that the coverage properties of the standard interval can be inconsistent even if …
