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- (Abstract Harmonic Analysis) Explicit machine computation and programs (not the theory of computation or programming) (1)
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- 20G05 Representation theory (1)
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Articles 1 - 6 of 6
Full-Text Articles in Algebra
Review: Crystal Bases Of Q-Deformed Kac Modules Over The Quantum Superalgebras Uq(Gl(Mln)), Gizem Karaali
Review: Crystal Bases Of Q-Deformed Kac Modules Over The Quantum Superalgebras Uq(Gl(Mln)), Gizem Karaali
Pomona Faculty Publications and Research
No abstract provided.
Review: The Relationships Among Multiplicities Of A J-Self-Adjoint Differential Operator's Eigenvalue, Stephan Ramon Garcia
Review: The Relationships Among Multiplicities Of A J-Self-Adjoint Differential Operator's Eigenvalue, Stephan Ramon Garcia
Pomona Faculty Publications and Research
No abstract provided.
What Is So Negative About Negative Exponents?, Geoffrey D. Dietz
What Is So Negative About Negative Exponents?, Geoffrey D. Dietz
Journal of Humanistic Mathematics
While teaching college-level mathematics (from College Algebra to Calculus to Abstract Algebra), I have observed that students are often uncomfortable using negative exponents in calculations. I believe the fault partially lies in the manner in which negative exponents are taught in Algebra 1 or Algebra 2 courses, especially in rigid instructions always to write answers using only positive exponents. After reviewing a sample of algebra texts used in the United States over the last two centuries, it appears that while attitudes toward negative exponents have varied from author to author over time, the current trend is to declare explicitly that …
A New Subgroup Chain For The Finite Affine Group, David Alan Lingenbrink Jr.
A New Subgroup Chain For The Finite Affine Group, David Alan Lingenbrink Jr.
HMC Senior Theses
The finite affine group is a matrix group whose entries come from a finite field. A natural subgroup consists of those matrices whose entries all come from a subfield instead. In this paper, I will introduce intermediate sub- groups with entries from both the field and a subfield. I will also examine the representations of these intermediate subgroups as well as the branch- ing diagram for the resulting subgroup chain. This will allow us to create a fast Fourier transform for the group that uses asymptotically fewer opera- tions than the brute force algorithm.
Fast Algorithms For Analyzing Partially Ranked Data, Matthew Mcdermott
Fast Algorithms For Analyzing Partially Ranked Data, Matthew Mcdermott
HMC Senior Theses
Imagine your local creamery administers a survey asking their patrons to choose their five favorite ice cream flavors. Any data collected by this survey would be an example of partially ranked data, as the set of all possible flavors is only ranked into subsets of the chosen flavors and the non-chosen flavors. If the creamery asks you to help analyze this data, what approaches could you take? One approach is to use the natural symmetries of the underlying data space to decompose any data set into smaller parts that can be more easily understood. In this work, I describe …
Finding Zeros Of Rational Quadratic Forms, John F. Shaughnessy
Finding Zeros Of Rational Quadratic Forms, John F. Shaughnessy
CMC Senior Theses
In this thesis, we introduce the notion of quadratic forms and provide motivation for their study. We begin by discussing Diophantine equations, the field of p-adic numbers, and the Hasse-Minkowski Theorem that allows us to use p-adic analysis determine whether a quadratic form has a rational root. We then discuss search bounds and state Cassels' Theorem for small-height zeros of rational quadratic forms. We end with a proof of Cassels' Theorem and suggestions for further reading.