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Patterns, Symmetries, And Mathematical Structures In The Arts, Sarah C. DeLoach 2020 Georgia Southern University

Patterns, Symmetries, And Mathematical Structures In The Arts, Sarah C. Deloach

University Honors Program Theses

Mathematics is a discipline of academia that can be found everywhere in the world around us. Mathematicians and scientists are not the only people who need to be proficient in numbers. Those involved in social sciences and even the arts can benefit from a background in math. In fact, connections between mathematics and various forms of art have been discovered since as early as the fourth century BC. In this thesis we will study such connections and related concepts in mathematics, dances, and music.


Oscillation In Mathematical Epidemiology, Meredith Greer 2019 Bates College

Oscillation In Mathematical Epidemiology, Meredith Greer

Annual Symposium on Biomathematics and Ecology: Education and Research

No abstract provided.


List-Distinguishing Cartesian Products Of Cliques, Michael Ferrara, Zoltan Füredi, Sogol Jahanbekam, Paul Wenger 2019 University of Colorado, Denver

List-Distinguishing Cartesian Products Of Cliques, Michael Ferrara, Zoltan Füredi, Sogol Jahanbekam, Paul Wenger

Sogol Jahanbekam

The distinguishing number of a graph G, denoted D(G), is the minimum number of colors needed to produce a coloring of the vertices of G so that every nontrivial isomorphism interchanges vertices of different colors. A list assignment L on a graph G is a function that assigns each vertex of G a set of colors. An L-coloring of G is a coloring in which each vertex is colored with a color from L(v). The list distinguishing number of G, denoted Dℓ(G) is the minimum k such that every list assignment L that assigns a list ...


A Tribute To Robert U. Ayres For A Lifetime Of Work In Technological Forecasting And Related Areas, Steven M. MILLER 2019 Singapore Management University

A Tribute To Robert U. Ayres For A Lifetime Of Work In Technological Forecasting And Related Areas, Steven M. Miller

Research Collection School Of Information Systems

Bob Ayres was born in the UnitedStates in 1932. For his university studies at the bachelors, masters and PhD levels, he concentrated in physics and mathematics. When we think of Bob today, we think of his pioneering work across the areas of technological forecasting, industrial metabolism and industrial ecology, and the role of energy and thermodynamics in economic growth. How did a person with a strong fundamental education as a physicist end up as a pioneering thinker and thought leader at the intersection of energy, environment and economics?


Minimum Rank, Maximum Nullity, And Zero Forcing Number Of Graphs, Shaun M. Fallat, Leslie Hogben 2019 University of Regina

Minimum Rank, Maximum Nullity, And Zero Forcing Number Of Graphs, Shaun M. Fallat, Leslie Hogben

Leslie Hogben

This chapter represents an overview of research related to a notion of the “rank of a graph" and the dual concept known as the “nullity of a graph," from the point of view of associating a fixed collection of symmetric or Hermitian matrices to a given graph. This topic and related questions have enjoyed a fairly large history within discrete mathematics, and have become very popular among linear algebraists recently, partly based on its connection to certain inverse eigenvalue problems, but also because of the many interesting applications (e.g., to communication complexity in computer science and to control of ...


Quantifying Iron Overload Using Mri, Active Contours, And Convolutional Neural Networks, Andrea Sajewski, Stacey Levine 2019 Duquesne University

Quantifying Iron Overload Using Mri, Active Contours, And Convolutional Neural Networks, Andrea Sajewski, Stacey Levine

Undergraduate Research and Scholarship Symposium

Iron overload, a complication of repeated blood transfusions, can cause tissue damage and organ failure. The body has no regulatory mechanism to excrete excess iron, so iron overload must be closely monitored to guide therapy and measure treatment response. The concentration of iron in the liver is a reliable marker for total body iron content and is now measured noninvasively with magnetic resonance imaging (MRI). MRI produces a diagnostic image by measuring the signals emitted from the body in the presence of a constant magnetic field and radiofrequency pulses. At each pixel, the signal decay constant, T2*, can be calculated ...


Lecture 8, Kannan Soundararajan 2019 University of Mississippi

Lecture 8, Kannan Soundararajan

NSF-CBMS Conference: L-functions and Multiplicative Number Theory

Continuation of Extreme values of L-functions.


Lecture 7, Kannan Soundararajan 2019 University of Mississippi

Lecture 7, Kannan Soundararajan

NSF-CBMS Conference: L-functions and Multiplicative Number Theory

Extreme values of L-functions.


Boundary Data Maps For Schrödinger Operators On A Compact Interval, Stephen L. Clark, Fritz Gesztesy, M. Mitrea 2019 Missouri University of Science and Technology

Boundary Data Maps For Schrödinger Operators On A Compact Interval, Stephen L. Clark, Fritz Gesztesy, M. Mitrea

Stephen L. Clark

We provide a systematic study of boundary data maps, that is, 2 x 2 matrix-valued Dirichlet-to-Neumann and more generally, Robin-to-Robin maps, associated with one-dimensional Schrödinger operators on a compact interval [0, R] with separated boundary conditions at 0 and R. Most of our results are formulated in the non-self-adjoint context. Our principal results include explicit representations of these boundary data maps in terms of the resolvent of the underlying Schrödinger operator and the associated boundary trace maps, Krein-type resolvent formulas relating Schrödinger operators corresponding to different (separated) boundary conditions, and a derivation of the Herglotz property of boundary data maps ...


Lecture 6, Kannan Soundararajan 2019 University of Mississippi

Lecture 6, Kannan Soundararajan

NSF-CBMS Conference: L-functions and Multiplicative Number Theory

Continuation of Progress towards moment conjectures -- upper and lower bounds.


Lecture 5, Kannan Soundararajan 2019 University of Mississippi

Lecture 5, Kannan Soundararajan

NSF-CBMS Conference: L-functions and Multiplicative Number Theory

Progress towards moment conjectures -- upper and lower bounds.


Forward Selection Via Distance Correlation, Ty Adams 2019 Rose-Hulman Institute of Technology

Forward Selection Via Distance Correlation, Ty Adams

Mathematical Sciences Technical Reports (MSTR)

No abstract provided.


High Moments Of L-Functions, Vorrapan Chandee 2019 Kansas State University

High Moments Of L-Functions, Vorrapan Chandee

NSF-CBMS Conference: L-functions and Multiplicative Number Theory

Abstract: Moments of L-functions on the critical line (Re(s) = 1/2) have been extensively studied due to numerous applications, for example, bounds for L-functions, information on zeros of L-functions, and connections to the generalized Riemann hypothesis. However, the current understanding of higher moments is very limited. In this talk, I will give an overview how we can achieve asymptotic and bounds for higher moments by enlarging the size of various families of L-functions and show some techniques that are involved.


Moments Of Cubic L-Functions Over Function Fields, Alexandra Florea 2019 Columbia University

Moments Of Cubic L-Functions Over Function Fields, Alexandra Florea

NSF-CBMS Conference: L-functions and Multiplicative Number Theory

Abstract: I will talk about some recent work with Chantal David and Matilde Lalin about the mean value of L-functions associated to cubic characters over F_q[t] when q=1 (mod 3). I will explain how to obtain an asymptotic formula which relies on obtaining cancellation in averages of cubic Gauss sums over functions fields. I will also talk about the corresponding non-Kummer case when q=2 (mod 3) and I will explain why this setting is somewhat easier to handle than the Kummer case, which allows us to prove some better results.


Lecture 4, Kannan Soundararajan 2019 University of Mississippi

Lecture 4, Kannan Soundararajan

NSF-CBMS Conference: L-functions and Multiplicative Number Theory

Larger values of L-functions on critical line -- moments, conjectures.


Lecture 3, Kannan Soundararajan 2019 University of Mississippi

Lecture 3, Kannan Soundararajan

NSF-CBMS Conference: L-functions and Multiplicative Number Theory

Continuation of Selberg's central limit theorem and analogues in families of L-functions (typical size of values on critical line).


An Effective Chebotarev Density Theorem For Families Of Fields, With An Application To Class Groups, Caroline Turnage-Butterbaugh 2019 Carleton College

An Effective Chebotarev Density Theorem For Families Of Fields, With An Application To Class Groups, Caroline Turnage-Butterbaugh

NSF-CBMS Conference: L-functions and Multiplicative Number Theory

This talk will present an effective Chebotarev theorem that holds for all but a possible zero-density subfamily of certain families of number fields of fixed degree. For certain families, this work is unconditional, and in other cases it is conditional on the strong Artin conjecture and certain conjectures on counting number fields. As an application, we obtain nontrivial average upper bounds on ℓ-torsion in the class groups of the families of fields.


Landau-Siegel Zeros And Their Illusory Consequences, Kyle Pratt 2019 University of Illinois

Landau-Siegel Zeros And Their Illusory Consequences, Kyle Pratt

NSF-CBMS Conference: L-functions and Multiplicative Number Theory

Updated time

Abstract: Researchers have tried for many years to eliminate the possibility of LandauSiegel zeros—certain exceptional counterexamples to the Generalized Riemann Hypothesis. Often one thinks of these zeros as being a severe nuisance, but there are many situations in which their existence allows one to prove spectacular, though illusory, results. I will review some of this history and some of these results. In the latter portion of the talk I will discuss recent work, joint with H. M. Bui and Alexandru Zaharescu, in which we show that the existence of Landau-Siegel zeros has implications for the behavior of ...


Lecture 2, Kannan Soundararajan 2019 University of Mississippi

Lecture 2, Kannan Soundararajan

NSF-CBMS Conference: L-functions and Multiplicative Number Theory

Selberg's central limit theorem and analogues in families of L-functions (typical size of values on critical line).


Lecture 1, Kannan Soundararajan 2019 University of Mississippi

Lecture 1, Kannan Soundararajan

NSF-CBMS Conference: L-functions and Multiplicative Number Theory

Introduction to the rest of lectures + value distribution of L-functions away from critical line.


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