Mathematics Commons^™

Convergence And Rate Of Convergence Of Approximate Greedy-Type Algorithms, Anton Dereventsov

Theses and Dissertations

In this dissertation we study the questions of convergence and rate of convergence of greedy-type algorithms under imprecise step evaluations. Such algorithms are in demand as the issue of calculation errors appears naturally in applications.

We address the question of strong convergence of the Chebyshev Greedy Algorithm (CGA), which is a generalization of the Orthogonal Greedy Algorithm (also known as the Orthogonal Matching Pursuit), and show that the class of Banach spaces for which the CGA converges for all dictionaries and objective elements is strictly between smooth and uniformly smooth Banach spaces.

We analyze an application-oriented modification of the CGA, …

Dynamics Of Gene Networks In Cancer Research, Paul Scott

College of Graduate Studies: Theses & Dissertations

Cancer prevention treatments are being researched to see if an optimized treatment schedule would decrease the likelihood of a person being diagnosed with cancer. To do this we are looking at genes involved in the cell cycle and how they interact with one another. Through each gene expression during the life of a normal cell we get an understanding of the gene interactions and test these against those of a cancerous cell. First we construct a simplified network model of the normal gene network. Once we have this model we translate it into a transition matrix and force changes on …

Fiber Products In Commutative Algebra, Keller Vandebogert

College of Graduate Studies: Theses & Dissertations

The purpose of this thesis is to introduce and illustrate some of the deep connections between commutative and homological algebra. We shall cover some of the fundamental definitions and introduce several important classes of commutative rings. The later chapters will consider a particular class of rings, the \emph{fiber product}, and, among other results, show that any Gorenstein fiber product is precisely a one dimensional hypersurface. It will also be shown that any Noetherian local ring with a (nontrivially) decomposable maximal ideal satisfies the Auslander-Reiten conjecture. To conclude, generalizations of results by Takahashi and Atkins-Vraciu shall be presented.

Hybrid Stochastic Systems: Numerical Methods, Limit Results, And Controls, Tuan A. Hoang

Wayne State University Dissertations

This dissertation is concerned with the so-called stochastic hybrid systems, which are

featured by the coexistence of continuous dynamics and discrete events and their interactions. Such systems have drawn much needed attentions in recent years. One of the main reasons is that such systems can be used to better reflect the reality for a wide range of applications in networked systems, communication systems, economic systems, cyber-physical systems, and biological and ecological systems, among others. Our main interest is centered around one class of such hybrid systems known as switching diffusions. In such a system, in addition to the driving force …

01: Quadratic Functions, Ruth Dover

Mathematica Notebooks for Pre-Calculus and Calculus

QuadraticFunctions.nb examines the path of the vertex of quadratic polynomial graphs as each parameter a, b, and c changes.

03: Poly Basics 2, Ruth Dover

Mathematica Notebooks for Pre-Calculus and Calculus

PolyBasics2.nb looks for patterns in polynomial graphs with three different factors when each factor is raised to various powers.

17: Plotting S(N), Ruth Dover

Mathematica Notebooks for Pre-Calculus and Calculus

PlottingS(n).nb animates the second section of the preceding notebook. After inputting the formula for a sequence, this animates both the sequence itself and the sequence of partial sums together as n increases.

01: Creating Derivative, Ruth Dover

Mathematica Notebooks for Pre-Calculus and Calculus

CreatingDerivative.nb takes any function and an x-window and animates a tangent line while plotting the value of the derivative.

04: Ivt, Ruth Dover

Mathematica Notebooks for Pre-Calculus and Calculus

IVT.nb allows the user to examine the Intermediate Value Theorem. Consider the graphs to examine whether or not the conclusions of the theorem hold.

07: Riemann Sums, Ruth Dover

Mathematica Notebooks for Pre-Calculus and Calculus

RiemannSums.nb allows the user to input a function, and x-interval, and a maximum value of n, the number of rectangles. This animates Riemann and trapezoidal sums.

14: Sequences And Series, Ruth Dover

Mathematica Notebooks for Pre-Calculus and Calculus

SequencesAndSeries.nb includes a couple of sections. The first asks the user to input a formula for a sequence. Then it generates a table of values for the sequence followed by a graph of the function. The second section does the same, though it shows the sequence as well as the sequence of partial sums.

A Comprehensive Analysis Of Team Streakiness In Major League Baseball: 1962-2016, Paul H. Kvam, Zezhong Chen

Department of Math & Statistics Faculty Publications

A baseball team would be considered “streaky” if its record exhibits an unusually high number of consecutive wins or losses, compared to what might be expected if the team’s performance does not really depend on whether or not they won their previous game. If an average team in Major League Baseball (i.e., with a record of 81-81) is not streaky, we assume its win probability would be stable at around 50% for most games, outside of peculiar details of day-to-day outcomes, such as whether the game is home or away, who is the starting pitcher, and so on.

In this …

Multipliers Of Sequence Spaces, Raymond Cheng, Javad Mashreghi, William T. Ross

Department of Math & Statistics Faculty Publications

This paper is selective survey on the space l_A^p and its multipliers. It also includes some connections of multipliers to Birkhoff-James orthogonality.

Birkhoff–James Orthogonality And The Zeros Of An Analytic Function, Raymond Cheng, Javad Mashreghi, William T. Ross

Department of Math & Statistics Faculty Publications

Bounds are obtained for the zeros of an analytic function on a disk in terms of the Taylor coefficients of the function. These results are derived using the notion of Birkhoff–James orthogonality in the sequence space ℓ^p with p ∈ (1,∞), along with an associated Pythagorean theorem. It is shown that these methods are able to reproduce, and in some cases sharpen, some classical bounds for the roots of a polynomial.

Approaching Cauchy’S Theorem, Stephan Ramon Garcia, William T. Ross

Department of Math & Statistics Faculty Publications

We hope to initiate a discussion about various methods for introducing Cauchy’s Theorem. Although Cauchy’s Theorem is the fundamental theorem upon which complex analysis is based, there is no “standard approach.” The appropriate choice depends upon the prerequisites for the course and the level of rigor intended. Common methods include Green’s Theorem, Goursat’s Lemma, Leibniz’ Rule, and homotopy theory, each of which has its positives and negatives.

Four Years With Russell, Gödel, And Erdős: An Undergraduate's Reflection On His Mathematical Education, Michael H. Boggess

CMC Senior Theses

Senior Thesis at CMC is often described institutionally as the capstone of one’s undergraduate education. As such, I wanted my own to accurately capture and reflect how I’ve grown as a student and mathematician these past four years. What follows is my attempt to distill lessons I learned in mathematics outside the curriculum, written for incoming undergraduates and anyone with just a little bit of mathematical curiosity. In it, I attempt to dispel some common preconceptions about mathematics, namely that it’s uninteresting, formulaic, acultural, or completely objective, in favor of a dynamic historical and cultural perspective, with particular attention paid …

Characterization Of Rectifying And Sphere Curves In R^3, Yun Myung Oh, Julie Logan

Faculty Publications

Studies of curves in 3D-space have been developed by many geometers and it is known that any regular curve in 3D space is completely determined by its curvature and torsion, up to position. Many results have been found to characterize various types of space curves in terms of conditions on the ratio of torsion to curvature. Under an extracondition on the constant curvature, Y.L. Seo and Y. M. Oh found the series solution when the ratio of torsion to curvature is a linear function. Furthermore, this solution is known to be a rectifying curve by B. Y. Chen’s work. This …

Some Extended Classes Of Distributions: Characterizations And Properties, Gholamhossein G. Hamedani, Gauss M. Cordeiro, M. C.S. Lima, A. D.C. Nascimento

Mathematics, Statistics and Computer Science Faculty Research and Publications

Based on a simple relationship between two truncated moments and certain functions of the th order statistic, we characterize some extended classes of distributions recently proposed in the statistical literature, videlicet Beta-G, Gamma-G, Kumaraswamy-G and McDonald-G. Several properties of these extended classes and some special cases are discussed. We compare these classes in terms of goodness-of-fit criteria using some baseline distributions by means of two real data sets.

Untangling The Most Probable Role For Vitamin D3 In Autism, Dianne E. Godar, Stephen J. Merrill

Mathematics, Statistics and Computer Science Faculty Research and Publications

Recent studies indicate an important role for vitamin D₃ in autism spectrum disorder (ASD), although its mechanism is not completely understood. The most puzzling aspect of ASD is that identical twins, who share identical DNA, do not have 100% concordance rates (∼88% for identical and ∼31% for fraternal twins). These findings provide major clues into the etiology: ASD must involve an environmental factor present in the prenatal milieu that both identical twins are not always exposed to because they do not always share it (i.e., placentas). Combined with the exponential increasing rates of ASD around the world, these observations …

All Sites But Skin Cancer Incidences Analyzed Worldwide By Sex, Age, And Skin Type Over Time (1955-2007), Advancing Age, And Uvb Dose Reveals Important Carcinogenic Drivers, Dianne E. Godar, Rossen Gurov, Stephen Merrill

Mathematics, Statistics and Computer Science Faculty Research and Publications

Because we observed increasing incidences over time, advancing age, higher estrogen levels, decreasing UVB (290-315 nm) doses, or lower vitamin D₃, and Human Papillomavirus hiding in immune-privileged sites of hair follicles play roles in melanoma, we wondered if the majority of cancers might have similar carcinogenic drivers. To investigate this possibility, we performed worldwide analysis of all sites but skin cancer over time (1955-2007), advancing age, and UVB doses for males and females with all skin types and ages (0-85+) and in five age groups using IARC data. To investigate Human Papillomavirus’s role, we analyzed the incidences of …