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2013

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Articles 301 - 330 of 1053

Full-Text Articles in Mathematics

Poincaré Polynomial Of Fjrw Rings And The Group-Weights Conjecture, Julian Boon Kai Tay Jun 2013

Poincaré Polynomial Of Fjrw Rings And The Group-Weights Conjecture, Julian Boon Kai Tay

Theses and Dissertations

FJRW-theory is a recent advancement in singularity theory arising from physics. The FJRW-theory is a graded vector space constructed from a quasihomogeneous weighted polynomial and symmetry group, but it has been conjectured that the theory only depends on the weights of the polynomial and the group. In this thesis, I prove this conjecture using Poincaré polynomials and Koszul complexes. By constructing the Koszul complex of the state space, we have found an expression for the Poincaré polynomial of the state space for a given polynomial and associated group. This Poincaré polynomial is defined over the representation ring of a group …

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Energy Flux Streamlines Versus Acoustic Rays For Modeling Interaction With Rigid Boundaries: Near Field Of Sound From A Circular Loudspeaker, Cleon Dean, James Braselton Jun 2013

Energy Flux Streamlines Versus Acoustic Rays For Modeling Interaction With Rigid Boundaries: Near Field Of Sound From A Circular Loudspeaker, Cleon Dean, James Braselton

Mathematical Sciences: Faculty Presentations (1991-2022)

Sound emitted by a circular loudspeaker can be treated as equivalent to a plane wave diffracted by a circular aperture in a rigid, sound absorbing screen. Axial symmetry leads one to expect constructive interference along the symmetry axis in the near field (the Poisson-Arago spot). An energy flux streamline model was developed to help visualize this and other features of the nearsound field. The model is used to draw out similarities and differences between energy flux streamlines and acoustic rays, particularly in the transition to the far field.

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Hilbert Space Theory And Applications In Basic Quantum Mechanics, Matthew Gagne Jun 2013

Hilbert Space Theory And Applications In Basic Quantum Mechanics, Matthew Gagne

Mathematics

We explore the basic mathematical physics of quantum mechanics. Our primary focus will be on Hilbert space theory and applications as well as the theory of linear operators on Hilbert space. We show how Hermitian operators are used to represent quantum observables and investigate the spectrum of various linear operators. We discuss deviation and uncertainty and briefly suggest how symmetry and representations are involved in quantum theory.

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Σary, Minnesota State University Moorhead, Mathematics Department Jun 2013

Σary, Minnesota State University Moorhead, Mathematics Department

Math Department Newsletters

No abstract provided.

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√(X2 + Μ) Is The Most Computationally Efficient Smooth Approximation To |X|: A Proof, Carlos Ramirez, Reinaldo Sanchez, Vladik Kreinovich, Miguel Argaez Jun 2013

√(X2 + Μ) Is The Most Computationally Efficient Smooth Approximation To |X|: A Proof, Carlos Ramirez, Reinaldo Sanchez, Vladik Kreinovich, Miguel Argaez

Departmental Technical Reports (CS)

In many practical situations, we need to minimize an expression of the type |c1| + ... + |cn|. The problem is that most efficient optimization techniques use the derivative of the objective function, but the function |x| is not differentiable at 0. To make optimization efficient, it is therefore reasonable to approximate |x| by a smooth function. We show that in some reasonable sense, the most computationally efficient smooth approximation to |x| is the function √(x2 + μ), a function which has indeed been successfully used in such optimization.

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Loops And Their Permutation Groups, Mark Greer Jun 2013

Loops And Their Permutation Groups, Mark Greer

Electronic Theses and Dissertations

This dissertation uses the connections between loops and their associated permutation groups to study certain varieties of loops. We first define a variety of loops generalizing commutative automorphic loops and show this new variety is power associative. We show a correspondence to Bruck loops of odd order and use this correspondence to give structural results for our new variety, which in turn hold for commutative automorphic loops. Next, we study a variety of loops that generalize both Moufang and Steiner loops. We extend on known results for Moufang loops and then extend two different doubling constructions for creating Moufang and …

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Insights On The Neyman - Pearson Lemma: Alternative Critical Regions, And Their Power., David E. Wetzell Jun 2013

Insights On The Neyman - Pearson Lemma: Alternative Critical Regions, And Their Power., David E. Wetzell

ACMS Conference Proceedings 2013

The Neyman-Pearson Lemma is a powerful fundamental lemma in the area of hypothesis testing in Statistics. It gives the best test when testing simple vs. simple hypotheses. In this talk we would like to investigate testing a population mean H0 μ = μ0 vs. H1 μ = μ1 > μ0. As a result of the N-P Lemma, the best test is of the form, “Reject H0 if x>c” , where c is chosen so that the Type I error probability is a. Let n be small. What are some alternative decision rules of size a, what …

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Service-Learning Panel, Dave Klanderman, Josh Wilkerson, Maria Zack Jun 2013

Service-Learning Panel, Dave Klanderman, Josh Wilkerson, Maria Zack

ACMS Conference Proceedings 2013

Many of us have wanted to incorporate service experiences in courses, or are being asked by our institutions to do so. Service-learning is a way of looking at service as being a partner with and leading to learning for our students. But in math, there are not a lot of resources to use! Our panelists will present classroom-tested ideas from several different levels of course, and we will end with a short time for more brainstorming among all participants.

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Pedagogical Enhancements To The Desymbol Logic Translator, Darren F. Provine, Nancy Lynn Tinkham Jun 2013

Pedagogical Enhancements To The Desymbol Logic Translator, Darren F. Provine, Nancy Lynn Tinkham

ACMS Conference Proceedings 2013

DeSymbol is a program that translates first-order predicate logic expressions into English. It is intended to be a practice tool for students who are learning logic for the first time or who are trying to refresh their memories if they need to use symbolic logic for an upper-level course. Students start with an English sentence and translate it by hand into symbolic logic notation; then they can check their work by using DeSymbol to translate their notation back into English. If the English sentence produced by DeSymbol differs significantly from the original English sentence, this helps the student to see …

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Mapping Biblical Commandments To An Iterated Prisoner’S Dilemma Framework, Nathan Gossett, Adam Johnson Jun 2013

Mapping Biblical Commandments To An Iterated Prisoner’S Dilemma Framework, Nathan Gossett, Adam Johnson

ACMS Conference Proceedings 2013

In his writings on Game Theory, an d the Iterated Prisoner’s Dilemma in particular, Robert Axelrod outlined four properties that are predictors of a successful strategy: Niceness, Reciprocity, Forgiveness, and Understandability. On the topic of Reciprocity, Axelrod makes the claim that not only does The Golden Rule lead to a suboptimal strategy, but that one of the most successful strategies (Tit for Tat) shows that a command of “An eye for an eye” leads to a much more optimal strategy. In this paper, we will discuss the details of Axelrod’s four properties, outline Biblical support for all four, and discuss …

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Open Source Software: What Is It, And Why Should We Care?, Karl-Dieter Crisman Jun 2013

Open Source Software: What Is It, And Why Should We Care?, Karl-Dieter Crisman

ACMS Conference Proceedings 2013

This paper examines the distinctions in talking about computer software that has implications for both mathematics and moral thought.

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Teaching Complex Analysis As A Lab-Type Course With A Focus On Geometric Interpretations Using Mathematics, William M. Kinney Jun 2013

Teaching Complex Analysis As A Lab-Type Course With A Focus On Geometric Interpretations Using Mathematics, William M. Kinney

ACMS Conference Proceedings 2013

I taught complex analysis for the first time in my career during the spring of 2013. I decided to do something “radical” and teach it as a lab-type course with a focus on geometric interpretations using the computer program Mathematica. The students and I met in a computer lab and, during most meetings, we spent a large portion of our time experimenting and exploring using Mathematica to visualize key concepts in complex analysis. Because of this, there was a heavy emphasis on viewing analytic functions as conformal mappings as well as considering associated vector fields and flows. Mathematica was used …

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Faith Integration Projects For First-Year Students, Doug Phillippy Jun 2013

Faith Integration Projects For First-Year Students, Doug Phillippy

ACMS Conference Proceedings 2013

This talk will consider the use of projects to motivate students to think deeply about how their faith connects with mathematics. This talk will begin by describing what a faith integration project is, including the goals and objectives of such a project. The talk will briefly describe a number of projects written by the speaker, with a more detailed look at one of those projects. The talk will conclude by discussing how these projects are being used to assess how students are doing at articulating a maturing understanding of the connection between faith and mathematics

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Philosophy Motivates Undergraduates In Mathematics, Dustin Wilson Jun 2013

Philosophy Motivates Undergraduates In Mathematics, Dustin Wilson

ACMS Conference Proceedings 2013

A talk on how elective seminars on the philosophy of mathematics can inspire undergraduate students to pursue and persist in mathematics.

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Mathematical Modeling Of The Regulatory T Cell Effects On Renal Cell Carcinoma Treatment, Lisette G. De Pillis, Trevor Caldwell '12, Elizabeth Sarapata '13, Heather Williams '12 Jun 2013

Mathematical Modeling Of The Regulatory T Cell Effects On Renal Cell Carcinoma Treatment, Lisette G. De Pillis, Trevor Caldwell '12, Elizabeth Sarapata '13, Heather Williams '12

All HMC Faculty Publications and Research

We present a mathematical model to study the effects of the regulatory T cells (Treg) on Renal Cell Carcinoma (RCC) treatment with sunitinib. The drug sunitinib inhibits the natural self-regulation of the immune system, allowing the effector components of the immune system to function for longer periods of time. This mathematical model builds upon our non-linear ODE model by de Pillis et al. (2009) [13] to incorporate sunitinib treatment, regulatory T cell dynamics, and RCC-specific parameters. The model also elucidates the roles of certain RCC-specific parameters in determining key differences between in silico patients whose immune profiles allowed them to …

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B Cell Chronic Lymphocytic Leukemia - A Model With Immune Response, Seema Nanda, Lisette G. De Pillis, Ami E. Radunskaya Jun 2013

B Cell Chronic Lymphocytic Leukemia - A Model With Immune Response, Seema Nanda, Lisette G. De Pillis, Ami E. Radunskaya

All HMC Faculty Publications and Research

B cell chronic lymphocytic leukemia (B-CLL) is known to have substantial clinical heterogeneity. There is no cure, but treatments allow for disease management. However, the wide range of clinical courses experienced by B-CLL patients makes prognosis and hence treatment a significant challenge. In an attempt to study disease progression across different patients via a unified yet flexible approach, we present a mathematical model of B-CLL with immune response, that can capture both rapid and slow disease progression. This model includes four different cell populations in the peripheral blood of humans: B-CLL cells, NK cells, cytotoxic T cells and helper T …

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Forming The Analytical Society At Cambridge University, Richard Stout Jun 2013

Forming The Analytical Society At Cambridge University, Richard Stout

ACMS Conference Proceedings 2013

The Analytical Society, an organization begun by students at Cambridge, was founded in 1812. Even though it was entirely student-led, the society was responsible for significant changes in the Cambridge mathematics curriculum and in the way mathematics was perceived in Britain throughout the nineteenth century. Its success was likely due to the outstanding students who formed the group, some of whom went on to become leaders in British science and mathematics for the next fifty years. In this paper we will briefly look at several of those who played important roles in forming and leading the society and we will …

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The Unity Of Knowledge And The Faithfulness Of God: The Theology Of Mathematical Physicist John Polkinghorne, Matt Delong Jun 2013

The Unity Of Knowledge And The Faithfulness Of God: The Theology Of Mathematical Physicist John Polkinghorne, Matt Delong

ACMS Conference Proceedings 2013

In this paper we will give a brief introduction to Polkinghorne's life and work. We will give an introduction to Polkinghorne's approach to philosophy and theology. We will introduce the two most significant influences on Polkinghorne's development as a theologian and philosopher of science. We will then give a necessarily telegraphic review of some of the topics addressed in Polkinghorne's theology, including his thoughts on science and religion, natural theology, evil, providence, prayer, resurrection, the soul and eschatology. We will then conclude with a few short examples of Polkinghorne's thoughts on mathematics.

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Leading A Successful Missions Trip In Your Discipline, Tom Nurkkala, Darci Nurkkala Jun 2013

Leading A Successful Missions Trip In Your Discipline, Tom Nurkkala, Darci Nurkkala

ACMS Conference Proceedings 2013

The global missions community goes wanting for skilled workers in almost every discipline. However, even students at a Christian institution that emphasizes global engagement remain largely unaware of the impact they can make in missions by leveraging their own academic specialty. In this paper, we draw on our experience leading discipline-specific missions trips as a means to encourage students to reframe their thinking about personal involvement in missions. We discuss the need for students to experience missions firsthand, and the student outcomes we have observed in intercultural awareness and spiritual formation. A key student outcome is an increased willingness to …

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Googol-Part Fugue: Another Imagination Of Divine Providence And Game Theory, Gideon Lee Jun 2013

Googol-Part Fugue: Another Imagination Of Divine Providence And Game Theory, Gideon Lee

ACMS Conference Proceedings 2013

The problem of evil presents an intellectual hurdle for some to believe in a good and omnipotent God. The emergence of open theism could be seen as an attempt to make a stronger case for the free will defense. However, in denying divine foreknowledge as traditionally understood, open theism contradicts biblical revelation not only in its direct claims, but also when its logical implications for divine providence are worked out. The open theist Alan Rhoda has sought to explain through game theory how some degree of divine providence is possible under open theism. That explanation is astonishing since the open …

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Life Lessons From Leibniz, Andrew J. Simoson Jun 2013

Life Lessons From Leibniz, Andrew J. Simoson

ACMS Conference Proceedings 2013

The tri-centennial of Leibniz’s death is nigh (2016). And 2013 is not too early to begin a special celebration of this man of mathematics. Besides being the co-discoverer of calculus and the implementer of binary numbers, formal logic, and formal languages, all of which foreshadowed the computer age, Leibniz is said to be one of the last to know almost everything that was known about almost anything. Professionally, his occupation was librarian in the princely court of Hanover in oldGermany. Serving under three different princes, the last of whom became George I of England, Leibniz had to continual lyre-invent himself—somewhat …

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Al-Khwārizmī: Founder Of Classical Algebra, Calvin Jongsma Jun 2013

Al-Khwārizmī: Founder Of Classical Algebra, Calvin Jongsma

ACMS Conference Proceedings 2013

Adopting a historically defensible definition of “algebra,” we will begin by exploring a few examples of algebra prior toal-Khwarizmi. We will then examine what algebra became through al-Khwarizmi’s work. In conclusion, we will assess thehistorical importance of al-Khwarizmi’s contributions for developments in European algebra.

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Expanding Jonathan Edwards’ Typology Program: The Bell Curve As A Type Of Christ, Jason Wilson Jun 2013

Expanding Jonathan Edwards’ Typology Program: The Bell Curve As A Type Of Christ, Jason Wilson

ACMS Conference Proceedings 2013

Over two hundred years after his death, an unfinished notebook of Jonathan Edwards’ was published for the first time in1993. Edwards was a father of the Evangelical movement, but because his work on typology was not published until recently, it has received almost no attention. In his notebook, Edwards makes an explicit argument for extending biblical typology to nature in a biblically grounded manner. This study is an attempt to extend that research program into mathematics/statistics.We will consider the following proposition, “The normal distribution (the graph of which is the bell curve) is a biblical type of Christ.” The basic …

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Knots In The Canonical Book Representation Of Complete Graphs, Dana Rowland, Andrea Politano Jun 2013

Knots In The Canonical Book Representation Of Complete Graphs, Dana Rowland, Andrea Politano

Mathematics Faculty Publications

We describe which knots can be obtained as cycles in the canonical book representation of the complete graph Kn, and we conjecture that the canonical book representation of Kn attains the least possible number of knotted cycles for any embedding of Kn. The canonical book representation of Kn contains a Hamiltonian cycle that is a composite knot if and only if n ≥12. When p and q are relatively prime, the (p, q) torus knot is a Hamiltonian cycle in the canonical book representation of K2p+q. …

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Delaware, Dickeson, Assessment And How You Can Help, Greg Crow, Maria Zack Jun 2013

Delaware, Dickeson, Assessment And How You Can Help, Greg Crow, Maria Zack

ACMS Conference Proceedings 2013

How much release time should a chair receive? What is the cost per unit for a particular academic program? What is a student credit hour (SCH) anyway and why would anyone care? Why are so many boards enamored of Delaware, Dickeson and Assessment? The answer to these and many related questions will be presented in this talk. Analytics and various“efficiency measures” are becoming increasingly important in higher education and mathematicians and computer scientists are being regularly recruited to help university administrators make meaning from large volumes of data. Come and learn about this trend and how you can be of …

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Topological Criteria For Schlichtness, Zach Teitler Jun 2013

Topological Criteria For Schlichtness, Zach Teitler

Mathematics Faculty Publications and Presentations

We give two sufficient criteria for schlichtness of envelopes of holomorphy in terms of topology. These are weakened converses of results of Kerner and Royden. Our first criterion generalizes a result of Hammond in dimension 2. Along the way, we also prove a generalization of Royden's theorem.

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Meromorphic Lévy-Khintchine Exponents With Poles Of Order Two, Guillaume Coqueret Jun 2013

Meromorphic Lévy-Khintchine Exponents With Poles Of Order Two, Guillaume Coqueret

Communications on Stochastic Analysis

No abstract provided.

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A Converse Comparison Theorem For Discrete-Time Finite-State Bsdes And Risk Measures Using G-Expectation, Robert Elliott, Yin Lin, Hailiang Yang Jun 2013

A Converse Comparison Theorem For Discrete-Time Finite-State Bsdes And Risk Measures Using G-Expectation, Robert Elliott, Yin Lin, Hailiang Yang

Communications on Stochastic Analysis

No abstract provided.

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A Hull And White Formula For A Stochastic Volatility Lévy Model With Infinite Activity, Hossein Jafari, Josep Vives Jun 2013

A Hull And White Formula For A Stochastic Volatility Lévy Model With Infinite Activity, Hossein Jafari, Josep Vives

Communications on Stochastic Analysis

No abstract provided.

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Fluctuation Properties Of Compound Poisson-Erlang Lévy Processes, Richard B Paris, Vladimir Vinogradov Jun 2013

Fluctuation Properties Of Compound Poisson-Erlang Lévy Processes, Richard B Paris, Vladimir Vinogradov

Communications on Stochastic Analysis

No abstract provided.

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