Mathematics Commons^™

Research On Correlation Effects Between Tianjin Port And Its Inland Ports Based On Modified Gravity Model, Yayun Zhao

World Maritime University Dissertations

No abstract provided.

Composite Dilation Wavelets With High Degrees, Tian-Xiao He

Scholarship

No abstract provided.

Climatology Of Medium-Scale Traveling Ionospheric Disturbances Observed By The Midlatitude Blackstone Superdarn Radar, N. A. Frissell, J. B. H. Baker, J. M. Ruohoniemi, A. J. Gerrard, E. S. Miller, J. P. Marini, M. L. West, W. A. Bristow

Department of Mathematics Faculty Scholarship and Creative Works

A climatology of daytime midlatitude medium-scale traveling ionospheric disturbances (MSTIDs) observed by the Blackstone Super Dual Auroral Radar Network (SuperDARN) radar is presented. MSTIDs were observed primarily from fall through spring. Two populations were observed: a dominant population heading southeast (centered at 147° geographic azimuth, ranging from 100° to 210°) and a secondary population heading northwest (centered at −50° azimuth, ranging from −75° to −25°). Horizontal velocities ranged from 50 to 250 m s−1 with a distribution maximum between 100 and 150 m s−1. Horizontal wavelengths ranged from 100 to 500 km with a distribution peak at 250 km, and …

Choosing Between Parametric And Non-Parametric Tests, Russ Johnson

Journal of Undergraduate Research at Minnesota State University, Mankato

A common question in comparing two sets of measurements is whether to use a parametric testing procedure or a non-parametric procedure. The question is even more important in dealing with smaller samples. Here, using simulation, several parametric and nonparametric tests, such as, t-test, Normal test, Wilcoxon Rank Sum test, van-der Waerden Score test, and Exponential Score test are compared.

On Sign-Solvable Linear Systems And Their Applications In Economics, Eric Hanson

Journal of Undergraduate Research at Minnesota State University, Mankato

Sign-solvable linear systems are part of a branch of mathematics called qualitative matrix theory. Qualitative matrix theory is a development of matrix theory based on the sign (¡; 0; +) of the entries of a matrix. Sign-solvable linear systems are useful in analyzing situations in which quantitative data is unknown or had to measure, but qualitative information is known. These situations arise frequently in a variety of disciplines outside of mathematics, including economics and biology. The applications of sign-solvable linear systems in economics are documented and the development of new examples is formalized mathematically. Additionally, recent mathematical developments about sign-solvable …

Asymptotic Expansions And Computation Of Generalized Stirling Numbers And Generalized Stirling Functions, Tian-Xiao He

Scholarship

Here presented is a unified approach to Stirling numbers and their generalizations as well as generalized Stirling functions by using generalized factorial functions, k-Gamma functions, and generalized divided difference. Previous well-known extensions of Stirling numbers due to Riordan, Carlitz, Howard, Charalambides-Koutras, Gould-Hopper, Hsu-Shiue, Tsylova Todorov, Ahuja-Enneking, and Stirling functions introduced by Butzer and Hauss, Butzer, Kilbas, and Trujilloet and others are included as particular cases of our generalization. Some basic properties related to our general pattern such as their recursive relations and generating functions are discussed. Some asymptotic expansions for the generalized Stirling functions and generalized Stirling numbers are established. …

Morphological Operations Applied To Digital Art Restoration, M. Kirbie Dramdahl

Scholarly Horizons: University of Minnesota, Morris Undergraduate Journal

This paper provides an overview of the processes involved in detecting and removing cracks from digitized works of art. Specific attention is given to the crack detection phase as completed through the use of morphological operations. Mathematical morphology is an area of set theory applicable to image processing, and therefore lends itself effectively to the digital art restoration process.

Explorations In Elementary And Analytic Number Theory, Scott Michael Dunn

Theses and Dissertations

In this dissertation, we investigate two distinct questions in number theory. Each question is dedicated its own chapter.

First, we consider arithmetic progressions in the polygonal numbers with a fixed number of sides. We will show that four-term arithmetic progressions cannot exist. We then describe explicitly how to find all three-term arithmetic progressions. Additionally we show that there are infinitely many three-term arithmetic progressions starting with an arbitrary polygonal number.

Second, we will show certain irreducibility criteria for polynomials. Let f(x) be a polynomial with non-negative integer coefficients such that f(b) is prime for some integer 2 ≤ b ≤ …

On The Group Of Transvections Of Ade-Diagrams, Marvin Jones

Theses and Dissertations

In this thesis we examine symplectic spaces with forms generated by the ADEdiagrams. Specifically, we determine the generators of the group of transvections for each space under the standard basis, S, of Kⁿ (where K is a field with characteristic 0) and the hyperbolic basis, H, we get from the classification theorem of symplectic spaces. Further, we examine how the generators of these groups are related via g : G_f,S ! SL(Z)_n where g(X) = P⁻¹XP where P is the change of basis matrix for S to H.

The Non-Existence Of A Covering System With All Moduli Distinct, Large And Square-Free, Melissa Kate Bechard

Theses and Dissertations

The work in this thesis is based on a paper written by Bob Hough in 2013. This thesis addresses the conjecture posed by Erdos that the least modulus for a covering system can be arbitrarily large. Hough proves the least modulus cannot be arbitrarily large. In this thesis, we present Hough’s proof for the case of square-free moduli.

Fake Real Quadratic Orders, Richard Michael Oh

Theses and Dissertations

The study of fake real quadratic orders is fascinating as their class group structure is similiar to real quadratic fields. Statistical data strongly agree with the heuristics of Cohen and Lenstra of real quadratics with class number one. We will investigate why this holds true as well as explore other analogues to open conjecture on real quadratic fields, such as the Ankeny-Artin-Chowla Conjecture, and present various results that mark the similiarities between real quadratic fields and fake real quadratic orders. Fake real quadratics are defined by inverting an ideal above any prime p which is split in OK where K …

Epistasis In Predator-Prey Relationships, Iuliia Inozemtseva, James P. Braselton

Mathematical Sciences: Faculty Publications

Epistasis is the interaction between two or more genes to control a single phenotype. We model epistasis of the prey in a two-locus two-allele problem in a basic predator-prey relationship. The resulting model allows us to examine both population sizes as well as genotypic and phenotypic frequencies. In the context of several numerical examples, we show that if epistasis results in an undesirable or desirable phenotype in the prey by making the particular genotype more or less susceptible to the predator or dangerous to the predator, elimination of undesirable phenotypes and then genotypes occurs.

Spatiotemporal Crime Analysis, James Q. Tay, Abish Malik, Sherry Towers, David Ebert

The Summer Undergraduate Research Fellowship (SURF) Symposium

There has been a rise in the use of visual analytic techniques to create interactive predictive environments in a range of different applications. These tools help the user sift through massive amounts of data, presenting most useful results in a visual context and enabling the person to rapidly form proactive strategies. In this paper, we present one such visual analytic environment that uses historical crime data to predict future occurrences of crimes, both geographically and temporally. Due to the complexity of this analysis, it is necessary to find an appropriate statistical method for correlative analysis of spatiotemporal data, as well …

Isometric Weighted Composition Operators, Valentin Matache

Mathematics Faculty Publications

A composition operator is an operator on a space of functions defined on the same set. Its action is by composition to the right with a fixed selfmap of that set. A composition operator followed by a multiplication operator is called a weighted composition operator. In this paper, we study when weighted composition operators on the Hilbert Hardy space of the open unit disc are isometric. We find their Wold decomposition in select cases and apply it to the computation of numerical ranges.

Calculation Of The Killing Form Of A Simple Lie Group, Sean A. Broughton

Mathematical Sciences Technical Reports (MSTR)

The Killing form of a simple Lie Algebra is determined from invariants of the extended root diagrams of the Lie algebra.

Math Talk: Preparing Your Conference Presentation, Gizem Karaali

Pomona Faculty Publications and Research

If you are a typical reader of this blog, then you recently wrapped up your finals week and then dutifully made a summer plan. And then came the summer. Your plan may have involved working on a manuscript, preparing for a qualifying exam or a new course coming up in the fall, drafting a grant proposal, learning a new language (human or machine), eating kale in four different forms, and perhaps some fun times under the sun. Some, like me, also made plans to travel to conferences and give talks. Gearing up to get ready for my first conference of …

Light Pollution Research Through Citizen Science, John Kanemoto

STAR Program Research Presentations

Light pollution (LP) can disrupt and/or degrade the health of all living things, as well as, their environments. The goal of my research at the NOAO was to check the accuracy of the citizen science LP reporting systems entitled: Globe at Night (GaN), Dark Sky Meter (DSM), and Loss of the Night (LoN). On the GaN webpage, the darkness of the night sky (DotNS) is reported by selecting a magnitude chart. Each magnitude chart has a different density/number of stars around a specific constellation. The greater number of stars implies a darker night sky. Within the DSM iPhone application, a …

Four Quotient Set Gems, Stephan Ramon Garcia, Michael Someck '14, Bob Lutz '13, Bryan Brown '15, Michael Dairyko '13

Pomona Faculty Publications and Research

Our aim in this note is to present four remarkable facts about quotient sets. These observations seem to have been overlooked by the MONTHLY, despite its intense coverage of quotient sets over the years.

Exponential Decay Of Reconstruction Error From Binary Measurements Of Sparse Signals, Richard Baraniuk, Simon Foucart, Deanna Needell, Yaniv Plan, Mary Wootters

CMC Faculty Publications and Research

Binary measurements arise naturally in a variety of statistical and engineering applications. They may be inherent to the problem—e.g., in determining the relationship between genetics and the presence or absence of a disease—or they may be a result of extreme quantization. A recent influx of literature has suggested that using prior signal information can greatly improve the ability to reconstruct a signal from binary measurements. This is exemplified by onebit compressed sensing, which takes the compressed sensing model but assumes that only the sign of each measurement is retained. It has recently been shown that the number of one-bit measurements …

Mathematical Content Knowledge For Teaching Elementary Mathematics: A Focus On Decimals, Signe Kastberg, Crystal Morton

The Mathematics Enthusiast

In the last 25 years a small collection of reports of studies focused on gaining insight into PTs’ knowledge of decimals has been published. Three themes are used to frame findings from papers published prior to 1998. Additional findings from papers published between 1998 and 2011 are discussed. Direction for future research that can contribute to the development of curriculum and instruction in mathematics teacher education is shared.