Mathematics Commons^™

On The Lagrangian Description And Uniqueness For The One-Dimensional Pressureless Euler System, Mark David Suder

Graduate Theses, Dissertations, and Problem Reports (ETD)

In this work we show that the one-dimensional pressureless Euler system admits a Lagragian characterization under fairly general initial conditions, extending recent results by Hynd [7]. Moreover, we show that if the initial velocity is right-continuous and bounded, then we have uniqueness of this Lagrangian solution (called Sticky Particles Flow, or SPF solution), which coincides with the Scalar Conservation Laws (or SCL) solution. An important tool we employed in order to prove existence is a result by Gangbo et al. [5], which establishes a canonical (i.e. the flow is given by the optimal maps pushing the Lebesgue measure restricted to …

Remediation Of Spatial Skills In First Semester Calculus Using Haptics-Based Applications, Kristen L. Murphy

Graduate Theses, Dissertations, and Problem Reports (ETD)

Spatial reasoning is required for many topics in undergraduate mathematics as well as other STEM fields. In calculus specifically, there are few interventions that assess students’ spatial skills and provide remediation. Haptic technology is a novel approach to spatial skills remediation due to its unfamiliarity to students and its flexibility with regard to models. The purpose of this dissertation is two-fold: first, to determine what level of spatial abilities students possess upon entering an undergraduate calculus course, and second, to determine whether haptic feedback will enhance an intervention for improving spatial skills.

The dissertation research was a mixed-methods study using …

Using Sentiment Analysis To Find The Public's Opinion On Iowa's Three State Schools, Alexa Ryan Bullock

Honors Program Theses

The purpose of this project was to create my own sentiment analysis that would allow me to analyze reviews of the three Iowa state schools: University of Iowa, Iowa State, and University of Northern Iowa, and organize them in a way that showed the strong and weak points of each university. I accomplished this by researching how sentiment analysis works, applying that to the construction of my own sentiment analysis, and then using it on reviews about these three schools. The goal of this project was to give my audience a greater understanding of how sentiment analysis works by creating …

Analyzing Applied Calculus Student Understanding Of Definite Integrals In Real-Life Applications, Cody Hood

Graduate Theses, Dissertations, and Problem Reports (ETD)

An individual’s knowledge of definite integrals can range from rote memorization to a strong foundational connection harkening back to its Riemann sum limit definition. In my research, I conducted seven task-based face-to-face interviews with Applied Calculus students. Through the use of real-life examples and guided reinvention, I analyzed ways in which these students, who all initially demonstrated rote memorization, could exhibit a Riemann sum based level of comprehension. This research was conducted in the confines of a student population with definite integral experience, but no formal instruction on limits. My results show that the lack of computational emphasis in class …

Heterogeneous Generalizations Of Vertex Coloring, Lucian Ciletti Mazza

Graduate Theses, Dissertations, and Problem Reports (ETD)

This dissertation proves a collection of results in some heterogeneous generalizations of vertex coloring, i.e. generalizations in which the relationship between the colors of two adjacent vertices may differ throughout the graph. For the most part, the results are from group coloring, group list coloring, and DP coloring. The main results are as follows: a group list coloring analogue of Brooks' Theorem for multigraphs, a result linking group structure (rather than only group size) with group coloring, some results involving coloring edge-disjoint unions, and an examination of the relationship between the group and DP coloring numbers of a multigraph and …

Exponential Random Graphs And A Generalization Of Parking Functions, Ryan Demuse

Electronic Theses and Dissertations

Random graphs are a powerful tool in the analysis of modern networks. Exponential random graph models provide a framework that allows one to encode desirable subgraph features directly into the probability measure. Using the theory of graph limits pioneered by Borgs et. al. as a foundation, we build upon the work of Chatterjee & Diaconis and Radin & Yin. We add complexity to the previously studied models by considering exponential random graph models with edge-weights coming from a generic distribution satisfying mild assumptions. In particular, we show that a large family of two-parameter, edge-weighted exponential random graphs display a phase …

Characterizations Of Student, Instructor, And Textbook Discourse Related To Basis And Change Of Basis In Quantum Mechanics, Kaitlyn Stephens Serbin, Megan Wawro, Rebecah Storms

School of Mathematical & Statistical Sciences Faculty Publications

Communities develop social languages in which utterances take on culturally specific situated meanings. As physics students interact in their classroom, they can learn the broader physics community’s social language by co-constructing meanings with their instructors. We provide an exposition of a systematic and productive use of idiosyncratic, socially acquired language in two classroom communities that we consider to be subcultures of the broader community of physicists. We perform a discourse analysis on twelve quantum mechanics students, two instructors, and the course text related to statements about basis and change of basis within a spin-½ probability problem. We classify the utterances’ …

Majorization And Minimal Energy On Spheres, Oleg R. Musin

School of Mathematical & Statistical Sciences Faculty Publications

In the present paper, we consider the majorization theorem (also known as Karamata's inequality) and the respective minima of the majorization (the so-called M-sets) for f-energy potentials of m-point configurations on the unit sphere. In particular, we show the optimality of regular simplexes, describe some M-sets of small cardinality, define and discuss spherical f-designs.

Analysis Of Intervention Effectiveness Using Early Outbreak Transmission Dynamics To Guide Future Pandemic Management And Decision-Making In Kuwait, Michael G. Tyshenko, Tamer Oraby, Joseph C. Longenecker, Harri Vainio, Janvier Gasana, Walid Q. Alali, Mohammad Alseaidan, Susie Elsaadany, Mustafa Al-Zoughool

School of Mathematical & Statistical Sciences Faculty Publications

Severe Acute Respiratory Syndrome Coronavirus 2 (SARS-CoV-2) is a World Health Organization designated pandemic that can result in severe symptoms and death that disproportionately affects older patients or those with comorbidities. Kuwait reported its first imported cases of COVID-19 on February 24, 2020. Analysis of data from the first three months of community transmission of the COVID-19 outbreak in Kuwait can provide important guidance for decision-making when dealing with future SARS-CoV-2 epidemic wave management. The analysis of intervention scenarios can help to evaluate the possible impacts of various outbreak control measures going forward which aim to reduce the effective reproduction …

Hexagon Tilings Of The Plane That Are Not Edge-To-Edge, D. Frettlöh, Alexey Glazyrin, Z. Lángi

School of Mathematical & Statistical Sciences Faculty Publications

An irregular vertex in a tiling by polygons is a vertex of one tile and belongs to the interior of an edge of another tile. In this paper we show that for any integer k≥3, there exists a normal tiling of the Euclidean plane by convex hexagons of unit area with exactly k irregular vertices. Using the same approach we show that there are normal edge-to-edge tilings of the plane by hexagons of unit area and exactly k many n-gons (n>6) of unit area. A result of Akopyan yields an upper bound for k depending on the maximal diameter …

Internet-Based Cognitive–Behavioural Therapy For Tinnitus: Secondary Analysis To Examine Predictors Of Outcomes, Hansapani Rodrigo, Eldré W. Beukes, Gerhard Andersson, Vinaya Manchaiah

School of Mathematical & Statistical Sciences Faculty Publications

Objectives The current study examined predictors of outcomes of internet-based cognitive–behavioural therapy (ICBT) for individuals with tinnitus.

Design Secondary analysis of intervention studies.

Setting Internet-based guided tinnitus intervention provided in the UK.

Participants 228 individuals who underwent ICBT.

Interventions ICBT.

Primary and secondary outcome measures The key predictor variables included demographic, tinnitus, hearing-related and treatment-related variables as well as clinical factors (eg, anxiety, depression, insomnia), which can have an impact on the treatment outcome. A 13-point reduction in Tinnitus Functional Index (TFI) scores has been defined as a successful outcome.

Results Of the 228 subjects who were included in the …

Geometric Properties Of Representation Varieties For An Elementary Abelian Group Of Rank 2 In Positive Characteristic, Eric Johnson

Graduate Research Theses & Dissertations

This dissertation’s motivation is the exploration of the irreducible components of Repn(kG), the affine variety whose points are n-dimensional representations of a finite group G over a field k. We let G = Z/pZ×Z/pZ and assume k is algebraically closed with char(k) = p > 0. In this case there is an isomorphism of affine varieties φ : Repn (kG) → C nil 1 (n) where C nil 1 (n) = {(x, y) Mn(k)×Mn(k) | x p = y p = xy−yx = 0}. Hence, for an irreducible component X of Repn (kG), φ(X) is an irreducible component of C nil …

Optimization Of Dynamic Objective Functions Using Path Integrals, Paramahansa Pramanik

Graduate Research Theses & Dissertations

Path integrals are used to find an optimal strategy for a firm under a Walrasian system. We define dynamic optimal strategies and develop an integration method to capture all non-additive non-convex strategies. We also show that the method can solve the non-linear case, for example Merton-Garman-Hamiltonian system, which the traditional Pontryagin maximum principle cannot solve in closed form. Furthermore, we assume that the strategy space and time are inseparable with respect to a contract. Under this assumption we show that the strategy spacetime is a dynamic curved Liouville-like 2-brane quantum gravity surface under asymmetric information and that traditional Euclidean geometry …

The Zorich Transform And Generalizing Koenigs Linearization Theorem To Quasiregular Maps, Jacob A. Pratscher

Graduate Research Theses & Dissertations

This dissertation investigates the role that a new tool called the Zorich transform plays in quasiregular dynamics as a generalization of the logarithmic transform in complex dynamics. In particular we use the Zorich transform to construct analogues of the logarithmic spiral maps and interpolation between radial stretch maps. These constructions are then used to completely classify the orbit space of a quasiregular map. Also, conditions are given in which a quasiregular map $f:D\to\R^n$, where $D\subset\R^n$ is a domain, that is quasiconformal in a neighborhood of a geometrically attracting fixed point can be conjugated by a quasiconformal map to the asymptotic …

Cheeger Constants Of Two Related Hyperbolic Riemann Surfaces, Ronald E. Hoagland

Masters Theses

This thesis concerns the study of the Cheeger constant of two related hyperbolic Riemann surfaces. The first surface R is formed by taking the quotient U²/Γ(4), where U² is the upper half-plane model of the hyperbolic plane and Γ(4) is a congruence subgroup of PSL2(Z), an isometry group of U² . This quotient is shown to form a Riemann surface which is constructed by gluing sides of a fundamental domain for Γ(4) together according to certain specified side pairings. To form the related Riemann surface R' , we follow a similar procedure, this time taking the …

Solutions For Fermi Questions, November 2021: Question 1: Chess Moves, Question 2: Cat Litter, Larry Weinstein

Physics Faculty Publications

Answers to the questions: How many chess moves are made by Americans each year? How much cat litter did Americans scoop last year?

Solutions For Fermi Questions, September 2021: Question 1: Cell Phone Gold, Question 2: Food For Thought, Larry Weinstein

Physics Faculty Publications

Answers to the questions: "How much gold is in a cell phone? Is it worth mining cell phones for gold?"

Question 1: Chess Moves; Question 2: Cat Litter, Larry Weinstein

Physics Faculty Publications

How many chess moves are made by Americans each year?

How much cat litter did Americans scoop last year?

Solutions For Femi Questions, October 2021: Rising Water Level: Popping Many Pimples, Larry Weinstein

Physics Faculty Publications

[Introduction] How much would sea levels rise if everyone jumped in the ocean? (Thanks to Bob Friedhoffer for suggesting the problem.)

To estimate this, we need to know the number of people, the average volume of a person, and the area of the oceans. This is the kind of estimation problem where the inputs are relatively well known, and we are calculating the answer to see its order of magnitude.

There are about 7 X 10⁹ people in the world. If each person has a mass of 100 kg (in round numbers), then they each have a volume …

On Coloring Oriented Graphs Of Large Girth, Michael Morris

Graduate Student Theses, Dissertations, & Professional Papers

No abstract provided.

Joint Modeling Of Rnaseq And Radiomics Data For Glioma Molecular Characterization And Prediction, Zeina A. Shboul, Norou Diawara, Arastoo Vossough, James Y. Chen, Khan M. Iftekharuddin

Electrical & Computer Engineering Faculty Publications

RNA sequencing (RNAseq) is a recent technology that profiles gene expression by measuring the relative frequency of the RNAseq reads. RNAseq read counts data is increasingly used in oncologic care and while radiology features (radiomics) have also been gaining utility in radiology practice such as disease diagnosis, monitoring, and treatment planning. However, contemporary literature lacks appropriate RNA-radiomics (henceforth, radiogenomics) joint modeling where RNAseq distribution is adaptive and also preserves the nature of RNAseq read counts data for glioma grading and prediction. The Negative Binomial (NB) distribution may be useful to model RNAseq read counts data that addresses potential shortcomings. …

Formal Power Series Approach To Nonlinear Systems With Static Output Feedback, G.S. Venkatesh, W. Steven Gray

Electrical & Computer Engineering Faculty Publications

The goal of this paper is to compute the generating series of a closed-loop system when the plant is described in terms of a Chen-Fliess series and static output feedback is applied. The first step is to reconsider the so called Wiener-Fliess connection consisting of a Chen-Fliess series followed by a memoryless function. Of particular importance will be the contractive nature of this map, which is needed to show that the closed-loop system has a Chen-Fliess series representation. To explicitly compute the generating series, two Hopf algebras are needed, the existing output feedback Hopf algebra used to describe dynamic output …

Combining Assumptions And Graphical Network Into Gene Expression Data Analysis, Demba Fofana, E. O. George, Dale Brown

School of Mathematical & Statistical Sciences Faculty Publications

Background

Analyzing gene expression data rigorously requires taking assumptions into consideration but also relies on using information about network relations that exist among genes. Combining these different elements cannot only improve statistical power, but also provide a better framework through which gene expression can be properly analyzed.

Material and methods

We propose a novel statistical model that combines assumptions and gene network information into the analysis. Assumptions are important since every test statistic is valid only when required assumptions hold. So, we propose hybrid p-values and show that, under the null hypothesis of primary interest, these p-values are …