Digital Commons Network^™

We Are Still Playing: A Meta-Analysis Of Game-Based Learning In Mathematics Education, Thomas Conmy

Doctoral Dissertations

The purpose of this meta-analysis was to investigate the effectiveness of the use of games as part of mathematics instruction on academic achievement in grades Kindergarten to 12 in the United States. There were 17 studies selected for investigation published from 2010 to 2023 that focused on game-based learning and mathematics. This meta-analysis fills the gap in the knowledge by examining classes that are using game based learning across three platforms of instruction: nondigital games, digital on computers, and mobile devices. The findings from this meta-analysis suggest that the usage of game-based learning in a classroom has a positive effect …

Borsuk–Ulam Type Theorems For G-Spaces With Applications To Tucker Type Lemmas, Oleg R. Musin, Alexey Yu. Volovikov

School of Mathematical & Statistical Sciences Faculty Publications

In this paper we consider several generalizations of the Borsuk–Ulam theorem for G-spaces and apply these results to Tucker type lemmas for G-simplicial complexes and PL-manifolds.

Efficient High Order Ensemble For Fluid Flow, John Carter

Doctoral Dissertations

"This thesis proposes efficient ensemble-based algorithms for solving the full and reduced Magnetohydrodynamics (MHD) equations. The proposed ensemble methods require solving only one linear system with multiple right-hand sides for different realizations, reducing computational cost and simulation time. Four algorithms utilize a Generalized Positive Auxiliary Variable (GPAV) approach and are demonstrated to be second-order accurate and unconditionally stable with respect to the system energy through comprehensive stability analyses and error tests. Two algorithms make use of Artificial Compressibility (AC) to update pressure and a solenoidal constraint for the magnetic field. Numerical simulations are provided to illustrate theoretical results and demonstrate …

Advances In Differentially Methylated Region Detection And Cure Survival Models, Daniel Ahmed Alhassan

Doctoral Dissertations

"This dissertation focuses on two areas of statistics: DNA methylation and survival analysis. The first part of the dissertation pertains to the detection of differentially methylated regions in the human genome. The varying distribution of gaps between succeeding genomic locations, which are represented on the microarray used to quantify methylation, makes it challenging to identify regions that have differential methylation. This emphasizes the need to properly account for the correlation in methylation shared by nearby locations within a specific genomic distance. In this work, a normalized kernel-weighted statistic is proposed to obtain an optimal amount of "information" from neighboring locations …

Essays On Conditional Heteroscedastic Time Series Models With Asymmetry, Long Memory, And Structural Changes, K C M R Anjana Bandara Yatawara

Doctoral Dissertations

"The volatility of asset returns is usually time-varying, necessitating the introduction of models with a conditional heteroskedastic variance structure. In this dissertation, several existing formulations, motivated by the Generalized Autoregressive Conditional Heteroskedastic (GARCH) type models, are further generalized to accommodate more dynamic features of asset returns such as asymmetry, long memory, and structural breaks. First, we introduce a hybrid structure that combines short-memory asymmetric Glosten, Jagannathan, and Runkle (GJR) formulation and the long-memory fractionally integrated GARCH (FIGARCH) process for modeling financial volatility. This formulation not only can model volatility clusters and capture asymmetry but also considers the characteristic of long …

Recurrent Event Data Analysis With Mismeasured Covariates, Ravinath Alahakoon Mudiyanselage

Doctoral Dissertations

"Consider a study with n units wherein every unit is monitored for the occurrence of an event that can recur with random end of monitoring. At each recurrence, p concomitant variables associated to the event recurrence are recorded with q (q ≤ p) collected with errors. Of interest in this dissertation is the estimation of the regression parameters of event time regression models accounting for the covariates. To circumvent the problem of bias and consistency associated with model's parameter estimation in the presence of measurement errors, we propose inference for corrected estimating functions with well-behaved roots under additive measurement errors …

Probabilistic Solutions Of Fractional Differential And Partial Differential Equations And Their Monte Carlo Simulations, Tamer Oraby, Erwin Suazo, Harrinson Arrubla

School of Mathematical & Statistical Sciences Faculty Publications

The work in this paper is four-fold. Firstly, we introduce an alternative approach to solve fractional ordinary differential equations as an expected value of a random time process. Using the latter, we present an interesting numerical approach based on Monte Carlo integration to simulate solutions of fractional ordinary and partial differential equations. Thirdly, we show that this approach allows us to find the fundamental solutions for fractional partial differential equations (PDEs), in which the fractional derivative in time is in the Caputo sense and the fractional in space one is in the Riesz–Feller sense. Lastly, using Riccati equation, we …

Long-Time Asymptotics Of A Complex Cubic Camassa-Holm Equation, Hongyi Zhang, Yufeng Zhang, Zhijun Qiao

School of Mathematical & Statistical Sciences Faculty Publications

n this paper, we study the Cauchy problem of the following complex cubic Camassa-Holm (ccCH) equation mt=bux+12[m(|u|2−|ux|2)]x−12m(uu¯x−uxu¯),m=u−uxx,

where b is an arbitrary real constant. %By applying ∂¯-steepest descent method, l Long-time asymptotics of the equation is obtained through the ∂¯-steepest descent method. Firstly, based on the spectral analysis of the Lax pair and scattering matrix, the solution of the equation is able to be constructed %can be expressed by %the solution of via solving the corresponding Riemann-Hilbert problem (RHP). Then, we present %obtain different long time asymptotic expansions of the solution u(y,t) in different space-time solitonic regions of ξ=y/t. The …

Quantization Dimension For Inhomogeneous Bi-Lipschitz Ifs, Amit Priyadarshi, Mrinal Kanti Roychowdhury, Manuj Verma

School of Mathematical & Statistical Sciences Faculty Publications

Let ν be a Borel probability measure on a d-dimensional Euclidean space Rd, d≥1, with a compact support, and let (p0,p1,p2,…,pN) be a probability vector with pj>0 for 1≤j≤N. Let {Sj:1≤j≤N} be a set of contractive mappings on Rd. Then, a Borel probability measure μ on Rd such that μ=∑Nj=1pjμ∘S−1j+p0ν is called an inhomogeneous measure, also known as a condensation measure on Rd. For a given r∈(0,+∞), the quantization dimension of order r, if it exists, denoted by Dr(μ), of a Borel probability measure μ on Rd represents the speed at which the nth quantization error of order r …

Quantization For A Set Of Discrete Distributions On The Set Of Natural Numbers, Juan Gomez, Haily Martinez, Mrinal Kanti Roychowdhury, Alexis Salazar, Daniel J. Vallez

School of Mathematical & Statistical Sciences Faculty Publications

The quantization scheme in probability theory deals with finding a best approximation of a given probability distribution by a probability distribution that is supported on finitely many points. In this paper, first we state and prove a theorem, and then give a conjecture. We verify the conjecture by a few examples. Assuming that the conjecture is true, for a set of discrete distributions on the set of natural numbers we have calculated the optimal sets of n-means and the nth quantization errors for all positive integers n. In addition, the quantization dimension is also calculated.

Note On Illuminating Constant Width Bodies, Alexey Glazyrin

School of Mathematical & Statistical Sciences Faculty Publications

Recently, Arman, Bondarenko, and Prymak constructed a constant width body in R n whose illumination number is exponential in n. In this note, we improve their bound by generalizing the construction. In particular, we construct a constant width body in R n whose illumination number is at least (τ + o(1))n, where τ ≈ 1.047.

Constrained Quantization For Probability Distributions, Megha Pandey, Mrinal Kanti Roychowdhury

School of Mathematical & Statistical Sciences Faculty Publications

In this paper, for a Borel probability measure P on a Euclidean space Rk, we extend the definitions of nth unconstrained quantization error, unconstrained quantization dimension, and unconstrained quantization coefficient, which traditionally in the literature known as nth quantization error, quantization dimension, and quantization coefficient, to the definitions of nth constrained quantization error, constrained quantization dimension, and constrained quantization coefficient. The work in this paper extends the theory of quantization and opens a new area of research. In unconstrained quantization, the elements in an optimal set are the conditional expectations in their own Voronoi regions, and it is not true …

A Covariance Formula For The Number Of Excursion Set Components Of Gaussian Fields And Applications, Dmitry Beliaev, Michael Mcauley, Stephen Muirhead

Articles

We derive a covariance formula for the number of excursion or level set components of a smooth stationary Gaussian field on R^d contained in compact domains. We also present two applications of this formula: (1) for fields whose correlations are integrable we prove that the variance of the component count in large domains is of volume order and give an expression for the leading constant, and (2) for fields with slower decay of correlation we give an upper bound on the variance which is of optimal order if correlations are regularly varying, and improves on best-known bounds if correlations …

2-Uniform Covering Groups Of Elementary Abelian 2-Groups, Dana Saleh, Rachel Quinlan

All Works

This article is concerned with the classification of Schur covering groups of the elementary abelian group of order (Formula presented.), up to isomorphism. We consider those covering groups possessing a generating set of n elements having only two distinct squares. We show that such groups may be represented by 2-vertex-colored and 2-edge-colored graphs of order n. We show that in most cases, the isomorphism type of the group is determined by that of the 2-colored graph, and we analyze the exceptions.

Oscillating Icebergs, John Adam

Mathematics & Statistics Faculty Publications

No abstract provided.

Exploding Haystacks, John Adam

Mathematics & Statistics Faculty Publications

No abstract provided.

Another Angle On Perspective: Solutions For Fermi Questions, May 2023, John Adam

Mathematics & Statistics Faculty Publications

No abstract provided.

Not Your Typical Tower Of Sauron, John Adam

Mathematics & Statistics Faculty Publications

The picture is of the tapering Chester Shot Tower, located in Chester, England. It was built in 1799 for the manufacture of lead shot for use in the Napoleonic Wars. Molten lead was poured through a sieve at the top of the tower, with the tiny droplets forming perfect spheres during the fall; these were then cooled in a vat of water at the base. This process was less labor intensive than an earlier method using molds. It is the oldest of the three remaining shot towers in the UK.

Question 1: Using the parked van at the base, estimate …

Dental Floss, Calculus, And Jail, John Adam

Mathematics & Statistics Faculty Publications

No abstract provided.

Dental Floss, Calculus, And Jail: Solutions For Fermi Questions, October 2023, John Adam

Mathematics & Statistics Faculty Publications

No abstract provided.

Jet Noise Reduction: A Fresh Start, Christopher K. Tam, Fang Q. Hu

Mathematics & Statistics Faculty Publications

Attempts to reduce jet noise began some 70 years ago. In the literature, there have been many publications written on this topic. By now, it is common knowledge that jet noise consists of a number of components. They possess different spectral and radiation characteristics and are generated by different mechanisms. It appears then that one may aim at the suppression of the noise of a single component instead of trying to reduce jet noise overall. The objective of the present project is to reduce large turbulence structures noise. It is the most dominant noise component radiating in the downstream direction. …

Charging Of Irregularly-Shaped Dust Grains Near Surfaces In Space, David Lund, Xiaoming He, Daoru Han

Mathematics and Statistics Faculty Research & Creative Works

This paper presents fully kinetic numerical investigation of the charging of dust grains in low temperature collision less plasmas (stationary) and collision less, cold-ion thermal-electron drifting plasmas. the Parallel Immersed-Finite-Element Particle-in-Cell (PIFE-PIC) code is utilized to self-consistently resolve the plasma environment and charging of immersed materials. This model explicitly includes the materials property (dielectric constant) of dust grains. Effects of materials property, inter-dust distance, and plasma conditions (stationery and drifting) will be investigated for both single-dust and multi-dust configurations.

Spectral Sequences And Khovanov Homology, Zachary J. Winkeler

Dartmouth College Ph.D Dissertations

In this thesis, we will focus on two main topics; the common thread between both will be the existence of spectral sequences relating Khovanov homology to other knot invariants. Our first topic is an invariant MKh(L) for links in thickened disks with multiple punctures. This invariant is different from but inspired by both the Asaeda-Pryzytycki-Sikora (APS) homology and its specialization to links in the solid torus. Our theory will be constructed from a Z^n-filtration on the Khovanov complex, and as a result we will get various spectral sequences relating MKh(L) to Kh(L), AKh(L), and APS(L). Our …

Spherical Aluthge Transform, Spherical P And Log-Hyponormality Of Commuting Pairs Of Operators Ii, Hyung Won Kim, Jaewoong Kim, Jasang Yoon

School of Mathematical & Statistical Sciences Faculty Publications

In this paper, we consider the notions of spherical p, log, and w-hyponormality of commuting pairs of operators and study their properties and relations. We first show that spherically p-hyponormal 2-variable weighted shifts of hyponormal operators are invariant under powers and the generalized spherical Aluthge transformation. Second, we study the relation between spherical p-hyponormality and spherical w-hyponormality. Third, we study whether the spherical p-hyponormality with 0<p< 1 is invariant under the spherical Aluthge transformation. Finally, we briefly discuss the relation between log-hyponormality in single operators and spherically log-hyponormality in commuting pairs of operators.

Classification On Boundary-Equilibria And Singular Continuums Of Continuous Piecewise Linear Systems, Hebai Chen, Zhaosheng Feng, Hao Yang, Linfeng Zhou

School of Mathematical & Statistical Sciences Faculty Publications

In this paper, we show that any switching hypersurface of n -dimensional continuous piecewise linear systems is an (n−1) -dimensional hyperplane. For two-dimensional continuous piecewise linear systems, we present local phase portraits and indices near the boundary equilibria (i.e. equilibria at the switching line) and singular continuum (i.e. continuum of nonisolated equilibria) between two parallel switching lines. The index of singular continuum is defined. Then we show that boundary-equilibria and singular continuums can appear with many parallel switching lines.

Equity In Focus : Investigating Gender Disparities In Glioblastoma Via Propensity Score Matching, Solomon Eshun

School of Mathematical & Statistical Sciences Faculty Publications

Gender disparities in health outcomes have garnered significant attention, prompting investigations into their underlying causes. Glioblastoma (GBM), a devastating and highly aggressive form of brain tumor, serves as a case for such inquiries. Despite the mounting evidence on gender disparities in GBM outcomes, investigations specific at the molecular level remain scarce and often limited by confounding biases in observational studies. In this study, I aimed to investigate the gender-related differences in GBM outcomes using propensity score matching (PSM) to control for potential confounding variables. The data used was accessed from the Cancer Genome Atlas (TCGA), encompassing factors such as gender, …

Resurgence Of Habiro Elements, Samuel Crew, Ankush Goswami, Robert Osburn

School of Mathematical & Statistical Sciences Faculty Publications

We prove resurgence properties for the Borel transform of elements in the Habiro ring which satisfy a general type of strange identity. As an application, we provide evidence for (and against) conjectures in quantum topology due to Costin and Garoufalidis.

Modeling Repairable System Failure Data Using Nhpp Reliability Growth Mode., Eunice Ofori-Addo

EWU Masters Thesis Collection

Stochastic point processes have been widely used to describe the behaviour of repairable systems. The Crow nonhomogeneous Poisson process (NHPP) often known as the Power Law model is regarded as one of the best models for repairable systems. The goodness-of-fit test rejects the intensity function of the power law model, and so the log-linear model was fitted and tested for goodness-of-fit. The Weibull Time to Failure recurrent neural network (WTTE-RNN) framework, a probabilistic deep learning model for failure data, is also explored. However, we find that the WTTE-RNN framework is only appropriate failure data with independent and identically distributed interarrival …

An Intertwined Cauchy––Schwarz–Type Inequality Based On A Lagrange–Type Identity, Iosif Pinelis

Michigan Tech Publications

Based on an apparently new Lagrange-type identity, a Cauchy–Schwarz-type inequality is proved. The mentioned identity is obtained by using certain “macro” variables; it is hoped that such a method can be used to prove or produce other identities and inequalities.

On Regular D-Handicap Tournaments, Bryan Freyberg, Melissa S. Keranen

Michigan Tech Publications, Part 1

k-regular d-handicap tournament is an incomplete tournament in which n teams, ranked according to the natural numbers, play exactly k < n − 1 different teams exactly once and the strength of schedule of the ith ranked team is d more than the (i − 1)st ranked team for some d ≥ 1. That is, strength of schedules increase arithmetically by d with strength of team. A d-handicap distance antimagic labeling of a graph (Formula Presented)forms an arithmetic sequence with difference d ≥ 1. A graph G which admits such a labeling is called a d-handicap graph. Constructing a k-regular d-handicap tournament on n teams is equivalent to finding a k-regular d-handicap graph of order n. For d = 1 and n even, the existence has recently been completely settled for all pairs (n, k), and some results are known for d = 2. For d > 2, the only known result is restricted to the case where n is divisible by 2d+2. In this paper, we construct infinite families of d-handicap graphs where the order is not restricted to a power of 2.