Applied Mathematics Commons^™

Asymptotic Behavior Of Random Defective Parking Functions, John T. Mann, Zecheng You, Mei Yin

DU Undergraduate Research Journal Archive

Suppose that m drivers each choose a preferred parking space in a linear car park with n spots. In order, each driver goes to their desired spot and parks there if possible. If the spot is already occupied then the car parks in the first available spot after that; if no such spot is available then the car leaves the street without parking. When m > n, there will always be defects–cars that are not able to park. Building upon the work in Cameron et al. "Counting defective parking functions," we introduce a multi-shuffle construction to defective parking functions and …

Du Undergraduate Showcase: Research, Scholarship, And Creative Works, Caitlyn Aldersea, Justin Bravo, Sam Allen, Anna Block, Connor Block, Emma Buechler, Maria De Los Angeles Bustillos, Arianna Carlson, William Christensen, Olivia Kachulis, Noah Craver, Kate Dillon, Muskan Fatima, Angel Fernandes, Emma Finch, Colleen Cassidy, Amy Fishman, Andrea Francis, Stacia Fritz, Simran Gill, Emma Gries, Rylie Hansen, Shannon Powers, Jacqueline Martinez, Zachary Harker, Ashley Hasty, Mykaela Tanino-Springsteen, Kathleen Hopps, Adelaide Kerenick, Colin Kleckner, Ci Koehring, Elijah Kruger, Braden Krumholz, Maddie Leake, Lyneé Alves, Seraphina Loukas, Yatzari Lozano Vazquez, Haley Maki, Emily Martinez, Sierra Mckinney, Audrey Mitchell, Kipling Newman, Audrey Ng, Megan Lucyshyn, Andrew Nguyen, Stevie Ostman, Casandra Pearson, Alexandra Penney, Julia Gielczynski, Tyler Ball, Anna Rini, Christina Rorres, Simon Ruland, Helayna Schafer, Emma Sellers, Sarah Schuller, Claire Shaver, Kevin Summers, Isabella Shaw, Madison Sinar, Claudia Pena, Apshara Siwakoti, Carter Sorensen, Madi Sousa, Anna Sparling, Alexandra Revier, Brandon Thierry, Dylan Tyree, Maggie Williams, Lauren Wols

DU Undergraduate Research Journal Archive

DU Undergraduate Showcase: Research, Scholarship, and Creative Works

Adaptive Multirate Infinitesimal Time Integration, Alex Fish

Mathematics Theses and Dissertations

As multiphysics simulations grow in complexity and application scientists desire more accurate results, computational costs increase greatly. Time integrators typically cater to the most restrictive physical processes of a given simulation\add{,} which can be unnecessarily computationally expensive for the less restrictive physical processes. Multirate time integrators are a way to combat this increase in computational costs by efficiently solving systems of ordinary differential equations that contain physical processes which evolve at different rates by assigning different time step sizes to the different processes. Adaptivity is a technique for further increasing efficiency in time integration by automatically growing and shrinking the …

Machine Learning In Finances, Elma Kastrat, Akinyemi Apampa, Satyanand Singh

Publications and Research

In our study we work on an optimization of an appropriate stock portfolio base on available information. Our work takes into consideration the average return and any associated risk. We produce an investment strategy that predictively allows a portfolio to grow with high yields.

Brief Review: Low Frequency Event Charts (G-Charts) In Healthcare, James Espinosa, David Ho, Alan Lucerna, Henry Schuitema

Rowan-Virtua Research Day

The ability to determine if a change in a system is actually an improvement—or worsening in function—is one of the essential desiderata of quality improvement efforts. There are many ways to look at the issue. A special problem occurs when the event being studied is low frequency by nature. By way of example, patient falls in a given hospital or division of a hospital may occur in a way that is low frequency—yet each event is important. Process engineering has developed an approach to low frequency events. Part of this approach may involve specialized charts that look at the “time-between-events”—as …

Effects Of Factors On The Market Price Of The Shares Using Design Of Experiment, Amir Ahmad Dar, Mohammad Shahfaraz Khan, Imran Azad, Tanveer Ahmad Tarray, N. Anuradha, Qaiser Farroq Dar

Applied Mathematics & Information Sciences

When the cost of capital, dividends and the price of the share at the beginning is known, Modigliani and Miller’s model can be used to estimate the price of the share at the end of the period. A design of experiment (Taguchi’s orthogonal array) is used in order to investigate the impact of three parameters on the price of the share at the end of the period. The main aim of this research article is to find which parameter is more significant on the price of the share at the end of the period. Taguchi’s methodology of design of the …

Listening For Common Ground In High School And Early Collegiate Mathematics, Gail Burrill, Henry Cohn, Yvonne Lai, Dev P. Sinha, Ji Y. Son, Katherine F. Stevenson

Department of Mathematics: Faculty Publications

Solutions to pressing and complex social challenges require that we reach for common ground. Only through cooperation among people with a broad range of backgrounds and expertise can progress be made on issues as challenging as improving student success in mathematics. In this spirit, the AMS Committee on Education held a forum in May 2022 entitled The Evolving Curriculum in High School and Early Undergraduate Mathematical Sciences Education.¹ This article is a report on that forum by the authors listed above, who were among the organizers and presenters.

Advancements In Fluid Simulation Through Enhanced Conservation Schemes, Sean Ingimarson

All Dissertations

To better understand and solve problems involving the natural phenomenon of fluid and air flows, one must understand the Navier-Stokes equations. Branching several different fields including engineering, chemistry, physics, etc., these are among the most important equations in mathematics. However, these equations do not have analytic solutions save for trivial solutions. Hence researchers have striven to make advancements in varieties of numerical models and simulations. With many variations of numerical models of the Navier-Stokes equations, many lose important physical meaningfulness. In particular, many finite element schemes do not conserve energy, momentum, or angular momentum. In this thesis, we will study …

An Integrated Experimental And Modeling Approach To Design Rotating Algae Biofilm Reactors (Rabrs) Via Optimizing Algae Biofilm Productivity, Nutrient Recovery, And Energy Efficiency, Gerald Benjamin Jones

All Graduate Plan B and other Reports, Spring 1920 to Spring 2023

Microalgae biofilms have been demonstrated to recover nutrients from wastewater and serve as biomass feedstock for bioproducts. However, there is a need to develop a platform to quantitatively describe microalgae biofilm production, which can provide guidance and insights for improving biomass areal productivity and nutrient uptake efficiency. This paper proposes a unified experimental and theoretical framework to investigate algae biofilm growth on a rotating algae biofilm reactor (RABR). The experimental laboratory setups are used to conduct controlled experiments on testing environmental and operational factors for RABRs. We propose a differential-integral equation-based mathematical model for microalgae biofilm cultivation guided by laboratory …

Dynamics Of Inertial And Non-Inertial Particles In Geophysical Flows, Nishanta Baral

Theses, Dissertations and Culminating Projects

We consider the dynamics of inertial and non-inertial particles in various flows. We investigate the underlying structures of the flow field by examining their Lagrangian coherent structures (LCS), which are found by computing finitetime Lyapunov exponents (FTLE). We compare the behavior of massless noninertial particles using the velocity fields from four models, the Duffing oscillator, the Bickley jet, the double-gyre flow, and a quasi-geostrophic geophysical flow model, with that of inertial particles. For inertial particles with finite size and mass, we use the Maxey-Riley equation to describe the particle’s motion. We explore the preferential aggregation of inertial particles and demonstrate …

Parameter Optimization For Excitable Cell Models, Amrit Parmar

Theses, Dissertations and Culminating Projects

The electrophysiology of nodose ganglia neurons is of great interest in the analysis of cell membrane currents and action potential behavior. This behavior was initially outlined in the Hodgkin-Huxley conductance model [1] using a system of nonlinear differential equations. Later, Schild et al. [2] developed an extension of the Hodgkin-Huxley model to provide a more exhaustive description of ion channels involved in nodose neuronal action potential activity. We consider a variety of methods to fit the parameters of both the Hodgkin-Huxley and Schild et al. models to an empirical stimulus response dataset. Our methods were validated using synthetic datasets, as …

Creating The Optimal Wedding Seating Chart, Madison Lane

Theses/Capstones/Creative Projects

The purpose of this project is to develop an effective seating arrangement for a wedding reception that enhances the comfort of guests. The ultimate aim is to create a harmonious and enjoyable atmosphere for all attendees. To achieve this, an integer program was designed to optimize the seating arrangement for the author’s upcoming wedding on May 27th, 2023. To ensure accuracy and feasibility, actual feedback was gathered from the guests to evaluate their compatibility and preferences. The proposed seating chart optimization not only addresses the placement of guests but also determines the number of tables required for the reception. The …

Asymptotic Properties And Separation Rates For Navier-Stokes Flows, Patrick Michael Phelps

Graduate Theses and Dissertations

In this dissertation, we investigate asymptotic properties of local energy solutions to the Navier-Stokes equations and develop an application which controls the separation of non-unique solutions in this class. Specifically, we quantify the rate at which two, possibly unique solutions evolving from the same data may separate pointwise away from a singularity. This is motivated by recent results on non-uniqueness for forced and unforced Navier-Stokes and analytical and numerical evidence suggesting non-uniqueness in the Leray class. Our investigation begins with discretely self-similar solutions known to exist globally in time and to be regular outside a space-time paraboloid. We prove decay …

Machine Learning-Based Data And Model Driven Bayesian Uncertanity Quantification Of Inverse Problems For Suspended Non-Structural System, Zhiyuan Qin

All Dissertations

Inverse problems involve extracting the internal structure of a physical system from noisy measurement data. In many fields, the Bayesian inference is used to address the ill-conditioned nature of the inverse problem by incorporating prior information through an initial distribution. In the nonparametric Bayesian framework, surrogate models such as Gaussian Processes or Deep Neural Networks are used as flexible and effective probabilistic modeling tools to overcome the high-dimensional curse and reduce computational costs. In practical systems and computer models, uncertainties can be addressed through parameter calibration, sensitivity analysis, and uncertainty quantification, leading to improved reliability and robustness of decision and …

Global Upper Bounds For The Landau Equation Of Plasma Physics In The Very Soft Potentials Case, Caleb Solomon

Theses and Dissertations

This paper explores global upper bounds for solutions of the Landau equation in the soft potentials case (γ < −2). In particular, this paper explores the case of γ ∈ [−3,−2). Working with a classical solution to the Landau equation weighted by a cut-off function χ and using the Moser iteration, an upper bound for the L∞v norm of the solution to the Landau equation f is obtained proportianally to the L2 v norm of f with the assumptions of positive, essentially bounded coefficients. The supremum of f for t ∈ [0, T], x ∈ R3, v ∈ BR for some large radius R is shown to be bounded polynomially in R.

Volatility Modeling Of Time Series Using Fractal And Self-Similarity Models, William Kubin

Open Access Theses & Dissertations

The study uses various methods to compare financial and geophysical time series scaling parameters and long-term memory behavior. The Cantor Detrended Fluctuation Analysis (CDFA) method is proposed to provide more accurate estimates of Hurst exponents. The CDFA method is applied to real-time series and the results are verified. The study also analyzes the memory behavior of daily Covid-19 cases before and after the announcement of effective vaccines. Low and high-frequency dataâ??s influence on the Hurst Index estimation is investigated, and a new PCDFA method is proposed. The stability of the Dow Jones Industrial Average is analyzed using a multi-scale normalized …

Recursive Forms For Determinant Of K-Tridiagonal Toeplitz Matrices, Eugene Agyei-Kodie

Open Access Theses & Dissertations

Toeplitz matrices have garnered renewed interest in recent years due to their practical applications in engineering and computational sciences. Additionally, research has shown their connection to other matrices and their significance in matrix theory. For example, one study demonstrated that any matrix can be expressed as the product of Toeplitz matrices \citep{ye2016every}, while another showed that any square matrix is similar to a Toeplitz matrix \citep{mackey1999every}.

Numerous studies have examined various properties of Toeplitz matrices, including ideals of lower triangular Toeplitz matrices \citep{dogan9some}, matrix power computation with band Toeplitz structures \citep{dogan2017matrix}, and norms of Toeplitz matrices. Moreover, the use of …

Inference For Multiple Utility In Time-Dependent Choice Pairs Under Copula-Based Models, Sasanka Adikari

Mathematics & Statistics Theses & Dissertations

Models for discrete choice experiments (DCE) are frequently used to analyze consumer choices about products and services. A family of DCE, best-worst scaling experiments, offers more in-depth insights into consumer preferences by eliciting a best and worst choice from a set of options, rather than just a single preference. Traditional approaches often assume that choices are mutually exclusive over time, which may not always be the case. This dissertation proposes a novel model for DCE that takes into account the changing nature of consumer choices over time and the priority constraint of transition probabilities. The model introduces a copula combination …

Numerical Evaluation Of Wavenumbers Of The Acoustic Waves Propagating In An Ice-Covered Ocean, Mohammad Khan

Masters Theses and Doctoral Dissertations

We consider acoustic wave propagation in a layered ocean waveguide covered by thick ice. The standard method of separation of variables leads to a Sturm-Liouville problem in the crosssection of the waveguide. We are specifically interested in the two leading modes, the separated solutions for the maximal eigenvalues. We first consider the homogeneous waveguide. We prove the differentiability of the eigenvalues with respect to the frequency, the monotonicity of the eigenvalues with respect to the frequency, and the existence of the cut-off frequency. We compare these eigenvalues with the eigenvalues for the case of a waveguide with a free surface. …

Invariants Of 3-Braid And 4-Braid Links, Mark Essa Sukaiti

Theses

In this study, we established a connection between the Chebyshev polynomial of the first kind and the Jones polynomial of generalized weaving knots of type W(3,n,m).
Through our analysis, we demonstrated that the coefficients of the Jones polynomial of weaving knots are essentially the Whitney numbers of Lucas lattices which allowed us to find an explicit formula for the Alexander polynomial of weaving knots of typeW(3,n).
In addition to confirming Fox’s trapezoidal conjecture, we also discussed the zeroes of the Alexander Polynomial of weaving knots of type W(3,n) as they relate to Hoste’s conjecture. In addition, …