Applied Mathematics Commons^™

A Mathematical Analysis Of The Wind Triangle Problem And An Inquiry Of True Airspeed Calculations In Supersonic Flight, Leonard T. Huang, Lisa I. Cummings

International Journal of Aviation, Aeronautics, and Aerospace

In the first half of this paper, we present a fresh perspective toward the Wind Triangle Problem in aerial navigation by deriving necessary and sufficient conditions, which we call "go/no-go conditions", for the existence/non-existence of a solution of the problem. Although our derivation is based on simple trigonometry and basic properties of quadratic functions, it is mathematically rigorous. We also offer examples to demonstrate how easy it is to check these conditions graphically. In the second half of this paper, we use function theory to re-examine another problem in aerial navigation, namely, that of computing true airspeed — even in …

A Gender And Race Theoretical And Probabilistic Analysis Of The Recent Title Ix Policy Changes, Jordan Wellington

Scripps Senior Theses

On May 6th, 2020, after extensive public comment and review, the Department of Education published the final rule for the new Title IX regulations, which took effect in schools on August 14th. Title IX is the nearly fifty year old piece of the Education Amendments that prohibits sexual discrimination in federally funded schools. Several of these changes, such as the inclusion of live hearings and cross examination of witnesses, have been widely criticized by victims’ rights advocates for potentially retraumatizing victims of sexual assault and discouraging students from pursuing a Title IX claim. While the impact of the new regulations …

Thermodynamic Entropy Of A Magnetized Ree-Eyring Particle-Fluid Motion With Irreversibility Process: A Mathematical Paradigm, M. M. Bhatti, Sara I. Abdelsalam

Basic Science Engineering

This article deals with the entropy generation and irreversibility process under the effects of partial slip on magnetic dusty liquid induced by peristaltic wave through a porous channel. The Ree-Eyring fluid model has been used for a governing flow. Mathematical modelling is based on Ohm's law, continuity equation, Darcy law and momentum equation. Analytical solutions are presented for fluid and particle phase. The effects of different pertinent parameters are considered for Newtonian and non-Newtonian cases. Numerical integration has been carried out using a computational software to analyse the pumping characteristics. The behaviour of velocity profile, trapping mechanism, entropy generation, Bejan …

New Numerical Approximations Of Geological Processes In Heterogeneous Systems Using Radial Basis Functions, Nadun Lakshitha Dissanayake Kulasekera Mudiyanselage

Dissertations, Master's Theses and Master's Reports

This dissertation includes four chapters. A brief description of each chapter is organized as follows. The first chapter provides an introduction to the RBF method. The chapter follows the historical progression of the Radial Basis Function (RBF) method while outlining the method’s advantages and disadvantages. A brief introduction about RBF interpolation, the RBF-FD method, and how to use it to solve PDEs is provided. Chapter 2 introduces a novel computationally efficient RBF-FD algorithm to solve the groundwater flow equation in the presence of an active well. We show that our method analytically handles the singularities in the PDE caused by …

Design Project: Smart Headband, John Michel, Jack Durkin, Noah Lewis

Williams Honors College, Honors Research Projects

Concussion in sports is a prevalent medical issue. It can be difficult for medical professionals to diagnose concussions. With the fast pace nature of many sports, and the damaging effects of concussions, it is important that any concussion risks are assessed immediately. There is a growing trend of wearable technology that collects data such as steps and provides the wearer with in-depth information regarding their performance. The Smart Headband project created a wearable that can record impact data and provide the wearer with a detailed analysis on their risk of sustaining a concussion. The Smart Headband uses accelerometers and gyroscopes …

Obstructive Wiring Patterns To Circular Planarity In Electrical Networks, Hannah Lebo

Williams Honors College, Honors Research Projects

In order for an electrical network to be printed on a flat surface without changing the network’s input or output, it is important to consider if any wires will cross and if this problem can be avoided. If a circular network can be printed so that no wires cross, the network is said to be circular planar. In this paper, we identify a number of wiring patterns that make circular planarity impossible. We find exactly 3 wiring patterns using circular pairs with sets of two nodes, and we find exactly 78 wiring patterns using circular pairs with sets of three …

Impact Of Vaccine Supplies And Delays On Optimal Control Of The Covid-19 Pandemic: Mapping Interventions For The Philippines, Carlo Delfin S. Estadilla, Joshua Uyheng, Elvira P. De Lara-Tuprio, Timothy Robin Y. Teng, Jay Michael R. Macalalag, Ma. Regina Justina E. Estuar

Mathematics Faculty Publications

Background

Around the world, controlling the COVID-19 pandemic requires national coordination of multiple intervention strategies. As vaccinations are globally introduced into the repertoire of available interventions, it is important to consider how changes in the local supply of vaccines, including delays in administration, may be addressed through existing policy levers. This study aims to identify the optimal level of interventions for COVID-19 from 2021 to 2022 in the Philippines, which as a developing country is particularly vulnerable to shifting assumptions around vaccine availability. Furthermore, we explore optimal strategies in scenarios featuring delays in vaccine administration, expansions of vaccine supply, and …

Scaling Up Exact Neural Network Compression By Relu Stability, Thiago Serra, Xin Yu, Abhinav Kumar, Srikumar Ramalingam

Faculty Conference Papers and Presentations

We can compress a rectifier network while exactly preserving its underlying functionality with respect to a given input domain if some of its neurons are stable. However, current approaches to determine the stability of neurons with Rectified Linear Unit (ReLU) activations require solving or finding a good approximation to multiple discrete optimization problems. In this work, we introduce an algorithm based on solving a single optimization problem to identify all stable neurons. Our approach is on median 183 times faster than the state-of-art method on CIFAR-10, which allows us to explore exact compression on deeper (5 x 100) and wider …

A New Mathematical Theory For The Dynamics Of Large Tumor Populations, A Potential Mechanism For Cancer Dormancy & Recurrence And Experimental Observation Of Melanoma Progression In Zebrafish, Adeyinka A. Lesi

Dissertations and Theses

Cancer, a family of over a hundred disease varieties, results in 600,000 deaths in the U.S. alone. Yet, improvements in imaging technology to detect disease earlier, pharmaceutical developments to shrink or eliminate tumors, and modeling of biological interactions to guide treatment have prevented millions of deaths. Cancer patients with initially similar disease can experience vastly different outcomes, including sustained recovery, refractory disease or, remarkably, recurrence years after apparently successful treatment. The current understanding of such recurrences is that they depend on the random occurrence of critical mutations. Clearly, these biological changes appear to be sufficient for recurrence, but are they …

Optimal Construction Of A Layer-Ordered Heap And Its Applications, Jake Pennington

Graduate Student Theses, Dissertations, & Professional Papers

The layer-ordered heap (LOH) is a simple data structure used in algorithms that perform optimal top-$k$ on $X+Y$, algorithms with the best known runtime for top-$k$ on $X_1+X_2+\cdots+X_m$, and the fastest method in practice for computing the most abundant isotopologue peaks in a chemical compound. In the analysis of these algorithms, the rank, $\alpha$, has been treated as a constant and $n$, the size of the array, has been treated as the sole parameter. Here, we explore the algorithmic complexity of LOH construction with $\alpha$ as a parameter, introduce a few algorithms for constructing LOHs, analyze their complexity in both …

New Results On Cyclic Compositions And Multicompositions, Silvana Ramaj

College of Graduate Studies: Theses & Dissertations

Integer compositions, cyclic compositions, and lately k-compositions, are an important topic in combinatorics and number theory. In this paper, we will explain, the general approach of using generating functions to study number sequences involving compositions, cyclic compositions, k-compositions, and the number of parts in each of them. After generating the data, some properties are observed and proved. Also, some interesting bijections involving Pell numbers and the Jacobsthal sequence are given.

Implementing A Neural Network For Supervised Learning With A Random Configuration Of Layers And Nodes, Kane A. Phillips

College of Graduate Studies: Theses & Dissertations

Deep learning has a substantial amount of real-life applications, making it an increasingly popular subset of artificial intelligence over the last decade. These applications come to fruition due to the tireless research and implementation of neural networks. This paper goes into detail on the implementation of supervised learning neural networks utilizing MATLAB, with the purpose being to generate a neural network based on specifications given by a user. Such specifications involve how many layers are in the network, and how many nodes are in each layer. The neural network is then trained based on known sample values of a function …

Arnold Transformations As Applied To Data Encryption, Haley N. Anderson

College of Graduate Studies: Theses & Dissertations

As our world becomes increasingly digital, data security becomes key. Data must be encrypted such that it can be easily encrypted only by the intended recipient. Arnold Transformations are a useful tool in this because of its unpredictable periodicity. Our goal is to outline a method for choosing an Arnold Transformation that is both secure and easy to implement. We find the necessary and sufficient condition that a key matrix has periodicity. The chosen key matrix has a random structure, and it has a periodicity that is sufficiently high. We apply this method to several image and data string examples …

Semiclassical Backreaction On Asymptotically Anti–De Sitter Black Holes, Peter Taylor, Cormac Breen

Articles

We consider a quantum scalar field on the classical background of an asymptotically anti–de Sitter black hole and the backreaction the field’s stress-energy tensor induces on the black hole geometry. The backreaction is computed by solving the reduced-order semiclassical Einstein field equations sourced by simple analytical approximations for the renormalized expectation value of the scalar field stress-energy tensor. When the field is massless and conformally coupled, we adopt Page’s approximation to the renormalized stress-energy tensor, while for massive fields we adopt a modified version of the DeWitt-Schwinger approximation. The latter approximation must be modified so that it possesses the correct …

Proper Orthogonal Decomposition: New Approximation Theory And A New Computational Approach, Sarah Katherine Locke

Doctoral Dissertations

“Proper orthogonal decomposition (POD) projection errors and error bounds for POD reduced order models of partial differential equations have been studied by many. In this research we obtain new results regarding POD data approximation theory and present a new difference quotient (DQ) approach for computing the POD modes of the data.

First, we improve on earlier results concerning POD projection errors by extending to a more general framework that allows for non-orthogonal POD projections and seminorms. We obtain new exact error formulas and convergence results for POD data approximation errors, and also prove new pointwise convergence results and error bounds …

A Learning Curve Model Accounting For The Flattening Effect In Production Cycles, Evan R. Boone, John J. Elshaw, Clay M. Koschnick, Jonathan D. Ritschel, Adedeji B. Badiru

Faculty Publications

We investigate production cost estimates to identify and model modifications to a prescribed learning curve. Our new model examines the learning rate as a decreasing function over time as opposed to a constant rate that is frequently used. The purpose of this research is to determine whether a new learning curve model could be implemented to reduce the error in cost estimates for production processes. A new model was created that mathematically allows for a “flattening effect,” which typically occurs later in the production process. This model was then compared to Wright’s learning curve, which is a popular method used …

Grouping Algorithms For Informative Array Testing In Disease Surveillance, David Sokolov

Graduate Theses, Dissertations, and Problem Reports (ETD)

In order to maintain normal operations and prevent unnecessary morbidity and mortality during times of disease outbreak, institutions find a need to conduct frequent and widespread testing of their constituents, often under significantly limited testing resource constraints. Faced with the challenge of how best to allo- cate these limited resources to maximum effect, institutions are increasingly turning to group (or “pooled”) testing, which involves testing strategically-chosen groups of patient samples rather than individual samples, producing significant testing resource savings under certain regimes of disease prevalence. While group test- ing can be conducted without any a priori knowledge of individual disease …

Development Of Synthetic Coal Char Simulant For Microwave Conversion Studies: A Computationally-Driven Approach, Kevin A. Hager

Graduate Theses, Dissertations, and Problem Reports (ETD)

Recent experimental demonstration of new reaction windows for coal char/methane reactions that are less energy-intensive, provides innovation for modular reactors. However, the correlation of the exact mechanism for the enhancement of these reaction windows is not certain. This study investigates the simplification of these experimental studies by developing a well-characterized coal char simulant. The approach involves using a computational approach to screen macroscopic composition to replicate the dielectric and compositional response of actual char. This study is focused on PRB coal char. A discrete element method (DEM) technique was used to simulate the packing of coal chars to give the …

Application Of Optimal Control Theory To A Malaria Model, Cassidy Hill

Murray State Theses and Dissertations

With malaria still prevalent and considered to be one of the most devastating infectious diseases in the world, many scientific efforts have been made to reduce its impact. One such effort includes the construction of mathematical models. Mathematical models can be used to analyze malaria transmission dynamics in the human population. The development of these models allows researchers to consider the control measures necessary to reduce the prevalence of malaria infection and possibly eliminate it.

The model presented in this thesis will provide the relationship of female Anopheles mosquitoes and insecticide treated paint acting as the control. A deterministic system …

Hands-On Developmental Playbook For Stem Clubs In Elementary Schools, James Lipuma, Bruce G. Bukiet, Cristo Leon

STEM for Success Resources

The following guide is the result of the work of NJIT researchers, staff, and student STEM role models along with the many public and private partners including Apple and the Us ARMY. The work was funded by the National Science Foundation through the NSF INCLUDES Life grant and support from Howmet Aerospace Foundation grants. The materials in the guide have been developed and tested with our New Jersey school district partners in Hillside, Long Branch, Morris Plains, Newark, Princeton, and Weehawken. See our strategic partners section for a more complete list of partners and collaborators.