Applied Mathematics Commons^™

Inexact Fixed-Point Proximity Algorithms For Nonsmooth Convex Optimization, Jin Ren

Mathematics & Statistics Theses & Dissertations

The aim of this dissertation is to develop efficient inexact fixed-point proximity algorithms with convergence guaranteed for nonsmooth convex optimization problems encountered in data science. Nonsmooth convex optimization is one of the core methodologies in data science to acquire knowledge from real-world data and has wide applications in various fields, including signal/image processing, machine learning and distributed computing. In particular, in the context of image reconstruction, compressed sensing and sparse machine learning, either the objective functions or the constraints of the modeling optimization problems are nondifferentiable. Hence, traditional methods such as the gradient descent method and the Newton method are …

Utilization Of Finite Element Analysis Techniques For Adolescent Idiopathic Scoliosis Surgical Planning, Michael A. Polanco

Mechanical & Aerospace Engineering Theses & Dissertations

Adolescent Idiopathic Scoliosis, a three-dimensional deformity of the thoracolumbar spine, affects approximately 1-3% of patients ages 10-18. Surgical correction and treatment of the spinal column is a costly and high-risk task that is consistently complicated by factors such as patient-specific spinal deformities, curve flexibility, and surgeon experience. The following dissertation utilizes finite element analysis to develop a cost-effective, building-block approach by which surgical procedures and kinematic evaluations may be investigated. All studies conducted are based off a volumetric, thoracolumbar finite element (FE) model developed from computer-aided design (CAD) anatomy whose components are kinematically validated with in-vitro data. Spinal ligament stiffness …

Evaluation Of Generative Models For Predicting Microstructure Geometries In Laser Powder Bed Fusion Additive Manufacturing, Andy Ramlatchan

Computer Science Theses & Dissertations

In-situ process monitoring for metals additive manufacturing is paramount to the successful build of an object for application in extreme or high stress environments. In selective laser melting additive manufacturing, the process by which a laser melts metal powder during the build will dictate the internal microstructure of that object once the metal cools and solidifies. The difficulty lies in that obtaining enough variety of data to quantify the internal microstructures for the evaluation of its physical properties is problematic, as the laser passes at high speeds over powder grains at a micrometer scale. Imaging the process in-situ is complex …

Academic Hats And Ice Cream: Two Optimization Problems, Valery F. Ochkov, Yulia V. Chudova

Journal of Humanistic Mathematics

This article describes the use of computer software to optimize the design of an academic hat and an ice cream cone!

Maintaining Ecosystem And Economic Structure In A Three-Species Dynamical System In Chesapeake Bay, Maila Hallare, Iordanka Panayotova

CODEE Journal

We consider a three-species fish dynamical system in Chesapeake Bay consisting of the Atlantic menhaden as the prey and its two competing predators, the striped bass and the catfish. Building on our previous work in this system, we consider the issue of balancing economic harvesting goals (financial gain for fishermen) with ecological harvesting goals (non-extinction of species). In particular, we investigate the bionomic equilibria, maximum sustainable yield, and the maximum economic yield. Analytical computations and numerical simulations are employed to provide some mathematical guidance on fisheries management policies.

Computational Models To Detect Radiation In Urban Environments: An Application Of Signal Processing Techniques And Neural Networks To Radiation Data Analysis, Jose Nicolas Gachancipa

Beyond: Undergraduate Research Journal

Radioactive sources, such as uranium-235, are nuclides that emit ionizing radiation, and which can be used to build nuclear weapons. In public areas, the presence of a radioactive nuclide can present a risk to the population, and therefore, it is imperative that threats are identified by radiological search and response teams in a timely and effective manner. In urban environments, such as densely populated cities, radioactive sources may be more difficult to detect, since background radiation produced by surrounding objects and structures (e.g., buildings, cars) can hinder the effective detection of unnatural radioactive material. This article presents a computational model …

Bbt Acoustic Alternative Top Bracing Cadd Data Set-Norev-2022jun28, Bill Hemphill

STEM Guitar Project’s BBT Acoustic Kit

This electronic document file set consists of an overview presentation (PDF-formatted) file and companion video (MP4) and CADD files (DWG & DXF) for laser cutting the ETSU-developed alternate top bracing designs and marking templates for the STEM Guitar Project’s BBT (OM-sized) standard acoustic guitar kit. The three (3) alternative BBT top bracing designs in this release are
(a) a one-piece base for the standard kit's (Martin-style) bracing,
(b) 277 Ladder-style bracing, and
(c) an X-braced fan-style bracing similar to traditional European or so-called 'classical' acoustic guitars.

The CADD data set for each of the three (3) top bracing designs includes …

Mathematics Textbook: Motivation, Experiences, And Didactical Aspect From Authors’ Perspectives, Deepak Basyal, Bhesh Raj Mainali

Mathematics and Statistics

Textbooks play a vital role in the Nepali education system since they are one of the main resources for teaching and learning mathematics. Because of poor physical infrastructure and inadequate educational resources, both teachers and students heavily rely on textbooks. In this regard, this study investigated the mathematics textbook authors' experiences and motivation, and what types of didactical knowledge were utilised while writing textbooks. A convenient yet purposeful sampling method was utilised to select four participants. The data analysis unveiled that each textbook author had different types of motivation and experiences, and only one participant was aware of the ideas …

An Iot Based Worker Safety Helmet Using Cloud Computing Technology, Yuthriya Iddi Khamis, Mahmoud Alawi, Waheed Muhammad Sanya

Tanzania Journal of Engineering and Technology (TJET)

Miner safety and security is a major challenge around the world due to the exposure to toxic gases that are frequently released in underground mines. Miners' health is adversely affected primarily by toxic gases, which endanger the workers' lives. Furthermore, human sensory abilities do not detect these dangerous gases. As a result, this paper proposes a safety monitoring system that includes a temperature sensor, humidity sensor, and gas sensors to detect harmful gases and alert miners to those harmful gases using the smart helmet they wear. These gases are transmitted to the control station via the cloud using Internet of …

Navier-Stokes Equations In One And Two Dimensions, Jon Nerdal

LSU Master's Theses

The Navier-Stokes equations are an important tool in understanding and describing fluid flow. We investigate different formulations of the incompressible Navier-Stokes equations in the one-dimensional case along an axis and in the two-dimensional case in a circular pipe without swirl. For the one-dimensional case we show that the velocity approximations are remarkably accurate and we suggest that understanding this simple axial behaviour is an important starting point for further exploration in higher dimensions. The complexity of the boundary is then increased with the two-dimensional case of fluid flow through the cross section of a circular pipe, where we investigate two …

Heterogeneity Of Gene Trees, Jonathan Nenye Odumegwu Unm

Mathematics & Statistics ETDs

Multilocus phylogenetic studies often show a high degree of gene tree heterogeneity —gene trees that have different topologies from each other as well as from the species tree topology. In some cases, this can lead to studies with hundreds of loci having distinct gene tree topologies. The degree of heterogeneity is expected to increase when there is a high degree of incomplete lineage sorting due to short branches (as measured in coalescent units) in the species tree. Other potential sources of heterogeneity include other biological processes such as introgression, recombination within genes, ancestral population structure, gene duplication and loss, and …

Many Cliques In Bounded-Degree Hypergraphs, Rachel Kirsch, J. Radcliffe

Department of Mathematics: Faculty Publications

Recently Chase determined the maximum possible number of cliques of size t in a graph on n vertices with given maximum degree. Soon afterward, Chakraborti and Chen answered the version of this question in which we ask that the graph have m edges and fixed maximum degree (without imposing any constraint on the number of vertices). In this paper we address these problems on hypergraphs. For s-graphs with s ≥ 3 a number of issues arise that do not appear in the graph case. For instance, for general s-graphs we can assign degrees to any i-subset of the vertex set …

Modelling Spherical Aberration Detection In An Analog Holographic Wavefront Sensor, Emma Branigan, Suzanne Martin, Matthew Sheehan, Kevin Murphy

Conference Papers

The analog holographic wavefront sensor (AHWFS) is a simple and robust solution to wavefront sensing in turbulent environments. Here, the ability of a photopolymer based AHWFS to detect refractively generated spherical aberration is modelled and verified.

Robust Sensor Design For The Novel Reduced Models Of The Mead-Marcus Sandwich Beam Equation, Ahmet Aydin

Masters Theses & Specialist Projects

Novel space-discretized Finite Differences-based model reductions are proposed for the partial differential equations (PDE) model of a multi-layer Mead-Marcus-type beam with (i) hinged-hinged and (ii) clamped-free boundary conditions. The PDE model describes transverse vibrations for a sandwich beam whose alternating outer elastic layers constrain viscoelastic core layers, which allow transverse shear. The major goal of this project is to design a single boundary sensor, placed at the tip of the beam, to control the overall dynamics on the beam.

For (i), it is first shown that the PDE model is exactly observable by the so-called nonharmonic Fourier series approach. However, …

On The Spectral Theory Of Linear Differential-Algebraic Operators With Periodic Coefficients, Bader Alshammari

Theses and Dissertations

In this thesis, the spectral theory of linear differential algebraic equations (DAEs) is considered in detail and extended to treat the weighted spectral theory which generalizes the classical theory, i.e., we develop the spectral theory for the most general DAEs: J df dt + Hf = λWf, (0.0.1) where J is a constant nonzero skew-Hermitian n×n-matrix, both H and W are dperiodic Hermitian n×n-matrices with Lebesgue measurable functions as entries, and W is positive semidefinite and invertible for a.e. t ∈ R (i.e., Lebesgue almost everywhere). Under weakest hypotheses on H and W currently known, called the local index-1 hypotheses, …

Numerical Solutions To The Robin Inverse Problem With Nonnegativity Constraints, Weifu Fang, Fu-Rong Lin

Mathematics and Statistics Faculty Publications

We present iterative numerical methods for solving the inverse problem of recovering the nonnegative Robin coefficient from partial boundary measurement of the solution to the Laplace equation. Based on the boundary integral equation formulation of the problem, nonnegativity constraints in the form of a penalty term are incorporated conveniently into least-squares iteration schemes for solving the inverse problem. Numerical implementation and examples are presented to illustrate the effectiveness of this strategy in improving recovery results.

Real-Time Data Analytics For Monitoring Electricity Consumption Using Iot Technology, Waheed Muhammad Sanya, Gaurav Bajpai, Omar Haji Kombo, Evariste Twahirwa

Tanzania Journal of Engineering and Technology (TJET)

Rising electricity bills as a result of climate variability and new home electrical and electronic appliances are becoming a major source of concern for most end users. Consumers are typically unaware of their household electricity consumption patterns and the costs associated with them, making proper planning and budgeting difficult. Monitoring and controlling energy consumption on appliances can reduce energy costs for end-users. The Internet of Things (IoT) has the potential to provide remote monitoring and control of devices via automated monitoring and control. In this study, we propose an IoT-enabled system for monitoring and controlling energy consumption in homes to …

Digital Skills And Self-Employment Among Graduates Of Technical Higher Education Institutions In Tanzania, Charles Raphael

Tanzania Journal of Engineering and Technology (TJET)

Digital skills are the driving forces for innovative, inclusive and sustainable growth through innovations and digitalization which in turn stimulate job creation, alleviate poverty, reducing inequality, facilitating the delivery of goods and services. However, large number of graduates is shown to be weak in digital skills in the industry hence affect their employability including self-employment. Recently, the Technical Higher Education Institutions (THEIs) took some initiatives to instill the digital skills to their respective students. This study therefore assessed the level of competence of digital skills among graduates following the initiatives taken by the THEIs and their influence on self-employment. It …

Applications Of Machine Learning Algorithms In Materials Science And Bioinformatics, Mohammed Quazi

Mathematics & Statistics ETDs

The piezoelectric response has been a measure of interest in density functional theory (DFT) for micro-electromechanical systems (MEMS) since the inception of MEMS technology. Piezoelectric-based MEMS devices find wide applications in automobiles, mobile phones, healthcare devices, and silicon chips for computers, to name a few. Piezoelectric properties of doped aluminum nitride (AlN) have been under investigation in materials science for piezoelectric thin films because of its wide range of device applicability. In this research using rigorous DFT calculations, high throughput ab-initio simulations for 23 AlN alloys are generated.

This research is the first to report strong enhancements of piezoelectric properties …

Mentoring Undergraduate Research In Mathematical Modeling, Glenn Ledder

Department of Mathematics: Faculty Publications

In writing about undergraduate research in mathematical modeling, I draw on my 31 years as a mathematics professor at the University of Nebraska–Lincoln, where I mentored students in honors’ theses, REU groups, and research done in a classroom setting, as well as my prior experience. I share my views on the differences between research at the undergraduate and professional levels, offer advice for undergraduate mentoring, provide suggestions for a variety of ways that students can disseminate their research, offer some thoughts on mathematical modeling and how to explain it to undergraduates, and discuss the challenges involved in broadening research participation …