Applied Mathematics Commons^™

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 …

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 …

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 …

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 …

Bloch Spectra For High Contrast Elastic Media, Jayasinghage Ruchira Nirmali Perera

LSU Doctoral Dissertations

The primary goal of this dissertation is to develop analytic representation formulas and power series to describe the band structure inside periodic elastic crystals made from high contrast inclusions. We use source free modes associated with structural spectra to represent the solution operator of the Lame' system inside phononic crystals. Then we obtain convergent power series for the Bloch wave spectrum using the representation formulas. An explicit bound on the convergence radius is given through the structural spectra of the inclusion array and the Dirichlet spectra of the inclusions. Sufficient conditions for the separation of spectral branches of the dispersion …

Analytic Solution Of 1d Diffusion-Convection Equation With Varying Boundary Conditions, Małgorzata B. Glinowiecka-Cox

University Honors Theses

A diffusion-convection equation is a partial differential equation featuring two important physical processes. In this paper, we establish the theory of solving a 1D diffusion-convection equation, subject to homogeneous Dirichlet, Robin, or Neumann boundary conditions and a general initial condition. Firstly, we transform the diffusion-convection equation into a pure diffusion equation. Secondly, using a separation of variables technique, we obtain a general solution formula for each boundary type case, subject to transformed boundary and initial conditions. While eigenvalues in the cases of Dirichlet and Neumann boundary conditions can be constructed easily, the Robin boundary condition necessitates solving a transcendental algebraic …

Differential Operators On Classical Invariant Rings Do Not Lift Modulo P, Jack Jeffries, Anurag K. Singh

Department of Mathematics: Faculty Publications

Levasseur and Stafford described the rings of differential operators on various classical invariant rings of characteristic zero; in each of the cases that they considered, the differential operators form a simple ring. Towards an attack on the simplicity of rings of differential operators on invariant rings of linearly reductive groups over the complex numbers, Smith and Van den Bergh asked if differential operators on the corresponding rings of positive prime characteristic lift to characteristic zero differential operators. We prove that, in general, this is not the case for determinantal hypersurfaces, as well as for Pfaffian and symmetric determinantal hypersurfaces. We …

Analyzing Domain Of Convergence For Broyden’S Method, Michael Bonthron

College of Science and Health Theses and Dissertations

Broyden’s method is a quasi-Newton iterative method used to find roots of non-linear systems of equations. Research has shown and improved the rate of convergence for special cases and specific applications of the method. However, there is limited literature regarding the well-posedness of the method. In practice, a numerical method must reliably converge to the appropriate root. This paper will discuss the domain of attraction for the roots of a system found by using Broyden’s method. A method of approximating the radius of convergence of a root will be described which considers the largest disk centered at the root such …

Opinion Profile Dynamics With Uniform Bounded Confidence: Analysis & Simulations, Jason Echevarria

College of Science and Health Theses and Dissertations

An opinion profile can describe a set of individuals, groups or entities that form an opinion over a topic. Given a number of agents, a time evolving opinion denoted by a vector can be described over time using the linear mode where is a time variable and the matrix (which might depend on time and the current profile) contains the weights that affect the dynamics of profile . With varying conditions over time, these profiles can form groups, polarize, fragment, or reach consensus. In this work, we investigate the uniform bounded confidence model: an agent adjusts their opinion over time …

Bbt Side Mold Assy, Bill Hemphill

STEM Guitar Project’s BBT Acoustic Kit

This electronic document file set covers the design and fabrication information of the ETSU Guitar Building Project’s BBT (OM-sized) Side Mold Assy for use with the STEM Guitar Project’s standard acoustic guitar kit. The extended 'as built' data set contains an overview file and companion video, the 'parent' CADD drawing, CADD data for laser etching and cutting a drill &/or layout template, CADD drawings in AutoCAD .DWG and .DXF R12 formats of the centerline tool paths for creating the mold assembly pieces on an AXYZ CNC router, and support documentation for CAM applications including router bit specifications, feeds, speed, multi-pass …

Introduction To Classical Field Theory, Charles G. Torre

All Complete Monographs

This is an introduction to classical field theory. Topics treated include: Klein-Gordon field, electromagnetic field, scalar electrodynamics, Dirac field, Yang-Mills field, gravitational field, Noether theorems relating symmetries and conservation laws, spontaneous symmetry breaking, Lagrangian and Hamiltonian formalisms.

Sparse Spectral-Tau Method For The Two-Dimensional Helmholtz Problem Posed On A Rectangular Domain, Gabriella M. Dalton

Mathematics & Statistics ETDs

Within recent decades, spectral methods have become an important technique in numerical computing for solving partial differential equations. This is due to their superior accuracy when compared to finite difference and finite element methods. For such spectral approximations, the convergence rate is solely dependent on the smoothness of the solution yielding the potential to achieve spectral accuracy. We present an iterative approach for solving the two-dimensional Helmholtz problem posed on a rectangular domain subject to Dirichlet boundary conditions that is well-conditioned, low in memory, and of sub-quadratic complexity. The proposed approach spectrally approximates the partial differential equation by means of …

(R1892) On The Asymptotic Stability Of A Neutral System With Nonlinear Perturbations And Constant Delay, Melek Gözen

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, we consider a nonlinear perturbed system of neutral delay integro-differential equations (NDIDEs). We prove two new theorems, Theorems 1 and 2, such that these theorems include sufficient conditions and are related to asymptotically stability of zero solution of the perturbed system of NDIDEs. The technique of the proofs depend upon the definitions of two new and more suitable Lyapunov- Krasovskiĭ functionals (LKFs). When we compared the results of this paper with those are found the literature related , our results improve and extend some classical results, and do new contributions to the topic of NDIDEs and literature.