Mathematics Commons^™

Squared Distance Matrix Of A Weighted Tree, Ravindra B. Bapat

Journal Articles

Let T be a tree with vertex set f1;: :: ; ng such that each edge is assigned a nonzero weight. The squared distance matrix of T; denoted by is the n n matrix with (i; j)-element d(i; j)2; where d(i; j) is the sum of the weights of the edges on the (ij)-path. We obtain a formula for the determinant of A formula for 1 is also obtained, under certain conditions. The results generalize known formulas for the unweighted case.

Spacetime Groups, Ian M. Anderson, Charles G. Torre

Publications

A spacetime group is a connected 4-dimensional Lie group G endowed with a left invariant Lorentz metric h and such that the connected component of the isometry group of h is G itself. The Newman-Penrose formalism is used to give an algebraic classification of spacetime groups, that is, we determine a complete list of inequivalent spacetime Lie algebras, which are pairs (g,η), with g being a 4-dimensional Lie algebra and η being a Lorentzian inner product on g. A full analysis of the equivalence problem for spacetime Lie algebras is given which leads to a completely algorithmic solution to the …

Ua66/10/1 Ogden College Of Science & Engineering Mathematics Administration, Wku Archives

WKU Archives Collection Inventories

Administrative records created by and about the Mathematics department.

Ua66/15/1 Ogden College Of Science & Engineering Mathematics & Computer Science Events, Wku Archives

WKU Archives Collection Inventories

Records related to events hosted by Mathematics & Computer Science.

Quantum Isometry Group Of Deformation: A Counterexample, Debashish Goswami, Arnab Mandal

Journal Articles

We give a counterexample to show that the quantum isometry group of a deformed finite dimensional spectral triple may not be isomorphic with a deformation of the quantum isometry group of the undeformed spectral triple.

Well-Posedness And Symmetry Properties Of Free Boundary Problems For Some Non-Linear Degenerate Elliptic Second Order Partial Differential Equations, Alaa Haj Ali

Wayne State University Dissertations

In the first part of this thesis, a bifurcation about the uniqueness of a solution of a singularly perturbed free boundary problem of phase transition associated with the $p$-Laplacian, subject to given boundary condition is proved in the first chapter. We show this phenomenon by proving the existence of a third solution through the Mountain Pass Lemma when the boundary data decreases below a threshold. In the second chapter and third chapter, we prove the convergence of an evolution to stable solutions, and show the Mountain Pass solution is unstable in this sense.

In the second part of this thesis, …

Neandertal Mandibular Molars From Hortus Cave, France: A Comparison Of Crown Shapes Using Elliptical Fourier Analysis, Frank L. Williams, Juliet K. Brophy, Gregory J. Matthews, Emilee Hart, Marie-Antoinette De Lumley, Gaël Becam

Mathematics and Statistics: Faculty Publications and Other Works

Neandertal permanent mandibular molars are well represented at Hortus Cave, France, Sub-Phase IVb and Vb, providing an opportunity to assess intrapopulation and intersite shape variation. We expected the mandibular molars from Hortus cave, comprising Hortus II, Hortus IV, Hortus V and Hortus VI to cluster together, compared to Neandertals close in proximity, such as Malarnaud and La Quina 5 as well as those more distantly located such as Arcysur- Cure 1, Engis 2 and Scladina 4A-1. A single Neolithic cave burial from Maurenne Caverne de la Cave, Belgium (n = 11) is used to contextualize the degree of variation in …

10. Corrections To Design And Analysis Of Experiments, Angela Dean, Dan Voss, Danel Draguljic

Design and Analysis of Experiments

Corrections for the provided by the authors for Design and Analysis of Experiments.

On Monochromatic Sets With Nondecreasing Diameter, Adam O’Neal

Theses, Dissertations and Capstones

Our problem comes from the field of combinatorics known as Ramsey theory. Ramsey theory, in a general sense, is about identifying the threshold for which a family of objects, associated with a particular parameter, goes from never or sometimes satisfying a certain property to always satisfying that property. Research in Ramsey theory has applications in design theory and coding theory. For integers m, r, and t, we say that a set of n integers colored with r colors is (m, r, t)-permissible if there exist t monochromatic subsets B₁, B₂, . . . , B_{t …}

An Inference-Driven Branch And Bound Optimization Strategy For Planning Ambulance Services, Kevin Mcdaniel

Theses, Dissertations and Capstones

Strategic placement of ambulances is important to the efficient functioning of emergency services. As part of an ongoing collaboration with Wayne County 911, we developed a strategy to optimize the placement of ambulances throughout Wayne County based on de-identified call and response data from 2016 and 2017. The primary goals of the optimization were minimizing annual operating cost and mean response time, as well as providing a constructive solution that could naturally evolve from the existing plan. This thesis details the derivation and implementation of one of the optimization strategies used in this project. It is based on parametric statistical …

Intermediate Cell States In Epithelial-To-Mesenchymal Transition, Yutong Sha, Daniel Haensel, Guadalupe Gutierrez, Huijing Du, Xing Dai, Qing Nie

Department of Mathematics: Faculty Publications

The transition of epithelial cells into a mesenchymal state (epithelial-to-mesenchymal transition or EMT) is a highly dynamic process implicated in various biological processes. During EMT, cells do not necessarily exist in ‘pure’ epithelial or mesenchymal states. There are cells with mixed (or hybrid) features of the two, which are termed as the intermediate cell states (ICSs). While the exact functions of ICS remain elusive, together with EMT it appears to play important roles in embryogenesis, tissue development, and pathological processes such as cancer metastasis. Recent single cell experiments and advanced mathematical modeling have improved our capability in identifying ICS and …

Free Market On The Free Way, Yuan Cheng

CGU Theses & Dissertations

Self-driving cars have the potential to decrease congestion and will probably become the future of efficient transportation. This dissertation presents a unique approach to implement sharing lanes on a freeway using the idea of option pricing. A macroscopic physical model (LWR) is implemented by adding noise to the speed which accounts for unexpected events. We then proceed to provide a fair price for lanes in real time.

Statistical Analysis Of Tandem Queues With Markovian Passages In Porous Mediums, Gboyega David Adepoju

Theses, Dissertations and Capstones

Queuing theory is the mathematical study of queues or waiting lines. A queue is formed whenever the demand for service exceeds the capacity to provide service at that point in time. In this thesis, the birth-and-death process is used to model the movement of customers or units into and out of a network of queues in tandem. We start with the theoretical analysis of M/M/1 queues with Poisson arrival and exponential service time with first-come first-served (FCFS) discipline and one service station. We derive the global balance equation for each network. Using both the iterative and the probability generating function, …

Local Lagged Adapted Generalized Method Of Moments: An Innovative Estimation And Forecasting Approach And Its Applications., Olusegun Michael Otunuga, Gandaram S. Ladde, Nathan G. Ladde

Mathematics Faculty Research

In this work, an attempt is made to apply the Local Lagged Adapted Generalized Method of Moments (LLGMM) to estimate state and parameters in stochastic differential dynamic models. The development of LLGMM is motivated by parameter and state estimation problems in continuous-time nonlinear and non-stationary stochastic dynamic model validation problems in biological, chemical, engineering, energy commodity markets, financial, medical, military, physical sciences and social sciences. The byproducts of this innovative approach (LLGMM) are the balance between model specification and model prescription of continuous-time dynamic process and the development of discrete-time interconnected dynamic model of local sample mean and variance statistic …

On The Existence Of Partitioned Incomplete Latin Squares With Five Parts, Jaromy Kuhl, Donald Mcginn, Michael W. Schroeder

Mathematics Faculty Research

Let a, b, c, d, e be positive integers such that a ≤ b ≤ c ≤ d ≤ e. Heinrich showed the existence of a partitioned incomplete Latin square (PILS) of type (a, b, c) and (a, b, c, d) if and only if a = b = c and 2a ≥ d. For PILS of type (a,b,c,d,e), it is necessary that a + b + c ≥ e, but not sufficient, and no characterization is currently known. In this talk we provide an additional …

Second-Order Generalized Differentiation Of Piecewise Linear-Quadratic Functions And Its Applications, Hong Do

Wayne State University Dissertations

The area of second-order variational analysis has been rapidly developing during the recent years with many important applications in optimization. This dissertation is devoted to the study and applications of the second-order generalized differentiation of a remarkable

class of convex extended-real-valued functions that is highly important in many aspects of nonlinear and variational analysis, specifically those related to optimization and stability.

The first goal of this dissertation is to compute the second-order subdifferential of the functions described above, which will be applied in the study of the stability of composite optimization problems associated with piecewise linear-quadratic functions, known as extended …

Linear Difference Equations: Integrated- Environmentalist Approach For Teaching Mathematics, John A. Adam

Mathematics & Statistics Faculty Publications

There are at least eight known approaches for teaching mathematics that have been described in the literature. These include the Integrated Environmentalist, Formative, Social-Constructivist, Structuralist, New Maths, Problem Solving, Cultural, and Behaviorist approaches (Neyland, 1995). This paper presents some examples for teaching mathematics using the Integrated-Environmentalist approach, which is based on the assumption that the content knowledge in mathematics cannot be separated from the meaningful context from which it is taken, and in which it can be explained. In this approach for teaching mathematics the environment is used as the main source of mathematical meaning, stimulation to do creative work …

An Examination Of Computational Methods Related To G/M/C Queueing, Thomas Michaud Ms

All Student Scholarship

The following examination of computational methods related to queues with general arrivals (i:i:d: but of unknown distribution), multiple identical servers with i:i:d: exponential service times, and ordinary first come, first served service (hereafter referred to as G/M/c to use existing naming conventions) seeks to investigate the current models and provide new results based on a draft convolution method proposed by El-Taha[3]. The new model will demonstrate the use of distributions with coefficients of variance ranging from zero to near infinity to provide flexibility in simulating a range of potential arrival distributions, and we include detailed results and software for both …

Mathematical Modeling Of Type 1 Diabetes, Gianna Wu

HMC Senior Theses

Type 1 Diabetes (T1D) is an autoimmune disease where the pancreas produces little to no insulin, which is a hormone that regulates blood glucose levels. This happens because the immune system attacks (and kills) the beta cells of the pancreas, which are responsible for insulin production. Higher levels of glucose in the blood could have very negative, long term effects such as organ damage and blindness.

To date, T1D does not have a defined cause nor cure, and research for this disease is slow and difficult due to the invasive nature of T1D experimentation. Mathematical modeling provides an alternative approach …

The Use Of 3-D Highway Differential Geometry In Crash Prediction Modeling, Kiriakos Amiridis

Theses and Dissertations--Civil Engineering

The objective of this research is to evaluate and introduce a new methodology regarding rural highway safety. Current practices rely on crash prediction models that utilize specific explanatory variables, whereas the depository of knowledge for past research is the Highway Safety Manual (HSM). Most of the prediction models in the HSM identify the effect of individual geometric elements on crash occurrence and consider their combination in a multiplicative manner, where each effect is multiplied with others to determine their combined influence. The concepts of 3-dimesnional (3-D) representation of the roadway surface have also been explored in the past aiming to …