Applied Mathematics Commons^™

Classification Of Symmetry Lie Algebras Of The Canonical Geodesic Equations Of Five-Dimensional Solvable Lie Algebras, Hassan Almusawa, Ryad Ghanam, Gerard Thompson

Mathematics and Applied Mathematics Publications

In this investigation, we present symmetry algebras of the canonical geodesic equations of the indecomposable solvable Lie groups of dimension five, confined to algebras A_{5,7}^{abc} to A_{18}^a. For each algebra, the related system of geodesics is provided. Moreover, a basis for the associated Lie algebra of the symmetry vector fields, as well as the corresponding nonzero brackets, are constructed and categorized.

Comparison Of Green's Functions For A Family Of Boundary Value Problems For Fractional Difference Equations, Paul W. Eloe, Catherine Kublik, Jeffrey T. Neugebauer

Mathematics Faculty Publications

In this paper, we obtain sign conditions and comparison theorems for Green's functions of a family of boundary value problems for a Riemann-Liouville type delta fractional difference equation. Moreover, we show that as the length of the domain diverges to infinity, each Green's function converges to a uniquely defined Green's function of a singular boundary value problem.

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 …

The 4-Dimensional Light Bulb Theorem, Elizabeth Gorton, Anna Jeffries, Nathan S. Sunukjian

Summer Research

"Topology" is the term used for the field of mathematics that looks at the geometrical relationships and properties of space. One way to think about this is if you have a big sheet of rubber that you can mess around with like PlayDoh. The classic illustration of topology is that, from a topological perspective, a doughnut and a coffee mug are the same thing.

Topology is not limited to only the 3rd dimension. In fact, the most interesting topology occurs in the 4th dimension, which is what the 4-dimensional light bulb theorem is about.

An Information Theory-Based Approach To Assessing Spatial Patterns In Complex Systems, Tarsha Eason, Wen Ching-Chuang, Shana Sundstrom, Heriberto Cabezas

School of Natural Resources: Faculty Publications

Given the intensity and frequency of environmental change, the linked and cross-scale nature of social-ecological systems, and the proliferation of big data, methods that can help synthesize complex system behavior over a geographical area are of great value. Fisher information evaluates order in data and has been established as a robust and effective tool for capturing changes in system dynamics, including the detection of regimes and regime shifts. The methods developed to compute Fisher information can accommodate multivariate data of various types and requires no a priori decisions about system drivers, making it a unique and powerful tool. However, the …

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 …

Prediction Of The Outcome In Cardiac Arrest Patients Undergoing Hypothermia Using Eeg Wavelet Entropy, Hana Moshirvaziri

CGU Theses & Dissertations

Cardiac arrest (CA) is the leading cause of death in the United States. Induction of hypothermia has been found to improve the functional recovery of CA patients after resuscitation. However, there is no clear guideline for the clinicians yet to determine the prognosis of the CA when patients are treated with hypothermia. The present work aimed at the development of a prognostic marker for the CA patients undergoing hypothermia. A quantitative measure of the complexity of Electroencephalogram (EEG) signals, called wavelet sub-band entropy, was employed to predict the patients’ outcomes. We hypothesized that the EEG signals of the patients who …

A Family Of Cantorvals, John Ferdinands, Timothy Ferdinands

University Faculty Publications and Creative Works

The set of subsums of the series Σn=1∞ xn is known to be one of three types: a finite union of intervals, homeomorphic to the Cantor set, or of the type known as a Cantorval. Bartoszewicz, Filipczak and Szymonik have described a family of series which contained all known examples of subsum sets which are Cantorvals. We construct another family of series which produces new examples of subsum sets which are Cantorvals.

A New Model For Lifting Condensation Levels Estimation, Nihad E. Daidzic

Aviation Department Publications

Knowledge of and the ability to predict lifting condensation levels (LCL) is important ingredient in weather predictions, cloud formation, planetary albedo and Earth’s energy balance. It is also essential topic in aviation safety and flight operations. In this article, we derive a new model of LCL and compare it to some older commonly-used models. This includes also the recently published Romps’ (2017) model. The new model presented here includes dependence, however weak, of the surface atmospheric pressure and the specific humidity on the LCL height and temperature. Such is not the case with widely used models and expressions by Espy …

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 …

Switching Diffusions: Applications To Ecological Models, And Numerical Methods For Games In Insurance, Trang Thi-Huyen Bui

Wayne State University Dissertations

Recently, a class of dynamic systems called ``hybrid systems" containing both continuous dynamics and discrete events has been adapted to treat a wide variety of situations arising in many real-world situations. Motivated by such development, this dissertation is devoted to the study of dynamical systems involving a Markov chain as the randomly switching process. The systems studied include hybrid competitive Lotka-Volterra ecosystems and non-zero-sum stochastic differential games between two insurance companies with regime-switching.

The first part is concerned with competitive Lotka-Volterra model with Markov switching. A novelty of the contribution is that the Markov chain has a countable state space. …

Local Hemodynamic Conditions Associated With Focal Changes In The Intracranial Aneurysm Wall, Juan R. Cebral, F. Detmer, Bong Jae Chung, J. Choque-Velasquez, B. Rezai, H. Lehto, R. Tulamo, J. Hernesniemi, M. Niemela, A. Yu, R. Williamson, Khaled Aziz, S. Sakur, S. Amin-Hanjani, F. Charbel, Y. Tobe, A. Robertson, J. Frösen

Department of Applied Mathematics and Statistics Faculty Scholarship and Creative Works

BACKGROUND AND PURPOSE: Aneurysm hemodynamics has been associated with wall histology and inflammation. We investigated associations between local hemodynamics and focal wall changes visible intraoperatively. MATERIALS AND METHODS: Computational fluid dynamics models were constructed from 3D images of 65 aneurysms treated surgically. Aneurysm regions with different visual appearances were identified in intraoperative videos: 1) “atherosclerotic” (yellow), 2) “hyperplastic” (white), 3) “thin” (red), 4) rupture site, and 5) “normal” (similar to parent artery), They were marked on 3D reconstructions. Regional hemodynamics was characterized by the following: wall shear stress, oscillatory shear index, relative residence time, wall shear stress gradient and divergence, …

Approximations In Reconstructing Discontinuous Conductivities In The Calderón Problem, George H. Lytle

Theses and Dissertations--Mathematics

In 2014, Astala, Päivärinta, Reyes, and Siltanen conducted numerical experiments reconstructing a piecewise continuous conductivity. The algorithm of the shortcut method is based on the reconstruction algorithm due to Nachman, which assumes a priori that the conductivity is Hölder continuous. In this dissertation, we prove that, in the presence of infinite-precision data, this shortcut procedure accurately recovers the scattering transform of an essentially bounded conductivity, provided it is constant in a neighborhood of the boundary. In this setting, Nachman’s integral equations have a meaning and are still uniquely solvable.

To regularize the reconstruction, Astala et al. employ a high frequency …

Decision Making Under Uncertainty With Applications To Geosciences And Finance, Laxman Bokati

Open Access Theses & Dissertations

In many practical situations, we need to make a decision. In engineering, we need to decide on the best design of a system, and, for existing systems â?? on the best control strategy. In financial applications, we need to decide what is the best way to invest money. In geosciences, we need to decide whether we should explore a possible mineral deposit â?? or whether we should perform more experiments and measurements (and what exactly). In some cases, we can compute the exact consequences of each decision - e.g., if we are controlling a satellite. However, in many other cases, …

Forecasting Crashes, Credit Card Default, And Imputation Analysis On Missing Values By The Use Of Neural Networks, Jazmin Quezada

Open Access Theses & Dissertations

A neural network is a system of hardware and/or software patterned after the operation of neurons in the human brain. Neural networks,- also called Artificial Neural Networks - are a variety of deep learning technology, which also falls under the umbrella of artificial intelligence, or AI. Recent studies shows that Artificial Neural Network has the highest coefficient of determination (i.e. measure to assess how well a model explains and predicts future outcomes.) in comparison to the K-nearest neighbor classifiers, logistic regression, discriminant analysis, naive Bayesian classifier, and classification trees. In this work, the theoretical description of the neural network methodology …

Stabilize Chaotic Flows In A Coupled Triple-Loop Thermosyphon System, Haley N. Anderson

Honors College Theses

This study addresses the control of chaotic dynamic systems represented by three coupled Lorenz systems. In application, Lorenz systems are commonly used to describe the one-dimensional motion of fluids in a tube when heated below and cooled above. This system, in particular, reflects the fluid motion in a coupled triple-loop thermosyphon system. The goal is to derive a system of nonlinear differential equations to help us study various flow patterns governed by such a high-dimensional nonlinear model numerically. Once the driving parameter (Rayleigh number) values are identified corresponding to the chaotic regime, a minimal number of proportional controllers are designed …

Using Social Network Analysis To Examine The Connections Within A Noyce Community’S Facebook Group, Amanda Jensen

Electronic Theses and Dissertations

One of the successes of the Rural Enhancement of Mathematics And Science Teachers (REMAST) Scholarship Program at South Dakota State University is the community we have built. This community has been built through a summer conference and a closed Facebook group. As we near the end of our Phase II Noyce funding, we are using social network analysis to examine the connections within the REMAST Facebook group. What we learn in this research project will be useful to other Noyce projects as it is a model for developing a strong professional learning community. In order to determine information about the …

Quasilinearization And Boundary Value Problems At Resonance For Caputo Fractional Differential Equations, Saleh S. Almuthaybiri, Paul W. Eloe, Jeffrey T. Neugebauer

Mathematics Faculty Publications

The quasilinearization method is applied to a boundary value problem at resonance for a Caputo fractional differential equation. The method of upper and lower solutions is first employed to obtain the uniqueness of solutions of the boundary value problem at resonance. The shift argument is applied to show the existence of solutions. The quasilinearization algorithm is then developed and sequences of approximate solutions are constructed that converge monotonically and quadratically to the unique solution of the boundary value problem at resonance. Two applications are provided to illustrate the main results.

Some Transitivity-Like Concepts In Abelian Groups, Gabor Braun, Brendan Goldsmith, Ketao Gong, Lutz Strungmann

Articles

The classical notions of transitivity and full transitivity in Abelian p-groups have natural extensions to concepts called Krylov and weak transitivity. The interconnections between these four types of transitivity are determined for Abelian p-groups; there is a marked difference in the relationships when the prime p is equal to 2. In the final section the relationship between full and Krylov transitivity is examined in the case of mixed Abelian groups which are p-local in the sense that multiplication by an integer relatively prime to p is an automorphism.