Applied Mathematics Commons^™

Rainbow Perfect Matchings And Hamilton Cycles In The Random Geometric Graph, Deepak C. Bal, Patrick Bennett, Xavier Pérez‐Giménez, Paweł Prałat

Department of Mathematics Faculty Scholarship and Creative Works

Given a graph on n vertices and an assignment of colours to the edges, a rainbow Hamilton cycle is a cycle of length n visiting each vertex once and with pairwise different colours on the edges. Similarly (for even n) a rainbow perfect matching is a collection of independent edges with pairwise different colours. In this note we show that if we randomly colour the edges of a random geometric graph with sufficiently many colours, then a.a.s. the graph contains a rainbow perfect matching (rainbow Hamilton cycle) if and only if the minimum degree is at least 1 (respectively, …

Superconvergence Of A Modified Weak Galerkin Approximation For Second Order Elliptic Problems By L^2 Projection Method, Betul Bogrek

Theses and Dissertations

In this dissertation, the general superconvergence result of a modified weak Galerkin finite element approximation for the second order elliptic problem by using L^2 projection method is introduced. The novel weak Galerkin finite element method, which was first proposed and analyzed by Wang J. and Ye X., uses the appropriately defined weak functions and discrete weak gradients on arbitrary shapes for higher order polynomial functions. The modified weak Galerkin finite element method was introduced by Wang X. & et al. It reduces the number of unknowns by modifying weak functions from the weak Galerkin finite element method. The superconvergence for …

Dynamics Of Multicultural Social Networks, Kristina B. Hilton

USF Tampa Graduate Theses and Dissertations

Historically human endeavors around the globe are in search of bilateral relationships. Knowledge and commerce has played a very significant role in increasing the ability for humans to connect for the betterment of the human species. As the means of communication improve, mutual benefits to the community as a whole also increase. Moreover, the benefits are filtered down to members of the overall community. Recent advancement in electronic communication technologies and in knowledge, in particular, physical, chemical, engineering and medical sciences and philosophies, have facilitated nearly instantaneous multi-cultural interactions. Local problems and solutions have become global. This has generated a …

Daily Fantasy Sports: Chance Or Skill?, Danielle Bergner

Honors Projects in Mathematics

Online daily fantasy sports is a billion dollar industry that has caused controversy for the last few years with states debating its legal status. As of today, under the current United States federal laws and regulations, betting money on daily fantasy sports online is considered legal. However, several states have decided to ban these games within their borders believing they are based on chance and should be considered gambling which they have ruled to be illegal online. Each state has the right to make their own rules of what they consider gambling even if the federal government has allowed it. …

Discrete Fractional Hermite-Hadamard Inequality, Aykut Arslan

Masters Theses & Specialist Projects

This thesis is comprised of three main parts: The Hermite-Hadamard inequality on discrete time scales, the fractional Hermite-Hadamard inequality, and Karush-Kuhn- Tucker conditions on higher dimensional discrete domains. In the first part of the thesis, Chapters 2 & 3, we define a convex function on a special time scale T where all the time points are not uniformly distributed on a time line. With the use of the substitution rules of integration we prove the Hermite-Hadamard inequality for convex functions defined on T. In the fourth chapter, we introduce fractional order Hermite-Hadamard inequality and characterize convexity in terms of this …

Stability Of Linear Difference Systems In Discrete And Fractional Calculus, Aynur Er

Masters Theses & Specialist Projects

The main purpose of this thesis is to define the stability of a system of linear difference equations of the form,

∇y(t) = Ay(t),

and to analyze the stability theory for such a system using the eigenvalues of the corresponding matrix A in nabla discrete calculus and nabla fractional discrete calculus. Discrete exponential functions and the Putzer algorithms are studied to examine the stability theorem.

This thesis consists of five chapters and is organized as follows. In the first chapter, the Gamma function and its properties are studied. Additionally, basic definitions, properties and some main theorem of discrete calculus are …

The Statistical Dynamics Of Nonequilibrium Control, Grant Murray Rotskoff '09

Doctoral Dissertations

Living systems, even at the scale of single molecules, are constantly adapting to changing environmental conditions. The physical response of a nanoscale system to external gradients or changing thermodynamic conditions can be chaotic, nonlinear, and hence difficult to control or predict. Nevertheless, biology has evolved systems that reliably carry out the cell’s vital functions efficiently enough to ensure survival. Moreover, the development of new experimental techniques to monitor and manipulate single biological molecules has provided a natural testbed for theoretical investigations of nonequilibrium dynamics. This work focuses on developing paradigms for both understanding the principles of nonequilibrium dynamics and also …

A Framework For Predicting Impacts On Ecosystem Services From (Sub)Organismal Responses To Chemicals, Valery E. Forbes, Chris J. Salice, Bjorn Birnir, Randy J.F. Bruins, Peter Calow, Virginie Ducrot, Nika Galic, Kristina Garber, Bret C. Harvey, Henriette Jager, Andrew Kanarek, Robert Pastorok, Steve F. Railsback, Richard Rebarber, Pernille Thorbek

Department of Mathematics: Faculty Publications

Protection of ecosystem services is increasingly emphasized as a risk-assessment goal, but there are wide gaps between current ecological risk-assessment endpoints and potential effects on services provided by ecosystems. The authors present a framework that links common ecotoxicological endpoints to chemical impacts on populations and communities and the ecosystem services that they provide. This framework builds on considerable advances in mechanistic effects models designed to span multiple levels of biological organization and account for various types of biological interactions and feedbacks. For illustration, the authors introduce 2 case studies that employ well-developed and validated mechanistic effects models: the inSTREAM individual-based …

Generalized Thomas-Fermi Equations As The Lampariello Class Of Emden-Fowler Equations, Haret C. Rosu, S.C. Mancas

Publications

A one-parameter family of Emden-Fowler equations defined by Lampariello’s parameter p which, upon using Thomas-Fermi boundary conditions, turns into a set of generalized Thomas-Fermi equations comprising the standard Thomas-Fermi equation for p = 1 is studied in this paper. The entire family is shown to be non integrable by reduction to the corresponding Abel equations whose invariants do not satisfy a known integrability condition. We also discuss the equivalent dynamical system of equations for the standard Thomas-Fermi equation and perform its phase-plane analysis. The results of the latter analysis are similar for the whole class.

An Rbf Interpolation Blending Scheme For Effective Shock-Capturing, M. Harris, Eduardo Divo, Alain J. Kassab

Publications

In recent years significant focus has been given to the study of Radial basis functions (RBF), especially in their use on solving partial differential equations (PDE). RBF have an impressive capability of inter- polating scattered data, even when this data presents localized discontinuities. However, for infinitely smooth RBF such as the Multiquadrics, inverse Multiquadrics, and Gaussian, the shape parameter must be chosen properly to obtain accurate approximations while avoiding ill-conditioning of the interpolating matrices. The optimum shape parameter can vary significantly depending on the field, particularly in locations of steep gradients, shocks, or discontinuities. Typically, the shape parameter is chosen …

A Coupled Localized Rbf Meshless/Drbem Formulation For Accurate Modeling Of Incompressible Fluid Flows, Leonardo Bueno, Eduardo Divo, Alain J. Kassab

Publications

Velocity-pressure coupling schemes for the solution of incompressible fluid flow problems in Computational Fluid Dynamics (CFD) rely on the formulation of Poisson-like equations through projection methods. The solution of these Poisson-like equations represent the pressure correction and the velocity correction to ensure proper satisfaction of the conservation of mass equation at each step of a time-marching scheme or at each level of an iteration process. Inaccurate solutions of these Poisson-like equations result in meaningless instantaneous or intermediate approximations that do not represent the proper time-accurate behavior of the flow. The fact that these equations must be solved to convergence at …

On The Classification Of The Second Minimal Orbits Of The Continuous Endomorphisms On The Real Line And Universality In Chaos, Naveed H. Iqbal

Theses and Dissertations

This dissertation presents full classification of second minimal odd periodic orbits of a continuous endomorphisms on the real line. A (2k + 1)-periodic orbit (k ≥ 3) is called second minimal for the map f , if 2k−1 is a minimal period of f in the Sharkovskii ordering. We prove that there are 4k−3 types of second minimal (2k+1)-orbits, each characterized with unique cyclic permutation and directed graph of transitions with accuracy up to inverses. The result is applied to the problem on the distribution of periodic windows within the chaotic regime of the bifurcation diagram of the one-parameter family …

Haar Wavelet Solution Of Poisson’S Equation And Their Block Structures, The British University In Egypt, Ain Shams University

Basic Science Engineering

The structure of the algebraic system which results from the use of Haar wavelet when solving Poisson’s equation is studied. Haar wavelet technique is used to solve Poisson’s equation on a unit square domain. The form of collocation points are used at the mid points of the subintervals i.e at the odd multiple of the sub interval length labeling. It is proved that the coefficient matrix has symmetric block structure. Comparison with the tridagonal block structure obtained by the finite difference with the natural ordering is introduced. The numerical results have illustrated the superiority of the use of Haar wavelet …

The Air Force Fitness Test: Creating New Fitness Assessment Charts Using Waist To Height Ratios, John R. Griffith

Theses and Dissertations

The Air Force currently uses AFI 36-2905 for fitness standards and evaluation, but no study to our knowledge has evaluated these standards using large databases. Using a 5.38 million record database from the Air Force Fitness Management System, we evaluated how the abdominal circumference, body mass index (BMI), waist to height ratio (WtHR), and height to weight ratio correlated to fitness as assessed by the 1.5 mile aerobic run in the Air Force Fitness Test. Whether individually or adjusting for age group and gender, WtHR performed better that the rest with an average rank score of 1.1 with a relative …

Classification Of Rectifying Space-Like Submanifolds In Pseudo-Euclidean Spaces, Bang Yen Chan, Yun Myung Oh

Faculty Publications

The notions of rectifying subspaces and of rectifying submanifolds were introduced in [B.-Y. Chen, Int. Electron. J. Geom 9 (2016), no. 2, 1–8]. More precisely, a submanifold in a Euclidean m-space Em is called a rectifying submanifold if its position vector field always lies in its rectifying subspace. Several fundamental properties and classification of rectifying submanifolds in Euclidean space were obtained in [B.-Y. Chen, op. cit.]. In this present article, we extend the results in [B.-Y. Chen, op. cit.] to rectifying space- like submanifolds in a pseudo-Euclidean space with arbitrary codimension. In particular, we completely classify all rectifying space-like submanifolds …

P26. Global Exponential Stabilization On So(3), Soulaimane Berkane

Western Research Forum

Global Exponential Stabilization on SO(3)

Computational Algorithms For Improved Representation Of The Model Error Covariance In Weak-Constraint 4d-Var, Jeremy A. Shaw

Dissertations and Theses

Four-dimensional variational data assimilation (4D-Var) provides an estimate to the state of a dynamical system through the minimization of a cost functional that measures the distance to a prior state (background) estimate and observations over a time window. The analysis fit to each information input component is determined by the specification of the error covariance matrices in the data assimilation system (DAS). Weak-constraint 4D-Var (w4D-Var) provides a theoretical framework to account for modeling errors in the analysis scheme. In addition to the specification of the background error covariance matrix, the w4D-Var formulation requires information on the model error statistics and …

Application Of Inverse Problems In Imaging, Xiaoyue Luo

Post-Grant Reports

In this project, we studied how to enhance image quality by denoising and deblurring a given image mathematically. We compared some existing state-of-the-art methods for image denoising and deblurring. We implemented the algorithms numerically using Matlab.

We studied the possibility of combining statistical analysis with the traditional image restoration methods including using wavelets and framelets and we derived some encouraging preliminary results.

My research student Alleta Maier gave a sequence of talks on the project including the Pacific Northwest Mathematical Association of America conference at Oregon State University in April, 2016; Linfield College Taylor Series in March, 2016, and Linfield …

P-31 Sufficient Conditions For The Existence Of Positive Solutions To An Elliptic Model, Timothy Robertson

Honors Scholars & Undergraduate Research Poster Symposium Programs

We study the existence of solutions to a general elliptic model. Specifically, we give conditions for the existence and non-existence of steady-state solutions to a general, nonlinear population model of two cooperating species.

Differences In Hemodynamics And Rupture Rate Of Aneurysms At The Bifurcation Of The Basilar And Internal Carotid Arteries, Ravi Doddasomayajula, Bong Jae Chung, Farid Hamzei-Sichani, Christopher M. Putman, Juan Cebral

Department of Applied Mathematics and Statistics Faculty Scholarship and Creative Works

BACKGROUND AND PURPOSE: Cerebral aneurysms in the posterior circulation are known to have a higher rupture risk than those in the anterior circulation. We sought to test the hypothesis that differences in hemodynamics can explain the difference in rupture rates.

MATERIALS AND METHODS: A total of 117 aneurysms, 63 at the tip of the basilar artery (27 ruptured, 36 unruptured, rupture rate = 43%) and 54 at the bifurcation of the internal carotid artery (11 ruptured, 43 unruptured, rupture rate = 20%) were analyzed with image-based computational fluid dynamics. Several hemodynamic variables were compared among aneurysms at each location and …

The Subject Librarian Newsletter, Mathematics, Spring 2017, Sandy Avila

Libraries' Newsletters

No abstract provided.

Utilizing Social Network Analysis To Study Communities Of Women In Conflict Zones, James R. Gatewood, Candice R. Price

Journal of Humanistic Mathematics

This article proposes to study the plight of women in conflict zones through the lens of social network analysis. We endorse the novel idea of building a social network within troubled regions to assist in understanding the structure of women's communities and identifying key individuals and groups that will help rebuild and empower the lives of women. Our main argument is that we can better understand the complexity of a society with quantitative measures using a network analysis approach. Given the foundation of this paper, one can develop a model that will represent the connections between women in these communities. …

Application Of An Rbf Blending Interpolation Method To Problems With Shocks, Michael Harris, Eduardo Divo, Alain J. Kassab

Publications

Radial basis functions (RBF) have become an area of research in recent years, especially in the use of solving partial differential equations (PDE). Radial basis functions have an impressive capability in interpolating scattered data, even for data with discontinuities. Although, for infinitely smooth radial basis functions such as the multi-quadrics and inverse multi-quadrics, the shape parameter must be chosen properly to obtain accurate approximations while avoiding ill-conditioning of the interpolating matrices. The optimum shape parameter can vary depending on the field, such as in locations of sharp gradients or shocks. Typically, the shape parameter is chosen to maintain a high …

On The Three Dimensional Interaction Between Flexible Fibers And Fluid Flow, Bogdan Nita, Ryan Allaire

Department of Mathematics Faculty Scholarship and Creative Works

In this paper we discuss the deformation of a flexible fiber clamped to a spherical body and immersed in a flow of fluid moving with a speed ranging between 0 and 50 cm/s by means of three dimensional numerical simulation developed in COMSOL . The effects of flow speed and initial configuration angle of the fiber relative to the flow are analyzed. A rigorous analysis of the numerical procedure is performed and our code is benchmarked against well established cases. The flow velocity and pressure are used to compute drag forces upon the fiber. Of particular interest is the behavior …

Extracting Geography From Datasets In Social Sciences, Yuke Li, Tianhao Wu, Nicholas Marshall, Stefan Steinerberger

Yale Day of Data

No abstract provided.

Steady State Probabilities In Relation To Eigenvalues, Pellegrino Christopher

The Kabod

By using the methods of Hamdy Taha, eigenvectors can be used in solving problems to compute steady state probabilities, and they work every time.

Numerical Simulation Of Acoustic Emission During Crack Growth In 3-Point Bending Test, Mihhail Berezovski, Arkadi Berezovski

Publications

Numerical simulation of acoustic emission by crack propagation in 3-point bending tests is performed to investigate how the interaction of elastic waves generates a detectable signal. It is shown that the use of a kinetic relation for the crack tip velocity combined with a simple crack growth criterion provides the formation of waveforms similar to those observed in experiments.

A Two-Species Stage-Structured Model For West Nile Virus Transmission, Taylor A. Beebe, Suzanne L. Robertson

Mathematics and Applied Mathematics Publications

We develop a host–vector model of West Nile virus (WNV) transmission that incorporates multiple avian host species as well as host stage-structure (juvenile and adult stages), allowing for both species-specific and stage-specific biting rates of vectors on hosts. We use this ordinary differential equation model to explore WNV transmission dynamics that occur between vectors and multiple structured host populations as a result of heterogeneous biting rates on species and/or life stages. Our analysis shows that increased exposure of juvenile hosts generally results in larger outbreaks of WNV infectious vectors when compared to differential host species exposure. We also find that …

A Theoretical Framework For Analyzing Coupled Neuronal Networks: Application To The Olfactory System, Andrea K. Barreiro, Shree Hari Gautam, Woodrow L. Shew, Cheng Ly

Mathematics and Applied Mathematics Publications

Determining how synaptic coupling within and between regions is modulated during sensory processing is an important topic in neuroscience. Electrophysiological recordings provide detailed information about neural spiking but have traditionally been confined to a particular region or layer of cortex. Here we develop new theoretical methods to study interactions between and within two brain regions, based on experimental measurements of spiking activity simultaneously recorded from the two regions. By systematically comparing experimentally-obtained spiking statistics to (efficiently computed) model spike rate statistics, we identify regions in model parameter space that are consistent with the experimental data. We apply our new technique …

Solitary Wave Solution Of Flat Surface Internal Geophysical Waves With Vorticity, Alan Compelli

Conference papers

A fluid system bounded by a flat bottom and a flat surface with an internal wave and depth-dependent current is con-sidered. The Hamiltonian of the system is presented and the dynamics of the system are discussed. A long-wave regime is then considered and extended to produce a KdV approximation. Finally, a solitary wave solution is obtained.