Mathematics Commons^™

Some Implications Of Chu's 10Ψ10 Generalization Of Bailey's 6Ψ6 Summation Formula, James Mclaughlin, Andrew Sills, Peter Zimmer

Mathematical Sciences: Faculty Publications

Lucy Slater used Bailey's 6ψ6 summation formula to derive the Bailey pairs she used to construct her famous list of 130 identities of the Rogers-Ramanujan type.

In the present paper we apply the same techniques to Chu's 10ψ10 generalization of Bailey's formula to produce quite general Bailey pairs. Slater's Bailey pairs are then recovered as special limiting cases of these more general pairs.

In re-examining Slater's work, we find that her Bailey pairs are, for the most part, special cases of more general Bailey pairs containing one or more free parameters. Further, we also find new …

Mathematical Modeling And Control Of Nonlinear Oscillators With Shape Memory Alloys, Mohamed Bendame

Theses and Dissertations (Comprehensive)

Shape memory alloys (SMAs) belong to an interesting type of materials that have attracted the attention of scientists and engineers over the last few decades. They have some interesting properties that made them the subject of extensive research to find the best ways to utilize them in different engineering, biomedical, and scientific applications. In this thesis, we develop a mathematical model and analyze the behavior of SMAs by considering a one degree of freedom nonlinear oscillator consisting of a mass connected to a fixed frame through a viscous damping and a shape memory alloy device. Due to the nonlinear and …

Diagonal Forms And The Rationality Of The Poincaré Series, Dibyajyoti Deb

University of Kentucky Doctoral Dissertations

The Poincaré series, Py(f) of a polynomial f was first introduced by Borevich and Shafarevich in [BS66], where they conjectured, that the series is always rational. Denef and Igusa independently proved this conjecture. However it is still of interest to explicitly compute the Poincaré series in special cases. In this direction several people looked at diagonal polynomials with restrictions on the coefficients or the exponents and computed its Poincaré series. However in this dissertation we consider a general diagonal polynomial without any restrictions and explicitly compute its Poincaré series, thus extending results of Goldman, Wang and Han. In a separate …

General Flips And The Cd-Index, Daniel J. Wells

University of Kentucky Doctoral Dissertations

We generalize bistellar operations (often called flips) on simplicial manifolds to a notion of general flips on PL-spheres. We provide methods for computing the cd-index of these general flips, which is the change in the cd-index of any sphere to which the flip is applied. We provide formulas and relations among flips in certain classes, paying special attention to the classic case of bistellar flips. We also consider questions of "flip-connecticity", that is, we show that any two polytopes in certain classes can be connected via a sequence of flips in an appropriate class.

[Introduction To] Ordinary And Particial Differential Equations: An Introduction To Dynamical Systems, John W. Cain, Angela M. Reynolds

Bookshelf

Differential equations arise in a variety of contexts, some purely theoretical and some of practical interest. As you read this textbook, you will find that the qualitative and quantitative study of differential equations incorporates an elegant blend of linear algebra and advanced calculus. This book is intended for an advanced undergraduate course in differential equations. The reader should have already completed courses in linear algebra, multivariable calculus, and introductory differential equations.

The Influence Of Inclusion On Langauge Arts Literacy And Math Achievement On Non-Disabled Middle School Students, Faye Brady

Seton Hall University Dissertations and Theses (ETDs)

.

Effects Of Multitemperature Nonequilibrium On Compressible Homogeneous Turbulence, Wei Liao, Yan Peng, Li-Shi Luo

Mathematics & Statistics Faculty Publications

We study the effects of the rotational-translational energy exchange on the compressible decaying homogeneous isotropic turbulence (DHIT) in three dimensions through direct numerical simulations. We use the gas-kinetic scheme coupled with multitemperature nonequilibrium based on the Jeans-Landau-Teller model. We investigate the effects of the relaxation time of rotational temperature, Z_R, and the initial ratio of the rotational and translational temperatures, T_R0 / T_L0, on the dynamics of various turbulence statistics including the kinetic energy K (t), the dissipation rate ε (t), the energy spectrum E (k,t), the root mean square of the velocity divergence θ′ …

Algorithms For Upper Bounds Of Low Dimensional Group Homology, Joshua D. Roberts

University of Kentucky Doctoral Dissertations

A motivational problem for group homology is a conjecture of Quillen that states, as reformulated by Anton, that the second homology of the general linear group over R = Z[1/p; ζ_p], for p an odd prime, is isomorphic to the second homology of the group of units of R, where the homology calculations are over the field of order p. By considering the group extension spectral sequence applied to the short exact sequence 1 → SL₂ → GL₂ → GL₁ → 1 we show that the calculation of the homology …

The Fibonacci Sequence, Arik Avagyan

A with Honors Projects

A review was made of the Fibonacci sequence, its characteristics and applications.

Using Mathematics As A Gateway To Literacy For English Language Learners, Krista Hemphill

Honors Program Theses

One teaching approach that alleviates language barriers involves teachers using what students know and can do to develop students‟ understanding of and ability in another area. Thus, 2 teachers can promote ELLs‟ literacy development by integrating knowledge and skills ELLs have from another subject area into their literacy instruction. Specifically, teachers can integrate mathematics into literacy instruction because research suggests that ELLs often understand and successfully carry out mathematical tasks. For example, Gunning (2003) points out that ELLs tend to perform well on mathematical computations. The universality of mathematical symbols seems to promote ELLs‟ understanding of mathematics instruction although lessons …

Multiscale Modeling Of Cellular Systems In Biology, J. C. Dallon

Faculty Publications

Here we review eight different multiscale modeling efforts dealing with cellular systems in biology. The first two models focus on collagen based tissue, one dealing with the biomechanical properties of the tissue and the other focusing on how the dermis is remodeled in scar tissue formation. The next two models deal with first avascular tumor growth and then the role of the vasculature in tumor growth. We then consider two models which use the Immersed Boundary method to model tissue properties and cell-cell adhesion. Finally we conclude with two models with treatments of the Cellular Potts Model. The first models …

Stochastic Orders In Heterogeneous Samples With Applications, Maochao Xu

Dissertations and Theses

The statistics literature has mostly focused on the case when the data available is in the form of a random sample. In many cases, the observations are not identically distributed. Such samples are called heterogeneous samples. The study of heterogeneous samples is of great interest in many areas, such as statistics, econometrics, reliability engineering, operation research and risk analysis.

Stochastic orders between probability distributions is a widely studied concept. There are several kinds of stochastic orders that are used to compare different aspects of probability distributions like location, variability, skewness, dependence, etc.

In this dissertation, most of the work is …

Numerical Computations For Pde Models Of Rocket Exhaust Flow In Soil, Brian Brennan

Electronic Theses and Dissertations

We study numerical methods for solving the nonlinear porous medium and Navier-Lame problems. When coupled together, these equations model the flow of exhaust through a porous medium, soil, and the effects that the pressure has on the soil in terms of spatial displacement. For the porous medium equation we use the Crank-Nicolson time stepping method with a spectral discretization in space. Since the Navier-Lame equation is a boundary value problem, it is solved using a finite element method where the spatial domain is represented by a triangulation of discrete points. The two problems are coupled by using approximations of solutions …

Initial-Value Technique For Singularly Perturbed Two Point Boundary Value Problems Via Cubic Spline, Luis G. Negron

Electronic Theses and Dissertations

A recent method for solving singular perturbation problems is examined. It is designed for the applied mathematician or engineer who needs a convenient, useful tool that requires little preparation and can be readily implemented using little more than an industry-standard software package for spreadsheets. In this paper, we shall examine singularly perturbed two point boundary value problems with the boundary layer at one end point. An initial-value technique is used for its solution by replacing the problem with an asymptotically equivalent first order problem, which is, in turn, solved as an initial value problem by using cubic splines. Numerical examples …

Detection And Approximation Of Function Of Two Variables In High Dimensions, Minzhe Pan

Electronic Theses and Dissertations

This thesis originates from the deterministic algorithm of DeVore, Petrova, and Wojtaszcsyk for the detection and approximation of functions of one variable in high dimensions. We propose a deterministic algorithm for the detection and approximation of function of two variables in high dimensions.

Linear Stochastic Systems: A White Noise Approach, Daniel Alpay, David Levanony

Mathematics, Physics, and Computer Science Faculty Articles and Research

Using the white noise setting, in particular the Wick product, the Hermite transform, and the Kondratiev space, we present a new approach to study linear stochastic systems, where randomness is also included in the transfer function. We prove BIBO type stability theorems for these systems, both in the discrete and continuous time cases. We also consider the case of dissipative systems for both discrete and continuous time systems. We further study ℓ1-ℓ2 stability in the discrete time case, and L2-L∞ stability in the continuous time case.

Heteroclinic Solutions To An Asymptotically Autonomous Second-Order Equation, Gregory S. Spradlin

Mathematics - Daytona Beach

We study the differential equation ẍ(t) = a(t)V '(x(t)), where V is a double-well potential with minima at x = ±1 and a(t) →l > 0 as |t| → 1. It is proven that under certain additional assumptions on a, there exists a heteroclinic solution x to the differential equation with x(t) → -1 as t → -1 and x(t) → 1 as t → ∞. The assumptions allow l - a(t) to change sign for arbitrarily large values of |t|, and do not restrict the decay rate of |l -a(t)| as |t| → ∞ © 2010 Texas State University - …

Regular Functions On The Space Of Cayley Numbers, Graziano Gentili, Daniele C. Struppa

Mathematics, Physics, and Computer Science Faculty Articles and Research

In this paper we present a new definition of regularity on the space Ç of Cayley numbers (often referred to as octonions), based on a Gateaux-like notion of derivative. We study the main properties of regular functions, and we develop the basic elements of a function theory on Ç. Particular attention is given to the structure of the zero sets of such functions.