Physical Sciences and Mathematics Commons^™

Partial Open Book Decompositions And The Contact Class In Sutured Floer Homology, Tolga Etgü, Burak Özbağci

Turkish Journal of Mathematics

We demonstrate how to combinatorially calculate the EH-class of a compatible contact structure in the sutured Floer homology group of a balanced sutured three manifold which is associated to an abstract partial open book decomposition. As an application we show that every contact three manifold (closed or with convex boundary) can be obtained by gluing tight contact handlebodies whose EH-classes are nontrivial.

C1 Modules With Respect To A Hereditary Torsion Theory, Tahi̇re Özen

Turkish Journal of Mathematics

An R-module M is said to be a C1-module if every closed submodule of M is a direct summand. In this paper we introduce and investigate the concept of the \tau-C1 module for a hereditary torsion theory \tau on Mod-R. \tau-C1 modules are a generalization of C1-modules.

Uniqueness For Meromorphic Functions And Differential Polynomials, Chao Meng

Turkish Journal of Mathematics

In this article, we deal with the uniqueness problems on meromorphic functions concerning differential polynomials and prove the following result: Let f and g be two transcendental meromorphic functions, \alpha be a meromorphic function such that T(r,\alpha)=o(T(r,f)+T(r,g)) and \alpha \not\equiv 0,\infty. Let a be a nonzero constant. Suppose that m,n are positive integers such that n>m+10. If \Psi_f' and \Psi_g' share ``(0,2)", then (i) if m\geq 2, then f(z)\equiv g(z); (ii) if m=1, either f(z)\equiv g(z) or f and g satisfy the algebraic equation R(f,g)\equiv 0, where R(\varpi_1,\varpi_2)=(n+1)(\varpi_1^{n+2}-\varpi_2^{n+2})-(n+2)(\varpi_1^{n+1} -\varpi_2^{n+1}). The results in this paper improve the results of Xiong-Lin-Mori …

A Perturbation Of M-Order Derivations On Banach Algebras, Yong-Soo Jung, Kyoo-Hong Park

Turkish Journal of Mathematics

Let \A be a unital Banach algebra and let m, 1 \leq m \leq 4, be an integer. If f: \A \to \A is an approximate m-order derivation in the sense of Hyers-Ulam-Rassias, then f: \A \to \A is an exact m-order derivation.

Intrinsic Equations For A Generalized Relaxed Elastic Line On An Oriented Surface In The Minkowski 3-Space E_1^3, Cumali̇ Eki̇ci̇, Ali̇ Görgülü

Turkish Journal of Mathematics

H. K. Nickerson and Gerald S. Manning [8] derived the intrinsic equations for a relaxed elastic line on an oriented surface in the Euclidean 3-dimensional space E^3. In this paper, we define a generalized relaxed elastic line and derive the intrinsic equations for a generalized of relaxed elastic line on an oriented surface in the Minkowski 3-dimensional space E_1^3 and give some applications of the result.

On The Dynamics Of Quasi-Self-Matings Of Generalized Starlike Complex Quadratics And The Structure Of The Mated Julia Sets, Ross Flek

Dissertations, Theses, and Capstone Projects

It has been shown that, in many cases, Julia sets of complex polynomials can be "glued" together to obtain a new Julia set homeomorphic to a Julia set of a rational map; the dynamics of the two polynomials are reflected in the dynamics of the mated rational map. Here, I investigate the Julia sets of self-matings of generalized starlike quadratic polynomials, which enjoy relatively simple combinatorics. The points in the Julia sets of the mated rational maps are completely classified according to their topology. The presence and location of buried points in these Julia sets are addressed. The interconnections between …

Applications Of New Diffusion Models To Barrier Option Pricing And First Hitting Time In Finance, Keang Ly

Theses and Dissertations (Comprehensive)

The main focus of this thesis is in the application of a new family of analytical solvable diffusion models to arbitrage-free pricing exotic financial derivatives, such as barrier options. The family of diffusions is the so-called “Drifted Bessel family” having nonlinear (smile-like) local volatility with multiple adjustable parameters. In particular, the drifted Bessel-K diffusion is used to model asset (stock) price processes under a risk-neutral measure whereby discounted asset price are martingales.

Closed-form spectral expansions for barrier option values are derived within the Bessel-K family of models. This follow from the closed-form spectral expansions for the transition probability …

First-Passage Time Models With A Stochastic Time Change In Credit Risk, Hui Li

Theses and Dissertations (Comprehensive)

Many authors have used a time-changed Brownian motion as a model of log-stock returns. Using a Levy process as a stochastic time change, one obtains well known asset price models such as the variance gamma (VG) and normal inverse Gaussian (NIG) models. Following on the heels of these asset price models, it is natural to extend structural credit models by using a time-changed geometric Brownian motion and other jump-diffusion processes to model the value of a firm. To avoid the difficulties that arise in computing the associated first passage time distribution and in analogy to the time-changed Markov chain models, …

Mathematical Modeling Of Quantum Dots With Generalized Envelope Functions Approximations And Coupled Partial Differential Equations, Dmytro Sytnyk

Theses and Dissertations (Comprehensive)

No abstract provided.

Gas-Kinetic Schemes For Direct Numerical Simulations Of Compressible Homogeneous Turbulence, Wei Liao, Yan Peng, Li-Shi Luo

Mathematics & Statistics Faculty Publications

We apply the gas-kinetic scheme (GKS) for the direct numerical simulations (DNSs) of compressible decaying homogeneous isotropic turbulence (DHIT). We intend to study the accuracy, stability, and efficiency of the gas-kinetic scheme for DNS of compressible homogeneous turbulence depending on both flow conditions and numerics. In particular, we study the GKS with multidimensional, quasi-one-dimensional, dimensional-splitting, and smooth-flow approximations. We simulate the compressible DHIT with the Taylor microscale Reynolds number Reλ =72.0 and the turbulence Mach number Ma_t between 0.1 and 0.6. We compute the low-order statistical quantities including the total kinetic energy K (t), the dissipation rate ε (t), …

On C2 -Smooth Surfaces Of Constant Width, Brendan Guilfoyle, Wilhelm Klingenberg

Publications

A number of results for C2 -smooth surfaces of constant width in Euclidean 3-space E 3 are obtained. In particular, an integral inequality for constant width surfaces is established. This is used to prove that the ratio of volume to cubed width of a constant width surface is reduced by shrinking it along its normal lines. We also give a characterization of surfaces of constant width that have rational support function. Our techniques, which are complex differential geometric in nature, allow us to construct explicit smooth surfaces of constant width in E 3 , and their focal sets. They also …

Dynamics And Rheology Of Biaxial Liquid Crystal Polymers, Sarthok K. Sircar

Theses and Dissertations

In this thesis we derive a hydrodynamical kinetic theory to study the orientational response of a mesoscopic system of nematic liquid crystals in the presence of an external flow field. Various problems have been attempted in this direction. First, we understand the steady-state behavior of uniaxial LCPs under an imposed elongational flow, electric and magnetic field respectively. We show that (1) the Smoluchowski equation can be cast into a generic form, (2) the external field is parallel to one of the eigenvectors of the second moment tensor, and (3) the steady state probability density function is of the Boltzmann type. …

Addressing The Principles For School Mathematics: A Case Study Of Elementary Teachers Pedagogy And Practices In An Urban High-Poverty School, Robert Q. Berry, Linda Bol, Sueanne E. Mckinney

Educational Foundations & Leadership Faculty Publications

The extent to which four novice teachers assigned to an urban high-poverty school implemented the Principles of School Mathematics during their mathematics instruction program was investigated using a case study design. The research team conducted 36 unannounced observations of the participating teachers and utilized a developed assessment to guide their observations. Results indicated that only one teacher was judged proficient for all the principles. The remaining three teachers fell short in the implementation and direction of the principles. Detailed descriptions of the pedagogical practices of the teachers are provided.

A Logistic Approximation To The Cumulative Normal Distribution, Shannon R. Bowling, Mohammad T. Khasawneh, Sittichai Kaewkuekool, Byung R. Cho

Engineering Management & Systems Engineering Faculty Publications

This paper develops a logistic approximation to the cumulative normal distribution. Although the literature contains a vast collection of approximate functions for the normal distribution, they are very complicated, not very accurate, or valid for only a limited range. This paper proposes an enhanced approximate function. When comparing the proposed function to other approximations studied in the literature, it can be observed that the proposed logistic approximation has a simpler functional form and that it gives higher accuracy, with the maximum error of less than 0.00014 for the entire range. This is, to the best of the authors’ knowledge, the …

Convergence And The Lebesgue Integral, Ryan Vail Thomas

MSU Graduate Theses

In this paper, we examine the theory of integration of functions of real variables. Background information in measure theory and convergence is provided and several examples are considered. We compare Riemann and Lebesgue integration and develop several important theorems. In particular, the Monotone Convergence Theorem and Dominated Convergence Theorem are considered under both pointwise convergence and convergence in measure.

A Finite Volume Method For Solving Parabolic Equations On Logically Cartesian Curved Surface Meshes, Donna Calhoun, Christiane Helzel

Donna Calhoun

We present a second-order, finite-volume scheme for the constant-coefficient diffusion equation on curved, parametric surfaces described via smooth or piecewise smooth mappings on logically Cartesian meshes. Our method does not require analytic metric terms, shows second-order accuracy, can be easily coupled to existing finite-volume solvers for logically Cartesian meshes and handles general mixed boundary conditions. We present numerical results demonstrating the accuracy of the scheme, and then use the scheme to solve advection-reaction-diffusion equations modeling biological pattern formation on surfaces.

Visualdsolve: Visualizing Differential Equations With Mathematica, Second Edition, Stan Wagon, Antonin Slavik, Dan Schwalbe

Stan Wagon, Retired

No abstract provided.

Geometric Ergodicity Of Gibbs Samplers (University Of Minnesota), Alicia Johnson

Alicia A. Johnson

No abstract provided.

Using A Personal Response System, John Hawkins, Bruce Mclean

John B. Hawkins

Over the years, we have consistently used the latest technology in our classes. It has made us more organized and has increased the understanding of our students. Now we have combined our old presentations and drawings from the past and placed them in PowerPoint presentations with imbedded questions. These questions can be multiple choice or questions that have numerical answers. Our University has settled upon one company to provide a personal response system, eInstruction’s Classroom Performance System (CPS). The students answer each question as it appears and we are able to evaluate our lectures in real time. Applets can still …

Easy Steps To Success: A Graphing Calculator Guide, Lisa Yocco, Ronald Harshbarger

Lisa S. Yocco

No abstract provided.

The Erdős-Lovász Tihany Conjecture For Quasi-Line Graphs, J. Balogh, A. V. Kostochka, N. Prince, M. Stiebitz

Noah Prince

Erdös and Lovász conjectured in 1968 that for every graph G with χ(G) > ω(G) and any two integers s, t ≥ 2 with s + t = χ(G) + 1, there is a partition (S,T) of the vertex set V(G) such that χ(G[S]) ≥ s and χ(G[T]) ≥ t . Except for a few cases, this conjecture is still unsolved. In this note we prove the conjecture for quasi-line graphs and for graphs with independence number 2.

Creating A Warmer Environment For Women In The Mathematical Sciences And In Philosophy, Samantha Brennan, Rob Corless

Samantha Brennan

No abstract provided.

Characterization Of Compactly Supported Renable Splines With Integer Matrix, Tian-Xiao He, Yujing Guana

Tian-Xiao He

Let M be an integer matrix with absolute values of all its eigenvalues being greater than 1. We give a characterization of compactly supported M-refinable splines f and the conditions that the shifts of f form a Riesz basis.

Modern Novels: How To Make Them More Relevant To High School Students, David Wendler, '09

Leah A. Nillas

There have been numerous studies conducted researching ways to reinvent how we teach outdated texts that are increasingly losing relevance to the current generation of students because of gaps in interest and culture. Because of this irrelevancy, students do not understand these books as well and are not thinking critically about the issues that they present. My research follows along the same lines, but deals specifically with the increasing irrelevancy of modern novels. I distributed a questionnaire to the class I observe at a local high school. My findings have been that modern novels, while lacking relevance with many students, …

Properties Of Multilevel Block $\Alpha$-Circulants, William F. Trench

William F. Trench

No abstract provided.

Inverses Of Lower Triangular Toeplitz Matrices, William F. Trench

William F. Trench

No abstract provided.

On Nonautonomous Linear Systems Of Differential And Difference Equations With $R$-Symmetric Coefficient Matrices, William F. Trench

William F. Trench

No abstract provided.

Problems Of Local Fractional Definite Integral Of The One-Variable Non-Differentiable Function, Yang Xiao-Jun

Xiao-Jun Yang

It is proposed that local fractional calculas introduced by Kolwankar and Gangal is extended by the concept of Jumarie’s fractional calculus and local fractional definite integral is redefined. The properties and the theorems of local fractional calculus are discussed in this paper.

My Trig Book, Bruce Kessler

Bruce Kessler

This is the MATH 117 Trigonometry text developed by Dr. Bruce Kessler for the Gatton Academy of Math and Science at Western Kentucky University for the Academy sections of the course. The text has also been used in two online course offerings. Revised 7/19/11.

Free readers are available for all of the files that accompany the book. Mathematica Player is available at http://www.wolfram.com/products/player/. QuickTime Player is available at http://www.apple.com/quicktime/.

Diamond Theory Collections. A Collection Of Papers And Fragments Towards Diamond Theory 2007-2009, Rudolf Kaehr

Rudolf Kaehr

No abstract provided.