Mathematics Commons^™

Approximation By Complex Potentials Generated By The Gamma Function, Sorin G. Gal

Turkish Journal of Mathematics

In this paper we find the exact orders of approximation of analytic functions by the complex versions of several potentials (including the Flett potential) generated by the Gamma function and by some singular integrals.

Cyclic Codes Over {Z_2+Uz_2+U^2z_2+\Ldots+U^{K-1}Z_2}, Mohammed Al Ashker, Mohammed Hamoudeh

Turkish Journal of Mathematics

In this paper, we study the structure of cyclic codes of an arbitrary length n over the ring Z_2+uZ_2+u^2Z_2+\ldots+u^{k-1}Z_2, where u^k=0. Also we study the rank for these codes, and we find their minimal spanning sets. This study is a generalization and extension of the work in reference [1].

Models For Discrete Quantum Gravity, S. Gudder

Mathematics Preprint Series

We first discuss a framework for discrete quantum processes (DQP). It is shown that the set of q-probability operators is convex and its set of extreme elements is found. The property of consistency for a DQP is studied and the quadratic algebra of suitable sets is introduced. A classical sequential growth process is “quantized” to obtain a model for discrete quantum gravity called a quantum sequential growth process (QSGP). Two methods for constructing concrete examples of QSGP are provided.

Vascular Countercurrent Network For 3d Triple-Layered Skin Structure With Radiation Heating, Xiaoqi Zeng

Doctoral Dissertations

Heat transfer in living tissue has become more and more attention for researchers, because high thermal radiation produced by intense fire, such as wild fires, chemical fires, accidents, warfare, terrorism, etc, is often encountered in human's daily life. Living tissue is a heterogeneous organ consisting of cellular tissue and blood vessels, and heat transfer in cellular tissue and blood vessel is quite different, because the blood vessels provide channels for fast heat transfer. The metabolic heat generation, heat conduction and blood perfusion in soft tissue, convection and perfusion of the arterial-venous blood through the capillary, and interaction with the environment …

Spectral Collocation Method For Compact Integral Operators, Can Huang

Wayne State University Dissertations

We propose and analyze a spectral collocation method for integral

equations with compact kernels, e.g. piecewise smooth kernels and

weakly singular kernels of the form $\frac{1}{|t-s|^\mu}, \;

0<\mu<1. $ We prove that 1) for integral equations, the convergence

rate depends on the smoothness of true solutions $y(t)$. If $y(t)$

satisfies condition (R): $\|y^{(k)}\|_{L^\infty[0,T]}\leq

ck!R^{-k}$}, we obtain a geometric rate of convergence; if $y(t)$

satisfies condition (M): $\|y^{(k)}\|_{L^{\infty}[0,T]}\leq cM^k $,

we obtain supergeometric rate of convergence for both Volterra

equations and Fredholm equations and related integro differential

equations; 2) for eigenvalue problems, the convergence rate depends

on the smoothness of eigenfunctions. The same convergence rate for

the largest modulus eigenvalue approximation …

Discrete Variable Representation Of The Angular Variables In Quantum Three-Body Scattering, David Caballero

CGU Theses & Dissertations

There are many numerical methods to study the quantum mechanical three-body scattering system using the Schrodinger equation. Traditionally, a partial-wave decomposition of the total wave function is carried out first, allowing the scattering system to be solved one partial wave at a time. This is convenient when the interaction is central, causing the total angular momentum to be conserved during the collision process. This is not possible in the presence of a non-central interaction such as a laser field, where the total angular momentum is not conserved during the collision process. The Discrete Variable Representation is a new method for …

Statistical Properties Of A Convoluted Beta-Weibull Distribution, Jianan Sun

Theses, Dissertations and Capstones

A new class of distributions recently developed involves the logit of the beta distribution. Among this class of distributions are the beta-normal (Eugene et.al. (2002)); beta-Gumbel (Nadarajah and Kotz (2004)); beta-exponential (Nadarajah and Kotz (2006)); beta-Weibull (Famoye et al. (2005)); beta-Rayleigh (Akinsete and Lowe (2008)); beta-Laplace (Kozubowski and Nadarajah (2008)); and beta-Pareto (Akinsete et al. (2008)), among a few others. Many useful statistical properties arising from these distributions and their applications to real life data have been discussed in the literature. One approach by which a new statistical distribution is generated is by the transformation of random variables having known …

Perspectives On Deepening Teachers’ Mathematics Content Knowledge: The Case Of The Oregon Mathematics Leadership Institute, Libby Knott, Martha Vancleave

Faculty Publications

The Oregon Mathematics Leadership Institute (OMLI) project served 180 Oregon teachers, and 90 administrators, across the K-12 grades from ten partner districts. OMLI offered a residential, three-week summer institute. Over the course of three consecutive summers, teachers were immersed in a total of six mathematics content classes– Algebra, Data & Chance, Discrete Mathematics, Geometry, Measurement & Change, and Number & Operations—along with an annual collegial leadership course. Each content class was designed and taught by a team of expert faculty from universities, community colleges, and K-12 districts. Each team chose a few “big ideas” on which to focus the course. …

High Order Compact Scheme For Discontinuous Differential Equations, James Louis Thompson

Mathematics Dissertations - Archive

A high order implicit second derivative compact method is given which is similar the Adams-Moulton method, but requiring only two steps for sixth order. This method is used in both predictor-corrector and Newton's method formulations, and although the compact scheme is not A-stable or stiffly stable, it's region of stability is over six times greater than the Sixth order Adams-Moulton method. This compact method has a small truncation error coefficient, and is more accurate than Enright's method within the region of stability. Fourth and sixth order explicit compact methods are derived as well, and the three step sixth order explicit …

Spreadsheets Across The Curriculum, 2: Assessing Our Success With Students At Eckerd College, Laura Reiser Wetzel

Numeracy

The Spreadsheets Across the Curriculum (SSAC) library consists of activities to reinforce or teach quantitative literacy or mathematical concepts and skills in context. Each SSAC “module” consists of a PowerPoint presentation with embedded Excel spreadsheets. Each student works through a presentation, thinks about the in-context problem, figures out how to solve it mathematically, and builds spreadsheets to calculate and examine answers.

To assess the effectiveness of SSAC modules, I surveyed Eckerd College undergraduates in two separate studies. Two undergraduate research assistants and I generated pre- and post-tests for 10 SSAC modules. We hired 21 undergraduates who conducted 62 individual module …

Numerics Of The Lattice Boltzmann Method: Effects Of Collision Models On The Lattice Boltzmann Simulations, Li-Shi Luo, Wei Liao, Xingwang Chen, Yan Peng, Wei Zhang

Mathematics & Statistics Faculty Publications

We conduct a comparative study to evaluate several lattice Boltzmann (LB) models for solving the near incompressible Navier-Stokes equations, including the lattice Boltzmann equation with the multiple-relaxation-time (MRT), the two-relaxation-time (TRT), the single-relaxation-time (SRT) collision models, and the entropic lattice Boltzmann equation (ELBE). The lid-driven square cavity flow in two dimensions is used as a benchmark test. Our results demonstrate that the ELBE does not improve the numerical stability of the SRT or the lattice Bhatnagar-Gross-Krook (LBGK) model. Our results also show that the MRT and TRT LB models are superior to the ELBE and LBGK models in terms of …

Analysis Of Biological Features Associated With Meiotic Recombination Hot And Cold Spots In Saccharomyces Cerevisiae, Loren Hansen, Nak-Kyeong Kim, Leonardo Mariño-Ramírez, David Landsman

Mathematics & Statistics Faculty Publications

Meiotic recombination is not distributed uniformly throughout the genome. There are regions of high and low recombination rates called hot and cold spots, respectively. The recombination rate parallels the frequency of DNA double-strand breaks (DSBs) that initiate meiotic recombination. The aim is to identify biological features associated with DSB frequency. We constructed vectors representing various chromatin and sequence-based features for 1179 DSB hot spots and 1028 DSB cold spots. Using a feature selection approach, we have identified five features that distinguish hot from cold spots in Saccharomyces cerevisiae with high accuracy, namely the histone marks H3K4me3, H3K14ac, H3K36me3, and H3K79me3; …

Convergence Of The Mean Shift Algorithm And Its Generalizations, Ting Hu

Electronic Theses and Dissertations

Mean shift is an effective iterative algorithm widely used in image analysis tasks like tracking, image segmentation, smoothing, filtering, edge detection and etc. It iteratively estimates the modes of the probability function of a set of sample data points based in a region. Mean shift was invented in 1975, but it was not widely used until the work by Cheng in 1995. After that, it becomes popular in computer vision. However the convergence, a key character of any iterative algorithm, has been rigorously proved only very recently, but with strong assumptions. In this thesis, the method of mean shift is …

Domination Polynomials Of Cubic Graphs Of Order 10, Saeid Alikhani, Yee-Hock Peng

Turkish Journal of Mathematics

Let G be a simple graph of order n. The domination polynomial of G is the polynomial D(G,x)=\sum_{i=\gamma(G)}^n d(G,i) x^i, where d(G,i) is the number of dominating sets of G of size i, and \gamma(G) is the domination number of G. In this paper we study the domination polynomials of cubic graphs of order 10. As a consequence, we show that the Petersen graph is determined uniquely by its domination polynomial.

Explicit Constructions Of Rip Matrices And Related Problems, Jean Bourgain, S J. Dilworth, Kevin Ford, Sergei Konyagin, Denka Kutzarova

Faculty Publications

We give a new explicit construction of n×N matrices satisfying the Restricted Isometry Property (RIP). Namely, for someε > 0, largeN, and any n satisfyingN1−ε ≤ n ≤ N, we construct RIP matrices of order k ≥ n1/2+ε and constant δ = n−ε. This overcomesthe natural barrier k = O(n1/2) for proofs based on small coherence, which areused in all previous explicit constructions of RIP matrices. Key ingredients in ourproof are new estimates for sumsets in product sets and for exponential sums with theproducts of sets possessing special additive structure. We also give a construction ofsets of n complex numbers whose …

A Primer Of Swarm Equilibria, Andrew J. Bernoff, Chad M. Topaz

All HMC Faculty Publications and Research

We study equilibrium configurations of swarming biological organisms subject to exogenous and pairwise endogenous forces. Beginning with a discrete dynamical model, we derive a variational description of the corresponding continuum population density. Equilibrium solutions are extrema of an energy functional and satisfy a Fredholm integral equation. We find conditions for the extrema to be local minimizers, global minimizers, and minimizers with respect to infinitesimal Lagrangian displacements of mass. In one spatial dimension, for a variety of exogenous forces, endogenous forces, and domain configurations, we find exact analytical expressions for the equilibria. These agree closely with numerical simulations of the underlying …

Evidence Of The Harmonic Faraday Instability In Ultrasonic Atomization Experiments With A Deep, Inviscid Fluid, Andrew P. Higginbotham '09, Aaron Guillen '11, Nathan C. Jones '10, Thomas D. Donnelly, Andrew J. Bernoff

All HMC Faculty Publications and Research

A popular method for generating micron-sized aerosols is to submerge ultrasonic (ω~MHz) piezoelectric oscillators in a water bath. The submerged oscillator atomizes the fluid, creating droplets with radii proportional to the wavelength of the standing wave at the fluid surface. Classical theory for the Faraday instability predicts a parametric instability driving a capillary wave at the subharmonic (ω/2) frequency. For many applications it is desirable to reduce the size of the droplets; however, using higher frequency oscillators becomes impractical beyond a few MHz. Observations are presented that demonstrate that smaller droplets may also be created by …

Strong Nonnegativity And Sums Of Squares On Real Varieties, Mohamed Omar, Brian Osserman

All HMC Faculty Publications and Research

Motivated by scheme theory, we introduce strong nonnegativity on real varieties, which has the property that a sum of squares is strongly nonnegative. We show that this algebraic property is equivalent to nonnegativity for nonsingular real varieties. Moreover, for singular varieties, we reprove and generalize obstructions of Gouveia and Netzer to the convergence of the theta body hierarchy of convex bodies approximating the convex hull of a real variety.

Applications Of Convex And Algebraic Geometry To Graphs And Polytopes, Mohamed Omar

All HMC Faculty Publications and Research

No abstract provided.

Designing And Teaching An Elementary School Enrichment Program: What The Students Were Taught And What I Learned, Angela M. Smart

The Mathematics Enthusiast

This article is a reflection on the experiences I had designing and teaching an elementary school enrichment program to gifted students in mathematics. In particular, I consider not just what I taught the students in the program but what I learned throughout the entire process. This article first focuses on a description of the program and my role within the program. I then describe in detail four of the lessons I designed and taught for the program. Central to the description of the lessons are my observations of the students’ reactions to the lessons and my own growth as the …