Escape Velocity, 2010 University of South Florida

#### Escape Velocity, Nikola Vlacic

*Undergraduate Journal of Mathematical Modeling: One + Two*

In this project, we investigated if it is feasible for a single staged rocket with constant thrust to attain escape velocity. We derived an equation for the velocity and position of a single staged rocket that launches vertically. From this equation, we determined if an ideal model of a rocket is able to reach escape velocity.

Optimal Location Of An Oil Storage Facility, 2010 University of South Florida

#### Optimal Location Of An Oil Storage Facility, Giovanni Quiel

*Undergraduate Journal of Mathematical Modeling: One + Two*

Given three oil drilling sites, we devise a method to determine the optimal location for a storage facility such that the total length of pipeline required to connect each site to the facility is minimized. First we represent the total distance of piping as the sum of the individual distances between the storage facility and each oil well. From this, both the optimal overall pipeline length and the location of the storage facility which realizes the minimal length can be determined through the first and second partial derivative tests.

Mastery Of Sixth-Grade Mathematics Expectations As Measured By The Seventh-Grade Michigan Education Assessment Program From 2005 To 2007, 2010 Andrews University

#### Mastery Of Sixth-Grade Mathematics Expectations As Measured By The Seventh-Grade Michigan Education Assessment Program From 2005 To 2007, Marian Prince

*Dissertations*

Purpose

The purpose of this study is to document sixth-grade mathematics mastery as measured by the seventh-grade Michigan Education Assessment Program (MEAP) over a period of 3 years: 2005, 2006, and 2007. This study investigated whether mathematics performance in Michigan is related to ethnicity by analyzing student responses on the seventh-grade MEAP which evaluates students’ mastery of the Michigan sixth-grade mathematics expectations.

Method

Data from the Michigan Department of Education (MDE) containing the student scores of individual test items on the mathematics Michigan Education Assessment Program (MEAP) for seventh-grade students in Michigan for 2005 to 2007 formed the basis for ...

Ordinary And Particial Differential Equations: An Introduction To Dynamical Systems, 2010 University of Richmond

#### 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.

Zorn Vector Matrices Over Commutative Rings And The Loops Arising From Their Construction, 2010 Iowa State University

#### Zorn Vector Matrices Over Commutative Rings And The Loops Arising From Their Construction, Andrew Thomas Wells

*Graduate Theses and Dissertations*

This thesis shows that the Zorn vector matrix construction which Paige used to construct simple nonassociative Moufang loops over finite fields can, in fact, be done over any commutative ring with the proper adjustments. The resulting loops are still Moufang, but no longer simple in general. Given a commutative ring and an ideal of that ring, the loop constructed over that ring can be decomposed into two pieces. In this way, it is shown that the loop

constructed over Z/4Z shares some structure with the Paige loop constructed over the finite field Z/2Z. An in depth study of ...

Effects Of Multitemperature Nonequilibrium On Compressible Homogeneous Turbulence, 2010 Old Dominion University

#### 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*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′ (t), the ...

_{L0},Bitopological Duality For Distributive Lattices And Heyting Algebras, 2010 New Mexico State University

#### Bitopological Duality For Distributive Lattices And Heyting Algebras, Guram Bezhanishvili, Nick Bezhanishvili, David Gabelaia, Alexander Kurz

*Engineering Faculty Articles and Research*

We introduce pairwise Stone spaces as a natural bitopological generalization of Stone spaces—the duals of Boolean algebras—and show that they are exactly the bitopological duals of bounded distributive lattices. The category PStone of pairwise Stone spaces is isomorphic to the category Spec of spectral spaces and to the category Pries of Priestley spaces. In fact, the isomorphism of Spec and Pries is most naturally seen through PStone by first establishing that Pries is isomorphic to PStone, and then showing that PStone is isomorphic to Spec. We provide the bitopological and spectral descriptions of many algebraic concepts important for ...

On Coalgebras Over Algebras, 2010 University Politehnica of Bucharest

#### On Coalgebras Over Algebras, Adriana Balan, Alexander Kurz

*Engineering Faculty Articles and Research*

We extend Barr’s well-known characterization of the final coalgebra of a Set-endofunctor as the completion of its initial algebra to the Eilenberg-Moore category of algebras for a Set-monad M for functors arising as liftings. As an application we introduce the notion of commuting pair of endofunctors with respect to the monad M and show that under reasonable assumptions, the final coalgebra of one of the endofunctors involved can be obtained as the free algebra generated by the initial algebra of the other endofunctor.

A Class Of Discontinuous Petrov–Galerkin Methods. Ii. Optimal Test Functions, 2010 University of Texas at Austin

#### A Class Of Discontinuous Petrov–Galerkin Methods. Ii. Optimal Test Functions, Leszek Demkowicz, Jay Gopalakrishnan

*Mathematics and Statistics Faculty Publications and Presentations*

We lay out a program for constructing discontinuous Petrov–Galerkin (DPG) schemes having test function spaces that are automatically computable to guarantee stability. Given a trial space, a DPG discretization using its optimal test space counterpart inherits stability from the well posedness of the undiscretized problem. Although the question of stable test space choice had attracted the attention of many previous authors, the novelty in our approach lies in the fact we identify a discontinuous Galerkin (DG) framework wherein test functions, arbitrarily close to the optimal ones, can be locally computed. The idea is presented abstractly and its feasibility illustrated ...

Phase-Linking And The Perceived Motion During Off-Vertical Axis Rotation, 2010 Portland State University

#### Phase-Linking And The Perceived Motion During Off-Vertical Axis Rotation, Jan Holly, Scott Wood, Gin Mccollum

*Mathematics and Statistics Faculty Publications and Presentations*

Human off-vertical axis rotation (OVAR) in the dark typically produces perceived motion about a cone, the amplitude of which changes as a function of frequency. This perception is commonly attributed to the fact that both the OVAR and the conical motion have a gravity vector that rotates about the subject. Little-known, however, is that this rotating-gravity explanation for perceived conical motion is inconsistent with basic observations about self-motion perception: (a) that the perceived vertical moves toward alignment with the gravito-inertial acceleration (GIA) and (b) that perceived translation arises from perceived linear acceleration, as derived from the portion of the GIA ...

Using Mathematics As A Gateway To Literacy For English Language Learners, 2010 University of Northern Iowa

#### 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 ...

On Baryon Number Non-Conservation In Two-Dimensional O(2n+1) Qcd, 2010 Massachusetts Institute of Technology

#### On Baryon Number Non-Conservation In Two-Dimensional O(2n+1) Qcd, Tamar Friedmann

*Mathematics and Statistics: Faculty Publications*

We construct a classical dynamical system whose phase space is a certain infinite dimensional Grassmannian manifold, and propose that it is equivalent to the large N limit of two-dimensional QCD with an O(2N + 1) gauge group. In this theory, we find that baryon number is a topological quantity that is conserved only modulo 2. We also relate this theory to the master field approach to matrix models.

Itineraries Of Rigid Rotations And Diffeomorphisms Of The Circle, 2010 Dickinson College

#### Itineraries Of Rigid Rotations And Diffeomorphisms Of The Circle, David S. Richeson, Paul Winkler, Jim Wiseman

*Faculty and Staff Publications By Year*

We examine the itinerary of 0 ∈ S^{1} = R/Z under the rotation by α ∈ R \ Q. The motivating question is: if we are given only the itinerary of 0 relative to *I* ⊂ *S*^{1} , a finite union of closed intervals, can we recover α and *I*? We prove that the itineraries do determine α and *I* up to certain equivalences. Then we present elementary methods for finding α and *I*. Moreover, if *g* : *S*^{1} → *S*^{1} is a *C*^{2} , orientation preserving diffeomorphism with an irrational rotation number, then we can use the orbit itinerary to recover the ...

Mathematical Modeling And Control Of Nonlinear Oscillators With Shape Memory Alloys, 2010 Wilfrid Laurier University

#### 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 ...

Solving Distance Geometry Problems For Protein Structure Determination, 2010 Iowa State University

#### Solving Distance Geometry Problems For Protein Structure Determination, Atilla Sit

*Graduate Theses and Dissertations*

A well-known problem in protein modeling is the determination of the structure of a protein with a given set of interatomic distances obtained from either physical experiments or theoretical estimates. A more general form of this problem is known as the distance geometry problem in mathematics, which can be solved in polynomial time if a complete set of exact distances is given, but is generally intractable for a general sparse set of distance data. We investigate the solution of the problem within a geometric buildup framework. We propose a new geometric buildup algorithm for solving the problem using special least-squares ...

High Performance Computing Techniques For Attacking Reduced Version Of Aes Using Xl And Xsl Methods, 2010 Iowa State University

#### High Performance Computing Techniques For Attacking Reduced Version Of Aes Using Xl And Xsl Methods, Elizabeth Kleiman

*Graduate Theses and Dissertations*

A known-plaintext attack on the Advanced Encryption Standard can be formulated as a system of quadratic multivariate polynomial equations in which the unknowns represent key bits. Algorithms such as XSL and XL use properties of the cipher to build a sparse system of linear equations over the field GF(2) from those multivariate polynomial equations. A scaled down version of AES called Baby Rijndael has structure similar to AES and can be attacked using the XL and XSL techniques among others. This results in a large sparse system of linear equations over the field GF(2) with an unknown number ...

On Hopf Algebras Of Dimension 4p, 2010 Iowa State University

#### On Hopf Algebras Of Dimension 4p, Yi-Lin Cheng

*Graduate Theses and Dissertations*

Some progress on classification problems for finite dimensional Hopf algebras has been made recently. In this thesis, we look at 4p-dimensional Hopf algebras over an algebraically closed field of characteristic zero. We show that a non-semisimple Hopf algebra of dimension 4p with an odd prime p is pointed if, and only if, this Hopf algebra contains more than two group-like elements. Moreover, we prove that non-semisimple Hopf algebras of dimensions 20, 28 and 44 are either pointed or dual-pointed, and this completes the classification of Hopf algebras of dimension 20, 28,and 44.

Ergodic And Combinatorial Proofs Of Van Der Waerden's Theorem, 2010 Claremont McKenna College

#### Ergodic And Combinatorial Proofs Of Van Der Waerden's Theorem, Matthew Samuel Rothlisberger

*CMC Senior Theses*

Followed two different proofs of van der Waerden's theorem. Found that the two proofs yield important information about arithmetic progressions and the theorem. van der Waerden's theorem explains the occurrence of arithmetic progressions which can be used to explain such things as the Bible Code.

Women And Math Performance: The Effects Of Stereotype Threat, Math Identity, And Gender Identity, 2010 Seton Hall University

#### Women And Math Performance: The Effects Of Stereotype Threat, Math Identity, And Gender Identity, Felicia W. Chu

*Seton Hall University Dissertations and Theses (ETDs)*

.

Analysis Of Models For Longitudinal And Clustered Binary Data, 2010 Old Dominion University

#### Analysis Of Models For Longitudinal And Clustered Binary Data, Weiming Yang

*Mathematics & Statistics Theses & Dissertations*

This dissertation deals with modeling and statistical analysis of longitudinal and clustered binary data. Such data consists of observations on a dichotomous response variable generated from multiple time or cluster points, that exhibit either decaying correlation or equi-correlated dependence. The current literature addresses modeling the dependence using an appropriate correlation structure, but ignores the feasible bounds on the correlation parameter imposed by the marginal means.

The first part of this dissertation deals with two multivariate probability models, the first order Markov chain model and the multivariate probit model, that adhere to the feasible bounds on the correlation. For both the ...