A Note On Acoustic Propagation In Power-Law Fluids: Compact Kinks, Mild Discontinuities, And A Connection To Finite-Scale Theory,
2012
University of New Orleans
A Note On Acoustic Propagation In Power-Law Fluids: Compact Kinks, Mild Discontinuities, And A Connection To Finite-Scale Theory, Dongming Wei
Mathematics Faculty Publications
Acoustic traveling waves in a class of viscous, power-lawfluids are investigated. Both bi-directional and unidirectional versions of the one-dimensional (1D), weakly-nonlinear equation of motion are derived; traveling wave solutions (TWS)s, special cases of which take the form of compact and algebraic kinks, are determined; and the impact of the bulk viscosity on the structure/nature of the kinks is examined. Most significantly, we point out a connection that exists between the power-law model considered here and the recently introduced theory of finite-scale equations.
The Hyperboloid Model Of Hyperbolic Geometry,
2012
Eastern Washington University
The Hyperboloid Model Of Hyperbolic Geometry, Zachery S. Lane Solheim
EWU Masters Thesis Collection
"The main goal of this thesis is to introduce and develop the hyperboloid model of Hyperbolic Geometry. In order to do that, some time is spent on Neutral Geometry as well as Euclidean Geometry; these are used to build several models of Hyperbolic Geometry. At this point the hyperboloid model is introduced, related to the other models visited, and developed using some concepts from physics as aids. After the development of the hyperboloid model, Fuchsian groups are briefly discussed and the more familiar models of Hyperbolic Geometry are further investigated"--Document.
Vortex Patterns Beyond Hypergeometric,
2012
Embry-Riddle Aeronautical University
Vortex Patterns Beyond Hypergeometric, Andrei Ludu
Publications
We prove that loop vortices are created by a point-like magnetic dipole in an infinite superconductor space. The geometry of the vortex system is obtained through analytic solutions of the linearized Ginzburg-Landau equation described in terms of Heun functions, generalizing the traditional hypergeometric behavior of such magnetic singularity.
Flow Over A Traveling Wavy Foil With A Passively Flapping Flat Plate,
2012
Old Dominion University
Flow Over A Traveling Wavy Foil With A Passively Flapping Flat Plate, Nansheng Liu, Yan Peng, Youwen Liang, Xiyun Lu
Mathematics & Statistics Faculty Publications
Flow over a traveling wavy foil with a passively flapping flat plate has been investigated using a multiblock lattice Boltzmann equation and the immersed boundary method. The foil undergoes prescribed undulations in the lateral direction and the rigid flat plate has passive motion determined by the fluid structure interaction. This simplified model is used to study the effect of the fish caudal fin and its flexibility on the locomotion of swimming animals. The flexibility of the caudal fin is modeled by a torsion spring acting about the pivot at the conjuncture of the wavy foil and the flat plate. The …
Upper Bounds In The Ohtsuki-Riley-Sakuma Partial Order On 2-Bridge Knots,
2012
University of California, Los Angeles
Upper Bounds In The Ohtsuki-Riley-Sakuma Partial Order On 2-Bridge Knots, Scott M. Garrabrant, Jim Hoste, Patrick D. Shanahan
Mathematics, Statistics and Data Science Faculty Works
In this paper we use continued fractions to study a partial order on the set of 2-bridge knots derived from the work of Ohtsuki, Riley, and Sakuma. We establish necessary and sufficient conditions for any set of 2-bridge knots to have an upper bound with respect to the partial order. Moreover, given any 2-bridge knot K we characterize all other 2-bridge knots J such that {K, J} has an upper bound. As an application we answer a question of Suzuki, showing that there is no upper bound for the set consisting of the trefoil and figure-eight knots.
Congrats You’Re Abd! Now What?,
2012
Loyola Marymount University
Congrats You’Re Abd! Now What?, Alissa Crans
Mathematics, Statistics and Data Science Faculty Works
No abstract provided.
Characterization Of Radially Symmetric Finite Time Blowup In Multidimensional Aggregation Equations,
2012
University of California, Los Angeles
Characterization Of Radially Symmetric Finite Time Blowup In Multidimensional Aggregation Equations, Andrea L. Bertozzi, John B. Garnett, Thomas Laurent
Mathematics, Statistics and Data Science Faculty Works
This paper studies the transport of a mass $\mu$ in $\mathbb{R}^d, d \geq 2,$ by a flow field $v= -\nabla K*\mu$. We focus on kernels $K=|x|^\alpha/ \alpha$ for $2-d\leq \alpha<2$ for which the smooth densities are known to develop singularities in finite time. For this range we prove the existence for all time of radially symmetric measure solutions that are monotone decreasing as a function of the radius, thus allowing for continuation of the solution past the blowup time. The monotone constraint on the data is consistent with the typical blowup profiles observed in recent numerical studies of these singularities. We prove monotonicity is preserved for all time, even after blowup, in contrast to the case $\alpha >2$ where radially symmetric solutions are known to lose monotonicity. In the case of the Newtonian potential ($\alpha=2-d$), under the assumption of radial symmetry the equation can be transformed into the inviscid Burgers equation on a half line. This enables us to prove preservation of monotonicity using the classical theory of conservation laws. In the case $2 -d < \alpha < 2$ and at the critical exponent p we exhibit initial data in $L^p$ for which the solution immediately develops a Dirac mass singularity. This extends recent work on the local ill-posedness of solutions at the critical exponent.
On Levi-Civita’S Alternating Symbol, Schouten’S Alternating Unit Tensors, Cpt, And Quantization,
2012
University of Houston
On Levi-Civita’S Alternating Symbol, Schouten’S Alternating Unit Tensors, Cpt, And Quantization, Evert Jan Post, Stan Sholar, Hooman Rahimizadeh, Michael Berg
Mathematics, Statistics and Data Science Faculty Works
The purpose of the present article is to demonstrate that by adopting a unifying differential geometric perspective on certain themes in physics one reaps remarkable new dividends in both microscopic and macroscopic domains. By replacing algebraic objects by tensor-transforming objects and introducing methods from the theory of differentiable manifolds at a very fundamental level we obtain a Kottler-Cartan metric-independent general invariance of the Maxwell field, which in turn makes for a global quantum superstructure for Gauss-Amp`ere and Aharonov-Bohm “quantum integrals.” Beyond this, our approach shows that postulating a Riemannian metric at the quantum level is an unnecessary concept and our …
Spatial Graphs With Local Knots,
2012
Loyola Marymount University
Spatial Graphs With Local Knots, Erica Flapan, Blake Mellor, Ramin Naimi
Mathematics, Statistics and Data Science Faculty Works
It is shown that for any locally knotted edge of a 3-connected graph in S3, there is a ball that contains all of the local knots of that edge and is unique up to an isotopy setwise fixing the graph. This result is applied to the study of topological symmetry groups of graphs embedded in S3.
Enhancements Of Rack Counting Invariants Via Dynamical Cocycles,
2012
Loyola Marymount University
Enhancements Of Rack Counting Invariants Via Dynamical Cocycles, Alissa S. Crans, Sam Nelson, Aparna Sarkar
Mathematics, Statistics and Data Science Faculty Works
We introduce the notion of N-reduced dynamical cocycles and use these objects to define enhancements of the rack counting invariant for classical and virtual knots and links. We provide examples to show that the new invariants are not determined by the rack counting invariant, the Jones polynomial or the generalized Alexander polynomial.
Convergence Of A Steepest Descent Algorithm For Ratio Cut Clustering,
2012
City University of Hong Kong
Convergence Of A Steepest Descent Algorithm For Ratio Cut Clustering, Xavier Bresson, Thomas Laurent, David Uminsky, James H. Von Brecht
Mathematics, Statistics and Data Science Faculty Works
Unsupervised clustering of scattered, noisy and high-dimensional data points is an important and difficult problem. Tight continuous relaxations of balanced cut problems have recently been shown to provide excellent clustering results. In this paper, we present an explicit-implicit gradient flow scheme for the relaxed ratio cut problem, and prove that the algorithm converges to a critical point of the energy. We also show the efficiency of the proposed algorithm on the two moons dataset.
How Well Do The Nsf Funded Elementary Mathematics Curricula Align With The Gaise Report Recommendations?,
2012
Loyola Marymount University
How Well Do The Nsf Funded Elementary Mathematics Curricula Align With The Gaise Report Recommendations?, Anna E. Bargagliotti
Mathematics, Statistics and Data Science Faculty Works
Statistics and probability have become an integral part of mathematics education. Therefore it is important to understand whether curricular materials adequately represent statistical ideas. The Guidelines for Assessment and Instruction in Statistics Education (GAISE) report (Franklin, Kader, Mewborn, Moreno, Peck, Perry, & Scheaffer, 2007), endorsed by the American Statistical Association, provides a two-dimensional (process and level) framework for statistical learning. This paper examines whether the statistics content contained in the NSF funded elementary curricula Investigations in Number, Data, and Space, Math Trailblazers, and Everyday Mathematics aligns with the GAISE recommendations. Results indicate that there are differences in the approaches used …
Characterizing Conflict In Wikipedia,
2012
Macalester College
Characterizing Conflict In Wikipedia, Nathaniel Miller
Mathematics, Statistics, and Computer Science Honors Projects
Wikipedia serves as the Internet's most widely viewed reference. In order to ensure its success, editors who create and maintain articles must resolve conflicts over appropriate article content. Previous research has measured Wikipedia conflict at two levels: single articles and categories of pages. I observe conflicts within small groups of articles, identifying their frequency, size, and intensity. Additionally, I identify individual conflicts spanning multiple articles and effects of conflict upon users' editing habits. I analyze cross-article conflict in three stages. First, I cluster a group of 1.4 million Wikipedia articles. Next, I find individual user conflicts within each article cluster …
The Best Mixing Time For Trees,
2012
Macalester College
The Best Mixing Time For Trees, Jeanmarie Youngblood
Mathematics, Statistics, and Computer Science Honors Projects
A graph G consists of a set of vertices connected in pairs by edges. Two vertices connected by an edge are called neighbors. A random walk on G is a sequence of vertices, where the next vertex is chosen randomly from the neighbors of the current vertex. Under mild assumptions, the distribution of a walk's current location converges to the stationary distribution. In this distribution, the probability of being at a given vertex is proportional to the size of its neighbor set. The expected time to convergence is called a mixing measure of G. There are a variety …
Geometry Of Partial Differential Equations,
2012
The University of Texas Rio Grande Valley
Geometry Of Partial Differential Equations, Paul Bracken
School of Mathematical & Statistical Sciences Faculty Publications
The study of partial differential equations has been the object of much investigation and seen a great many advances recently. This is primarily due to the fact that certain classes of these equations fall under the category of being integrable. These kinds of equations have many useful properties such as the existence of Lax pairs, Backlund transformations, explicit solutions and the existence of a correspondence with geometric manifolds. There have also been many applications of solutions to these equations in the study of solitons and other objects which have seen applications in physics. It is the objective here to study …
The Distribution Of Individual Stock Returns In A Modified Black-Scholes Option Pricing Model,
2012
Georgia Southern University
The Distribution Of Individual Stock Returns In A Modified Black-Scholes Option Pricing Model, Daniel Lee Richey
College of Graduate Studies: Theses & Dissertations
Author's abstract: There have been many attempts to find a model that can accurately price options. These models are built on many assumptions, including which probability distribution stock returns follow. In this paper, we test several distributions to see which best fit the log returns of 20 different companies over a period between November 1, 2006 to October 31, 2011. If a "best" distribution is found, a modified Black-Scholes model will be defined by modifying the Weiner process. We use Monte Carlo simulations to generate estimated prices under specified parameters, and compare these prices to those simulated by the model …
Berry-Esseen Bounds For Nonlinear Statistics, And Asymptotic Relative Efficiency Between Correlation Statistics,
2012
Michigan Technological University
Berry-Esseen Bounds For Nonlinear Statistics, And Asymptotic Relative Efficiency Between Correlation Statistics, Raymond E. Molzon
Dissertations, Master's Theses and Master's Reports - Open
Four papers, written in collaboration with the author’s graduate school advisor, are presented. In the first paper, uniform and non-uniform Berry-Esseen (BE) bounds on the convergence to normality of a general class of nonlinear statistics are provided; novel applications to specific statistics, including the non-central Student’s, Pearson’s, and the non-central Hotelling’s, are also stated. In the second paper, a BE bound on the rate of convergence of the F-statistic used in testing hypotheses from a general linear model is given. The third paper considers the asymptotic relative efficiency (ARE) between the Pearson, Spearman, and Kendall …
Groupoids, Imaginaries And Internal Covers,
2012
TÜBİTAK
Groupoids, Imaginaries And Internal Covers, Ehud Hrushovski
Turkish Journal of Mathematics
Let T be a first-order theory. A correspondence is established between internal covers of models of T and definable groupoids within T. We also consider amalgamations of independent diagrams of algebraically closed substructures, and find strong relation between covers, uniqueness for 3-amalgamation, existence of 4-amalgamation, imaginaries of T^\si, and definable groupoids. As a corollary, we describe the imaginary elements of families of finite-dimensional vector spaces over pseudo-finite fields.
On Normality Of Meromorphic Functions With Multiple Zeros And Sharing Values,
2012
TÜBİTAK
On Normality Of Meromorphic Functions With Multiple Zeros And Sharing Values, Youming Wang
Turkish Journal of Mathematics
In this paper we study the problem of normal families of meromorphic functions concerning shared values. Let F be a family of meromorphic functions in the plane domain D \subseteq C and n be a positive integer. Let a, b be two finite complex constants such that a \neq 0. If n \geq 3 and f + a(f')^n and g + a(g')^n share b in D for every pair of functions f, g \in F, then F is normal in D. And some examples are provided to show the result is sharp.
Invariant Subspaces Of Weakly Compact-Friendly Operators,
2012
TÜBİTAK
Invariant Subspaces Of Weakly Compact-Friendly Operators, Mert Çağlar, Remzi̇ Tunç Misirlioğlu
Turkish Journal of Mathematics
We prove that if a non-zero weakly compact-friendly operator B on a Banach lattice with topologically full center is locally quasi-nilpotent, then the super right-commutant [B\rangle of B has a non-trivial closed invariant ideal. An example of a weakly compact-friendly operator which is not compact-friendly is also provided.
