Physical Sciences and Mathematics Commons^™

Problem Posing From The Foundations Of Mathematics, Libby Knott

The Mathematics Enthusiast

This reflective paper develops a repertoire of questions for teachers to use in their classrooms during episodes of mathematics discussions with and among students. These questions are motivated by an examination of questions posed by Wittgenstein in Zettel, and are connected to underlying tacit assumptions about mathematics, most of which lie subtly below the generally accepted milieu of math-talk. Once classrooms norms have been established to encourage participation by all students in a democratic and just classroom environment, these questions can be used effectively to stimulate meaningful discourse. These questions provide important examples of problem posing designed to encourage student …

Theoretical Properties And Estimation In Weighted Weibull And Related Distributions, Ryan Roman

Electronic Theses and Dissertations

The Weibull distribution is a well known and common distribution. In this thesis, theoretical properties of weighted Weibull distributions are presented. Properties of the non-weighted Weibull distribution are also reiterated for comparison. The probability density functions, cumulative distribution functions, survival functions, hazard functions and reverse hazard functions are given for each distribution. In addition, Glaser's Lemma is applied to determine the behavior of the hazard functions. The standardized moments, differential entropy, Fisher information and results based on the likelihood function are given for each distribution as well. These results are also shown for the Rayleigh distribution, a special case of …

Semi-Parametric Likelihood Functions For Bivariate Survival Data, S. H. Sathish Indika

Mathematics & Statistics Theses & Dissertations

Because of the numerous applications, characterization of multivariate survival distributions is still a growing area of research. The aim of this thesis is to investigate a joint probability distribution that can be derived for modeling nonnegative related random variables. We restrict the marginals to a specified lifetime distribution, while proposing a linear relationship between them with an unknown (error) random variable that we completely characterize. The distributions are all of positive supports, but one class has a positive probability of simultaneous occurrence. In that sense, we capture the absolutely continuous case, and the Marshall-Olkin type with a positive probability of …

Post-Processing Techniques And Wavelet Applications For Hammerstein Integral Equations, Khomsan Neamprem

Mathematics & Statistics Theses & Dissertations

This dissertation is focused on the varieties of numerical solutions of nonlinear Hammerstein integral equations. In the first part of this dissertation, several acceleration techniques for post-processed solutions of the Hammerstein equation are discussed. The post-processing techniques are implemented based on interpolation and extrapolation. In this connection, we generalize the results in [29] and [28] to nonlinear integral equations of the Hammerstein type. Post-processed collocation solutions are shown to exhibit better accuracy. Moreover, an extrapolation technique for the Galerkin solution of Hammerstein equation is also obtained. This result appears new even in the setting of the linear Fredholm equation.

In …

Boundary Type Quadrature Formulas Over Axially Symmetric Regions, Tian-Xiao He

Scholarship

A boundary type quadrature formula (BTQF) is an approximate integration formula with all its of evaluation points lying on the Boundary of the integration domain. This type formulas are particularly useful for the cases when the values of the integrand functions and their derivatives inside the domain are not given or are not easily determined. In this paper, we will establish the BTQFs over sonic axially symmetric regions. We will discuss time following three questions in the construction of BTQFs: (i) What is the highest possible degree of algebraic precision of the BTQF if it exists? (ii) What is the …

Women Belonging In The Social Worlds Of Graduate Mathematics, Abbe H. Herzig

The Mathematics Enthusiast

The participation of women in post-graduate mathematics still lags substantially behind that of men. Drawing upon sociocultural theories of learning, I argue that success in graduate school necessitates learning mathematical content, participating in mathematical practices, and developing a sense of belonging in mathematics. Using an institutional ethnography approach, I interviewed 12 women graduate students from three mathematics departments in the U.S. to document their experiences within the social relations of graduate mathematics. They described both intrinsic and extrinsic obstacles to belonging, including a tension between their desire to belong and their needs to distance themselves from what they perceived to …

Chaos In Physics And Recurrence In Arithmetic Sets, Jean Dayantis

The Mathematics Enthusiast

After briefly recalling the concepts of recurrence and chaos in physics, the recurrence properties of arithmetic sets are examined following Gauss’ method, as exposed in part three of his Disquisitiones Arithmeticae. This problem in number theory is related to the physical problem of recurrence in deterministic chaos. Most possible forms of moduli are examined in detail with respect to their recurrence properties, for application to the generalized Bernoulli mapping. The emphasis is put on period lengths, rather than on congruences. In an annex the recurrence properties of Arnold’s cat map are briefly examined.

Rehearsal Or Reorganization: Two Patterns Of Literacy Strategy Use In Secondary Mathematics Classes, Anne Adams

The Mathematics Enthusiast

This study presents two critical cases illustrating distinct patterns in teachers' use of literacy strategies in secondary mathematics classes. The cases are part of a professional development project designed to enhance teachers' pedagogical skills by developing content literacy strategies for use in secondary mathematics and science classrooms. Teachers' beliefs about teaching mathematics, their uses of writing and vocabulary development strategies, and goals for student learning were examined via interviews, classroom observations, reflections on teaching, and teacher posts to an online discussion forum. Results show patterns of literacy strategy use were related to teachers' views of pedagogy and of mathematics. Ned, …

Duffing-Van Der Pol Type Oscillator, Guangyue Gao

Theses and Dissertations - UTB/UTPA

The nonlinear Duffing-van der Pol oscillator system is studied by means of the Lie symmetry reduction method and the Preller-Singer method. With the particular case of coefficients, this system has physical relevance as a simple model in certain flow-induced structural vibration problems. Under certain parametric conditions, we are concerned with the first integrals of the Duffing-van der Pol oscillator system. After making a series of variable transformations, we apply the Preller-Singer method and the Lie symmetry reduction method to obtain the first integrals of the simplified equations without complicated calculations.

Soliton Solutions To Integrable Equations, Haiqi Wang

Theses and Dissertations - UTB/UTPA

In recent years, integrable systems and soliton theory play an important role in the study of nonlinear water wave equations. In this thesis, we will focus on the procedure of how to get soliton solutions for integrable equations. The fundamental idea is to use the traveling wave setting to convert a partial differential equation to an ordinary differential equation and to solve ordinary differential equations yields soliton solutions for the integrable equations under certain boundary conditions at both negative and positive infinities. In our work, we will consider five integrable equations and present their solitons solutions, one of which will …

Modeling Instabilities Of Electrically Driven Jets With Finite Conductivity Under Constant Or Variable Applied Field, Saulo I. Orizaga

Theses and Dissertations - UTB/UTPA

We investigate the problem of spatial (S), combined spatial and temporal (CST), and non-linear temporal instability (NLT) of electrically driven viscous jets with finite electrical conductivity and in the presence of either a constant or a variable applied electric field. A mathematical model, which is developed and used for the spatially growing disturbances in electrically driven jet flows, leads to a lengthy equation for the unknown growth rate and frequency of the disturbances. This equation is solved numerically using Newton‟s Method. For neutral temporal stability boundary, we find, in particular, two new spatial modes of instability under certain conditions. One …

Boundary Type Quadrature Formulas Over Axially Symmetric Regions, Tian-Xiao He

Tian-Xiao He

A boundary type quadrature formula (BTQF) is an approximate integration formula with all its of evaluation points lying on the Boundary of the integration domain. This type formulas are particularly useful for the cases when the values of the integrand functions and their derivatives inside the domain are not given or are not easily determined. In this paper, we will establish the BTQFs over sonic axially symmetric regions. We will discuss time following three questions in the construction of BTQFs: (i) What is the highest possible degree of algebraic precision of the BTQF if it exists? (ii) What is the …

LP Estimates For The Maximal Functions, Alexander M. Stokolos

Department of Mathematical Sciences Faculty Presentations

This talk was given during the Jozef Marcinkiewicz Centenary Conference.

Gender Bias In Education In West Bengal., Chayanika Mitra Dr.

Doctoral Theses

There exists a vast literature with evidences of gender discrimination against females in allocation of goods and services at regional/national level in India. Evidence of gender bias on Indian data include, among many others, studies by Subramanian and Deaton (1991), Azam and Kingdon (2013), Kingdon (2005), Drèze and Kingdon (2001), Zimmerman (2012) and Lancaster, Maitra, and Ray (2008). India has a history of preference for sons over daughters for cultural and economic reasons. This is manifested through high birth sex ratios, which is possibly a result of female foeticide. The child sex ratio is within the normal natural range in …

Hopf Differentials And Smoothing Sobolev Homeomorphisms, Tadeusz Iwaniec, Leonid V. Kovalev, Jani Onninen

Mathematics - All Scholarship

We prove that planar homeomorphisms can be approximated by diffeomorphisms in the Sobolev space W^1,2 and in the Royden algebra. As an application, we show that every discrete and open planar mapping with a holomorphic Hopf differential is harmonic.

Topology Of Cyclo-Octane Energy Landscape, Evangelos A. Coutsias, Shawn Martin, Aidan Thompson, Jean-Paul Watson

Branch Mathematics and Statistics Faculty and Staff Publications

Understanding energy landscapes is a major challenge in chemistry and biology. Although a wide variety of methods have been invented and applied to this problem, very little is understood about the actual mathematical structures underlying such landscapes. Perhaps the most general assumption is the idea that energy landscapes are low-dimensional manifolds embedded in high-dimensional Euclidean space. While this is a very mild assumption, we have discovered an example of an energy landscape which is nonmanifold, demonstrating previously unknown mathematical complexity. The example occurs in the energy landscape of cyclo-octane, which was found to have the structure of a reducible algebraic …

A Characteristic Free Tilting Bundle For Grassmannians, Ragar-Olaf Buchweitz, Graham J. Leuschke, Michel Van Den Bergh

Mathematics - All Scholarship

We construct a characteristic free tilting bundle on Grassmannians.

Agnostic Science. Towards A Philosophy Of Data Analysis, Domenico Napoletani, Marco Panza, Daniele C. Struppa

MPP Published Research

In this paper we will offer a few examples to illustrate the orientation of contemporary research in data analysis and we will investigate the corresponding role of mathematics. We argue that the modus operandi of data analysis is implicitly based on the belief that if we have collected enough and sufficiently diverse data, we will be able to answer most relevant questions concerning the phenomenon itself. This is a methodological paradigm strongly related, but not limited to, biology, and we label it the microarray paradigm. In this new framework, mathematics provides powerful techniques and general ideas which generate new …

The Minimum Rank, Inverse Inertia, And Inverse Eigenvalue Problems For Graphs, Mark Condie Kempton

Theses and Dissertations

For a graph G we define S(G) to be the set of all real symmetric n by n matrices whose off-diagonal zero/nonzero pattern is described by G. We show how to compute the minimum rank of all matrices in S(G) for a class of graphs called outerplanar graphs. In addition, we obtain results on the possible eigenvalues and possible inertias of matrices in S(G) for certain classes of graph G. We also obtain results concerning the relationship between two graph parameters, the zero forcing number and the path cover number, related to the minimum rank problem.

Approximation Of Stationary Statistical Properties Of Dissipative Dynamical Systems: Time Discretization, Xiaoming Wang

Mathematics and Statistics Faculty Research & Creative Works

We consider temporal approximation of stationary statistical properties of dissipative infinite-dimensional dynamical systems. We demonstrate that stationary statistical properties of the time discrete approximations, i.e., numerical scheme, converge to those of the underlying continuous dissipative infinite-dimensional dynamical system under three very natural assumptions as the time step approaches zero. the three conditions that are sufficient for the convergence of the stationary statistical properties are: (1) uniform dissipativity of the scheme in the sense that the union of the global attractors for the numerical approximations is pre-compact in the phase space; (2) convergence of the solutions of the numerical scheme to …

Wild Low-Dimensional Topology And Dynamics, Mark H. Meilstrup

Theses and Dissertations

In this dissertation we discuss various results for spaces that are wild, i.e. not locally simply connected. We first discuss periodic properties of maps from a given space to itself, similar to Sharkovskii's Theorem for interval maps. We study many non-locally connected spaces and show that some have periodic structure either identical or related to Sharkovskii's result, while others have essentially no restrictions on the periodic structure. We next consider embeddings of solenoids together with their complements in three space. We differentiate solenoid complements via both algebraic and geometric means, and show that every solenoid has an unknotted embedding …

Preface

Communications on Stochastic Analysis

No abstract provided.

On The Non-Classical Infinite Divisibility Of Power Semicircle Distributions, Octavio Arizmendi, Victor Pérez-Abreu

Communications on Stochastic Analysis

No abstract provided.

What Is A Gaussian State?, K R Parthasarathy

Communications on Stochastic Analysis

No abstract provided.

Persistence Of Invertibility In The Wiener Space, A S Üstünel

Communications on Stochastic Analysis

No abstract provided.

An Anticipative Stochastic Calculus Approach To Pricing In Markets Driven By Lévy Process, Bernt Øksendal, Agnès Sulem

Communications on Stochastic Analysis

No abstract provided.

The Asymptotic Dependence Behavior Of Ornstein-Uhlenbeck Semi-Stable Processes, Balram S Rajput

Communications on Stochastic Analysis

No abstract provided.

Set-Valued Stochastic Differential Equation In M-Type 2 Banach Space, Itaru Mitoma, Yoshiaki Okazaki, Jinping Zhang

Communications on Stochastic Analysis

No abstract provided.

Stochastic Magneto-Hydrodynamic System Perturbed By General Noise, P Sundar

Communications on Stochastic Analysis

No abstract provided.

A Stochastic Finite Element Method For Stochastic Parabolic Equations Driven By Purely Spatial Noise, Chia Ying Lee, Boris Rozovskii

Communications on Stochastic Analysis

No abstract provided.