Physical Sciences and Mathematics Commons^™

Topics In Analytic Number Theory, Kevin James Powell

Theses and Dissertations

The thesis is in two parts. The first part is the paper “The Distribution of k-free integers” that my advisor, Dr. Roger Baker, and I submitted in February 2009. The reader will note that I have inserted additional commentary and explanations which appear in smaller text. Dr. Baker and I improved the asymptotic formula for the number of k-free integers less than x by taking advantage of exponential sum techniques developed since the 1980's. Both of us made substantial contributions to the paper. I discovered the exponent in the error term for the cases k=3,4, and worked the case k=3 …

The Effects Of The Use Of Technology In Mathematics Instruction On Student Achievement, Ron Y. Myers

FIU Electronic Theses and Dissertations

The purpose of this study was to examine the effects of the use of technology on students’ mathematics achievement, particularly the Florida Comprehensive Assessment Test (FCAT) mathematics results. Eleven schools within the Miami-Dade County Public School System participated in a pilot program on the use of Geometers Sketchpad (GSP). Three of these schools were randomly selected for this study. Each school sent a teacher to a summer in-service training program on how to use GSP to teach geometry. In each school, the GSP class and a traditional geometry class taught by the same teacher were the study participants. Students’ mathematics …

The Maximum Rectilinear Crossing Number Of The N Dimensional Cube Graph, Matthew Alpert, Elie Feder, Heiko Harborth, Sheldon Klein

Publications and Research

We find a.nd prove the maximum rectilinear crossing n1.1mber of the three-dimensional cube graph (Q₃). We demonstrate a method of drawing then-cube graph, Q_n., with many crossings, and thus find a lower bound for the maximum rectilinear crossing number of Q_n. We conjecture that this bound is sharp. We also prove an upper bound for the maximum rectilinear crossing number of Q_n.

Studies On Construction And List Decoding Of Codes On Some Towers Of Function Fields., M. Prem Laxman Das Dr.

Doctoral Theses

In everyday life, there arise many situations where two parties, sender and receiver, need to communicate. The channel through which they communicate is assumed to be binary symmetric, that is, it changes 0 to 1 and vice versa with equal probability. At the receiver’s end, the sent message has to be recovered from the corrupted received word using some reasonable mechanism. This real life problem has attracted a lot of research in the past few decades. A solution to this problem is obtained by adding redundancy in a systematic manner to the message to construct a codeword. The collection of …

Harmonic Mappings Of An Annulus, Nitsche Conjecture And Its Generalizations, Tadeusz Iwaniec, Leonid V. Kovalev, Jani Onninen

Mathematics - All Scholarship

As long ago as 1962 Nitsche conjectured that a harmonic homeomorphism h: A(r,R) ^onto-> A(r_*, R_*) between planar annuli exists if and only if R_*/r_* > 1/2 ((R/r) + (r/R)). We prove this conjecture when the domain annulus is not too wide; explicitly, when log(R/r) < 3/2. For general A(r,R) the conjecture is proved under additional assumption that either h or its normal derivative have vanishing average on the inner boundary circle. This is the case for the critical Nitsche mapping which yields equality in the above inequality. The Nitsche mapping represents so-called free evolution of circles of the annulus A(r,R). It will be shown on the other hand that forced harmonic evolution results in greater ratio R_*/r_*. To this end, we introduce the underlying differential operators for the circular means of the forced evolution and use them to obtain sharp lower bounds of R_*/r_*.

Using The Ti-Nspire As A Tool To Explore Real Applications, Lisa Yocco

Lisa S. Yocco

No abstract provided.

Proportional Reasoning 101, Laurie O. Cavey

Laurie O. Cavey

No abstract provided.

Alternating Links And Subdivision Rules, Brian Craig Rushton

Theses and Dissertations

The study of geometric group theory has suggested several theorems related to subdivision tilings that have a natural hyperbolic structure. However, few examples exist. We construct subdivision tilings for the complement of every nonsingular, prime alternating link and all torus links, and explore some of their properties and applications. Several examples are exhibited with color coding of tiles.

Creating Multi Objective Value Functions From Non-Independent Values, Christopher D. Richards

Theses and Dissertations

Decisions are made every day and by everyone. As these decisions become more important, involve higher costs and affect a broader group of stakeholders it becomes essential to establish a more rigorous strategy than simply intuition or "going with your gut". In the past several decades, the concept of Value Focused Thinking (VFT) has gained much acclaim in assisting Decision Makers (DMs) in this very effort. By identifying and organizing what a DM values VFT is able to decompose the original problem and create a mathematical model to score and rank alternatives to be chosen. But what if the decision …

Transitional Probabilities For The Four-State Random Walk On A Lattice In The Presence Of Partially Reflecting Boundaries, Ramakrishna Janaswamy

Ramakrishna Janaswamy

The four-state random walk (4RW) model, wherein the particle is endowed with two states of spin and two states of directional motion in each space coordinate, permits a stochastic solution of the Schrödinger equation (or the equivalent parabolic equation) without resorting to the usual analytical continuation in complex space of the particle trajectories. Analytical expressions are derived here for the various transitional probabilities in a 4RW by employing generating functions and eigenfunction expansions when the particle moves on a 1+1 space-time lattice with two-point boundary conditions. The most general case of dissimilar boundaries with partially reflecting boundary conditions is treated …

A Simulated Annealing Approach To Communication Network Design, Stephen J. Sugden, Marcus Randall, Graham Mcmahon

Stephen Sugden

This paper explores the use of the meta-heuristic search algorithm Simulated Annealing for solving a minimum cost network synthesis problem. This problem is a common one in the design of telecommunication networks. The formulation we use models a number of practical problems with hop-limit, degree and capacity constraints. Emphasis is placed on a new approach that uses a knapsack polytope to select amongst a number of pre-computed traffic routes in order to synthesise the network. The advantage of this approach is that a subset of the best routes can be used instead of the whole set, thereby making the process …

Reverse Mathematics, Computability, And Partitions Of Trees, Jennifer Chubb, Jeffry L. Hirst, Timothy H. Mcnicholl

Mathematics

We examine the reverse mathematics and computability theory of a form of Ramsey’s theorem in which the linear n-tuples of a binary tree are colored.

Parameterizing The Growth-Decline Boundary For Uncertain Population Projection Models, Joan Lubben, Derek Boeckner, Richard Rebarber, Stuart Townley, Brigitte Tenhumberg

Department of Mathematics: Faculty Publications

We consider discrete time linear population models of the form n(t + 1) = An(t) where A is a population projection matrix or integral projection operator, and represents a structured population at time t. It is well known that the asymptotic growth or decay rate of n(t) is determined by the leading eigenvalue of A. In practice, population models have substantial parameter uncertainty, and it might be difficult to quantify the effect of this uncertainty on the leading eigenvalue. For a large class of matrices and integral operators A, we …

Interpolation Theorems For Self-Adjoint Operators, Shijun Zheng

Department of Mathematical Sciences Faculty Publications

We prove a complex and a real interpolation theorems on Besov spaces and Triebel-Lizorkin spaces associated with a self adjoint operator L, without assuming the gradient estimate for its spectral kernel. The result applies to the cases where L is a uniformly elliptic operator or a Schrödinger operator with electro-magnetic potential.

A Conceptual Framework For Cross-Curricular Teaching, Astrid Beckmann

The Mathematics Enthusiast

The Montana Mathematics Enthusiast is pleased to present a special supplemental issue this year focused on the issue of interdisciplinarity in the curriculum and classroom. This book is based on the longitudinal research carried out by Prof. Astrid Beckmann of the University of Education, Schwäbisch Gmünd- Germany, who is one of the co-founders of the Mathematics and its Connections to the Arts and Sciences international group (MACAS).

Neutrosophic Logic, Wave Mechanics, And Other Stories: Selected Works 2005-2008, Florentin Smarandache, Victor Christianto

Branch Mathematics and Statistics Faculty and Staff Publications

There is beginning for anything; we used to hear that phrase. The same wisdom word applies to us too. What began in 2005 as a short email on some ideas related to interpretation of the Wave Mechanics results in a number of papers and books up to now. Some of these papers can be found in Progress in Physics or elsewhere. It is often recognized that when a mathematician meets a physics-inclined mind then the result is either a series of endless debates or publication. In our story, we prefer to publish rather than perish. Therefore, our purpose with this …

Topology Explains Why Automobile Shades Fold Oddly, Ramin Naimi, Curtis Feist

Ramin Naimi

We use braids and linking number to explain why automobile shades fold into an odd number of loops.

Image And Video Compression Using Block Truncation Coding And Pattern Fitting For Fast Decoding., Bibhas Chandra Dhara Dr.

Doctoral Theses

In the present era of multimedia, the requirement of image/video storage and transmission for video conferencing, image and video retrieval, video playback, etc. are increasing exponentially. As a result, the need for better compression technology is always in demand. The limited bandwidth of internet also asks for transmission of desired objects only. Progressive image transmission provides such facilities, where transmission is done in steps and the transmission of undesired image can be stopped at an early stage. Modern applications, in addition to high compression ratio, also demand for efficient encoding and decoding processes, so that computational constraint of many real-time …

Homogeneous Operators In The Cowen-Douglas Class., Subrata Shyam Roy Dr.

Doctoral Theses

Although, we have used techniques developed in the paper of Cowen-Douglas [18, 20], a systematic account of Hilbert space operators using a variety of tools from several different areas of mathematics is given in the book [26]. This book provides, what the authors call, a sheaf model for a large class of commuting Hilbert space operators. It is likely that these ideas will play a significant role in the future development of the topics discussed here.

Spectral Analysis And Synthesis For Radial Sections Of Homogenous Vector Bundles On Certain Noncompath Riemannian Symmetric Spaces., Sanjoy Pusti Dr.

Doctoral Theses

We consider two classical theorems of real analysis which deals with translation invariant subspaces of integrable and smooth functions on R respectively. The first one is a theorem of Norbert Wiener [63] which states that if the Fourier transform of a function f ∈ L 1 (R) has no real zeros then the finite linear combinations of translations f(x − a) of f with complex coefficients form a dense subspace in L 1 (R), equivalently, span{g ∗ f | g ∈ L 1 (R)} is dense in L 1 (R). This theorem is well known as the Wiener-Tauberian Theorem (WTT). …

Look Behind The Scenes With The Ti-Nspire, Lisa Yocco

Lisa S. Yocco

No abstract provided.

Web Surfer Models: Preprocessing, Page Ranking, And Quantitative Evaluation., Narayan L. Bhamidipati Dr.

Doctoral Theses

The World Wide Web [12] (usually referred to as the Web, WWW or W3) is an enormous collection of data available over the Internet, which is a vast network of computers. It was created in the year 1990 by Tim Berners-Lee, while he worked at CERN, Switzerland, and was made available over the Internet in 1991. The World Wide Web Consortium [136] authoritatively defines the Web as the universe of network-accessible information, the embodiment of human knowledge. The Web consists of objects, also called documents or pages in a generic sense, that are identified using a Uniform Resource Identifier (URI), …

Order-Restricted Covariate Effects And Hazard Regression Models., Arnab Bhattacharjee Dr.

Doctoral Theses

The proportional hazards (PH) model, but more speciÖcally its special case the Cox regression model (Cox, 1972), plays an important role in the theory and practice of lifetime and duration data analysis. This is because the PH model (and the Cox regression model) provides a convenient way to evaluate the ináuence of one or several covariates on the probability of conclusion of lifetime or duration spells. However, the PH speciÖcation substantially restricts interdependence between the explanatory variables and the lifetime in determining the hazard. In particular, the Cox regression model model restricts the coe¢ cients of the regressors in the …

Placement And Range Assignment In Power-Aware Radio Networks., Gautam Kumar Das Dr.

Doctoral Theses

Due to the extraordinary growth of demand in mobile communication facility, design of efficient systems for providing specialized services has become an important issue in wireless mobility research. Broadly speaking, there are two major models for wireless networking: single-hop and multi-hop. The single-hop model [110] is based on the cellular network, and it provides one-hop wireless connectivity between the host and the static nodes known as base stations. single-hop networks rely on a fixed backbone infrastructure that interconnects all the base stations by high speed wired links. On the other hand, the multi-hop model requires neither fixed wired infrastructure nor …

Data Assimilation, Adaptive Observations And Applications, Humberto Carlos Godinez Vasquez

Dissertations and Theses

Sensitivity analysis, data assimilation and targeting observation strategies are methods that are applied to various complex mathematical models of fluid dynamics. In this research we investigate new directions to improve on the current strategies used to deploy additional observational resources (targeting strategies) for data assimilation in dynamical systems of fluid mechanics.

Targeting strategies aim to determine optimal locations where additional observations will improve the solution of the data assimilation process by identifying regions where state errors in the model have a high potential to grow.

Properly accounting for nonlinear error growth is an unresolved issue in targeted observations for numerical …

Quasi-Anosov Diffeomorphisms Of 3-Manifolds, Todd L. Fisher, Hertz M. Rodriguez

Faculty Publications

In 1969, Hirsch posed the following problem: given a diffeomorphism f:N → N and a compact invariant hyperbolic set Λ of f, describe the topology of Λ and the dynamics of f restricted to Λ. We solve the problem where Λ=M^3 is a closed 3-manifold: if M^3 is orientable, then it is a connected sum of tori and handles; otherwise it is a connected sum of tori and handles quotiented by involutions.

First-Order Bias Correction For Fractionally Integrated Time Series, Jaechoul Lee, Kyungduk Ko

Mathematics Faculty Publications and Presentations

Most of the long memory estimators for stationary fractionally integrated time series models are known to experience non-negligible bias in small and finite samples. Simple moment estimators are also vulnerable to such bias, but can easily be corrected. In this paper, we propose bias reduction methods for a lag-one sample autocorrelation-based moment estimator. In order to reduce the bias of the moment estimator, we explicitly obtain the exact bias of lag-one sample autocorrelation up to the order n−1. An example where the exact first-order bias can be noticeably more accurate than its asymptotic counterpart, even for large samples, is presented. …

A Survey On Semilinear Differential Equations And Inclusions Involving Riemann-Liouville Fractional Derivative, Ravi P. Agarwal, Mohammed Belmekki, Mouffak Benchohra

Mathematics and System Engineering Faculty Publications

We establish sufficient conditions for the existence of mild solutions for some densely defined semilinear functional differential equations and inclusions involving the Riemann-Liouville fractional derivative. Our approach is based on the C0-semigroups theory combined with some suitable fixed point theorems.

Faculty Colloquium Examines “Applied Modal Logic”, Heather Lindquist ’09

News and Events

No abstract provided.

Second-Order Analysis Of Polyhedral Systems In Finite And Infinite Dimensions With Applications To Robust Stability Of Variational Inequalities, René Henrion, Boris S. Mordukhovich, Nguyen Mau Nam

Mathematics Research Reports

This paper concerns second-order analysis for a remarkable class of variational systems in finite-dimensional and infinite-dimensional spaces, which is particularly important for the study of optimization and equilibrium problems with equilibrium constraints. Systems of this type are described via variational inequalities over polyhedral convex sets and allow us to provide a comprehensive local analysis by using appropriate generalized differentiation of the normal cone mappings for such sets. In this paper we efficiently compute the required coderivatives of the normal cone mappings exclusively via the initial data of polyhedral sets in reflexive Banach spaces. This provides the main tools of second-order …