Open Access. Powered by Scholars. Published by Universities.®

Mathematics Commons™

Open Access. Powered by Scholars. Published by Universities.®

2011

Discipline
Institution
Keyword
Publication
Publication Type
File Type

Articles 691 - 720 of 882

Full-Text Articles in Mathematics

Women In Mathematics: An Historical Account Of Women's Experiences And Achievement, Kendra D. Huff Jan 2011

Women In Mathematics: An Historical Account Of Women's Experiences And Achievement, Kendra D. Huff

CMC Senior Theses

For a long time, women have struggled to gain complete acceptance in the mathematics field. The purpose of this paper is to explore the history of women in the field of mathematics, the impact and experiences of current female mathematicians, and the common trends for women in the mathematics field, through literature review and personal interviews. This paper looks at the lives of four famous female mathematicians, as well as female mathematicians in the Claremont Colleges who were interviewed for this paper. Specifically this paper examines the discrimination they faced and how they overcame this discrimination, as well as the …

Go to article

Regression Model Fitting With Quadratic Term Leads To Different Conclusion In Economic Analysis Of Washington State Smoking Ban, Marshal Ma, Scott Mcclintock Jan 2011

Regression Model Fitting With Quadratic Term Leads To Different Conclusion In Economic Analysis Of Washington State Smoking Ban, Marshal Ma, Scott Mcclintock

Mathematics Faculty Publications

No abstract provided.

Go to article

Estimation For The Cox Model With Various Types Of Censored Data, Tonya Riddlesworth Jan 2011

Estimation For The Cox Model With Various Types Of Censored Data, Tonya Riddlesworth

Electronic Theses and Dissertations

In survival analysis, the Cox model is one of the most widely used tools. However, up to now there has not been any published work on the Cox model with complicated types of censored data, such as doubly censored data, partly-interval censored data, etc., while these types of censored data have been encountered in important medical studies, such as cancer, heart disease, diabetes, etc. In this dissertation, we first derive the bivariate nonparametric maximum likelihood estimator (BNPMLE) F[subscript n](t,z) for joint distribution function F[sub 0](t,z) of survival time T and covariate Z, where T is subject to right censoring, noting …

Go to article

Hückel Energy Of A Graph: Its Evolution From Quantum Chemistry To Mathematics, Steven Zimmerman Jan 2011

Hückel Energy Of A Graph: Its Evolution From Quantum Chemistry To Mathematics, Steven Zimmerman

Electronic Theses and Dissertations

The energy of a graph began with German physicist, Erich H¨uckel’s 1931 paper, Quantenttheoretische Beitr¨age zum Benzolproblem. His work developed a method for computing the binding energy of the π-electrons for a certain class of organic molecules. The vertices of the graph represented the carbon atoms while the single edge between each pair of distinct vertices represented the hydrogen bonds between the carbon atoms. In turn, the chemical graphs were represented by an n × n matrix used in solving Schr¨odinger’s eigenvalue/eigenvector equation. The sum of the absolute values of these graph eigenvalues represented the total π-electron energy. The criteria …

Go to article

Finding Dud Vertices In Defensive Alliances And Secure Sets Using Computational Tools, George Worley Ii Jan 2011

Finding Dud Vertices In Defensive Alliances And Secure Sets Using Computational Tools, George Worley Ii

Electronic Theses and Dissertations

Defensive alliances are a way of using graphs to model the defense of resources (people, buildings, countries, etc.) against attacks where the number of potential attackers against each resource is known. The initial study of defensive alliances focused on questions of minimal defensive alliances in a graph and the minimum possible size of a defensive alliance in a graph, but in order to apply defensive alliances in modeling real-world situations, additional considerations are important. In particular, since each vertex in a defensive alliance represents some real-world object that has a cost associated with remaining in the defensive alliance, it is …

Go to article

Fractal Spectral Measures In Two Dimensions, Beng Oscar Alrud Jan 2011

Fractal Spectral Measures In Two Dimensions, Beng Oscar Alrud

Electronic Theses and Dissertations

We study spectral properties for invariant measures associated to affine iterated function systems. We present various conditions under which the existence of a Hadamard pair implies the existence of a spectrum for the fractal measure. This solves a conjecture proposed by Dorin Dutkay and Palle Jorgensen, in several special cases in dimension 2.

Go to article

Kernel-Based Interior-Point Methods For Cartesian P*(Κ)-Linear Complementarity Problems Over Symmetric Cones, Goran Lesaja Jan 2011

Kernel-Based Interior-Point Methods For Cartesian P*(Κ)-Linear Complementarity Problems Over Symmetric Cones, Goran Lesaja

Mathematical Sciences: Faculty Publications

We present an interior point method for Cartesian P*(k)-Linear Complementarity Problems over Symmetric Cones (SCLCPs). The Cartesian P*(k)-SCLCPs have been recently introduced as the generalization of the more commonly known and more widely used monotone SCLCPs. The IPM is based on the barrier functions that are defined by a large class of univariate functions called eligible kernel function which have recently been successfully used to design new IPMs for various optimization problems. Eligible barrier (kernel) functions are used in calculating the Nesterov-Todd search directions and the default step-size which leads to a very good complexity results for the method. For …

Go to article

A Multi-Agent Prediction Market Based On Boolean Network Evolution, Janyl Jumadinova, Mihaela Teodora Matache, Prithviraj Dasgupta Jan 2011

A Multi-Agent Prediction Market Based On Boolean Network Evolution, Janyl Jumadinova, Mihaela Teodora Matache, Prithviraj Dasgupta

Mathematics Faculty Proceedings & Presentations

—Prediction markets have been shown to be a useful tool in forecasting the outcome of future events by aggregating public opinion about the events’ outcome. Previous research on prediction markets has mostly analyzed the prediction markets by building complex analytical models. In this paper, we posit that simpler yet powerful Boolean rules can be used to adequately describe the operations of a prediction market. We have used a multi-agent based prediction market where Boolean network based rules are used to capture the evolution of the beliefs of the market’s participants, as well as to aggregate the prices in the market. …

Go to article

Composition Operators Whose Symbols Have Orthogonal Powers, Valentin Matache Jan 2011

Composition Operators Whose Symbols Have Orthogonal Powers, Valentin Matache

Mathematics Faculty Publications

Composition operators on the Hilbert Hardy space H2 whose symbols are analytic selfmaps of the open unit disk having orthogonal powers are considered. The spectra and essential spectra of such operators are described. In the general case of an arbitrary analytic selfmap of the open unit disk, it is proved that the composition operator induced by that map has essential spectral radius less than 1 if and only if the map under consideration is a non–inner map with a fixed point in the unit disk. The canonical decomposition of a non–unitary composition contraction is determined.

Go to article

Boolean Modeling Of Biochemical Networks, Tomáš Helikar, Naomi Kochi, John Konvalina, Jim A. Rogers Jan 2011

Boolean Modeling Of Biochemical Networks, Tomáš Helikar, Naomi Kochi, John Konvalina, Jim A. Rogers

Mathematics Faculty Publications

The use of modeling to observe and analyze the mechanisms of complex biochemical network function is becoming an important methodological tool in the systems biology era. Number of different approaches to model these networks have been utilized-- they range from analysis of static connection graphs to dynamical models based on kinetic interaction data. Dynamical models have a distinct appeal in that they make it possible to observe these networks in action, but they also pose a distinct challenge in that they require detailed information describing how the individual components of these networks interact in living cells. Because this level of …

Go to article

Fully Nonlinear Boundary Value Problems With Impulse, Paul Eloe, Muhammad Usman Jan 2011

Fully Nonlinear Boundary Value Problems With Impulse, Paul Eloe, Muhammad Usman

Mathematics Faculty Publications

An impulsive boundary value problem with nonlinear boundary conditions for a second order ordinary differential equation is studied. In particular, sufficient conditions are provided so that a compression- expansion cone theoretic fixed point theorem can be applied to imply the existence of positive solutions. The nonlinear forcing term is assumed to satisfy usual sublinear or superlinear growth as t → ∞ or t → 0 +. The nonlinear impulse terms and the nonlinear boundary terms are assumed to satisfy the analogous asymptotic behavior.

Go to article

Prospective Teachers' Use Of Representations In Solving Statistical Tasks With Dynamic Statistical Software, Hollylynne Lee, Shannon O. Driskell, Suzanne R. Harper, Keith R. Leatham, Gladis Kersaint, Robin L. Angotti Jan 2011

Prospective Teachers' Use Of Representations In Solving Statistical Tasks With Dynamic Statistical Software, Hollylynne Lee, Shannon O. Driskell, Suzanne R. Harper, Keith R. Leatham, Gladis Kersaint, Robin L. Angotti

Mathematics Faculty Publications

This study examined a random stratified sample (n=62) of prospective teachers' work across eight institutions on three tasks that utilized dynamic statistical software. Our work was guided by considering how teachers may utilize their statistical knowledge and technological statistical knowledge to engage in cycles of investigation. Although teachers did not tend to take full advantage of dynamic linking capabilities, they utilized a large variety of graphical representations and often added statistical measures or other augmentations to graphs as part of their analysis.

Go to article

Non-Normality Points Of Β X\X, William Fleissner, Lynne Yengulalp Jan 2011

Non-Normality Points Of Β X\X, William Fleissner, Lynne Yengulalp

Mathematics Faculty Publications

We seek conditions implying that (β X\X) \ {y} is not normal. Our main theorem: Assume GCH and all uniform ultrafilters are regular. If X is a locally compact metrizable space without isolated points, then (β X\X) \ {y} is not normal for all y ∈ β X\X. In preparing to prove this theorem, we generalize the notions “uniform”, “regular”, and “good” from set ultrafilters to z-ultrafilters. We discuss non-normality points of the product of a discrete space and the real line. We topologically embed a nonstandard real line into the remainder of this product space.

Go to article

Algorithms For Area Preserving Flows, Catherine Kublik, Selim Esedoglu, Jeffrey A. Fessler Jan 2011

Algorithms For Area Preserving Flows, Catherine Kublik, Selim Esedoglu, Jeffrey A. Fessler

Mathematics Faculty Publications

We propose efficient and accurate algorithms for computing certain area preserving geometric motions of curves in the plane, such as area preserving motion by curvature. These schemes are based on a new class of diffusion generated motion algorithms using signed distance functions. In particular, they alternate two very simple and fast operations, namely convolution with the Gaussian kernel and construction of the distance function, to generate the desired geometric flow in an unconditionally stable manner. We present applications of these area preserving flows to large scale simulations of coarsening.

Go to article

Upper And Lower Solutions For Regime-Switching Diffusions With Applications In Financial Mathematics, Paul W. Eloe, R. H. Liu Jan 2011

Upper And Lower Solutions For Regime-Switching Diffusions With Applications In Financial Mathematics, Paul W. Eloe, R. H. Liu

Mathematics Faculty Publications

This paper develops a method of upper and lower solutions for a general system of second-order ordinary differential equations with two-point boundary conditions. Our motivation of study stems from a class of financial mathematics problems under regime-switching diffusion models. Two examples are double barrier option valuation and optimal selling rules in asset trading. We establish the existence of a unique C2 solution of the two-point boundary value problem. We construct monotone sequences of upper and lower solutions that are shown to converge to the unique solution of the boundary value problem. This construction provides a feasible numerical method to compute …

Go to article

Optimal Intervals For Uniqueness Of Solutions For Nonlocal Boundary Value Problems, Paul W. Eloe, Johnny Henderson Jan 2011

Optimal Intervals For Uniqueness Of Solutions For Nonlocal Boundary Value Problems, Paul W. Eloe, Johnny Henderson

Mathematics Faculty Publications

For the nth order differential equation (see PDF for equation) we obtain optimal bounds on the length of intervals on which solutions are unique for certain nonlocal three point boundary value problems. These bounds are obtained through an application of the Pontryagin Maximum Principle from the theory of optimal control.

Go to article

2011 Program And Abstracts, University Of Dayton. Department Of Mathematics Jan 2011

2011 Program And Abstracts, University Of Dayton. Department Of Mathematics

Undergraduate Mathematics Day: Programs, Lectures, Promotional Materials

Program and abstracts of papers presented at the 2011 Undergraduate Mathematics Day held at the University of Dayton.

Go to article

Perfect And Abundant Numbers - A Perfect And Abundant Source For Undergraduate Research Projects (Abstract), Judy Holdener Jan 2011

Perfect And Abundant Numbers - A Perfect And Abundant Source For Undergraduate Research Projects (Abstract), Judy Holdener

Undergraduate Mathematics Day: Programs, Lectures, Promotional Materials

In June of 2009, the 47th perfect number was discovered by the Great Internet Mersenne Prime Search (GIMPS), a collaborative computing project involving volunteers from all over the world. Like all known perfect numbers before it, this number is even. Does an odd perfect number exist? Are there infinitely many perfect numbers?

Go to article

Personal And Professional Numeracy: A Unit For Pre-Service Teachers At The University Of Tasmania, Jane M. Watson Jan 2011

Personal And Professional Numeracy: A Unit For Pre-Service Teachers At The University Of Tasmania, Jane M. Watson

Numeracy

This paper addresses issues associated with the development of a unit preparing pre-service teachers to be quantitatively literate in three respects. These issues surround (i) the need to be aware of numeracy demands across the curriculum, (ii) the need to model numerate behavior in all interactions of teachers, and (iii) the need to be able to interpret and use system data provided from local and national testing programs. The context for the unit described is Australia, where a national testing program for literacy and numeracy requires teachers to analyze extensive data on their students, a national curriculum requires teachers of …

Go to article

Twisted Virtual Biracks, Jessica Ceniceros Jan 2011

Twisted Virtual Biracks, Jessica Ceniceros

CMC Senior Theses

This thesis will take a look at a branch of topology called knot theory. We will first look at what started the study of this field, classical knot theory. Knot invariants such as the Bracket polynomial and the Jones polynomial will be introduced and studied. We will then explore racks and biracks along with the axioms obtained from the Reidemeister moves. We will then move on to generalize classical knot theory to what is now known as virtual knot theory which was first introduced by Louis Kauffman. Finally, we take a look at a newer aspect of knot theory, twisted …

Go to article

The Mathematical Landscape, Antonio Collazo Jan 2011

The Mathematical Landscape, Antonio Collazo

CMC Senior Theses

The intent of this paper is to present the reader will enough information to spark a curiosity in to the subject.  By no means is the following a complete formulation of any of the topics covered.  I want to give the reader a tour of the mathematical landscape.  There are plenty of further details to explore in each section, I have just touched the tip the iceberg.  The work is basically in four sections: Numbers, Geometry, Functions, Sets and Logic, which are the basic building blocks of Math.  The first sections are a exposition into the mathematical objects and their …

Go to article

Determining A Patient Recovery From A Total Knee Replacement Using Fuzzy Logic And Active Databases, Robert Azarbod Jan 2011

Determining A Patient Recovery From A Total Knee Replacement Using Fuzzy Logic And Active Databases, Robert Azarbod

All Graduate Theses, Dissertations, and Other Capstone Projects

The purpose of the knowledge-based system is to predict the rehabilitation timeline of a patient in physical therapy for a total knee replacement. All patients have various attributes that contribute to their rehabilitation rate such as: weight, gender, smoking habit, medications, physical ability, or other medical problems. A combination of any one or several of these attributes will affect the recovery process. The proposed FRTP (Fuzzy Rehabilitation Timeline Predictor) is a fuzzy data mining model that can predict the recovery length of a patient in physical therapy for a total knee replacement and provide feedback to experts for revision of …

Go to article

On The Singular Weyl-Titchmarsh Function Of Perturbed Spherical Schrödinger Operators, Aleksey Kostenko, Gerald Teschl Jan 2011

On The Singular Weyl-Titchmarsh Function Of Perturbed Spherical Schrödinger Operators, Aleksey Kostenko, Gerald Teschl

Articles

We investigate the singular Weyl–Titchmarsh m-function of perturbed spherical Schrödinger operators (also known as Bessel operators) under the assumption that the perturbation q(x) satisfies xq(x) ∈ L1(0, 1). We show existence plus detailed properties of a fundamental system of solutions which are entire with respect to the energy parameter. Based on this we show that the singular mfunction belongs to the generalized Nevanlinna class and connect our results with the theory of super singular perturbations.

Go to article

On The (Non)-Integrability Of Kdv Hierarchy With Self-Consistent Sources, Vladimir Gerdjikov, Georgi Grahovski, Rossen Ivanov Jan 2011

On The (Non)-Integrability Of Kdv Hierarchy With Self-Consistent Sources, Vladimir Gerdjikov, Georgi Grahovski, Rossen Ivanov

Articles

Nonholonomic deformations of integrable equations of the KdV hierarchy are studied by using the expansions over the so-called “squared solutions” (squared eigenfunctions). Such deformations are equivalent to a perturbed model with external (self-consistent) sources. In this regard, the KdV6 equation is viewed as a special perturbation of KdV. Applying expansions over the symplectic basis of squared eigenfunctions, the integrability properties of the KdV6 equation are analysed. This allows for a formulation of conditions on the perturbation terms that preserve its integrability. The perturbation corrections to the scattering data and to the corresponding action-angle (canonical) variables are studied. The analysis shows …

Go to article

Rational Bundles And Recursion Operators For Integrable Equations On A.Iii-Type Symmetric Spaces, Vladimir Gerdjikov, Georgi Grahovski, Alexander Mikhailov, Tihomir Valtchev Jan 2011

Rational Bundles And Recursion Operators For Integrable Equations On A.Iii-Type Symmetric Spaces, Vladimir Gerdjikov, Georgi Grahovski, Alexander Mikhailov, Tihomir Valtchev

Articles

We analyze and compare the methods of construction of the recursion operators for a special class of integrable nonlinear differential equations related to A.III-type symmetric spaces in Cartan’s classification and having additional reductions.

Go to article

Polynomial Bundles And Generalised Fourier Transforms For Integrable Equations On A.Iii-Type Symmetric Spaces, Vladimir Gerdjikov, Georgi Grahovski, Alexander V. Mikhailov, Tihomir Valchev Jan 2011

Polynomial Bundles And Generalised Fourier Transforms For Integrable Equations On A.Iii-Type Symmetric Spaces, Vladimir Gerdjikov, Georgi Grahovski, Alexander V. Mikhailov, Tihomir Valchev

Articles

A certain class of integrable nonlinear differential equations related to A.III-type symmetric spaces and having additional reductions is analysed via the Inverse Scattering Method (ISM). The class contains systems of nonlinear evolution equations (NLEEs) associated with a Lax operator (for the time-evolution) polynomial in the spectral parameter. Using the Wronskian relations, the mapping between the potential and the minimal sets of scattering data is constructed. Furthermore, completeness relations for the `squared solutions' (generalised exponentials) are derived. Next, expansions of Q and its variation are obtained. This demonstrates that the interpretation of the inverse scattering method as a generalized Fourier transform …

Go to article

A Duality Theory For The Algebraic Invariants Of Substitution Tiling Spaces, Jeffrey Myers Ford Jan 2011

A Duality Theory For The Algebraic Invariants Of Substitution Tiling Spaces, Jeffrey Myers Ford

All Graduate Theses, Dissertations, and Other Capstone Projects

We present here a method for computing the homology of a substitution tiling space. There is a well established cohomology theory that uses simple matrix computations to determine if two tiling spaces are dierent. We will show how to compute Putnam's homology groups for these spaces using simple linear algebra. We construct a Markov Partition based on the substitution rules, and exploit the properties of this partition as a shift of finite type to construct algebraic invariants for the tiling space. These invariants form a chain complex, of which we can compute the homology. In our examples we will demonstrate …

Go to article

A Characterization Of Connected (1,2)-Domination Graphs Of Tournaments, Kim A. S. Factor, Larry J. Langley Jan 2011

A Characterization Of Connected (1,2)-Domination Graphs Of Tournaments, Kim A. S. Factor, Larry J. Langley

Mathematics, Statistics and Computer Science Faculty Research and Publications

Recently. Hedetniemi et aI. introduced (1,2)-domination in graphs, and the authors extended that concept to (1, 2)-domination graphs of digraphs. Given vertices x and y in a digraph D, x and y form a (1,2)-dominating pair if and only if for every other vertex z in D, z is one step away from x or y and at most two steps away from the other. The (1,2)-dominating graph of D, dom1,2 (D), is defined to be the graph G = (V, E ) , where V (G) = V (D), and xy is …

Go to article

Multi-Dimensional Weiss Operators, Sergey Bori̇senok, Mehmet Hakan Erkut, Yaşar Polatoğlu, Rüştü Murat Demi̇rer Jan 2011

Multi-Dimensional Weiss Operators, Sergey Bori̇senok, Mehmet Hakan Erkut, Yaşar Polatoğlu, Rüştü Murat Demi̇rer

Turkish Journal of Mathematics

We present a solution of the Weiss operator family generalized for the case of R^d and formulate a d-dimensional analogue of the Weiss Theorem. Most importantly, the generalization of the Weiss Theorem allows us to find a subset of null class functions for a partial differential equation with the generalized Weiss operators. We illustrate the significance of our approach through several examples of both linear and non-linear partial differential equations.

Go to article

A Class Of Generalized Shannon-Mcmillan Theorems For Arbitrary Discrete Information Source, Kangkang Wang Jan 2011

A Class Of Generalized Shannon-Mcmillan Theorems For Arbitrary Discrete Information Source, Kangkang Wang

Turkish Journal of Mathematics

In this study, a class of strong limit theorems for the relative entropy densities of random sum of arbitrary information source are discussed by constructing the joint distribution and nonnegative super martingales. As corollaries, some Shannon-McMillan theorems for arbitrary information source, mth-order Markov information source and non-memory information source are obtained and some results for the discrete information source which have been obtained by authors are extended.

Go to article

First Prev Next Last