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2013

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Articles 1 - 30 of 108

Full-Text Articles in Other Mathematics

Model Spaces: A Survey, William T. Ross, Stephan Ramon Garcia Dec 2013

Model Spaces: A Survey, William T. Ross, Stephan Ramon Garcia

Department of Math & Statistics Faculty Publications

This is a brief and gentle introduction, aimed at graduate students, to the subject of model subspaces of the Hardy space.


Principal Angles And Approximation For Quaternionic Projections [Dataset], Terry A. Loring Dec 2013

Principal Angles And Approximation For Quaternionic Projections [Dataset], Terry A. Loring

Math and Statistics Datasets

We extend Jordan's notion of principal angles to work for two subspaces of quaternionic space, and so have a method to analyze two orthogonal projections in the matrices over the real, complex or quaternionic field (or skew field). From this we derive an algorithm to turn almost commuting projections into commuting projections that minimizes the sum of the displacements of the two projections. We quickly prove what we need using the universal real C*-algebra generated by two projections.


Estimating Norms Of Commutators [Dataset], Terry A. Loring, Freddy Vides Dec 2013

Estimating Norms Of Commutators [Dataset], Terry A. Loring, Freddy Vides

Math and Statistics Datasets

We find estimates on the norm of a commutator of the form [f(x),y] in terms of the norm of [x,y], assuming that x and y are bounded linear operators on Hilbert space, with x normal and with spectrum within the domain of f. In particular we discuss |[x^2,y]| and |[x^{1/2},y]| for 0leq x leq 1. For larger values of delta = |[x,y]| we can rigorous calculate the best possible upper bound |[f(x),y]| leq eta_f(delta) for many f. In other cases we have conducted numerical experiments that strongly suggest that we have in many cases found the correct formula for the …


On The Exact Distribution Of The Maximum Of The Exponential Of The Generalized Normal-Inverse Gaussian Process With Respect To A Martingale Measure, Roman V Ivanov Dec 2013

On The Exact Distribution Of The Maximum Of The Exponential Of The Generalized Normal-Inverse Gaussian Process With Respect To A Martingale Measure, Roman V Ivanov

Communications on Stochastic Analysis

No abstract provided.


Local Time Of A Multifractional Gaussian Process, Aissa Sghir Dec 2013

Local Time Of A Multifractional Gaussian Process, Aissa Sghir

Communications on Stochastic Analysis

No abstract provided.


Generalization Of The Anticipative Girsanov Theorem, Hui-Hsiung Kuo, Yun Peng, Benedykt Szozda Dec 2013

Generalization Of The Anticipative Girsanov Theorem, Hui-Hsiung Kuo, Yun Peng, Benedykt Szozda

Communications on Stochastic Analysis

No abstract provided.


Vertical Martingales, Stochastic Calculus And Harmonic Sections, Simão N Stelmastchuk Dec 2013

Vertical Martingales, Stochastic Calculus And Harmonic Sections, Simão N Stelmastchuk

Communications on Stochastic Analysis

No abstract provided.


Analytically Weak Solutions To Linear Spdes With Unbounded Time-Dependent Differential Operators And An Application, Benedict Baur, Martin Grothaus, Thanh Tan Mai Dec 2013

Analytically Weak Solutions To Linear Spdes With Unbounded Time-Dependent Differential Operators And An Application, Benedict Baur, Martin Grothaus, Thanh Tan Mai

Communications on Stochastic Analysis

No abstract provided.


Mathematical Model Of Heavy Diffusion Particles System With Drift, Vitalii Konarovskyi Dec 2013

Mathematical Model Of Heavy Diffusion Particles System With Drift, Vitalii Konarovskyi

Communications on Stochastic Analysis

No abstract provided.


A New Type Of Reflected Backward Doubly Stochastic Differential Equations, Auguste Aman, Yong Ren Dec 2013

A New Type Of Reflected Backward Doubly Stochastic Differential Equations, Auguste Aman, Yong Ren

Communications on Stochastic Analysis

No abstract provided.


Random Search Models Of Foraging Behavior: Theory, Simulation, And Observation., Ben C. Nolting Dec 2013

Random Search Models Of Foraging Behavior: Theory, Simulation, And Observation., Ben C. Nolting

Department of Mathematics: Dissertations, Theses, and Student Research

Many organisms, from bacteria to primates, use stochastic movement patterns to find food. These movement patterns, known as search strategies, have recently be- come a focus of ecologists interested in identifying universal properties of optimal foraging behavior. In this dissertation, I describe three contributions to this field. First, I propose a way to extend Charnov's Marginal Value Theorem to the spatially explicit framework of stochastic search strategies. Next, I describe simulations that compare the efficiencies of sensory and memory-based composite search strategies, which involve switching between different behavioral modes. Finally, I explain a new behavioral analysis protocol for identifying the …


Computing A Logarithm Of A Unitary Matrix With General Spectrum [Dataset], Terry A. Loring Nov 2013

Computing A Logarithm Of A Unitary Matrix With General Spectrum [Dataset], Terry A. Loring

Math and Statistics Datasets

We analyze an algorithm for computing a skew-Hermitian logarithm of a unitary matrix, and also skew-Hermitian approximate logarithms for nearly unitary matrices. This algorithm is very easy to implement using standard software and it works well even for unitary matrices with no spectral conditions assumed. Certain examples, with many eigenvalues near -1, lead to very non-Hermitian output for other basic methods of calculating matrix logarithms. Altering the output of these algorithms to force an Hermitian output creates accuracy issues which are avoided by the considered algorithm. A modification is introduced to deal properly with the J-skew symmetric unitary matrices. Applications …


Leslie Matrices For Logistic Population Modeling, Bruce Kessler Nov 2013

Leslie Matrices For Logistic Population Modeling, Bruce Kessler

Mathematics Faculty Publications

Leslie matrices are taught as a method of modeling populations in a discrete-time fashion with more detail in the tracking of age groups within the population. Leslie matrices have limited use in the actual modeling of populations, since when the age groups are summed, it is basically equivalent to discrete-time modeling assuming exponential population growth. The logistic model of population growth is more realistic, since it takes into account a carrying capacity for the environment of the population. This talk will describe an adjustment to the Leslie matrix approach for population modeling that is both takes into account the carrying …


Leslie Matrices For Logistic Population Modeling, Bruce Kessler Nov 2013

Leslie Matrices For Logistic Population Modeling, Bruce Kessler

Bruce Kessler

Leslie matrices are taught as a method of modeling populations in a discrete-time fashion with more detail in the tracking of age groups within the population. Leslie matrices have limited use in the actual modeling of populations, since when the age groups are summed, it is basically equivalent to discrete-time modeling assuming exponential population growth. The logistic model of population growth is more realistic, since it takes into account a carrying capacity for the environment of the population. This talk will describe an adjustment to the Leslie matrix approach for population modeling that is both takes into account the carrying …


A Primer For Mathematical Modeling, Marla A. Sole Oct 2013

A Primer For Mathematical Modeling, Marla A. Sole

Publications and Research

With the implementation of the National Council of Teachers of Mathematics recommendations and the adoption of the Common Core State Standards for Mathematics, modeling has moved to the forefront of K-12 education. Modeling activities not only reinforce purposeful problem-solving skills, they also connect the mathematics students learn in school with the mathematics they will use outside of school. Instructors have found mathematical modeling difficult to teach. To successfully incorporate modeling activities I believe that curricular changes should be accompanied by professional development for curriculum developers, classroom teachers, and higher education professionals. This article serves as an introduction to modeling by …


Mathematical Reasoning: Writing And Proof, Ted Sundstrom Sep 2013

Mathematical Reasoning: Writing And Proof, Ted Sundstrom

Ted Sundstrom, Professor of Mathematics

Mathematical Reasoning: Writing and Proof is designed to be a text for the first course in the college mathematics curriculum that introduces students to the processes of constructing and writing proofs and focuses on the formal development of mathematics. The primary goals of the text are to help students: • Develop logical thinking skills and to develop the ability to think more abstractly in a proof oriented setting. • Develop the ability to construct and write mathematical proofs using standard methods of mathematical proof including direct proofs, proof by contradiction, mathematical induction, case analysis, and counterexamples. • Develop the ability …


A Clark-Ocone Type Formula Under Change Of Measure For Lévy Processes With L^2-Lévy Measure, Ryoichi Suzuki Sep 2013

A Clark-Ocone Type Formula Under Change Of Measure For Lévy Processes With L^2-Lévy Measure, Ryoichi Suzuki

Communications on Stochastic Analysis

No abstract provided.


Positive Harris Recurrence Of The Cir Process And Its Applications, Peng Jin, Vidyadhar Mandrekar, Barbara Rüdiger, Chiraz Trabelsi Sep 2013

Positive Harris Recurrence Of The Cir Process And Its Applications, Peng Jin, Vidyadhar Mandrekar, Barbara Rüdiger, Chiraz Trabelsi

Communications on Stochastic Analysis

No abstract provided.


Identities And Inequalities For Cdo Tranche Sensitivities, Claas Becker, Ambar N Sengupta Sep 2013

Identities And Inequalities For Cdo Tranche Sensitivities, Claas Becker, Ambar N Sengupta

Communications on Stochastic Analysis

No abstract provided.


Stein's Method For Brownian Approximations, L Coutin, L Decreusefond Sep 2013

Stein's Method For Brownian Approximations, L Coutin, L Decreusefond

Communications on Stochastic Analysis

No abstract provided.


The Generalized Sub-Fractional Brownian Motion, Aissa Sghir Sep 2013

The Generalized Sub-Fractional Brownian Motion, Aissa Sghir

Communications on Stochastic Analysis

No abstract provided.


A Bochner-Type Representation Of Positive Definite Mappings On The Dual Of A Compact Group, Herbert Heyer Sep 2013

A Bochner-Type Representation Of Positive Definite Mappings On The Dual Of A Compact Group, Herbert Heyer

Communications on Stochastic Analysis

No abstract provided.


Itô Formula And Girsanov Theorem For Anticipating Stochastic Integrals, Hui-Hsiung Kuo, Yun Peng, Benedykt Szozda Sep 2013

Itô Formula And Girsanov Theorem For Anticipating Stochastic Integrals, Hui-Hsiung Kuo, Yun Peng, Benedykt Szozda

Communications on Stochastic Analysis

No abstract provided.


On Optimal Proportional Reinsurance And Investment In A Partial Markovian Regime-Switching Economy, Xin Zhang Sep 2013

On Optimal Proportional Reinsurance And Investment In A Partial Markovian Regime-Switching Economy, Xin Zhang

Communications on Stochastic Analysis

No abstract provided.


A Bayesian Model For Cluster Detection, Jonathan Wakefield, Albert Y. Kim Sep 2013

A Bayesian Model For Cluster Detection, Jonathan Wakefield, Albert Y. Kim

Statistical and Data Sciences: Faculty Publications

The detection of areas in which the risk of a particular disease is significantly elevated, leading to an excess of cases, is an important enterprise in spatial epidemiology. Various frequentist approaches have been suggested for the detection of “clusters” within a hypothesis testing framework. Unfortunately, these suffer from a number of drawbacks including the difficulty in specifying a p-value threshold at which to call significance, the inherent multiplicity problem, and the possibility of multiple clusters. In this paper, we suggest a Bayesian approach to detecting “areas of clustering” in which the study region is partitioned into, possibly multiple, “zones” …


Examples Where The Conjunctive And Dempster’S Rules Are Insensitive, Florentin Smarandache, Jean Dezert, Valeri Kroumov Sep 2013

Examples Where The Conjunctive And Dempster’S Rules Are Insensitive, Florentin Smarandache, Jean Dezert, Valeri Kroumov

Branch Mathematics and Statistics Faculty and Staff Publications

In this paper we present several counter-examples to the Conjunctive rule and to Dempster rule of combinations in information fusion.


Elementary Teacher Candidates' Images Of Mathematics, Diverse Students, And Teaching: An Exploratory Study With Implications For Culturally Responsive Mathematics Education, Bernd Richard Ferner Aug 2013

Elementary Teacher Candidates' Images Of Mathematics, Diverse Students, And Teaching: An Exploratory Study With Implications For Culturally Responsive Mathematics Education, Bernd Richard Ferner

Dissertations and Theses

Children from many culturally diverse backgrounds do not achieve in mathematics at the same rates as their counterparts from the dominant White, European-American culture (Gay, 2010). This so-called achievement gap is an artifact of an educational system that continues to fail to provide equal learning opportunities to culturally diverse children (Ladson-Billings, 2006; Nieto & Bode, 2011). Teachers who employ culturally responsive teaching (Gay, 2010) may help to close this opportunity gap and hence, the achievement gap. This study investigated, "How do elementary teacher candidates perceive teaching mathematics in a multicultural environment"; Using a critical constructivism research paradigm, this qualitative instrumental …


Field Control Of The Surface Electroclinic Effect In Liquid Crystal Displays, Dana Hipolite Aug 2013

Field Control Of The Surface Electroclinic Effect In Liquid Crystal Displays, Dana Hipolite

Physics

Liquid crystals (LCs) are a fascinating class of materials exhibiting a range of phases intermediate between liquid and crystalline. Smectic LCs consist of elongated molecules arranged in a periodic stack (along z) of liquid like layers. In the smectic-A (Sm-A) phase, the average molecular long axis (director) points along z. In the smectic-C (Sm-C) phase, it is tilted relative to z, thus picking out a special direction within the layers. Typically, the Sm-A* to Sm- C* transition will occur as temperature is decreased. In chiral smectics (Sm-*A or Sm-C*) it is possible to induce director titling (i.e. the Sm-C* phase) …


Development And Application Of Difference And Fractional Calculus On Discrete Time Scales, Tanner J. Auch Aug 2013

Development And Application Of Difference And Fractional Calculus On Discrete Time Scales, Tanner J. Auch

Department of Mathematics: Dissertations, Theses, and Student Research

The purpose of this dissertation is to develop and apply results of both discrete calculus and discrete fractional calculus to further develop results on various discrete time scales. Two main goals of discrete and fractional discrete calculus are to extend results from traditional calculus and to unify results on the real line with those on a variety of subsets of the real line. Of particular interest is introducing and analyzing results related to a generalized fractional boundary value problem with Lidstone boundary conditions on a standard discrete domain N_a. We also introduce new results regarding exponential order for functions on …


A Math Therapy Exercise, Gary Stogsdill Jul 2013

A Math Therapy Exercise, Gary Stogsdill

Journal of Humanistic Mathematics

Math anxiety prevents many liberal arts undergraduates from appreciating mathematics and realizing their potential in math courses and math-related endeavors. The author describes his development and use of a "math therapy exercise" that enables students to move beyond the paralyzing grip of math anxiety and cultivate a more positive relationship with mathematics.