Deterministic And Stochastic Bellman's Optimality Principles On Isolated Time Domains And Their Applications In Finance, 2011 Western Kentucky University

#### Deterministic And Stochastic Bellman's Optimality Principles On Isolated Time Domains And Their Applications In Finance, Nezihe Turhan

*Masters Theses & Specialist Projects*

The concept of dynamic programming was originally used in late 1949, mostly during the 1950s, by Richard Bellman to describe decision making problems. By 1952, he refined this to the modern meaning, referring specifically to nesting smaller decision problems inside larger decisions. Also, the Bellman equation, one of the basic concepts in dynamic programming, is named after him. Dynamic programming has become an important argument which was used in various fields; such as, economics, finance, bioinformatics, aerospace, information theory, etc. Since Richard Bellman's invention of dynamic programming, economists and mathematicians have formulated and solved a huge variety of sequential ...

Development Of Fractional Trigonometry And An Application Of Fractional Calculus To Pharmacokinetic Model, 2011 Western Kentucky University

#### Development Of Fractional Trigonometry And An Application Of Fractional Calculus To Pharmacokinetic Model, Amera Almusharrf

*Masters Theses & Specialist Projects*

No abstract provided.

Discrete Geometric Homotopy Theory And Critical Values Of Metric Spaces, 2011 University of Tennessee, Knoxville

#### Discrete Geometric Homotopy Theory And Critical Values Of Metric Spaces, Leonard Duane Wilkins

*Doctoral Dissertations*

Building on the work of Conrad Plaut and Valera Berestovskii regarding uniform spaces and the covering spectrum of Christina Sormani and Guofang Wei developed for geodesic spaces, the author defines and develops discrete homotopy theory for metric spaces, which can be thought of as a discrete analog of classical path-homotopy and covering space theory. Given a metric space, X, this leads to the construction of a collection of covering spaces of X - and corresponding covering groups - parameterized by the positive real numbers, which we call the [epsilon]-covers and the [epsilon]-groups. These covers and groups evolve dynamically as the ...

Explicit Lp-Norm Estimates Of Infinitely Divisible Random Vectors In Hilbert Spaces With Applications, 2011 University of Tennessee, Knoxville

#### Explicit Lp-Norm Estimates Of Infinitely Divisible Random Vectors In Hilbert Spaces With Applications, Matthew D Turner

*Doctoral Dissertations*

I give explicit estimates of the Lp-norm of a mean zero infinitely divisible random vector taking values in a Hilbert space in terms of a certain mixture of the L2- and Lp-norms of the Levy measure. Using decoupling inequalities, the stochastic integral driven by an infinitely divisible random measure is defined. As a first application utilizing the Lp-norm estimates, computation of Ito Isomorphisms for different types of stochastic integrals are given. As a second application, I consider the discrete time signal-observation model in the presence of an alpha-stable noise environment. Formulation is given to compute the optimal linear estimate of ...

Solving Equations Applet Project, 2011 Utah State University

#### Solving Equations Applet Project, Kimberly Thatcher

*All Graduate Plan B and other Reports*

The purpose of this paper is to summarize a Masters Project for the MMath Degree. The purpose of the project was to create and evaluate an applet that maintains the advantages of the existent manipulatives (Hands-On Equations® and the NLVM applet) while also overcoming the limitations of each. Another product of this project is accompanying lesson plans for teachers.

Collecting, Analyzing And Interpreting Bivariate Data From Leaky Buckets: A Project-Based Learning Unit, 2011 Utah State University

#### Collecting, Analyzing And Interpreting Bivariate Data From Leaky Buckets: A Project-Based Learning Unit, Florence Funmilayo Obielodan

*All Graduate Plan B and other Reports*

Despite the significance and the emphasis placed on mathematics as a subject and field of study, achieving the right attitude to improve students‟ understanding and performance is still a challenge. Previous studies have shown that the problem cuts across nations around the world, both developing countries and developed alike. Teachers and educators of the subject have responsibilities to continuously develop innovative pedagogical approaches that will enhance students‟ interests and performance. Teaching approaches that emphasize real life applications of the subject have become imperative. It is believed that this will stimulate learners‟ interest in the subject as they will be able ...

Ranking Score Vectors Of Tournaments, 2011 Utah State University

#### Ranking Score Vectors Of Tournaments, Sebrina Ruth Cropper

*All Graduate Plan B and other Reports*

Given , a tournament on vertices, Landau derived a method to determine how close is to being transitive or regular. This comparison is based on the tournament’s hierarchy number, ̅, a value derived from its score vector ̅ ( ). Let be the set of all score vectors of tournaments on vertices with the entries listed in non-decreasing order. A partial order, poset, exists on the set using the following binary relation. Given ̅ ̅ such that ̅ ̅, let ̅ ̅ if Σ Σ for and Σ Σ . Let this poset be represented as ( ) ( ) where {( ̅ ̅) ̅ ̅}. The value ̅ can also be used to define a partial order on the set ...

Some Dense Subsets Of Real Numbers And Their Applications, 2011 Illinois Wesleyan University

#### Some Dense Subsets Of Real Numbers And Their Applications, Tian-Xiao He, Peter Shiue, Xiaoya Zha

*Tian-Xiao He*

We give a collection of subsets which are dense in the set of real numbers. Several applications of the dense sets are also presented.

Characterizations Of Orthogonal Generalized Gegenbauer-Humbert Polynomials And Orthogonal Sheffer-Type Polynomials, 2011 Illinois Wesleyan University

#### Characterizations Of Orthogonal Generalized Gegenbauer-Humbert Polynomials And Orthogonal Sheffer-Type Polynomials, Tian-Xiao He

*Tian-Xiao He*

We present characterizations of the orthogonal generalized Gegen-bauer-Humbert polynomial sequences and the orthogonal Sheffer-type polynomial sequences. Using a new polynomial sequence transformation technique presented in [12], we give a method to evaluate the measures and their supports of some orthogonal generalized Gegenbauer-Humbert polynomial sequences.

Sequences Of Non-Gegenbauer-Humbert Polynomials Meet The Generalized Gegenbauer-Humbert Polynomials, 2011 Illinois Wesleyan University

#### Sequences Of Non-Gegenbauer-Humbert Polynomials Meet The Generalized Gegenbauer-Humbert Polynomials, Tian-Xiao He, Peter Shiue

*Tian-Xiao He*

Here,we present a connection between a sequence of polynomials generated by a linear recurrence relation of order 2 and sequences of the generalized Gegenbauer Humbert polynomials. Many new and known transfer formulas between non-Gegenbauer-Humbert polynomials and generalized Gegenbauer-Humbert polynomials are given. The applications of the relationship to the construction of identities of polynomial sequences defined by linear recurrence relations are also discussed.

Symmetry Breaking, Coupling Management, And Localized Modes In Dual-Core Discrete Nonlinear-Schrödinger Lattices, 2011 UMASS, Amherst

#### Symmetry Breaking, Coupling Management, And Localized Modes In Dual-Core Discrete Nonlinear-Schrödinger Lattices, H. Susanto, Panos Kevrekidis, F. Kh. Abdullaev, Boris A. Malomed

*Panos Kevrekidis*

We introduce a system of two linearly coupled discrete nonlinear Schr\"{o}dinger equations (DNLSEs), with the coupling constant subject to a rapid temporal modulation. The model can be realized in bimodal Bose-Einstein condensates (BEC). Using an averaging procedure based on the multiscale method, we derive a system of averaged (autonomous) equations, which take the form of coupled DNLSEs with additional nonlinear coupling terms of the four-wave-mixing type. We identify stability regions for fundamental onsite discrete symmetric solitons (single-site modes with equal norms in both components), as well as for two-site in-phase and twisted modes, the in-phase ones being completely ...

“Drawing” Upon Your Students’ Creativity: Teaching (Your Subject Here) With Comic Books, 2011 Western Kentucky University

#### “Drawing” Upon Your Students’ Creativity: Teaching (Your Subject Here) With Comic Books, Bruce Kessler

*Mathematics Faculty Publications*

During Spring 2009, Dr. Kessler created and published a comic book series that embedded math content into the story for 4th-6th grade students. The comics were well received in the classrooms at Cumberland Trace Elementary. Dr. Kessler contends that this approach to teaching and learning can be used in any content area, and is useful for engaging students who might not be as interested otherwise. This session will explore ways of utilizing the skills of your students to construct learning comics in your classes, regardless of the funds, technology, and artistic experience at your disposal. The session will include a ...

“Drawing” Upon Your Students’ Creativity: Teaching (Your Subject Here) With Comic Books, 2011 Western Kentucky University

#### “Drawing” Upon Your Students’ Creativity: Teaching (Your Subject Here) With Comic Books, Bruce Kessler

*Bruce Kessler*

During Spring 2009, Dr. Kessler created and published a comic book series that embedded math content into the story for 4th-6th grade students. The comics were well received in the classrooms at Cumberland Trace Elementary. Dr. Kessler contends that this approach to teaching and learning can be used in any content area, and is useful for engaging students who might not be as interested otherwise. This session will explore ways of utilizing the skills of your students to construct learning comics in your classes, regardless of the funds, technology, and artistic experience at your disposal. The session will include a ...

2011 Sonia Kovalevsky Math For Girls Day Flyer, 2011 Lincoln University

#### 2011 Sonia Kovalevsky Math For Girls Day Flyer, Association For Women In Mathematics, Lincoln University Of Missouri, Donna L. Stallings

*Math for Girls Day Documents*

6th Annual Lincoln University Sonia Kovalevsky Math for Girls Day program flyer on April 29, 2011.

2011 Sonia Kovalevsky Math For Girls Day Evaluation Forms, 2011 Lincoln University

#### 2011 Sonia Kovalevsky Math For Girls Day Evaluation Forms, Association For Women In Mathematics, Lincoln University Of Missouri, Donna L. Stallings

*Math for Girls Day Documents*

Presenter, student and teacher evaluation forms for the 6th Annual Lincoln University Sonia Kovalevsky Math for Girls Day program flyer on April 29, 2011.

Quasidiscrete Microwave Solitons In A Split-Ring-Resonator-Based Left-Handed Coplanar Waveguide, 2011 UMass, Amherst

#### Quasidiscrete Microwave Solitons In A Split-Ring-Resonator-Based Left-Handed Coplanar Waveguide, G. P. Veldes, J. Cuevas, Panos Kevrekidis, D. J. Frantzeskakis

*Panos Kevrekidis*

We study the propagation of quasidiscrete microwave solitons in a nonlinear left-handed coplanar waveguide coupled with split-ring resonators. By considering the relevant transmission line analog, we derive a nonlinear lattice model which is studied analytically by means of a quasidiscrete approximation. We derive a nonlinear Schrödinger equation, and find that the system supports bright envelope soliton solutions in a relatively wide subinterval of the left-handed frequency band. We perform systematic numerical simulations, in the framework of the nonlinear lattice model, to study the propagation properties of the quasidiscrete microwave solitons. Our numerical findings are in good agreement with the analytical ...

Estimation Of Hazard Function For Right Truncated Data, 2011 Georgia State University

#### Estimation Of Hazard Function For Right Truncated Data, Yong Jiang

*Mathematics Theses*

This thesis centers on nonparametric inferences of the cumulative hazard function of a right truncated variable. We present three variance estimators for the Nelson-Aalen estimator of the cumulative hazard function and conduct a simulation study to investigate their performances. A close match between the sampling standard deviation and the estimated standard error is observed when an estimated survival probability is not close to 1. However, the problem of poor tail performance exists due to the limitation of the proposed variance estimators. We further analyze an AIDS blood transfusion sample for which the disease latent time is right truncated. We compute ...

A Review Of Cross Validation And Adaptive Model Selection, 2011 Georgia State University

#### A Review Of Cross Validation And Adaptive Model Selection, Ali R. Syed

*Mathematics Theses*

We perform a review of model selection procedures, in particular various cross validation procedures and adaptive model selection. We cover important results for these procedures and explore the connections between different procedures and information criteria.

A New Jackknife Empirical Likelihood Method For U-Statistics, 2011 Georgia State University

#### A New Jackknife Empirical Likelihood Method For U-Statistics, Zhengbo Ma

*Mathematics Theses*

U-statistics generalizes the concept of mean of independent identically distributed (i.i.d.) random variables and is widely utilized in many estimating and testing problems. The standard empirical likelihood (EL) for U-statistics is computationally expensive because of its onlinear constraint. The jackknife empirical likelihood method largely relieves computation burden by circumventing the construction of the nonlinear constraint. In this thesis, we adopt a new jackknife empirical likelihood method to make inference for the general volume under the ROC surface (VUS), which is one typical kind of U-statistics. Monte Carlo simulations are conducted to show that the EL confidence intervals perform ...

Computing, Symbols And Math, 2011 The University of Western Ontario

#### Computing, Symbols And Math, Stephen M. Watt

*Computer Science Presentations*

No abstract provided.