Set: The Probabilities And Possibilities,
2011
University of Lynchburg
Set: The Probabilities And Possibilities, Tabitha K. Bollinger
Undergraduate Theses and Capstone Projects
The card game SET involves finding groups o f three cards called SETs. Choices are based upon the individual card characteristics, including shape, pattern, number, and color. Previously, the maximum number o f cards that can be played without creating a SET has been determined as 20 cards by extensive computer work. This report further explored the probabilities and possibilities o f the game. Using discrete mathematics and probability, we explored how many SETs are possible and what strategies led to the most points. Additionally, this project exercised undergraduate logic and reasoning to generalize the results in order to be …
Operator Splitting Method And Applications For Semilinear Parabolic Partial Differential Equations,
2011
George Fox University
Operator Splitting Method And Applications For Semilinear Parabolic Partial Differential Equations, R. Corban Harwood
Faculty Publications - Department of Mathematics
This dissertation presents a redefined operator splitting method used in solving semilinear parabolic partial differential equations. As one such form, the reaction-diffusion equation is highly prevalent in mathematical modeling. Besides being physically meaningful as a separation of two distinct physical processes in this equation, operator splitting simplifies the solution method in several ways. The super-linear speed-up of computations is a rewarding simplification as it presents great benefits for large-scale systems. In solving these semilinear equations, we will develop a condition for oscillation-free methods, a condition independent of the usual stability condition. This numerical consideration is important to fully embody our …
Strategic Treatment Interruptions During Imatinib Treatment Of Chronic Myelogenous Leukemia,
2011
California Polytechnic State University - San Luis Obispo
Strategic Treatment Interruptions During Imatinib Treatment Of Chronic Myelogenous Leukemia, Dana C. Paquin, Peter S. Kim, Peter P. Lee, Doron Levy
Mathematics
Although imatinib is an effective treatment for chronic myelogenous leukemia (CML), and nearly all patients treated with imatinib attain some form of remission, imatinib does not completely eliminate leukemia. Moreover, if the imatinib treatment is stopped, most patients eventually relapse (Cortes et al. in Clin. Cancer Res. 11:3425–3432, 2005). In Kim et al. (PLoS Comput. Biol. 4(6):e1000095, 2008), the authors presented a mathematical model for the dynamics of CML under imatinib treatment that incorporates the anti-leukemia immune response. We use the mathematical model in Kim et al. (PLoS Comput. Biol. 4(6):e1000095, 2008) to study and numerically simulate strategic treatment interruptions …
Continuous Blooming Of Convex Polyhedra,
2011
Massachusetts Institute of Technology
Continuous Blooming Of Convex Polyhedra, Erik D. Demaine, Martin L. Demaine, Vi Hart, Joan Iacono, Stefan Langerman, Joseph O'Rourke
Computer Science: Faculty Publications
We construct the first two continuous bloomings of all convex polyhedra. First, the source unfolding can be continuously bloomed. Second, any unfolding of a convex polyhedron can be refined (further cut, by a linear number of cuts) to have a continuous blooming.
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
Scholarship
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.
Hermite Polynomials And Sylvester Type Determinants,
2011
University at Albany, State University of New York
Hermite Polynomials And Sylvester Type Determinants, Kelly C. Stange
Mathematics and Statistics
In this paper, we first recall Hermite polynomials, a particular family of orthogonal polynomials. We then evaluate their recurrence relations in terms of Sylvester type determinants of certain tridiagnoal matrix.
Algebraic Solutions To Overdefined Systems With Applications To Cryptanalysis,
2011
Rose-Hulman Institute of Technology
Algebraic Solutions To Overdefined Systems With Applications To Cryptanalysis, Eric Crockett
Mathematical Sciences Technical Reports (MSTR)
Cryptographic algorithms are based on a wide variety of difficult problems in mathematics. One of these problems is finding a solution to a system of multivariate quadratic equations (MQ). A generalization of this problem is to find a solution to a system of higher order non-linear equations. Both of these problems are NP-hard over any field. Many cryptosystems such as AES, Serpent, Toyocrypt, and others can be reduced to some form of the MQ problem. In this paper we analyze the relinearization and XL algorithms for solving overdetermined systems of non-linear equations, as well as two variations of the XL …
A Range And Existence Theorem For Pseudomonotone Perturbations Of Maximal Monotone Operators,
2011
Missouri University of Science and Technology
A Range And Existence Theorem For Pseudomonotone Perturbations Of Maximal Monotone Operators, Vy Khoi Le
Mathematics and Statistics Faculty Research & Creative Works
In this paper, we prove a range and existence theorem for multivalued pseudomonotone perturbations of maximal monotone operators. We assume a general coercivity condition on the sum of a maximal monotone and a pseudomonotone operator instead of a condition on the pseudomonotone operator only. An illustrative example of a variational inequality in a Sobolev space with variable exponent is given.
Bias In Monte Carlo Simulations Due To Pseudo-Random Number Generator Initial Seed Selection,
2011
Beaumont Health System
Bias In Monte Carlo Simulations Due To Pseudo-Random Number Generator Initial Seed Selection, Jack C. Hill, Shlomo S. Sawilowsky
Theoretical and Behavioral Foundations of Education Faculty Publications
Pseudo-random number generators can bias Monte Carlo simulations of the standard normal probability distribution function with initial seeds selection. Five generator designs were initial-seeded with values from 10000HEX to 1FFFFHEX, estimates of the mean were calculated for each seed, the distribution of mean estimates was determined for each generator and simulation histories were graphed for selected seeds.
Rated Extremal Principles For Finite And Infinite Systems,
2011
Wayne State University
Rated Extremal Principles For Finite And Infinite Systems, Hung M. Phan, Boris S. Mordukhovich
Mathematics Research Reports
In this paper we introduce new notions of local extremality for finite and infinite systems of closed sets and establish the corresponding extremal principles for them called here rated extremal principles. These developments are in the core geometric theory of variational analysis. We present their applications to calculus and optimality conditions for problems with infinitely many constraints.
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 unstable. The …
A Multiple Regression Analysis Of Personality’S Impact On Actuarial Exam Performance,
2011
Bryant University
A Multiple Regression Analysis Of Personality’S Impact On Actuarial Exam Performance, Matthew Ciaffone
Honors Projects in Mathematics
Existing literature indicates that there is some connection between personality and both academic and work-related performance. The author's intent for the research described herein is to explore this connection for students majoring in actuarial mathematics with regard to their performance on actuarial certification exams. Specifically, using the five-factor model of personality, the author seeks to predict the number of attempts required to pass the first two exams in the process (Exam 1/P - probability; Exam 2/FM - financial mathematics) using measures of the five dimensions of the five-factor model (openness to experience, conscientiousness, extraversion, agreeableness, and emotional stability) through regression …
Factors Related To Math Performance And Potential Benefits Of One-On-One Instruction,
2011
Bryant University
Factors Related To Math Performance And Potential Benefits Of One-On-One Instruction, Amanda Zagame
Honors Projects in Mathematics
This fall 2010 study of Bryant University students enrolled in freshman-level math courses considered factors related to college-level math performance, including gender, math self-efficacy, math anxiety, and utilization of professors’ office hours and/or tutoring center services. Female students at Bryant reported lower levels of math self-efficacy and higher levels of math anxiety, both of which research has shown to be negatively correlated with test scores. The use of one-on-one instruction was expected to provide a potential counterweight to this equation. Results from the 287 initial and 229 final surveys administered in this study did not support this hypothesis. This phenomenon …
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, Spring 1920 to Spring 2023
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 …
Solving Equations Applet Project,
2011
Utah State University
Solving Equations Applet Project, Kimberly Thatcher
All Graduate Plan B and other Reports, Spring 1920 to Spring 2023
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.
Mathematical Justification Of Introductory Hypothesis Tests And Development Of Reference Materials,
2011
Utah State University
Mathematical Justification Of Introductory Hypothesis Tests And Development Of Reference Materials, Jennifer L. Loveland
All Graduate Plan B and other Reports, Spring 1920 to Spring 2023
This purpose of this project was to create a set of reference material for an introductory level statistics course. The focus was on the Neyman-Pearson approach to hypothesis testing. A brief historical development of the Neyman-Pearson approach is followed by mathematical proofs of each of the hypothesis tests covered in the reference material. The reference material includes the basic hypothesis tests taught in an introductory statistics course, the accompanying distributions, and prerequisite information.
Estimation Of Beta In A Simple Functional Capital Asset Pricing Model For High Frequency Us Stock Data,
2011
Utah State University
Estimation Of Beta In A Simple Functional Capital Asset Pricing Model For High Frequency Us Stock Data, Yan Zhang
All Graduate Plan B and other Reports, Spring 1920 to Spring 2023
This project applies the methods of functional data analysis (FDA) to intra-daily returns of US corporations. It focuses on an extension of the Capital Asset Pricing Model (CAPM) to such returns. The CAPM is essentially a linear regression with the slope coefficient β. Returns of an asset are regressed on index return. We compare the estimates of β obtained for the daily and intra-daily returns. The variability of these estimates is assessed by two bootstrap methods. All computations are performed using statistical software R. Customized functions are developed to process the raw data, estimate the parameters and assess their variability. …
Ranking Score Vectors Of Tournaments,
2011
Utah State University
Ranking Score Vectors Of Tournaments, Sebrina Ruth Cropper
All Graduate Plan B and other Reports, Spring 1920 to Spring 2023
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 ( ) ( ) …
The Minimum-Norm Least-Squares Solution Of A Linear System And Symmetric Rank-One Updates,
2011
Fitchburg State University
The Minimum-Norm Least-Squares Solution Of A Linear System And Symmetric Rank-One Updates, Xuzhou Chen, Jun Ji
Faculty and Research Publications
In this paper, we study the Moore-Penrose inverse of a symmetric rank-one perturbed matrix from which a finite method is proposed for the minimum-norm least-squares solution to the system of linear equations Ax = b. This method is guaranteed to produce the required result.
Finding The Beat In Music: Using Adaptive Oscillators,
2011
Harvey Mudd College
Finding The Beat In Music: Using Adaptive Oscillators, Kate M. Burgers
HMC Senior Theses
The task of finding the beat in music is simple for most people, but surprisingly difficult to replicate in a robot. Progress in this problem has been made using various preprocessing techniques (Hitz 2008; Tomic and Janata 2008). However, a real-time method is not yet available. Methods using a class of oscillators called relay relaxation oscillators are promising. In particular, systems of forced Hopf oscillators (Large 2000; Righetti et al. 2006) have been used with relative success. This work describes current methods of beat tracking and develops a new method that incorporates the best ideas from each existing method and …
