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Counting Conjugates Of Colored Compositions, Jesus Omar Sistos Barron
Counting Conjugates Of Colored Compositions, Jesus Omar Sistos Barron
Honors College Theses
The properties of n-color compositions have been studied parallel to those of regular compositions. The conjugate of a composition as defined by MacMahon, however, does not translate well to n-color compositions, and there is currently no established analogous concept. We propose a conjugation rule for cyclic n-color compositions. We also count the number of self-conjugates under these rules and establish a couple of connections between these and regular compositions.
Zeckendorf Representation Analysis On Third Order Fibonacci Sequences That Do Not Satisfy The Uniqueness Property, Samuel A. Aguilar
Zeckendorf Representation Analysis On Third Order Fibonacci Sequences That Do Not Satisfy The Uniqueness Property, Samuel A. Aguilar
Honors College Theses
Zeckendorf's Theorem states that every natural number can be expressed uniquely as the sum of distinct non-consecutive terms of the shifted Fibonacci sequence (i.e. 1, 2, 3, 5, ...). This theorem has motivated the study of representation of integers by the sum of non-adjacent terms of Nth order Fibonacci sequences, including the characterization of the uniqueness of Zeckendorf representation based on the initial terms of the sequence. Moreover, when this uniqueness property is satisfied for third order Fibonacci sequences, the ratio of integers less than a given number X that have a Zeckendorf representation has been estimated by Dr. Sungkon …
Teacher Influence On Elementary School Students’ Participation In Science, Technology, Engineering, And Mathematics, Courtney Hartman
Teacher Influence On Elementary School Students’ Participation In Science, Technology, Engineering, And Mathematics, Courtney Hartman
Honors College Theses
The purpose of this study is to explore the influence of elementary school teachers on encouraging students’ interest and participation in Science, Technology, Engineering, and Mathematics. The researcher sought to understand what methods teachers use in their classrooms to encourage students to participate in STEM subjects and programs. This mixed methods study consisted of a questionnaire to collect quantitative data, as well as an interview of selected teachers who participated in the questionnaire to collect qualitative data. The data was analyzed to determine the overall perceptions of teachers regarding the importance of encouraging students to participate in STEM. The qualitative …
Numerical Solutions To The Gross-Pitaevskii Equation For Bose-Einstein Condensates, Luigi Galati
Numerical Solutions To The Gross-Pitaevskii Equation For Bose-Einstein Condensates, Luigi Galati
Electronic Theses and Dissertations
In this thesis we compare various potential operators for the two-dimensional (2D) Gross-Pitaevskii equation (GPE) for Bose-Einstein condensates. Both the 2D and the 1D models are scaled to get a three parameter model. Smoothness of initial conditions is considered and choice of method (Split-Step Fourier method with Strang Splitting) is justied. Numerical simulations provide graphical evidence of properties of both focusing and nonfocusing cases.
Integer Compositions, Gray Code, And The Fibonacci Sequence, Linus Lindroos
Integer Compositions, Gray Code, And The Fibonacci Sequence, Linus Lindroos
Electronic Theses and Dissertations
In this thesis I show the relation of binary and Gray Code to integer compositions and the Fibonacci sequence through the use of analytic combinatorics, Zeckendorf's Theorem, and generating functions.