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Full-Text Articles in Mathematics

Helping At-Risk Students Add Up: Motivational Lessons For Students In High School Mathematics, Karen Beckner Dec 2001

Helping At-Risk Students Add Up: Motivational Lessons For Students In High School Mathematics, Karen Beckner

Mahurin Honors College Capstone Experience/Thesis Projects

No abstract provided.


A Construction Of Compactly-Supported Biorthogonal Scaling Vectors And Multiwavelets On $R^2$, Bruce Kessler Jul 2001

A Construction Of Compactly-Supported Biorthogonal Scaling Vectors And Multiwavelets On $R^2$, Bruce Kessler

Mathematics Faculty Publications

In \cite{K}, a construction was given for a class of orthogonal compactly-supported scaling vectors on $\R^{2}$, called short scaling vectors, and their associated multiwavelets. The span of the translates of the scaling functions along a triangular lattice includes continuous piecewise linear functions on the lattice, although the scaling functions are fractal interpolation functions and possibly nondifferentiable. In this paper, a similar construction will be used to create biorthogonal scaling vectors and their associated multiwavelets. The additional freedom will allow for one of the dual spaces to consist entirely of the continuous piecewise linear functions on a uniform subdivision of the …


Elgenvalues Of Fibonacci-Like Sequences, Elyssa Hurst May 2001

Elgenvalues Of Fibonacci-Like Sequences, Elyssa Hurst

Masters Theses & Specialist Projects

The familiar Fibonacci sequence 1,1,2,3,5,8,13,... can be described by the recurrence relation x(0) = 1, x(1) = 1, x(n) = x(n-1) + x(n-2). For this relation, as n → oo, x(n+1) → 1 +√5 x(n) 2 ' which is the familiar golden ratio. This value is also the dominant eigenvalue of the above recurrence relation. In this series, we consider the dominant eigenvalue of some Fibonacci-like sequence of the form x(n) = ∑n-1/k+1 ak Zk (n-k) where the Zk's are independent random variables with Zk = {+1 with probability p - 1 with probability q, with p + q = …


Power Series Solutions To Ordinary Differential Equations, John Lagrange May 2001

Power Series Solutions To Ordinary Differential Equations, John Lagrange

Masters Theses & Specialist Projects

In this thesis, the reader will be made aware of methods for finding power series solutions to ordinary differential equations. In the case that a solution to a differential equation may not be expressed in terms of elementary functions, it is practical to obtain a solution in the form of an infinite series, since many differential equations which yield such a solution model an actual physical situation. In this thesis, we introduce conditions that guarantee existence and uniqueness of analytic solutions, both in the linear and nonlinear case. Several methods for obtaining analytic solutions are introduced as well. For the …