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A Quadratic Volterra Integral Equation and Its Solution for Various Kernels
(University of Texas at Arlington, 1997)
**Please note that the full text is embargoed** ABSTRACT: Consider the Volterra integral equation [see pdf for notation], ^ is a parameter Solutions of this equation are discussed for separable and difference kernels using ...
Ray Optics on Surfaces
(University of Texas at Arlington, 1997)
**Please note that the full text is embargoed** ABSTRACT: Variational techniques are used to find path of light rays on surfaces. Using Fermat's principle of least time the problem is treated as a constraint optimization ...
Controlling Curvature in the Minkowski Plane
(University of Texas at Arlington, 1997)
**Please note that the full text is embargoed** ABSTRACT: Pontryagin's maximum principle is used to find the curve of shortest length with bounded Minkowskian curvature passing through two points with given initial and ...
Snell's Law in Normed Linear Planes
(University of Texas at Arlington, 1997)
**Please note that the full text is embargoed** ABSTRACT: The method of Lagrange multipliers is used to find a reflection principle in a real normed linear plane with smooth unit circle. A generalization of Snell's law of ...
Geometry of Post's Correspondence Problem
(University of Texas at Arlington, 1997)
**Please note that the full text is embargoed** ABSTRACT: Orthogonality of vectors with integer coordinates in an n-dimensional Euclidean space is used to show that Post's correspondence problem is solvable for words over ...
A Quadratic Fredholm Integral Equation and its Solution for Various Kernels
(University of Texas at Arlington, 1999-02)
**Please note that the full text is embargoed** ABSTRACT:Consider the Fredholm integral equation [see pdf for notation], a parameter.
The solution of this equation is discussed for separable, difference and distribution ...
Heron's Problem in the Minkowski Plane
(University of Texas at Arlington, 1995)
**Please note that the full text is embargoed** ABSTRACT: Heron's problem in the Euclidean plane is that of minimizing the length of a path
that joins two points on one side of a line and intersects the line. A ...
Self-Circumference of Rotors
(University of Texas at Arlington, 1996)
**Please note that the full text is embargoed** ABSTRACT: The law of cosines from trigonometry is used to obtain elliptic integrals of the second kind to calculate the "self-circumference" of a Reuleaux triangle and the ...
Minimum Path Problems in Normed Spaces, Reflection and Refraction
(University of Texas at Arlington, 1996)
**Please note that the full text is embargoed** ABSTRACT: The main minimum (or extremum) path problem in this paper deals with the "law of refraction" at a curve separating the plane into two parts with different norms. ...
Tennis, Geometric Progression, Probability and Basketball
(University of Texas at Arlington, 1999-03)
The following problem about a tennis match is well—known. See Halmos [1, 2]. Consider 2n tennis players playing a single elimination match. Ask the question: what are the number of games played? The answer can be obtained ...