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Now showing items 1-10 of 18

#### A Quadratic Fredholm Integral Equation and its Solution for Various Kernels

(University of Texas at Arlington, 1999-02)

Consider the Fredholm integral equation [see pdf for notation], a parameter.
The solution of this equation is discussed for separable, difference and distribution kernels. Existence, uniqueness and bifurcation questions ...

#### Geometry of Post's Correspondence Problem

(University of Texas at Arlington, 1997)

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 one-symbol alphabet. We also use orthogonality to discover ...

#### A Quadratic Volterra Integral Equation and Its Solution for Various Kernels

(University of Texas at Arlington, 1997)

Consider the Volterra integral equation [see pdf for notation], ^ is a parameter Solutions of this equation are discussed for separable and difference kernels using Laplace transform and differential equation techniques. ...

#### Snell's Law in Normed Linear Planes

(University of Texas at Arlington, 1997)

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 refraction with two different norms is given. The case ...

#### A Geometric Inequality in Pharmacokinetics

(University of Texas at Arlington, 2006-02)

The arithmetic-geometric mean inequality is used to give a lower bound for the average concentration in a two-compartmental model in pharmacokinetics. A geometric interpretation is given to relate concentration to the area ...

#### Geometrical Problems in Engineering Mechanics

(University of Texas at Arlington, 2005-11)

Four problems in two dimensional geometry are presented, which are applicable to education of the basic courses, statics. These problems represent geometrical concepts that are understandable by engineering students. For ...

#### The Laplace Transform of the Linear Car-following Model

(University of Texas at Arlington, 2008)

Laplace transform is used to analyze the differential-difference equation for the linear car-following model. The car-following model has been developed to describe the dynamics of a platoon of vehicles initially traveling ...

#### Restricted Curvature in the Minkowski Plane

(University of Texas at Arlington, 2008)

A geometric proof for the following problem is given: Let E be the unit circle in a Minkowski plane. Let C be any continuously differentiable closed curve with length l(C)(measured in Minkowski metric). Assume [see pdf for ...

#### 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 ...

#### The Reflection Property in Normed Linear Planes with Applications to Generalized Conics

(University of Texas at Arlington, 2005-07)

The ancient Greek mathematician Heron was the first to solve the problem of finding the shortest path from point A to point B on one side of the line L, subject to the condition that the path goes from A to L and then to ...