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Now showing items 1-10 of 18

#### A Modified Greenberg Speed-flow Traffic Model

(University of Texas at Arlington, 2008)

A modified Greenberg speed-flow model is proposed. We assume speed is a logarithmic function of free-flow speed, concentration and a minimum constant density. Optimization techniques are used to maximize the flow. Taylor's ...

#### Minkowski's Inequality for Convex Curves

(University of Texas at Arlington, 2001-05)

Minkowski's inequality is a relation between mixed areas of two curves and their respective areas. The concept of mixed area is defined. A variational technique is used to give a proof of Minkowski's inequality. As a special ...

#### 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 ...

#### Heron's Problem in the Minkowski Plane

(University of Texas at Arlington, 1995)

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 generalization
in the Minkowski plane is given and used to discuss ...

#### 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 ...

#### 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. ...

#### Controlling Curvature in the Minkowski Plane

(University of Texas at Arlington, 1997)

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 terminal tangents.

#### 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 ...

#### 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 ...