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Now showing items 1-10 of 18
A Geometric Inequality for Convex Polygons
(University of Texas at Arlington, 2001-05)
**Please note that the full text is embargoed** ABSTRACT: Consider a regular polygon with vertices P1, P2, , Pn. Assume P
is an interior point. Let [see pdf for notation] denote the Euclidean distance from P to Pi, i = ...
Minkowski's Inequality for Convex Curves
(University of Texas at Arlington, 2001-05)
**Please note that the full text is embargoed** ABSTRACT: 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 ...
Geometrical Problems in Engineering Mechanics
(University of Texas at Arlington, 2005-11)
**Please note that the full text is embargoed** ABSTRACT: Four problems in two dimensional geometry are presented, which are applicable to education of the basic courses, statics. These problems represent geometrical ...
Restricted Curvature in the Minkowski Plane
(University of Texas at Arlington, 2008)
**Please note that the full text is embargoed** ABSTRACT: 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 ...
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 ...
A Modified Greenberg Speed-flow Traffic Model
(University of Texas at Arlington, 2008)
**Please note that the full text is embargoed** ABSTRACT: 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. ...
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 ...