Browsing Department of Mathematics by Author "Ghandehari, Mostafa"

Now showing items 1-18 of 18

    • Controlling Curvature in the Minkowski Plane 

      Ghandehari, Mostafa (University of Texas at ArlingtonDepartment of Mathematics, 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 ...

    • A Geometric Inequality for Convex Polygons 

      Ghandehari, Mostafa (University of Texas at ArlingtonDepartment of Mathematics, 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 = ...

    • A Geometric Inequality in Pharmacokinetics 

      Holyk, Jennifer; Ghandehari, Mostafa (University of Texas at ArlingtonDepartment of Mathematics, 2006-02)
      **Please note that the full text is embargoed** ABSTRACT: 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 ...

    • Geometrical Problems in Engineering Mechanics 

      Kashefi, Feraydune; Ghandehari, Mostafa (University of Texas at ArlingtonDepartment of Mathematics, 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 ...

    • Geometry of Post's Correspondence Problem 

      Ghandehari, Mostafa (University of Texas at ArlingtonDepartment of Mathematics, 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 ...

    • Heron's Problem in the Minkowski Plane 

      Ghandehari, Mostafa (University of Texas at ArlingtonDepartment of Mathematics, 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 ...

    • The Laplace Transform of the Linear Car-following Model 

      Ardekani, Siamak; Ghandehari, Mostafa (University of Texas at ArlingtonDepartment of Mathematics, 2008)
      **Please note that the full text is embargoed** ABSTRACT: 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 ...

    • Minimum Path Problems in Normed Spaces, Reflection and Refraction 

      Golomb, Michael; Ghandehari, Mostafa (University of Texas at ArlingtonDepartment of Mathematics, 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. ...

    • Minkowski's Inequality for Convex Curves 

      Ghandehari, Mostafa (University of Texas at Arlingtonhttp://hdl.handle.net/10106/2458, 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 ...

    • A Modified Greenberg Speed-flow Traffic Model 

      Ardekani, Siamak; Ghandehari, Mostafa (University of Texas at ArlingtonDepartment of Mathematics, 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. ...

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

      Nestell, Merlynd K.; Ghandehari, Mostafa (University of Texas at ArlingtonDepartment of Mathematics, 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 ...

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

      Nestell, Merlynd K.; Ghandehari, Mostafa (University of Texas at ArlingtonDepartment of Mathematics, 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 

      Ghandehari, Mostafa (University of Texas at ArlingtonDepartment of Mathematics, 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 ...

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

      O'Neill, Edward J.; Ghandehari, Mostafa (University of Texas at ArlingtonDepartment of Mathematics, 2005-07)
      **Please note that the full text is embargoed** ABSTRACT: 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 ...

    • Restricted Curvature in the Minkowski Plane 

      Ghandehari, Mostafa (University of Texas at ArlingtonDepartment of Mathematics, 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 ...

    • Self-Circumference of Rotors 

      O'Neill, Edward J.; Ghandehari, Mostafa (University of Texas at ArlingtonDepartment of Mathematics, 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 ...

    • Snell's Law in Normed Linear Planes 

      Ghandehari, Mostafa (University of Texas at ArlingtonDepartment of Mathematics, 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 ...

    • Tennis, Geometric Progression, Probability and Basketball 

      Ghandehari, Mostafa (University of Texas at ArlingtonDepartment of Mathematics, 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 ...