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Exact solution of some new planar polygon models. Plus aspects of a ”new” SAW model
planar polygon models new SAW model
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2015/3/19
Exact solution of some new planar polygon models. Plus aspects of a ”new” SAW model.
Finding the Maximum Area Parallelogram in a Convex Polygon
Maximum Area Parallelogram Convex Polygon
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2012/12/3
We consider the problem of finding the maximum area parallelogram (MAP) inside a given convex polygon. Our main result is an algorithm for computing the MAP
in an n-sided polygon in O(n2) time. Achie...
On the polygonal diameter of the interior, resp. exterior, of a simple closed polygon in the plane
Jordan-Brouwer theorem Jordan exterior (interior) Jordan’s curve theorem
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2011/2/21
We give a tight upper bound on the polygonal diameter of the interior, resp. exterior, of a simple n-gon, n ≥ 3, in the plane as a function of n, and describe an n-gon (n ≥ 3) for which both upper bou...
Behavior of the singular solutions of the problem governed by the adjunct of the Laplace operator affected by a weight function near the tops of plane polygon
Singularity Polygon function
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2010/9/21
In this work, we study the behavior of the singular solutions of the problem governed by the adjunct of the laplacian operator affected by a weight function in a polygon. First, the study will be done...
On an elliptic boundary problem governed by a Laplacian operator perturbed by a spectral parameter and affected by a weight function in a plane polygon
Spectral prameter Polygon
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2010/9/21
In this work, we study the problem governed by the laplacian operator perturbed by a spectral parameter and affected by a weight function in a polygon. First, the study will be done in a plane sector....
We study the Casimir energy of a scalar field for a regular polygon with N sides.
Casimir energy scalar field regular polygon
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2011/2/25
We study the Casimir energy of a scalar field for a regular polygon with N sides.The scalar field obeys Dirichlet boundary conditions at the perimeter of the polygon.
Looking for a Billiard Table which is not a Lattice Polygon but Satisfies Veech's Dichotomy
Billiard Table Lattice Polygon Satisfies Veech's Dichotomy
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2010/11/19
Over the course of studying billiard dynamics, several questions were raised. One of the questions was, which surfaces satisfy the following property (which is called Veech's dichotomy): Any directio...
On Isosceles Triangles and Related Problems in a Convex Polygon
Isosceles Triangles and Related Problems Convex Polygon
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2010/12/15
Given any convex n-gon, in this article, we: (i) prove that its vertices can form at most n2/2 + (n log n) isosceles trianges with two sides of unit length and show that this bound is optimal in the ...