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Exact solution of some new planar polygon models. Plus aspects of a ”new” SAW model.
Ice wedges are widespread periglacial features in the landscape of Adventdalen, Svalbard. The networks of ice wedges have created areas with well-developed polygonal terrains in the lowest fluvial ter...
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...
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...
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...
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.The scalar field obeys Dirichlet boundary conditions at the perimeter of the polygon.
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...
We show that the notion of induction introduced by Cassaigne, Ferenczi and Zamboni for trees of relations arising in the context of interval exchange relations can be generalised to the case of an arb...
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 ...

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