In this paper we study the following problem: how to divide a cake among the children attending a birthday party such that all the children get the same amount of cake and the same amount of icing. This leads us to the study of the following. A perfect k-partitioning of a convex set S is a partitioning of S into k convex pieces such that each piece has the same area and 1 k of the perimeter of ...

In this paper, a numerical method is proposed for solving optimal control problem of Volterra integral equations using radial basis functions (RBFs) for approximating unknown function. Actually, the method is based on interpolation by radial basis functions including multiquadrics (MQs), to determine the control vector and the corresponding state vector in linear dynamic system while minimizing...

We study the radial-hedgehog solution on a unit ball in three dimensions, with homeotropic boundary conditions, within the Landau-de Gennes theory for nematic liquid crystals. The radial-hedgehog solution is a candidate for a globally stable configuration in this model framework and is also a prototype configuration for studying isolated point defects in condensed matter physics. We use a combi...

‎In this paper‎, ‎indirect collocation approach based on compactly supported radial basis function (CSRBF) is applied for solving Volterra's population model. The method reduces the solution of this problem to the solution of a system of algebraic equations‎. ‎Volterra's model is a non-linear integro-differential equation where the integral term represents the effect of toxin‎. ‎To solve the pr...

We propose new measures to evaluate to which extent the shape of a given convex polygon is close to the shape of some regular polygon. We prove that our parameters satisfy several reasonable requirements and provide algorithms for their efficient computation. The properties we mostly focus on are the facts that regular polygons are equilateral, equiangular and have radial symmetry.

In this work, we give a priori height and gradient estimates for solutions of the prescribed constant Gauss curvature equation in Euclidean space. We shall consider convex radial graphs with positive constant mean curvature. The estimates are established by considering in such a graph, the Riemannian metric given by the second fundamental form of the immersion. r 2003 Elsevier Inc. All rights r...

We consider the following problem stated in 1993 by Buttazzo and Kawohl (Math Intell 15:7–12, 1993): minimize functional $${\int \limits } {\int }_{\Omega (1 + |\nabla u(x,y)|^{2})^{-1} dx dy$$ class of concave functions u : Ω → [0,M], where $${\Omega \subset \mathbb {R}^{2}$$ is a convex domain M > 0. It generalizes classical minimization problem, which was initially I. Newton 1687 more restri...