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In this paper we introduce a new class of geometric robot motion planning problems that we call incremental problems. W e also introduce the concept of incremental algorithms to solve this class of problems. As a n example, we describe an incremental critical curve based exact cell decomposition algorithm for a line segment robot moving freely amidst polpgonal obstacles. In the example, after c...
Background: Identify the optimal technique of radiotherapy for patients with high grade glioma. Our initial year of experience with RapidArc radiation therapy. Materials and Methods: Planning CT scans of 50 patients with grade IV glioma were reviewed and three plan sets by 3D Conformal Radiotherapy (3DCRT), Intensity Modulated Radiotherapy (IMRT) and Rapid Arc (RA) were generated and the plans ...
We study the large time behavior of the solutions of the Cauchy problem for the Anderson model restricted to the upper half space D = Zd−1 × Z+ and/or D = Rd−1 × R+ when the potential is a homogeneous random field concentrated on the boundary ∂D. In other words we consider the problem: ∂u(t, z) ∂t = κ∆u(t, z) + ξ(x)u(t, z) z = (x, y), with y ≥ 0 and t ≥ 0 with an appropriate initial condition. ...
In this paper we present a new approach for finding periodic orbits in dynamical systems modeled by differential equations. It is based on the Homotopy Analysis Method (HAM) but it differs from the usual way it is applied. We apply the HAM to construct approximations of a formal series solution of the equation. These approximations exist for any value of the frequency. They can be obtained by c...
In the paper is studied, in the diiusive scaling, the limiting behaviour of the Goldstein-Taylor model in a box, for a large class of initial and boundary conditions. It is shown that, in the limit, the evolution of the mass density is governed by the heat equation, with initial conditions depending only on the initial data of the hyperbolic system, and conditions on the boundary depending only...
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