We study the uniqueness of multiple-spike solutions for some singularly perturbed Neumann problem in a ball. We are able to completely classify all two-peaked solutions. We can also classify all threepeaked solutions except some degenerate situations. Our main idea is by using the method of moving planes to show that two-peaks must be located on a line with the origin and the three-peaks must l...

A simple isoparametric geometry mapping is applied to incorporate irregular four-node quadrilateral elements into Modified Nodal Integral Method for the two-dimensional, time-dependent, incompressible Navier-Stokes equations. The modified scheme has been applied to solve the twodimensional lid driven cavity problem with exact solution, solved over a sub-domain that necessitate non-rectangular e...

We investigate the problem of finding the twodimensional convex hull of a set of points on a coarsegrained parallel computer. Recently Goodrich has devised a parallel sorting algorithm for n items on P processors which achieves an optimal number of communication phases for all ranges of P n. Ferreira et al. have recently introduced a deterministic convex hull algorithm with a constant number of...

We consider Brownian motion in a bounded domain Ω on a twodimensional Riemannian manifold (Σ, g). We assume that the boundary ∂Ω is smooth and reflects the trajectories, except for a small absorbing arc ∂Ωa ⊂ ∂Ω. As ∂Ωa is shrunk to zero the expected time to absorption in ∂Ωa becomes infinite. The narrow escape problem consists in constructing an asymptotic expansion of the expected lifetime, d...

Considering the relationship between the deformation on Hough planes and the affine transformation on raw images, the authors have proposed a matching algorithm ; four-dimensional optimization problem to search rotation, scale, and two-translation parameters has been decomposed into two-stages of one-dimensional and one stage of twodimensional optimization problems. The algorithm achieves the r...

Is it possible for humans to navigate in the natural environment wherein the path taken between various destinations is ‘optimal’ in some way? In the domain of optimization this challenge is traditionally framed as the “Traveling Salesman Problem” (TSP). What strategies and ecological considerations are plausible for human navigation? When given a twodimensional map-like presentation of the des...

This paper addresses the capacitated vehicle routing problem with twodimensional loading constraints (2L-CVRP). The 2L-CVRP is a combination of the two most important problems in distribution logistics, which are loading of freight into vehicles, and the successive routing of the vehicles to satisfy customer demand. The objective is to minimize the transportation cost. All vehicles must start a...

This paper discusses a structural optimization method that optimizes shape and topology based on the phase field method. The proposed method has the same functional capabilities as a structural optimization method based on the level set method incorporating perimeter control functions. The advantage of the method is the simplicity of computation, since extra operations such as reinitialization ...

Talk Abstract This paper concerns the switching on of twodimensional time-harmonic scalar waves. We consider the diffraction of a time-harmonic plane wave by a halfline, determining the rate at which the solution of the time domain ‘switching on’ problem converges to the solution of the corresponding frequency domain problem (the classical ‘Sommerfeld problem’) as the time since the wave was sw...

In this study, a dynamic programming approach to deal with the unconstrained twodimensional non-guillotine cutting problem is presented. The method extends the recently introduced recursive partitioning approach for the manufacturer’s pallet loading problem. The approach involves two phases and uses bounds based on unconstrained two-staged and non-staged guillotine cutting. Since a counterexamp...