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Scattering from the coated targets embedded in a multilayered medium has attracted much interest during recent years for extensive applications, such as sea radar target detection and underwater radar...
We consider the obstacle problem for a nonlocal elliptic operator, like the integral fractional Laplacian of order $s \in (0,1)$. We derive regularity results in weighted Sobolev spaces, where the wei...
A tiny obstacle course for bacteria has shown researchers how E. coli changes its behavior to rapidly clear obstructions to food. The work holds implications for biology and medicine, and for robotic ...
Random Homogenization of Fractional Obstacle Problems     Random Homogenization  Fractional Obstacle Problems       font style='font-size:12px;'> 2015/10/15
We use a characterization of the fractional Laplacian as a Dirichlet to Neumann operator for an appropriate differential equation to study its obstacle problem in perforated domains.
Random Homogenization of an Obstacle Problem     Random Homogenization  Obstacle Problem       font style='font-size:12px;'> 2015/10/15
We study the homogenization of an obstacle problem in a perforated domain, when the holes are periodically distributed and have random shape and size. The main assumption concerns the capacity of the ...
This paper describes a method for estimating the distance between a robot and its surrounding environment using best ellipsoid fit. The method consists of the following two stages. First we approximat...
The boundary integral method is an efficient approach for solving time-harmonic obstacle scattering problems by a bounded scatterer. This paper presents the directional preconditioner for the iterativ...
This paper, we develop a numerical method for solving a unilateral obstacle problem by using the cubic spline collocation method and the generalized Newton method. This method converges quadratically ...
We study a two-player zero-sum stochastic differential game with both players adopting impulse controls, on a finite time horizon. The Hamilton-Jacobi-Bellman-Isaacs (HJBI) partial differential equati...
The Heston stochastic volatility process is a degenerate diffusion process where the degeneracy in the diffusion coefficient is proportional to the square root of the distance to the boundary of the h...
In this paper, we consider the free boundary for the inho-mogeneous obstacle problem with zero obstacle. We firstly establish the growth rates for the solution u(x) and the gradient of u(x), awa...
Computing the obstacle number of a plane graph     obstacle number of a plane graph  Computational Geometry       font style='font-size:12px;'> 2011/10/9
Abstract: An obstacle representation of a plane graph G is V(G) together with a set of opaque polygonal obstacles such that G is the visibility graph on V(G) determined by the obstacles. We investigat...
Abstract: In this paper a wave is generated by an initial data whose support is localized at the outside of unknown obstacles and observed in a limited time on a known closed surface or the same posit...
In this study, we use B-spline functions to solve the linear and nonlinear special systems of differential equations associated with the category of obstacle, unilateral, and contact problems. The pro...
An obstacle representation of a graph G is a set of points on the plane together with a set of polygonal obstacles that determine a visibility graph isomorphic to G. The obstacle number of G is the mi...

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