We study the nodal set of the Steklov eigenfunctions on the boundary of a smooth bounded domain in Rn – the eigenfunctions of the Dirichlet-to-Neumann map Λ. For a bounded Lipschitz domain Ω ⊂ Rn, this map associates to each function u defined on the boundary ∂Ω, the normal derivative of the harmonic function on Ω with boundary data u. Under the assumption that the domain Ω is C2, we prove a do...

Abstract: In this paper, we introduce and study the extended Newton-type method for solving the variational inclusion 0∈ f (x)+g(x)+F(x), where f :Ω⊆X→Y is Fréchet differentiable in a neighborhood Ω of a point x̄ in X, g:Ω⊆X→Y is linear and differentiable at point x̄, and F is a set-valued mapping with closed graph acting in Banach spaces X and Y. Semilocal and local convergence of the extended N...

In this paper we present a numerical solution method for the Bernoulli free boundary value problem for the Laplace equation in three dimensions. We extend a nonlinear integral equation approach for the free boundary reconstruction [21] from the two-dimensional to the three-dimensional case. The idea of the method consists in reformulating Bernoulli’s problem as a system of boundary integral equ...

In [1], it is established that a convergent observer with an infinite gain margin can be designed for a given nonlinear system when a Riemannian metric showing that the system is differentially detectable (i.e., the Lie derivative of the Riemannian metric along the system vector field is negative in the space tangent to the output function level sets) and the level sets of the output function a...

We show that in the presense of disruptive selection, spatial distributions of sexually reproducing organisms with local mating neighborhoods give rise to symmetry breaking and spontaneous pattern formation in the genetic composition of local populations. Global dynamics follows conventional coarsening of systems with non-conserved order parameters in statistical physics. These patterns interac...

We propose a new numerical method for the solution of Bernoulli’s free boundary value problem for a harmonic function w in a doubly connected domain D in R2 where an unknown free boundary Γ0 is determined by prescribed Cauchy data of w on Γ0 in addition to a Dirichlet condition on the known boundary Γ1. Our method is based on a two-by-two system of boundary integral equations for the unknown bo...

In this paper, we propose a novel local feature descriptor, Local Gaussian Structural Pattern (LGSP), for face recognition that encodes the directional information of the face’s textures (i.e., the texture’s structure), producing a more discriminant code than other state-of-the-art methods. Each micro-pattern’s structure is computed by using a derivative-Gaussian compass mask, which is more rob...

The synthesis of increasingly complex polymers has created daunting, sometimes insurmountable problems for their chemical analysis. The importance is magnified by outsourcing of production and their use in consumer products, including medical devices and food storage, and therefore requires a new generation of technology for quality assurance. Here, we report capturing subtle differences at the...

This paper presents a novel LDP based image descriptor which is more robust to temporal face changes. LDP is a framework to encode directional pattern based on local derivative variations, hence LDP is highly directional. However texture based features extracted globally tend to average over the image area. Hence this paper proposes to divide the face image into multiple regions and perform LDP...

the acute intravenous toxicities of a selection of three potential long-acting local anaesthetics belonging to the series of2- phenoxyethyldialkylamine were determined in mice. two of the compounds were tertiary amines and the third a quaternary ammonium derivative.the i.v. median lethal dose, (ldso) of one of the tertiary compounds, 21a [n, n- diethyl-2- (2,6- diisopropyl) ethyl amine hydrochl...