We study domain monotonicity of the principal eigenvalue λ1 (α) corresponding to ∆u = λ(α)u in Ω, ∂u ∂ν = αu on ∂Ω, with Ω ⊂ Rn a C0,1 bounded domain, and α a fixed real. We show that contrary to intuition domain monotonicity might hold if one of the two domains is a ball.

The paper deals with the well–posedness of the problem 8 >< >: utt −∆u = 0 in R× Ω, utt = kuν on R× Γ, u(0, x) = u0(x), ut(0, x) = v0(x) in Ω, where u = u(t, x), t ∈ R, x ∈ Ω, ∆ = ∆x denotes the Laplacian operator respect to the space variable, Ω is a bounded regular (C∞) open domain of RN (N ≥ 1), Γ = ∂Ω, ν is the outward normal to Ω, k is a constant. We prove that it is ill–posed if N ≥ 2, wh...

Let M either be a closed real analytic Riemannian manifold or a closed C∞-Riemannian surface. We estimate from below the volume of a nodal domain component in an arbitrary ball, provided that this component enters the ball deeply enough.

The article presents the steps required to reconstruct a 3D trajectory of a golf ball flight, bounces and roll in short game. Two video cameras were used to capture the last parts of the trajectories including the bounces and roll. Each video sequence is processed and the ball is detected and tracked until is stops. Detected positions from both video sequences are then matched and 3D trajectory...

Recently there has been great deal of interest in making system that enables an audience to view sports event from any arbitrary viewpoint. The rapid development of networks and computers will soon make it possible to provide a form of real-time video that allows the viewer to select any desired view of the action. This paper introduces a novel method for generating an arbitrary view of a scene...

this paper concerns the design and analysis, of a ball type continuously variable transmission, (b-cvt). this b-cvt has a simple kinematic structure, and same as a toroidal cvt, transmits power by friction on the contact points between input and output discs, that are connected to each other by balls. after, a brief introduction of our b-cvt structure, the performance and traction efficiency of...

We consider a class of singular systems of Lane-Emden type      ∆u + λu p 1 v q 1 = 0, x ∈ D, a smooth domain in R n. In case the system is sublinear we prove existence of a positive solution. If D is a ball in R n , we prove both existence and uniqueness of positive radially symmetric solution.

We investigate a variation of the transitivity problem for proximinality properties of subspaces and intersection properties of balls in Banach spaces. For instance, we prove that if Z ⊆ Y ⊆ X, where Z is a finite co-dimensional subspace of X which is strongly proximinal in Y and Y is an M -ideal in X, then Z is strongly proximinal in X. Towards this, we prove that a finite co-dimensional proxi...