Let $K$ be a locally compact hypergroup with left Haar measure and let $L^1(K)$ be the complex Lebesgue space associated with it. Let $L^infty(K)$ be the dual of $L^1(K)$. The purpose of this paper is to present some necessary and sufficient conditions for $L^infty(K)^*$ to have a topologically left invariant mean. Some characterizations of amenable hypergroups are given.

we study connected orientable spacelike hypersurfaces $x:m^{n}rightarrowm_q^{n+1}(c)$, isometrically immersed into the riemannian or lorentzian space form of curvature $c=-1,0,1$, and index $q=0,1$, satisfying the condition $~l_kx=ax+b$,~ where $l_k$ is the $textit{linearized operator}$ of the $(k+1)$-th mean curvature $h_{k+1}$ of the hypersurface for a fixed integer $0leq k

Airborne laser scanning (ALS)-based forest inventories are being increasingly used. The two main approaches in deriving forest information from small-footprint laser scanner data are the area-based and individual tree detection (ITD) methods. In the present study we test the accuracies of an area-based k-nearest neighbour (k-NN)-method and ITD with a practical low-pulse density (1.8/m) ALS data...

Motivation Data clustering, which aims at identifying a varying number of clusters and unique cluster assignments in a fully unsupervised manner, is an important topic in machine learning and computer vision. Many of the available methods in this field such as k-means or mean shift are based on a Euclidean assumption. In this work we overcome the shortcomings of such an assumption by considerin...