Shapes of finite-dimensional compacta

Three-dimensional beta shapes

The Voronoi diagram of a point set has been extensively used in various disciplines ever since it was first proposed. Its application realms have been even further extended to estimate the shape of point clouds when Edelsbrunner and Mücke introduced the concept of α-shape based on the Delaunay triangulation of a point set. In this paper, we present the theory of β-shape for a set of three-dimen...

Finite Posets and Ferrers Shapes

Synthesis of Supported Pt Alloy three Dimensional Rhombus Shapes Nanoparticles for Oxygen Reduction Reaction

In this study PtFeCo ternary alloys nanoparticles of three dimentional (3D) rhombus shapes dispersed on graphene nanosheets (PtFeCo/Gr) were successfully prepared and studied as electrocatalysts for oxygen reduction reaction (ORR) in polymer-electrolyte fuel cells. A combination of analytical techniques including powder X-ray diffraction, X-ray photoelectron spectra, inductively coupled plasma-...

Comparative study of 12 thread shapes of dental implant designs: a three-dimensional finite element analysis

The purpose of this study was to determine the optimal thread shape for an experimental cylinder implant. Twelve three-dimensional finite element models with an implant of different thread shape were created: 1mm, 2mm, and 3mm square designs (S-1, S-2, and S-3); 90, 60, and 30 V-shaped designs (V-1, V-2, and V-3); 45, 30, and 15 buttress designs (B-1, B-2, and B-3); 45, 30, and 15 reverse buttr...

Remarks on Actions on Compacta by Some Infinite-dimensional Groups

We discuss some techniques related to equivariant compactifications of uniform spaces and amenability of topological groups. In particular, we give a new proof of a recent result by Glasner and Weiss describing the universal minimal flow of the infinite symmetric group S∞ with the standard Polish topology, and extend Bekka’s concept of an amenable representation, enabling one to deduce non-amen...