Schrödinger–Poisson systems in the 3-sphere

Bonnet Pairs in the 3 - Sphere

Two non-congruent surfaces that are isometric and have the same mean curvature at corresponding points are called a Bonnet pair of surfaces or simply a Bonnet pair. The interest in such pairs arises from the following considerations: One of the fundamental problems of surface theory is to find invariants which characterize surfaces geometrically. The Bonnet theorem states that a surface is dete...

Sphere packings in 3-space

In this paper we survey results on packings of congruent spheres in 3-dimensional spaces of constant curvature. The topics discussed are as follows: Hadwiger numbers of convex bodies and kissing numbers of spheres; Touching numbers of convex bodies; Newton numbers of convex bodies; One-sided Hadwiger and kissing numbers; Contact graphs of finite packings and the combinatorial Kepler problem; Is...

Sphere Packings in 3 Dimensions

The Kepler conjecture asserts that no packing of equal balls in three dimensions can have density exceeding that of the facecentered cubic packing. The density of this packing is π/ √ 18, or about 0.74048. This conjecture was proved in 1998 [H]. In superficial terms, the proof takes over 270 pages of mathematical text, extensive computer resources, including 3 gigabytes of data, well over 40 th...

Recommender Systems in the Web 2.0 Sphere

Recommender Systems (RS) are software solutions that help users deal with the information overload and find the information they need. From a technical perspective, RS have their origins in different fields such as information filtering and data mining and are built using a broad array of statistical methods and algorithms. Since their beginnings in the early 1990s, boosted by the enormous grow...

On Involutions of the 3-Sphere