Wave Geometry. (Geometry in Microscopic Space)

Editorial: Brain Extracellular Space: Geometry, Matrix and Physiological Importance

Some Banach Space Geometry

Notation. ε is an arbitrarily small positive number. L(X,Y ) is the Banach space of bounded linear operators T : X → Y . B(X) is the closed unit ball {x ∈ X : ‖x‖ 6 1}. N := N ∪ {∞} is the one-point compactification of the discrete space N. All operators are bounded and linear. A compact (topological) space always means a compact Hausdorff space. (We sometimes add “Hausdorff” explicitly for emp...

Geometry of face space

The geometrical character of face space is investigated, and is analyzed within the framework of eigenface decompositions. To deal with the sparse data problem, which occurs when not enough data is present to fill the space, we construct and test a range of probabilistic models. A key tool in this investigation is the decomposition of the eigenfaces representation of face space into odd and eve...

Super coset space geometry

Super coset spaces play an important role in the formulation of supersymmetric theories. The aim of this paper is to review and discuss the geometry of super coset spaces with particular focus on the way the geometrical structures of the super coset space G/H are inherited from the super Lie group G. The isometries of the super coset space are discussed and a definition of Killing supervectors ...

Space Geometry with Metapost *

METAPOST is a tool especially well-suited for the inclusion of technical drawings in a document. In this article, we show how METAPOST can be used to represent objects in space and especially how it can be used for drawing geometric constructions involving lines, planes, as well as their intersections, orthogonal planes, etc. All the features belong to a new METAPOST package aimed at all those ...