Mathematical computational tools for the analysis of data with geometric content, such images, videos, 3D scans, GPS traces -- as well as for other data embedded into geometric spaces.
The account is quasi-formal, rather than simply formal, in that it gives geometric content an irreduciable role in Euclid's proofs.
They thus made it their goal not merely to describe but to calculate the angular positions of the planets on the basis of the numerical and geometric content of the theory.
Also known as planar quaternions, the representation allows us to formulate the kinematic constraints in an algebraic form with rich geometric content.
The mean (geometric) content of individual compounds varied from 1 μg kg− 1 for acenaphtylene to 55 μg kg− 1 for fluoranthene with the highest contributions (11.6%–12.9%) of phenanthrene, fluoranthene and pyrene.
The advantage of this approach comes from the highly sparse representation properties of the shearlet framework that is especially designed to robustly extract the fundamental geometric content of an image.
We show that the Lp Busemann Petty centroid inequality provides an elementary and powerful tool to the study of some sharp affine functional inequalities with a geometric content, like log-Sobolev, Sobolev and Gagliardo Nirenberg inequalities.
By fully exploiting the phase structure of these theories (discovered in earlier works) we are able to clearly identify their geometric content.
We also discuss some other models with unusual phase diagrams that highlight some subtle features regarding the geometric content of conformal theories.
The first part is about Geometric Analysis and Conformal Geometry; this modern field lies at the intersection of many branches of mathematics (Riemannian, Conformal, Complex or Algebraic Geometry, Calculus of Variations, PDE's, etc) and relates directly to the physical world, since many natural phenomena posses an intrinsic geometric content.
