A simple proof of polar decomposition in pseudo-Euclidean geometry

A simple proof of Zariski's Lemma

‎Our aim in this very short note is to show that the proof of the‎ ‎following well-known fundamental lemma of Zariski follows from an‎ ‎argument similar to the proof of the fact that the rational field‎ ‎$mathbb{Q}$ is not a finitely generated $mathbb{Z}$-algebra.

A simple proof of Kashin’s decomposition theorem∗†

Compressive Sensing techniques are used in a short proof of Kashin’s decomposition theorem generalized to `p-spaces for p ≤ 1. The proof is based on the observation that the null-space of a properly-sized matrix with restricted isometry property is almost Euclidean when endowed with the `p-quasinorm. Kashin’s decomposition theorem states that, for any integer m ≥ 1, `2m 1 is the orthogonal sum ...

Pseudo-Convex Decomposition of Simple Polygons

We extend a dynamic-programming algorithm of Keil and Snoeyink for finding a minimum convex decomposition of a simple polygon to the case when both convex polygons and pseudo-triangles are allowed. Our algorithm determines a minimum pseudo-convex decomposition of a simple polygon in O(n) time where n is the number of the vertices of the polygon. In this way we obtain a well-structured decomposi...

Euclidean «-planes in Pseudo-euclidean Spaces and Differential Geometry of Cartan Domains

Spatial Analysis in curved spaces with Non-Euclidean Geometry

The ultimate goal of spatial information, both as part of technology and as science, is to answer questions and issues related to space, place, and location. Therefore, geometry is widely used for description, storage, and analysis. Undoubtedly, one of the most essential features of spatial information is geometric features, and one of the most obvious types of analysis is the geometric type an...