Sentence examples for deep results from inspiring English sources

This is a vast subject with many deep results.

It went on to say that his name was "forever attached to deep results and important concepts within Riemannian geometry, symplectic geometry, string theory and group theory".

There was AltaVista, and Ask Jeeves, and HotBot, and Excite, and Infoseek, and Northern Light — with its deep results and its elegant floating schooner logo — and if you wanted to drag through several oceans at once, there was MetaCrawler.

In this talk, I'll discuss a beautiful recent work on reproving and generalizing the results of Faltings using a method which sidesteps the associated deep results on abelian varieties and semisimplicity in his original work.

Specifically, deep results in classical harmonic analysis and ergodic theory, due to Bochner, de Leeuw and Glicksberg, Forelli, and others are all extensions of the classical F. & M. Riesz Theorem.

Many of the deep results of point set topology still remain valid, however, when open sets are abandoned and generalizations of the closure operator are used as the foundation of the mathematical theory.

He also gave the first proof of the law of quadratic reciprocity, a deep result previously glimpsed by Euler.

The removal of the constant-rank condition whenp=q=2 involves the use of a deep result of Lojasiewicz from singularity theory.

Also a different proof, of a deep result of J. Diestel, W. Ruess, W. Schachermayer about weak compactness in L1(E), is given.

Secondly, in weekly individual and group meetings over the next four years, Tom exemplified that the best research occurs when there is a simple surprise in the understanding of what might be thought of as a deep result.

A main tool in proving this deep result was some results concerning asphericity of convex bodies.