Crystals may seem flawless, but deep inside they contain tiny structural imperfections that dramatically influence their ...

Crystals are known far and wide for their beauty and elegance. But even though they may appear perfect on the outside, their ...

The Langlands programme has inspired and befuddled mathematicians for more than 50 years. A major advance has now opened up ...

Researchers from The University of Osaka have developed a mathematical model for Volterra defects using differential geometry to analyze the relationships between different types of defects. Their ...

Let M be a Riemannian manifold with constant scalar curvature K which admits an infinitesimal conformal transformation. A necessary and sufficient condition in order that it be isometric with a sphere ...

Recently, manifold learning has been widely exploited in pattern recognition, data analysis, and machine learning. This paper presents a novel framework, called Riemannian manifold learning (RML), ...

This manifold turns out to be decisive in characterizing solutions of Riemann problems, in particular because the origin is connected to this manifold by means of a right characteristic 1-Lax shock.