Rubidum and Caesium (Perel'man, F. M.)

Krasner $F^{(m, n)}$-Hyperrings

$!!!!$ In this paper, the notion of fuzzy $!$ Krasner $!(m, n)$-hyperrings($!F^{(m, n)}!$-hyperrings) by using the notion of$F^m$-hyperoperations and $F^n$-operations is introduced and somerelated properties are investigated. In this regards,relationships between Krasner $F^{(m, n)}$-hyperrings and Krasner$(m, n)$-hyperrings are considered. We shall prove that everyKrasner $F^{(m, n)}$-hyperrin...

Seed dormancy in pistacia mutica F. & M.

Perelman, Poincaré, and the Ricci Flow

In this expository article, we introduce the topological ideas and context central to the Poincaré Conjecture. Our account is intended for a general audience, providing intuitive definitions and spatial intuition whenever possible. We define surfaces and their natural generalizations, manifolds. We then discuss the classification of surfaces as it relates to the Poincaré and Thurston Geometriza...

Perelman Proves Poincaré

In 1904, Henri Poincaré conjectured: Every compact, connected, simply-connected 3-manifold is the 3-sphere. This conjecture has been near the center of a maelstrom of activity in topology, geometry, analysis, and many allied and sub-disciplines for a hundred years. Recently, Grisha Perelman announced a proof of the conjecture – in fact of the stronger Geometrization Conjecture of William Thurst...

On Perelman ’ S Papers

These are notes on Perelman’s papers “The Entropy Formula for the Ricci Flow and its Geometric Applications” [40] and “Ricci Flow with Surgery on Three-Manifolds’ [41]. In these two remarkable preprints, which were posted on the ArXiv in 2002 and 2003, Grisha Perelman announced a proof of the Poincaré Conjecture, and more generally Thurston’s Geometrization Conjecture, using the Ricci flow appr...