Crystal mathematics
WebAbstract. This paper is concerned with a simplified hydrodynamic equation, proposed by Ericksen and Leslie, modeling the flow of nematic liquid crystals. In dimension two, we establish both interior and boundary regularity theorems for such a flow under smallness conditions. As a consequence, we establish the existence of global (in time) weak ... WebA lattice is the symmetry group of discrete translational symmetry in n directions. A pattern with this lattice of translational symmetry cannot have more, but may have less symmetry than the lattice itself. [1] As a group (dropping its geometric structure) a lattice is a finitely-generated free abelian group, and thus isomorphic to .
Crystal mathematics
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WebSep 1, 2024 · This is a survey paper of the theory of crystal bases, global bases and the cluster algebra structure on the quantum coordinate rings. ... Representation Theory (math.RT); Quantum Algebra (math.QA) MSC classes: 13F60, 81R50, 16G, 17B37: Cite as: arXiv:1809.00114 [math.RT] WebJul 30, 2024 · Google’s quantum computing team made headlines in 2024 when they performed the first-ever computation that ordinary computers weren’t thought to be able …
WebNov 20, 2012 · About Crystal Clear Mathematics; Contact Me; Donation; Videos & Learning Resources. History of Mathematics. Anecdotes; Biographies; Famous … WebSouth Africa's best website for past papers. Learn Online! Other reosurces available. We have resources for many subjects. Mathematics, Accounting and more!
WebCrystallica is a Wolfram Language application for crystal and molecular structures. The user can manipulate structures and create plots with a variety of elements like atoms, bonds, … WebAug 31, 2024 · The strong ionic bond between the ions in the crystal makes it very hard and brittle. Ionic crystals have high melting points and are good conductors of electricity. Salt is an ionic crystal solid.
In mathematics, crystals are Cartesian sections of certain fibered categories. They were introduced by Alexander Grothendieck (1966a), who named them crystals because in some sense they are "rigid" and "grow". In particular quasicoherent crystals over the crystalline site are analogous to quasicoherent modules over a scheme. An isocrystal is a crystal up to isogeny. They are $${\displaystyle p}$$-adic analogues of -adic étale
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