Definition & Betydelse | Engelska ordet COMPACTIFICATION

Definition av COMPACTIFICATION

1. kompaktifiering

Exempel på hur man kan använda COMPACTIFICATION i en mening

• In mathematics, in general topology, compactification is the process or result of making a topological space into a compact space.
• Stone–Čech compactification, a process that turns a completely regular Hausdorff space into a compact Hausdorff space, may be described as adjoining limits of certain nonconvergent nets to the space.
• The map c is a Hausdorff compactification if and only if X is a locally compact, noncompact Hausdorff space.
• Just as the Möbius group requires the Riemann sphere, a compact space, for a complete description, so the alternative complex planes require compactification for complete description of conformal mapping.
• Degenerate conics, as with degenerate algebraic varieties generally, arise as limits of non-degenerate conics, and are important in compactification of moduli spaces of curves.
• Urysohn, Alexandrov showed the full meaning of this concept; in particular, he proved the first general metrization theorem and the famous compactification theorem of any locally compact Hausdorff space by adding a single point.
• Resolution says that such singularities can be handled rather as a (complicated) sort of compactification, ending up with a compact manifold (for the strong topology, rather than the Zariski topology, that is).
• Maldacena–Nunez no-go theorem: any compactification of type IIB string theory on an internal compact space with no brane sources will necessarily have a trivial warp factor and trivial fluxes.
• To have a moduli space as a scheme is on one side a question about characterising schemes as representable functors (as the Grothendieck school would see it); but geometrically it is more like a compactification question, as the stability criteria revealed.
• In 2015 Emanuello & Nolder performed the compactification by first embedding the motor plane into a torus, and then making it projective by identifying antipodal points.
• In 1978, together with Bernard Julia and Joël Scherk, he co-developed eleven-dimensional supergravity theory and proposed a mechanism of spontaneous compactification in field theory.
• Shepherd-Barron works in various aspects of algebraic geometry, such as: singularities in the minimal model program; compactification of moduli spaces; the rationality of orbit spaces, including the moduli spaces of curves of genus 4 and 6; the geography of algebraic surfaces in positive characteristic, including a proof of Raynaud's conjecture; canonical models of moduli spaces of abelian varieties; the Schottky problem at the boundary; the relation between algebraic groups and del Pezzo surfaces; the period map for elliptic surfaces.
• The points of the Wallman compactification ωX of a space X are the maximal proper filters in the poset of closed subsets of X.
• Moore's research has focused on: D-branes on Calabi–Yau manifolds and BPS state counting; relations to Borcherds products, automorphic forms, black-hole entropy, and wall-crossing; applications of the theory of automorphic forms to conformal field theory, string compactification, black hole entropy counting, and the AdS/CFT correspondence; potential relation between string theory and number theory; effective low energy supergravity theories in string compactification and the computation of nonperturbative stringy effects in effective supergravities; topological field theories, and applications to invariants of manifolds; string cosmology and string field theory.
• The compactification of Teichmüller space by adding measured foliations is essential in the definition of the ending laminations of a hyperbolic 3-manifold.
• The analysis can also be reduced to this case because all points in the complex algebra (or its compactification) lie in an image of the polydisk (or polysphere) under the unitary structure group.
• In the 2000s he focused on the expansion of the AdS/CFT correspondence to low supersymmetric and non-conformal gauge theories, the construction of four-dimensional effective Lagrangians for lower energies from the compactification of magnetised D-brane models, and the high-energy scattering of closed strings in the framework of the theory of D-branes.
• In 1985 Horowitz published an influential paper with Philip Candelas, Andrew Strominger and Edward Witten on the compactification of superstrings in Calabi-Yau spaces.
• Given an algebraic torus and a connected closed subvariety of that torus, a compactification of the subvariety is defined as a closure of it in a toric variety of the original torus.
• In 2010 he had with Yuji Tachikawa and Luis Alday, developed the AGT correspondence (named after the authors), a duality in the 6D (2,0) superconformal field theory with compactification on a surface to a conformal field theory on the surface (Liouville field theory).

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