C L 1 ~ R 2 C L S1 R C S2
... Question 5: (Numerical) Even the smoothest surfaces are "rough'' when viewed at a scale of 100 nm. When two very smooth metal surfaces are placed in contact with each other, the actual distance between the surfaces varies from 0 nm at points of contacts to about 100 nm. Take the average distance bet ...
... Question 5: (Numerical) Even the smoothest surfaces are "rough'' when viewed at a scale of 100 nm. When two very smooth metal surfaces are placed in contact with each other, the actual distance between the surfaces varies from 0 nm at points of contacts to about 100 nm. Take the average distance bet ...
Octonion model of dark matter
... electromagnetic forces. The nonbaryonic dark matter [20, 21, 22] includes neutrinos, and possibly hypothetical entities such as axions, or supersymmetric particles. Unlike baryonic dark matter, nonbaryonic dark matter does not contribute to the formation of the elements in the early universe and so ...
... electromagnetic forces. The nonbaryonic dark matter [20, 21, 22] includes neutrinos, and possibly hypothetical entities such as axions, or supersymmetric particles. Unlike baryonic dark matter, nonbaryonic dark matter does not contribute to the formation of the elements in the early universe and so ...
Multidimensional Hypergeometric Functions in Conformai Field
... where co is a differential form of the Orlik-Solomon algebra. Hypergeometric forms form a finite-dimensional complex, as the differential of a hypergeometric form is a hypergeometric form: d(lao>) = L E «(//) dfH/fH A co. The weight local system ^(a) on the complement of a configuration is the compl ...
... where co is a differential form of the Orlik-Solomon algebra. Hypergeometric forms form a finite-dimensional complex, as the differential of a hypergeometric form is a hypergeometric form: d(lao>) = L E «(//) dfH/fH A co. The weight local system ^(a) on the complement of a configuration is the compl ...
Renormalization
In quantum field theory, the statistical mechanics of fields, and the theory of self-similar geometric structures, renormalization is any of a collection of techniques used to treat infinities arising in calculated quantities.Renormalization specifies relationships between parameters in the theory when the parameters describing large distance scales differ from the parameters describing small distances. Physically, the pileup of contributions from an infinity of scales involved in a problem may then result in infinities. When describing space and time as a continuum, certain statistical and quantum mechanical constructions are ill defined. To define them, this continuum limit, the removal of the ""construction scaffolding"" of lattices at various scales, has to be taken carefully, as detailed below.Renormalization was first developed in quantum electrodynamics (QED) to make sense of infinite integrals in perturbation theory. Initially viewed as a suspect provisional procedure even by some of its originators, renormalization eventually was embraced as an important and self-consistent actual mechanism of scale physics in several fields of physics and mathematics. Today, the point of view has shifted: on the basis of the breakthrough renormalization group insights of Kenneth Wilson, the focus is on variation of physical quantities across contiguous scales, while distant scales are related to each other through ""effective"" descriptions. All scales are linked in a broadly systematic way, and the actual physics pertinent to each is extracted with the suitable specific computational techniques appropriate for each.