Search results
Results from the WOW.Com Content Network
In quantum optics, superradiance is a phenomenon that occurs when a group of N emitters, such as excited atoms, interact with a common light field. If the wavelength of the light is much greater than the separation of the emitters, [2] then the emitters interact with the light in a collective and coherent fashion. [3]
Despite the original model of the superradiance the quantum electromagnetic field is totally neglected here. The oscillators may be assumed to be placed for example on the cubic lattice with the lattice constant in the analogy to the crystal system of the condensed matter. The worse scenario of the defect of the absence of the two out-of-the ...
Epigraph of a function A function (in black) is convex if and only if the region above its graph (in green) is a convex set.This region is the function's epigraph. In mathematics, the epigraph or supergraph [1] of a function: [,] valued in the extended real numbers [,] = {} is the set = {(,) : ()} consisting of all points in the Cartesian product lying on or above the function's graph. [2]
A graph with three vertices and three edges. A graph (sometimes called an undirected graph to distinguish it from a directed graph, or a simple graph to distinguish it from a multigraph) [4] [5] is a pair G = (V, E), where V is a set whose elements are called vertices (singular: vertex), and E is a set of unordered pairs {,} of vertices, whose elements are called edges (sometimes links or lines).
For disconnected graphs, definitions vary: the diameter may be defined as infinite, or as the largest diameter of a connected component, or it may be undefined. diamond The diamond graph is an undirected graph with four vertices and five edges. diconnected Strong ly connected. (Not to be confused with disconnected) digon
Given a function: from a set X (the domain) to a set Y (the codomain), the graph of the function is the set [4] = {(, ()):}, which is a subset of the Cartesian product.In the definition of a function in terms of set theory, it is common to identify a function with its graph, although, formally, a function is formed by the triple consisting of its domain, its codomain and its graph.
Graph theory, the study of graphs and networks, is often considered part of combinatorics, but has grown large enough and distinct enough, with its own kind of problems, to be regarded as a subject in its own right. [14] Graphs are one of the prime objects of study in discrete mathematics.
Finally, the adjective strong or the adverb strongly may be added to a mathematical notion to indicate a related stronger notion; for example, a strong antichain is an antichain satisfying certain additional conditions, and likewise a strongly regular graph is a regular graph meeting stronger conditions. When used in this way, the stronger ...