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Since G is a connected group with a continuous action by conjugation on a discrete group Γ, it must act trivially, so that Γ has to be a subgroup of the center of G. In particular π 1 (H) = Γ is an abelian group; this can also easily be seen directly without using covering spaces. The group G is called the universal covering group of H.
Various methods have been proposed for measuring influence. [3] [4] Assume an estimated regression = +, where is an n×1 column vector for the response variable, is the n×k design matrix of explanatory variables (including a constant), is the n×1 residual vector, and is a k×1 vector of estimates of some population parameter .
A sphere of influence (SOI) in astrodynamics and astronomy is the oblate spheroid-shaped region where a particular celestial body exerts the main gravitational influence on an orbiting object. This is usually used to describe the areas in the Solar System where planets dominate the orbits of surrounding objects such as moons , despite the ...
Thus, a planar graph has genus 0, because it can be drawn on a sphere without self-crossing. The non-orientable genus of a graph is the minimal integer n such that the graph can be drawn without crossing itself on a sphere with n cross-caps (i.e. a non-orientable surface of (non-orientable) genus n). (This number is also called the demigenus.)
A non-closed curve may also be called an open curve. If the domain of a topological curve is a closed and bounded interval = [,], the curve is called a path, also known as topological arc (or just arc). A curve is simple if it is the image of an interval or a circle by an injective continuous function.
The radius of the sphere of influence is called the "(gravitational) influence radius". There are two definitions in common use for the radius of the sphere of influence. The first [ 1 ] is given by r h = G M BH σ 2 {\displaystyle r_{h}={\frac {GM_{\text{BH}}}{\sigma ^{2}}}} where M BH is the mass of the black hole, σ is the stellar velocity ...
An influence diagram (ID) (also called a relevance diagram, decision diagram or a decision network) is a compact graphical and mathematical representation of a decision situation. It is a generalization of a Bayesian network , in which not only probabilistic inference problems but also decision making problems (following the maximum expected ...
A universal graph is a graph that contains as subgraphs all graphs in a given family of graphs, or all graphs of a given size or order within a given family of graphs. 2. A universal vertex (also called an apex or dominating vertex) is a vertex that is adjacent to every other vertex in the graph.