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In the study of non-associative algebra, there are at least two different notions of what the half-Bol identity is. Throughout, let L be an algebraic loop and let x, y, and z ...

Refer to the above figures. Let X be the point of intersection, with X^' ahead of X on one manifold and X^('') ahead of X of the other. The mapping of each of these points ...

The logarithmic capacity of a compact set E in the complex plane is given by gamma(E)=e^(-V(E)), (1) where V(E)=inf_(nu)int_(E×E)ln1/(|u-v|)dnu(u)dnu(v), (2) and nu runs over ...

An operator A:f^((n))(I)|->f(I) assigns to every function f in f^((n))(I) a function A(f) in f(I). It is therefore a mapping between two function spaces. If the range is on ...

An element of an adèle group, sometimes called a repartition in older literature (e.g., Chevalley 1951, p. 25). Adèles arise in both number fields and function fields. The ...

A map projection. The inverse equations for phi are computed by iteration. Let the angle of the projection plane be theta_b. Define a={0 for theta_b=1/2pi; ...

The base manifold in a bundle is analogous to the domain for a set of functions. In fact, a bundle, by definition, comes with a map to the base manifold, often called pi or ...

In a dynamical system, a bifurcation is a period doubling, quadrupling, etc., that accompanies the onset of chaos. It represents the sudden appearance of a qualitatively ...

The colon is the symbol ":". It is used in a number of different ways in mathematics. 1. To denote ratio or odds, as in 2:1 (voiced "two to one"). 2. To mean such that in ...

A commutative diagram is a collection of maps A_i-->^(phi_i)B_i in which all map compositions starting from the same set A and ending with the same set B give the same ...