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In general, groups are not Abelian. However, there is always a group homomorphism h:G->G^' to an Abelian group, and this homomorphism is called Abelianization. The ...

Differential entropy differs from normal or absolute entropy in that the random variable need not be discrete. Given a continuous random variable X with a probability density ...

A series suma(n)e^(-lambda(n)z), where a(n) and z are complex and {lambda(n)} is a monotonic increasing sequence of real numbers. The numbers lambda(n) are called the ...

The normal to an ellipse at a point P intersects the ellipse at another point Q. The angle corresponding to Q can be found by solving the equation (P-Q)·(dP)/(dt)=0 (1) for ...

In predicate calculus, an existential formula is a prenex normal form formula (i.e., a formula written as a string of quantifiers and bound variables followed by a ...

A variation of chess involving a change in the form of the board, the rules of play, or the pieces used. For example, the normal rules of chess can be used but with a ...

The fourth group isomorphism theorem, also called the lattice group isomorphism theorem, lets G be a group and let N⊴G, where N⊴G indicates that N is a normal subgroup of G. ...

Also known as the Serret-Frenet formulas, these vector differential equations relate inherent properties of a parametrized curve. In matrix form, they can be written [T^.; ...

A presentation of a group is a description of a set I and a subset R of the free group F(I) generated by I, written <(x_i)_(i in I)|(r)_(r in R)>, where r=1 (the identity ...

The upper central series of a group G is the sequence of groups (each term normal in the term following it) 1=Z_0<=Z_1<=Z_2<=...<=Z_n<=... that is constructed in the ...