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The double bar symbol | is used to denote certain kinds of norms in mathematics (e.g., ||x|| or ||x||_2). It is also used to denote parallel lines, as in A∥B, and in an older ...

A number which can be specified implicitly or explicitly by exponential, logarithmic, and algebraic operations.

The general ellipsoid, also called a triaxial ellipsoid, is a quadratic surface which is given in Cartesian coordinates by (x^2)/(a^2)+(y^2)/(b^2)+(z^2)/(c^2)=1, (1) where ...

Given a triangle DeltaA_1A_2A_3, the points A_1, I, and J_1 lie on a line, where I is the incenter and J_1 is the excenter corresponding to A_1. Furthermore, the circle with ...

Exponential decay is the decrease in a quantity N according to the law N(t)=N_0e^(-lambdat) (1) for a parameter t and constant lambda (known as the decay constant), where e^x ...

A group action phi:G×X->X is called faithful if there are no group elements g (except the identity element) such that gx=x for all x in X. Equivalently, the map phi induces ...

Any collineation from P(V) to P(V), where V is a three-dimensional vector space, is associated with a semilinear map from V to V.

If A is a unital Banach algebra where every nonzero element is invertible, then A is the algebra of complex numbers.

The Diophantine equation x^2+y^2=p can be solved for p a prime iff p=1 (mod 4) or p=2. The representation is unique except for changes of sign or rearrangements of x and y. ...

A method for predicting the onset of widespread chaos. It is based on the hypothesis that the dissolution of an invariant torus can be associated with the sudden change from ...