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The homomorphism S which, according to the snake lemma, permits construction of an exact sequence (1) from the above commutative diagram with exact rows. The homomorphism S ...

The Ackermann function is the simplest example of a well-defined total function which is computable but not primitive recursive, providing a counterexample to the belief in ...

A symmetric polynomial on n variables x_1, ..., x_n (also called a totally symmetric polynomial) is a function that is unchanged by any permutation of its variables. In other ...

The spherical harmonics Y_l^m(theta,phi) are the angular portion of the solution to Laplace's equation in spherical coordinates where azimuthal symmetry is not present. Some ...

The base 8 notational system for representing real numbers. The digits used are 0, 1, 2, 3, 4, 5, 6, and 7, so that 8_(10) (8 in base 10) is represented as 10_8 ...

A 15-sided polygon, sometimes also called the pentakaidecagon. For a regular pentadecagon with side length 1, the inradius r, circumradius R, and area A are r = ...

Let A^~, B^~, ... be operators. Then the commutator of A^~ and B^~ is defined as [A^~,B^~]=A^~B^~-B^~A^~. (1) Let a, b, ... be constants, then identities include [f(x),x] = 0 ...

If A moves along a known curve, then P describes a pursuit curve if P is always directed toward A and A and P move with uniform velocities. Pursuit curves were considered in ...

Cis(x) is another name for the complex exponential, Cis(x)=e^(ix)=cosx+isinx. (1) It has derivative d/(dz)Cis(z)=ie^(iz) (2) and indefinite integral intCis(z)dz=-ie^(iz). (3)

A moment sequence is a sequence {mu_n}_(n=0)^infty defined for n=0, 1, ... by mu_n=int_0^1t^ndalpha(t), where alpha(t) is a function of bounded variation in the interval ...