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A condition used in the definition of a mathematical object, commonly denoted : or |. For example, the rationals Q can be defined by Q={p/q:q!=0,p,q in Z}, read as "the set ...

Summation by parts for discrete variables is the equivalent of integration by parts for continuous variables Delta^(-1)[v(x)Deltau(x)]=u(x)v(x)-Delta^(-1)[Eu(x)Deltav(x)], ...

For a discrete function f(n), the summatory function is defined by F(n)=sum_(k in D)^nf(k), where D is the domain of the function.

Let M be an oriented regular surface in R^3 with normal N. Then the support function of M is the function h:M->R defined by h(p)=p·N(p).

A symplectic form on a smooth manifold M is a smooth closed 2-form omega on M which is nondegenerate such that at every point m, the alternating bilinear form omega_m on the ...

The symbol tau (the lower case Greek letter tau) has many common uses in mathematics, as summarized in the following table. 1. tau(n) is an alternate notation for the divisor ...

The function defined by T_n(x)=((-1)^(n-1))/(sqrt(n!))Z^((n-1))(x), where Z(x)=1/(sqrt(2pi))e^(-x^2/2) and Z^((k))(x) is the kth derivative of Z(x).

Coordinates useful for plotting projective three-dimensional curves of the form f(x_0,x_1,x_2,x_3)=0 which are defined by x_0 = 1-z-sqrt(2)x (1) x_1 = 1-z+sqrt(2)x (2) x_2 = ...

The topological entropy of a map M is defined as h_T(M)=sup_({W_i})h(M,{W_i}), where {W_i} is a partition of a bounded region W containing a probability measure which is ...

One of a set of numbers defined in terms of an invariant generated by the finite cyclic covering spaces of a knot complement. The torsion numbers for knots up to 9 crossings ...