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Let A be a C^*-algebra, then an element a in A is called normal if aa^*=a^*a.

A function f(n) has the normal order F(n) if f(n) is approximately F(n) for almost all values of n. More precisely, if (1-epsilon)F(n)<f(n)<(1+epsilon)F(n) for every positive ...

g_(ij)=[0 1 0 0; 1 0 0 0; 0 0 0 -1; 0 0 -1 0]. It can be expressed as g_(ab)=l_an_b+l_bn_a-m_am^__b-m_bm^__a.

A broad area of mathematics connected with functional analysis, differential equations, index theory, representation theory, and mathematical physics.

A metric defined by d(z,w)=sup{|ln[(u(z))/(u(w))]|:u in H^+}, where H^+ denotes the positive harmonic functions on a domain. The part metric is invariant under conformal maps ...

Let A be a C^*-algebra, then an element u in A is called a partial isometry if uu^*u=u.

All elementary functions can be extended to the complex plane. Such definitions agree with the real definitions on the x-axis and constitute an analytic continuation.

A tensor notation which considers the Riemann tensor R_(lambdamunukappa) as a matrix R_((lambdamu)(nukappa)) with indices lambdamu and nukappa.

The motion along a phase curve as a function of time (Tabor 1989, p. 14).

For a function with 2 degrees of freedom, the 2-dimensional phase space that is accessible to the function or object is called its phase plane.