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A paracompact space is a T2-space such that every open cover has a locally finite open refinement. Paracompactness is a very common property that topological spaces satisfy. ...

The Poisson integral with n=0, J_0(z)=1/piint_0^picos(zcostheta)dtheta, where J_0(z) is a Bessel function of the first kind.

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.

Given a sequence {a_k}_(k=1)^n, a partial sum of the first N terms is given by S_N=sum_(k=1)^Na_k.

I((chi_s^2)/(sqrt(2(k-1))),(k-3)/2)=(Gamma(1/2chi_s^2,(k-1)/2))/(Gamma((k-1)/2)), where Gamma(x) is the gamma function.

2^(50)=1024^5 bytes. Although the term petabyte is sometimes used to refer to 1024^5 bytes, such usage is deprecated in favor of the standard SI naming convention of 1 ...

The pentagonal rotunda is a convex polyhedron consisting of half of an icosidodecahedron, with the base being filled in by a decagon. It has 10 triangular and five pentagonal ...

The pentagrammic deltohedron (Har'El 1993) is the dual polyhedron of the pentagrammic antiprism U_(79).

A characteristic of some systems making a transition to chaos. Doubling is followed by quadrupling, etc. An example of a map displaying period doubling is the logistic map.