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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 ...

A perfect cubic polynomial can be factored into a linear and a quadratic term, x^3+y^3 = (x+y)(x^2-xy+y^2) (1) x^3-y^3 = (x-y)(x^2+xy+y^2). (2)

A perfect field is a field F such that every algebraic extension is separable. Any field in field characteristic zero, such as the rationals or the p-adics, or any finite ...

F(x,s) = sum_(m=1)^(infty)(e^(2piimx))/(m^s) (1) = psi_s(e^(2piix)), (2) where psi_s(x) is the polygamma function.

If a circular pizza is divided into 8, 12, 16, ... slices by making cuts at equal angles from an arbitrary point, then the sums of the areas of alternate slices are equal. ...

The plumbing of a p-sphere and a q-sphere is defined as the disjoint union of S^p×D^q and D^p×S^q with their common D^p×D^q, identified via the identity homeomorphism. This ...

The symbol +/- is used to denote a quantity which should be both added and subtracted, as in a+/-b. The symbol can be used to denote a range of uncertainty, or to denote a ...

Every Lie algebra L is isomorphic to a subalgebra of some Lie algebra A^-, where the associative algebra A may be taken to be the linear operators over a vector space V.

Poinsot's spirals are the two polar curves with equations r = acsch(ntheta) (1) r = asech(ntheta). (2)

The hypothesis is that, for X is a measure space, f_n(x)->f(x) for each x in X, as n->infty. The hypothesis may be weakened to almost everywhere convergence.