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Given a set X, let F be a nonempty set of subsets of X. Then F is a ring if, for every pair of sets in F, the intersection, union, and set difference is also in F. F is ...

A topological space that is not connected, i.e., which can be decomposed as the disjoint union of two nonempty open subsets. Equivalently, it can be characterized as a space ...

The first solution to Lamé's differential equation, denoted E_n^m(x) for m=1, ..., 2n+1. They are also called Lamé functions. The product of two ellipsoidal harmonics of the ...

The exponent laws, also called the laws of indices (Higgens 1998) or power rules (Derbyshire 2004, p. 65), are the rules governing the combination of exponents (powers). The ...

A field automorphism of a field F is a bijective map sigma:F->F that preserves all of F's algebraic properties, more precisely, it is an isomorphism. For example, complex ...

A general quartic surface defined by x^4+y^4+z^4+a(x^2+y^2+z^2)^2+b(x^2+y^2+z^2)+c=0 (1) (Gray 1997, p. 314). The above two images correspond to (a,b,c)=(0,0,-1), and ...

Any locally compact Hausdorff topological group has a unique (up to scalars) nonzero left invariant measure which is finite on compact sets. If the group is Abelian or ...

The Hadamard product is a representation for the Riemann zeta function zeta(s) as a product over its nontrivial zeros rho, ...

A Hermitian metric on a complex vector bundle assigns a Hermitian inner product to every fiber bundle. The basic example is the trivial bundle pi:U×C^k->U, where U is an open ...

A Hessenberg decomposition is a matrix decomposition of a matrix A into a unitary matrix P and a Hessenberg matrix H such that PHP^(H)=A, where P^(H) denotes the conjugate ...