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In the study of non-associative algebra, there are at least two different notions of what the half-Bol identity is. Throughout, let L be an algebraic loop and let x, y, and z ...

For a prime constellation, the Hardy-Littlewood constant for that constellation is the coefficient of the leading term of the (conjectured) asymptotic estimate of its ...

The harmonic conjugate to a given function u(x,y) is a function v(x,y) such that f(x,y)=u(x,y)+iv(x,y) is complex differentiable (i.e., satisfies the Cauchy-Riemann ...

The Heine-Borel theorem states that a subspace of R^n (with the usual topology) is compact iff it is closed and bounded. The Heine-Borel theorem can be proved using the ...

A continuum is hereditarily decomposable if each of its subcontinua is decomposable. An interval is hereditarily decomposable, as is a circle, whereas the buckethandle (also ...

A Hermitian inner product on a complex vector space V is a complex-valued bilinear form on V which is antilinear in the second slot, and is positive definite. That is, it ...

An integer n>1 is said to be highly cototient if the equation x-phi(x)=n has more solutions than the equations x-phi(x)=k for all 1<k<n, where phi is the totient function. ...

Given a nonzero finitely generated module M over a commutative Noetherian local ring R with maximal ideal M and a proper ideal I of R, the Hilbert-Samuel function of M with ...

Let H be a Hilbert space and (e_i)_(i in I) is an orthonormal basis for H. The set S(H) of all operators T for which sum_(i in I)||Te_i||^2<infty is a self-adjoint ideal of ...

Given a number field K, there exists a unique maximal unramified Abelian extension L of K which contains all other unramified Abelian extensions of K. This finite field ...