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If A is a unital Banach algebra where every nonzero element is invertible, then A is the algebra of complex numbers.

The proposition that every consistent generalized theory has a model. The theorem is true if the axiom of choice is assumed.

Let the vertices of a graph G be numbered with distinct integers 1 to |G|. Then the dilation of G is the maximum (absolute) difference between integers assigned to adjacent ...

A graph G is Hamilton-connected if every two vertices of G are connected by a Hamiltonian path (Bondy and Murty 1976, p. 61). In other words, a graph is Hamilton-connected if ...

Harmonic coordinates satisfy the condition Gamma^lambda=g^(munu)Gamma_(munu)^lambda=0, (1) or equivalently, partial/(partialx^kappa)(sqrt(g)g^(lambdakappa))=0. (2) It is ...

The study, first developed by Boole, of shift-invariant operators which are polynomials in the differential operator D^~. Heaviside calculus can be used to solve any ordinary ...

A Heegaard splitting of a connected orientable 3-manifold M is any way of expressing M as the union of two (3,1)-handlebodies along their boundaries. The boundary of such a ...

The second-order ordinary differential equation (Moon and Spencer 1961, p. 157; Zwillinger 1997, p. 166).

A function S_n(z) which satisfies the recurrence relation S_(n-1)(z)-S_(n+1)(z)=2S_n^'(z) together with S_1(z)=-S_0^'(z) is called a hemicylindrical function.

The hemisphere function is defined as H(x,y)={sqrt(a-x^2-y^2) for sqrt(x^2+y^2)<=a; 0 for sqrt(x^2+y^2)>a. (1) Watson (1966) defines a hemispherical function as a function S ...