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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.

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 ...

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 ...

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 ...

Let A be a C^*-algebra. A C^*-subalgebra (that is a closed *-subalgebra) B of A is called hereditary if bab^' in B for all b,b^' in B and a in A, or equivalently if for a in ...

An irregular dodecahedron which is also a trapezohedron.

A homology class in a singular homology theory is represented by a finite linear combination of geometric subobjects with zero boundary. Such a linear combination is ...