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Let X be a topological vector space and for an arbitrary point x in X, denote by N_(x) the collection of all neighborhoods of x in X. A local base at x is any set B subset ...

If Omega subset= C is a domain and phi:Omega->C is a one-to-one analytic function, then phi(Omega) is a domain, and area(phi(Omega))=int_Omega|phi^'(z)|^2dxdy (Krantz 1999, ...

A line along a normal vector (i.e., perpendicular to some tangent line). If K subset R^d is a centrosymmetric set which has a twice differentiable boundary, then there are ...

Let A be a C^*-algebra. An element a in A is called positive if a=a* and sp(a) subset= R^+, or equivalently if there exists an element b in A such that a=bb^*. For example, ...

A function on the reals R is a step function if it can be written as a finite linear combination of semi-open intervals [a,b) subset= R. Therefore, a step function f can be ...

Catalan's constant is a constant that commonly appears in estimates of combinatorial functions and in certain classes of sums and definite integrals. It is usually denoted K ...

The detour index omega(G) of a graph G is a graph invariant defined as half the sum of all off-diagonal matrix elements of the detour matrix of G. Unless otherwise stated, ...

The Fourier transform is a generalization of the complex Fourier series in the limit as L->infty. Replace the discrete A_n with the continuous F(k)dk while letting n/L->k. ...

Let f be a fractional coloring of a graph G. Then the sum of values of f is called its weight, and the minimum possible weight of a fractional coloring is called the ...

A function tau(n) related to the divisor function sigma_k(n), also sometimes called Ramanujan's tau function. It is defined via the Fourier series of the modular discriminant ...