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Grünbaum conjectured that for every m>1, n>2, there exists an m-regular, m-chromatic graph of girth at least n. This result is trivial for n=2 and m=2,3, but only a small ...

The Heaviside step function is a mathematical function denoted H(x), or sometimes theta(x) or u(x) (Abramowitz and Stegun 1972, p. 1020), and also known as the "unit step ...

An elliptic partial differential equation given by del ^2psi+k^2psi=0, (1) where psi is a scalar function and del ^2 is the scalar Laplacian, or del ^2F+k^2F=0, (2) where F ...

A hexahedron is a polyhedron with six faces. The figure above shows a number of named hexahedra, in particular the acute golden rhombohedron, cube, cuboid, hemicube, ...

The Hilbert curve is a Lindenmayer system invented by Hilbert (1891) whose limit is a plane-filling function which fills a square. Traversing the polyhedron vertices of an ...

The hypersine (n-dimensional sine function) is a function of a vertex angle of an n-dimensional parallelotope or simplex. If the content of the parallelotope is P and the ...

p^x is an infinitary divisor of p^y (with y>0) if p^x|_(y-1)p^y, where d|_kn denotes a k-ary Divisor (Guy 1994, p. 54). Infinitary divisors therefore generalize the concept ...

The proof theories of propositional calculus and first-order logic are often referred to as classical logic. Intuitionistic propositional logic can be described as classical ...

What space-filling arrangement of similar cells of equal volume has minimal surface area? This questions arises naturally in the theory of foams when the liquid content is ...

In mathematics, a knot is defined as a closed, non-self-intersecting curve that is embedded in three dimensions and cannot be untangled to produce a simple loop (i.e., the ...