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Let G=(V,E) be a finite graph, let Omega be the set Omega={0,1}^E whose members are vectors omega=(omega(e):e in E), and let F be the sigma-algebra of all subsets of Omega. A ...

Ede (1958) enumerates 13 basic series of stellations of the rhombic triacontahedron, the total number of which is extremely large. Pawley (1973) gave a set of restrictions ...

The set of fixed points which do not move as a knot is transformed into itself is not a knot. The conjecture was proved in 1978 (Morgan and Bass 1984). According to Morgan ...

One or both of the square bracket symbols [ and ] are used in many different contexts in mathematics. 1. Square brackets are occasionally used in especially complex ...

The tetrahedral equation, by way of analogy with the icosahedral equation, is a set of related equations derived from the projective geometry of the octahedron. Consider a ...

The thin plate spline is the two-dimensional analog of the cubic spline in one dimension. It is the fundamental solution to the biharmonic equation, and has the form ...

A vector space V is a set that is closed under finite vector addition and scalar multiplication. The basic example is n-dimensional Euclidean space R^n, where every element ...

Wolfram (2002, p. 123) considered the sequence related to the Collatz problem obtained by iterating w_n={3/2w_(n-1) for w_(n-1) even; 3/2(w_(n-1)+1) for w_(n-1) odd (1) ...

A knot property, also called the twist number, defined as the sum of crossings p of a link L, w(L)=sum_(p in C(L))epsilon(p), (1) where epsilon(p) defined to be +/-1 if the ...

A graph is k-edge-connected if there does not exist a set of k-1 edges whose removal disconnects the graph (Skiena 1990, p. 177). The maximum edge connectivity of a given ...