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A set of n magic circles is a numbering of the intersections of the n circles such that the sum over all intersections is the same constant for all circles. The above sets of ...

The sum of the values of an integral of the "first" or "second" sort int_(x_0,y_0)^(x_1,y_1)(Pdx)/Q+...+int_(x_0,y_0)^(x_N,y_N)(Pdx)/Q=F(z) and ...

An addition chain for a number n is a sequence 1=a_0<a_1<...<a_r=n, such that each member after a_0 is the sum of two earlier (not necessarily distinct) ones. The number r is ...

A knot or link L^n in S^(n+2) is said to be fibered if there exists a fibration f:S^(n+2)-L->S^1 and if the fibration is well-behaved near L (Rolfsen 1976, p. 323). Examples ...

A metric on a bunch of segments with a common endpoint O, which defines the distance between two points P_1 and P_2 as the length of the shortest path connecting them inside ...

Any vector field v satisfying [del ·v]_infty = 0 (1) [del xv]_infty = 0 (2) may be written as the sum of an irrotational part and a solenoidal part, v=-del phi+del xA, (3) ...

A linear transformation A:R^n->R^n is hyperbolic if none of its eigenvalues has modulus 1. This means that R^n can be written as a direct sum of two A-invariant subspaces E^s ...

Let Q_i denote anything subject to weighting by a normalized linear scheme of weights that sum to unity in a set W. The Kolmogorov axioms state that 1. For every Q_i in W, ...

Let G=(V,E) be a (not necessarily simple) undirected edge-weighted graph with nonnegative weights. A cut C of G is any nontrivial subset of V, and the weight of the cut is ...

Let the true value of a quantity be x and the measured or inferred value x_0. Then the relative error is defined by deltax=(Deltax)/x=(x_0-x)/x=(x_0)/x-1, where Deltax is the ...