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A family composed of countably many discrete families.

A smooth map f:S^1->R^3 whose image has singularities. In particular, in the theory of Vassiliev's knot invariants, singular knots with a finite number of ordinary double ...

A space which is isomorphic to a Borel subset B of a Polish space equipped with its sigma-algebra of Borel sets.

Defined for samples x_i, i=1, ..., N by alpha_r=1/Nsum_(i=1)^Nz_i^r=(mu_r)/(sigma^r), (1) where z_i=(x_i-x^_)/(s_x). (2) The first few are alpha_1 = 0 (3) alpha_2 = 1 (4) ...

The symbol ∼ used to denote similarity, equivalence relations, or asymptosy.

A symmetry group is a group of symmetry-preserving operations, i.e., rotations, reflections, and inversions (Arfken 1985, p. 245).

An ordering of permutations in which each two adjacent permutations differ by the transposition of two elements. For the permutations of {1,2,3} there are two listings which ...

A group of three elements, also called a triad. A triple is therefore a 3-tuple.

A generalization of spun knots due to Zeeman. This method produces four-dimensional knot types that cannot be produced by ordinary spinning.

An R-module M is said to be unital if R is a commutative ring with multiplicative identity 1=1_R and if 1m=m for all elements m in M.