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Given an original knot K, the knots produced by mutations together with K itself are called mutant knots. Mutant knots are often difficult to distinguish. For instance, ...

The natural domain of a function is the maximal chain of domains on which it can be analytically continued to a single-valued function.

A natural transformation Phi={Phi_C:F(C)->D(C)} between functors F,G:C->D of categories C and D is said to be a natural isomorphism if each of the components is an ...

where del is the backward difference.

Let N be a nilpotent, connected, simply connected Lie group, and let D be a discrete subgroup of N with compact right quotient space. Then N/D is called a nilmanifold.

A module M is Noetherian if it obeys the ascending chain condition with respect to inclusion, i.e., if every set of increasing sequences of submodules eventually becomes ...

Any irreducible curve may be carried by a factorable Cremona transformation into one with none but ordinary singular points.

The nullity of a linear transformation f:V->W of vector spaces is the dimension of its null space. The nullity and the map rank add up to the dimension of V, a result ...

An algebraic surface of degree eight. The maximum number of ordinary double points known to exist on an octic surface is 168 (the Endraß octics), although the rigorous upper ...

A set of maximum degree to which all other degrees of recursively enumerable sets can be one-one reduced. If set A is many-one complete, then it is one-one complete, and vice ...