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A cross-handle is a topological structure which can be thought of as the object produced by puncturing a surface twice, attaching a zip around each puncture travelling in the ...

The cyclic group C_(11) is unique group of group order 11. An example is the integers modulo 11 under addition (Z_(11)). No modulo multiplication group is isomorphic to ...

Darboux's formula is a theorem on the expansion of functions in infinite series and essentially consists of integration by parts on a specific integrand product of functions. ...

An embedding of a 1-sphere in a 3-manifold which exists continuously over the 2-disk also extends over the disk as an embedding. An alternate phrasing is that if a knot group ...

Given a set X, let F be a nonempty set of subsets of X. Then F is a ring if, for every pair of sets in F, the intersection, union, and set difference is also in F. F is ...

The group D_5 is one of the two groups of order 10. Unlike the cyclic group C_(10), D_5 is non-Abelian. The molecule ruthenocene (C_5H_5)_2Ru belongs to the group D_(5h), ...

A disk algebra is an algebra of functions which are analytic on the open unit disk in C and continuous up to the boundary. A representative measure for a point x in the ...

The normal to an ellipse at a point P intersects the ellipse at another point Q. The angle corresponding to Q can be found by solving the equation (P-Q)·(dP)/(dt)=0 (1) for ...

Two statements in logic are said to be equipollent if they are deducible from each other. Two sets A and B are said to be equipollent iff there is a one-to-one correspondence ...

A curve on the unit sphere S^2 is an eversion if it has no corners or cusps (but it may be self-intersecting). These properties are guaranteed by requiring that the curve's ...