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In a cochain complex of modules ...->C^(i-1)->^(d^(i-1))C^i->^(d^i)C^(i+1)->... the module Z^i of i-cocycles Z^i is the kernel of d^i, which is a submodule of C^i.

A continuous vector bundle is a vector bundle pi:E->M with only the structure of a topological manifold. The map pi is continuous. It has no smooth structure or bundle metric.

The system of partial differential equations u_t = (u^2-u_x+2v)_x (1) v_y = (2uv+v_x)_x. (2)

A binary relation associated with an instance of the stable marriage problem. Stable marriages correspond to vertices with outdegree 0 in the divorce digraph (Skiena 1990, p. ...

A curve in two dimensions on which the value of a function f(x,y) is a constant. Other synonymous terms are isarithm, isopleth, and contour line. A plot of several ...

The knots that make up a knot sum of a composite knot are known as factor knots (Adams 1994, p. 8).

Let the vertices of a graph G be numbered with distinct integers 1 to |G|. Then the dilation of G is the maximum (absolute) difference between integers assigned to adjacent ...

The hexyl circle is the circumcircle of the hexyl triangle. Amazingly, its center is at the incenter I and its radius is 2R, where R is the circumradius. Its circle function ...

A necessary and sufficient condition for a measure which is quasi-invariant under a transformation to be equivalent to an invariant probability measure is that the ...

A transformation of an algebraic curve which is of the same type as its inverse. A Jonquière's transformation is always factorable.