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A set of identities involving n-dimensional visible lattice points was discovered by Campbell (1994). Examples include product_((a,b)=1; ...

Let f be a contraction mapping from a closed subset F of a Banach space E into F. Then there exists a unique z in F such that f(z)=z.

Let A be a closed convex subset of a Banach space and assume there exists a continuous map T sending A to a countably compact subset T(A) of A. Then T has fixed points.

An algorithm for partitioning (or clustering) N data points into K disjoint subsets S_j containing N_j data points so as to minimize the sum-of-squares criterion ...

The partitioning of a plane with n points into convex polygons such that each polygon contains exactly one generating point and every point in a given polygon is closer to ...

A surface possessing a saddle point.

The value at a stationary point.

When a point P moves along a line through the circumcenter of a given triangle Delta, the pedal circle of P with respect to Delta passes through a fixed point (the Griffiths ...

A point of discontinuity, also called a leap.

For every partition of all the points on a line into two nonempty sets such that no point of either lies between two points of the other, there is a point of one set which ...