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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 ...

Let [a_0;a_1,a_2,...] be the simple continued fraction of a "generic" real number, where the numbers a_i are the partial quotients. Then the Khinchin (or Khintchine) harmonic ...

The continued fraction for K is [2; 1, 2, 5, 1, 1, 2, 1, 1, ...] (OEIS A002211). A plot of the first 256 terms of the continued fraction represented as a sequence of binary ...

Given a sum and a set of weights, find the weights which were used to generate the sum. The values of the weights are then encrypted in the sum. This system relies on the ...

The Lemoine hexagon is a cyclic hexagon with vertices given by the six concyclic intersections of the parallels of a reference triangle through its symmedian point K. The ...

A Lie group is a group with the structure of a manifold. Therefore, discrete groups do not count. However, the most useful Lie groups are defined as subgroups of some matrix ...

A representation of a Lie algebra g is a linear transformation psi:g->M(V), where M(V) is the set of all linear transformations of a vector space V. In particular, if V=R^n, ...

A bounded entire function in the complex plane C is constant. The fundamental theorem of algebra follows as a simple corollary.

Infinite series of various simple functions of the logarithm include sum_(k=1)^^^inftylnk = 1/2ln(2pi) (1) sum_(k=1)^^^infty(-1)^klnk = 1/2ln(1/2pi) (2) ...

The Markström graph is a cubic planar graph on 24 vertices which lacks cycles of length 4 and 8 but contains cycles of length 16. (In particular, it contains cycles of ...