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For d>=1, Omega an open subset of R^d, p in [1;+infty] and s in N, the Sobolev space W^(s,p)(R^d) is defined by W^(s,p)(Omega)={f in L^p(Omega): forall ...

While early soccer balls were constructed in a number of ways, a fairly stadard 32-panel ball was designed by Danish national team goalkeeer Eigil Nielsen in 1962. This was ...

Sociable numbers are numbers that result in a periodic aliquot sequence, where an aliquot sequence is the sequence of numbers obtained by repeatedly applying the restricted ...

The theory of analyzing a decision between a collection of alternatives made by a collection of n voters with separate opinions. Any choice for the entire group should ...

Twenty golfers wish to play in foursomes for 5 days. Is it possible for each golfer to play no more than once with any other golfer? The answer is yes, and the following ...

The socle of a group G is the subgroup generated by its minimal normal subgroups. For example, the symmetric group S_4 has two nontrivial normal subgroups: A_4 and ...

Socrates is reported to have stated: "One thing I know is that I know nothing."

Given three mutually tangent circles, there exist exactly two nonintersecting circles which are tangent circles to all three original circles. These are called the inner and ...

Given three noncollinear points, construct three tangent circles such that one is centered at each point and the circles are pairwise tangent to one another. Then there exist ...

The triangle line that passes through the inner and outer Soddy centers S and S^'. The Soddy line is central line L_(657) and has trilinear equation ...