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The average number of regions N(n) into which n lines divide a square is N^_(n)=1/(16)n(n-1)pi+n+1 (Santaló 1976; Finch 2003, p. 481). The maximum number of sequences is ...

The square knot, also called the reef knot, is a composite knot of six crossings consisting of a knot sum of a trefoil knot and its mirror image (Rolfsen 1976, p. 220). The ...

A collection of subsets of a topological space that is contained in a basis of the topology and can be completed to a basis when adding all finite intersections of the ...

In the tabu search category of meta-heuristics, the essential idea is to 'forbid' search moves to points already visited in the (usually discrete) search space, at least for ...

Given a doubled knot with the unknot taken as the base knot K_1, the companion knot K_2 of K_1 is called a twist knot with q twists. As illustrated above, the following knots ...

An unduloid, also called an onduloid, is a surface of revolution with constant nonzero mean curvature. It is a roulette obtained from the path described by the foci of a ...

A topological space that contains a homeomorphic image of every topological space of a certain class. A metric space U is said to be universal for a family of metric spaces M ...

Vardi's integral is the beautiful definite integral int_(pi/4)^(pi/2)lnlntanxdx = pi/2ln[sqrt(2pi)(Gamma(3/4))/(Gamma(1/4))] (1) = pi/4ln[(4pi^3)/(Gamma^4(1/4))] (2) = ...

The Weierstrass constant is defined as the value sigma(1|1,i)/2, where sigma(z|omega_1,omega_2) is the Weierstrass sigma function with half-periods omega_1 and omega_2. ...

A statistic w on the symmetric group S_n is called a weighted inversion statistic if there exists an upper triangular matrix W=(w_(ij)) such that ...