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Betting odds are written in the form r:s ("r to s") and correspond to the probability of winning P=s/(r+s). Therefore, given a probability P, the odds of winning are ...

A noncompact manifold without boundary.

Let A:D(A)->H and B:D(B)->H be linear operators from domains D(A) and D(B), respectively, into a Hilbert space H. It is said that B extends A if D(A) subset D(B) and if Bv=Av ...

The fraction eta of a volume filled by a given collection of solids.

An ideal I of a partial order P is a subset of the elements of P which satisfy the property that if y in I and x<y, then x in I. For k disjoint chains in which the ith chain ...

A change in a knot projection such that a pair of oppositely oriented strands are passed through another pair of oppositely oriented strands.

The percentage error is 100% times the relative error.

Consider n intersecting ellipses. The maximal number of regions into which these divide the plane are N(n)=2n^2-2n+2=2(n^2-n+1), giving values for n=1, 2, ... of 2, 6, 14, ...

A point lattice is a regularly spaced array of points. In the plane, point lattices can be constructed having unit cells in the shape of a square, rectangle, hexagon, etc. ...

A triangle center is said to be polynomial iff there is a triangle center function f that is a polynomial in a, b, and c (Kimberling 1998, p. 46).