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Exchanges branches of the hyperbola x^'y^'=xy. x^' = mu^(-1)x (1) y^' = -muy. (2)

A series s_1,s_2,... for which s_1>=s_2>=....

By analogy with the divisor function sigma_1(n), let pi(n)=product_(d|n)d (1) denote the product of the divisors d of n (including n itself). For n=1, 2, ..., the first few ...

A pair of overdots placed over a symbol, as in x^.., most commonly used to denote a second derivative with respect to time, i.e., x^..=d^2x/dt^2.

Johnson solid J_(18).

The three diagonal points of a complete quadrilateral are never collinear.

Any bivariate distribution function with marginal distribution functions F and G satisfies max{F(x)+G(y)-1,0}<=H(x,y)<=min{F(x),G(y)}.

For n players, n-1 games are needed to fairly determine first place, and n-1+lg(n-1) are needed to fairly determine first and second place.

The generalized law of sines applies to a simplex in space of any dimension with constant Gaussian curvature. Let us work up to that. Initially in two-dimensional space, we ...

Grünbaum conjectured that for every m>1, n>2, there exists an m-regular, m-chromatic graph of girth at least n. This result is trivial for n=2 and m=2,3, but only a small ...