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Let a hotel have a denumerable set of rooms numbered 1, 2, 3, .... Then any finite number n of guests can be accommodated without evicting the current guests by moving the ...

The second-order ordinary differential equation (d^2y)/(dx^2)+[theta_0+2sum_(n=1)^inftytheta_ncos(2nx)]y=0, (1) where theta_n are fixed constants. A general solution can be ...

A minimal embedded surface discovered in 1992 consisting of a helicoid with a hole and handle (Science News 1992). It has the same topology as a punctured sphere with a ...

A point where a stable and an unstable separatrix (invariant manifold) from the same fixed point or same family intersect. Therefore, the limits lim_(k->infty)f^k(X) and ...

Hyperreal numbers are an extension of the real numbers to include certain classes of infinite and infinitesimal numbers. A hyperreal number x is said to be finite iff |x|<n ...

The idempotent numbers are given by B_(n,k)(1,2,3,...)=(n; k)k^(n-k), where B_(n,k) is a Bell polynomial and (n; k) is a binomial coefficient. A table of the first few is ...

A matrix is ill-conditioned if the condition number is too large (and singular if it is infinite).

Define the "information function" to be I=-sum_(i=1)^NP_i(epsilon)ln[P_i(epsilon)], (1) where P_i(epsilon) is the natural measure, or probability that element i is populated, ...

Let (A,<=) be a well ordered set. Then the set {a in A:a<k} for some k in A is called an initial segment of A (Rubin 1967, p. 161; Dauben 1990, pp. 196-197; Moore 1982, pp. ...

There are at least two distinct notions of an intensity function related to the theory of point processes. In some literature, the intensity lambda of a point process N is ...