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States that for a nondissipative Hamiltonian system, phase space density (the area between phase space contours) is constant. This requires that, given a small time increment ...

The longest increasing scattered subsequence is the longest subsequence of increasing terms, where intervening nonincreasing terms may be dropped. Finding the largest ...

A maximal independent edge set of a graph is an independent edge set that cannot be expanded to another independent edge set by addition of any edge in the graph. Note that a ...

The natural norm induced by the L1-norm is called the maximum absolute column sum norm and is defined by ||A||_1=max_(j)sum_(i=1)^n|a_(ij)| for a matrix A. This matrix norm ...

This problem is NP-complete (Garey and Johnson 1983).

Given an original triangle (thick line), find the medial triangle (outer thin line) and its incircle. Take the pedal triangle (inner thin line) of the medial triangle with ...

For x>0, J_0(x) = 2/piint_0^inftysin(xcosht)dt (1) Y_0(x) = -2/piint_0^inftycos(xcosht)dt, (2) where J_0(x) is a zeroth order Bessel function of the first kind and Y_0(x) is ...

(1) where H_n(x) is a Hermite polynomial (Watson 1933; Erdélyi 1938; Szegö 1975, p. 380). The generating function ...

det(i+j+mu; 2i-j)_(i,j=0)^(n-1)=2^(-n)product_(k=0)^(n-1)Delta_(2k)(2mu), where mu is an indeterminate, Delta_0(mu)=2, ...

A bounded plane convex region symmetric about a lattice point and with area >4 must contain at least three lattice points in the interior. In n dimensions, the theorem can be ...