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Two points P,Q on a compact Riemann surface such that P lies on every geodesic passing through Q, and conversely. An oriented surface where every point belongs to a ...

Let E_n(f) be the error of the best uniform approximation to a real function f(x) on the interval [-1,1] by real polynomials of degree at most n. If alpha(x)=|x|, (1) then ...

Any partition of the plane into regions of equal area has perimeter at least that of the regular hexagonal grid (i.e., the honeycomb, illustrated above). Pappus refers to the ...

Consider the Fibonacci-like recurrence a_n=+/-a_(n-1)+/-a_(n-2), (1) where a_0=0, a_1=1, and each sign is chosen independently and at random with probability 1/2. ...

A polyomino is a generalization of the domino to a collection of n squares of equal size arranged with coincident sides. Polyominos were originally called "super-dominoes" by ...

Differential Equations

Let {a_i}_(i=1)^n be a set of positive numbers. Then sum_(i=1)^n(a_1a_2...a_i)^(1/i)<=esum_(i=1)^na_i (which is given incorrectly in Gradshteyn and Ryzhik 2000). Here, the ...

The detour polynomial of a graph G is the characteristic polynomial of the detour matrix of G. Precomputed detour polynomials for many named graphs are available in the ...

The determination of a test for the equality of means for two normal distributions with different variances given samples from each. There exists an exact test which, ...

A minimal cover is a cover for which removal of any single member destroys the covering property. For example, of the five covers of {1,2}, namely {{1},{2}}, {{1,2}}, ...