Search Results for ""

A paracompact space is a T2-space such that every open cover has a locally finite open refinement. Paracompactness is a very common property that topological spaces satisfy. ...

The first and second Pöschl-Teller differential equations are given by y^('')-{a^2[(kappa(kappa-1))/(sin^2(ax))+(lambda(lambda-1))/(cos^2(ax))]-b^2}y=0 and ...

In the theory of special functions, a class of functions is said to be "of the third kind" if it is similar to but distinct from previously defined functions already defined ...

Let H_nu^((iota))(x) be a Hankel function of the first or second kind, let x,nu>0, and define w=sqrt((x/nu)^2-1). Then ...

The nine-point circle, also called Euler's circle or the Feuerbach circle, is the circle that passes through the perpendicular feet H_A, H_B, and H_C dropped from the ...

Linnik's constant L is the constant appearing in Linnik's theorem. Heath-Brown (1992) has shown that L<=5.5, and Schinzel, Sierpiński, and Kanold (Ribenboim 1989) have ...

In 1891, Chebyshev and Sylvester showed that for sufficiently large x, there exists at least one prime number p satisfying x<p<(1+alpha)x, where alpha=0.092.... Since the ...

A manifold possessing a metric tensor. For a complete Riemannian manifold, the metric d(x,y) is defined as the length of the shortest curve (geodesic) between x and y. Every ...

Given a group of n men arranged in a circle under the edict that every mth man will be executed going around the circle until only one remains, find the position L(n,m) in ...

There are a number of attractive cube 20-compounds that can be constructed by taking the duals of the octahedra in the two octahedron 20-compounds. The second of these was ...