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The Gram series is an approximation to the prime counting function given by G(x)=1+sum_(k=1)^infty((lnx)^k)/(kk!zeta(k+1)), (1) where zeta(z) is the Riemann zeta function ...

A Hamiltonian walk on a connected graph is a closed walk of minimal length which visits every vertex of a graph (and may visit vertices and edges multiple times). For ...

In cylindrical coordinates, the scale factors are h_r=1, h_theta=r, h_z=1, so the Laplacian is given by del ...

Given a 111×111 (0,1)-matrix, fill 11 spaces in each row in such a way that all columns also have 11 spaces filled. Furthermore, each pair of rows must have exactly one ...

Using the notation of Byerly (1959, pp. 252-253), Laplace's equation can be reduced to (1) where alpha = cint_c^lambda(dlambda)/(sqrt((lambda^2-b^2)(lambda^2-c^2))) (2) = ...

In spherical coordinates, the scale factors are h_r=1, h_theta=rsinphi, h_phi=r, and the separation functions are f_1(r)=r^2, f_2(theta)=1, f_3(phi)=sinphi, giving a Stäckel ...

There are several types of numbers that are commonly termed "lucky numbers." The first is the lucky numbers of Euler. The second is obtained by writing out all odd numbers: ...

A system of curvilinear coordinates in which two sets of coordinate surfaces are obtained by revolving the curves of the elliptic cylindrical coordinates about the y-axis ...

A quintic nonhamiltonian graph is a quintic graph that is nonhamiltonian. A number of such graphs are illustrated above. Owens (1980) showed that there exists a ...

Sphere line picking is the selection of pairs of points corresponding to vertices of a line segment with endpoints on the surface of a sphere. n random line segments can be ...