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N. Nielsen (1909) and Ramanujan (Berndt 1985) considered the integrals a_k=int_1^2((lnx)^k)/(x-1)dx. (1) They found the values for k=1 and 2. The general constants for k>3 ...

Define a pebbling move as a transer of two pebbles from one vertex of a graph edge to an adjacent vertex with one of the pebbles being removed in transit as a toll. The ...

For some authors (e.g., Bourbaki, 1964), the same as principal ideal domain. Most authors, however, do not require the ring to be an integral domain, and define a principal ...

A prolate spheroid is a spheroid that is "pointy" instead of "squashed," i.e., one for which the polar radius c is greater than the equatorial radius a, so c>a (called ...

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 x-axis, ...

Quasi-Monte Carlo integration is a method of numerical integration that operates in the same way as Monte Carlo integration, but instead uses sequences of quasirandom numbers ...

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 ...

The reversal of a positive integer abc...z is z...cba. The reversal of a positive integer n is implemented in the Wolfram Language as IntegerReverse[n]. A positive integer ...

In his famous paper of 1859, Riemann stated that the number N(T) of Riemann zeta function zeros sigma+it with 0<t<=T is asymptotically given by ...

Every smooth nonzero vector field on the 3-sphere has at least one closed orbit. The conjecture was proposed in 1950 and proved true for Hopf maps. The conjecture was ...