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A minimum vertex cut of a graph is a vertex cut of smallest possible size. A vertex cut set of size 1 in a connected graph corresponds to an articulation vertex. The size of ...

In many cases, the Hausdorff dimension correctly describes the correction term for a resonator with fractal perimeter in Lorentz's conjecture. However, in general, the proper ...

There are four fixed points (mod 1) of Minkowski's question mark function ?(x), namely x=0, 1/2, f and 1-f, where f<1/2 is a constant known as the Minkowski-Bower constant ...

There exist lattices in n dimensions having hypersphere packing densities satisfying eta>=(zeta(n))/(2^(n-1)), where zeta(n) is the Riemann zeta function. However, the proof ...

Polynomials M_k(x) which form the associated Sheffer sequence for f(t)=(e^t-1)/(e^t+1) (1) and have the generating function sum_(k=0)^infty(M_k(x))/(k!)t^k=((1+t)/(1-t))^x. ...

If a function analytic at the origin has no singularities other than poles for finite x, and if we can choose a sequence of contours C_m about z=0 tending to infinity such ...

The group Gamma of all Möbius transformations of the form tau^'=(atau+b)/(ctau+d), (1) where a, b, c, and d are integers with ad-bc=1. The group can be represented by the 2×2 ...

The unique 8_3 configuration. It is transitive and self-dual, but cannot be realized in the real projective plane. Its Levi graph is the Möbius-Kantor graph.

Tiling of a Möbius strip can be performed immediately by carrying over a tiling of a rectangle with the same two-sided surface area. However, additional tilings are possible ...

The theorem of Möbius tetrads, also simply called Möbius's theorem by Baker (1925, p. 18), may be stated as follows. Let P_1, P_2, P_3, and P_4 be four arbitrary points in a ...