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The projective plane crossing number of a graph is the minimal number of crossings with which the graph can be drawn on the real projective plane. A graph with projective ...

Proper covers are defined as covers of a set X which do not contain the entire set X itself as a subset (Macula 1994). Of the five covers of {1,2}, namely {{1},{2}}, {{1,2}}, ...

A positive proper divisor is a positive divisor of a number n, excluding n itself. For example, 1, 2, and 3 are positive proper divisors of 6, but 6 itself is not. The number ...

A Proth number is a number of the form N=k·2^n+1 for odd k, n a positive integer, and 2^n>k. The 2^n>k condition is needed since otherwise, every odd number >1 would be a ...

A pseudoforest is an undirected graph in which every connected component contains at most one graph cycle. A pseudotree is therefore a connected pseudoforest and a forest ...

The case of the Weierstrass elliptic function with invariants g_2=-1 and g_3=0. The half-periods for this case are L(1+i)/4 and L(-1+i)/4, where L is the lemniscate constant ...

The pseudosmarandache function Z(n) is the smallest integer such that sum_(k=1)^(Z(n))k=1/2Z(n)[Z(n)+1] is divisible by n. The values for n=1, 2, ... are 1, 3, 2, 7, 4, 3, 6, ...

A pseudotree is a connected pseudoforest, i.e., an undirected connected graph that contains at most one graph cycle. Connected acyclic graphs (i.e., trees), are therefore ...

For a cyclic quadrilateral, the sum of the products of the two pairs of opposite sides equals the product of the diagonals AB×CD+BC×DA=AC×BD (1) (Kimberling 1998, p. 223). ...

Quinn et al. (2007) investigated a class of N coupled oscillators whose bifurcation phase offset had a conjectured asymptotic behavior of sinphi∼1-c_1/N, with an experimental ...