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An orthogonal transformation is a linear transformation T:V->V which preserves a symmetric inner product. In particular, an orthogonal transformation (technically, an ...

Given a set X, a set function mu^*:2^X->[0,infty] is said to be an outer measure provided that mu^*(emptyset)=0 and that mu^* is countably monotone, where emptyset is the ...

A number of graphs are associated with P. J. Owens. The 76-node Owens graph (Owens 1980) provides the smallest known example of a polyhedral quintic nonhamiltonian graph. It ...

The pair group of a group G is the group that acts on the 2-subsets of {1,...,p} whose permutations are induced by G. Pair groups can be calculated using PairGroup[g] in the ...

A simple unlabeled graph on n vertices is called pancyclic if it contains cycles of all lengths, 3, 4, ..., n. Since a pancyclic graph must contain a cycle of length n, ...

A pandiagonal perfect magic cube is a perfect magic cube that remains perfect when any single orthogonal section is "restacked" cyclically so that the ordering of any set of ...

A fraction containing each of the digits 1 through 9 is called a pandigital fraction. The following table gives the number of pandigital fractions which represent simple unit ...

A linkage invented in 1630 by Christoph Scheiner for making a scaled copy of a given figure. The linkage is pivoted at O; hinges are denoted circledot . By placing a pencil ...

A system of curvilinear coordinates in which two sets of coordinate surfaces are obtained by revolving the parabolas of parabolic cylindrical coordinates about the x-axis, ...

The parabolic cylinder differential equation is the second-order ordinary differential equation y^('')+(nu+1/2-1/4z^2)y=0 (1) whose solution is given by ...