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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 ...

Given two paired sets X_i and Y_i of n measured values, the paired t-test determines whether they differ from each other in a significant way under the assumptions that the ...

An expanded paper bag, cushion, or pillow has a distinctive shape. Given the dimensions of a flat rectangular bag with dimensions a, b, bounds for the maximum volume of ...

The parabiaugmented truncated dodecahedron is a convex equilateral solid that is Johnson solid J_(69). The unit parabiaugmented truncated dodecahedron has volume ...

The parabididiminished rhombicosidodecahedron is a convex equilateral solid that is Johnson solid J_(820). The unit parabididiminished rhombicosidodecahedron ...

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 ...

A system of curvilinear coordinates. There are several different conventions for the orientation and designation of these coordinates. Arfken (1970) defines coordinates ...

Parallel curves, frequently called "offset curves" in computer graphics applications, are curves which are displaced from a base curve by a constant offset, either positive ...

Move a point Pi_0 along a line from an initial point to a final point. It traces out a line segment Pi_1. When Pi_1 is translated from an initial position to a final ...