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Two nodes connected to the same node which are same distance from the root vertex in a rooted tree are called siblings. A function to return the siblings of a vertex v in a ...

The socle of a group G is the subgroup generated by its minimal normal subgroups. For example, the symmetric group S_4 has two nontrivial normal subgroups: A_4 and ...

The line segment connecting opposite polyhedron vertices (i.e., two polyhedron vertices which do not share a common face) in a parallelepiped or other similar solid. Also ...

A spherical shell is a generalization of an annulus to three dimensions. A spherical shell is therefore the region between two concentric spheres of differing radii. The ...

Teichmüller's theorem asserts the existence and uniqueness of the extremal quasiconformal map between two compact Riemann surfaces of the same genus modulo an equivalence ...

The difference X_1-X_2 of two uniform variates on the interval [0,1] can be found as P_(X_1-X_2)(u) = int_0^1int_0^1delta((x-y)-u)dxdy (1) = 1-u+2uH(-u), (2) where delta(x) ...

Jacobi theta functions can be used to uniformize all elliptic curves. Jacobi elliptic functions may also be used to uniformize some hyperelliptic curves, although only two ...

Dürer's solid, also known as the truncated triangular trapezohedron, is the 8-faced solid depicted in an engraving entitled Melencolia I by Albrecht Dürer (The British ...

In 1803, Malfatti posed the problem of determining the three circular columns of marble of possibly different sizes which, when carved out of a right triangular prism, would ...

The Weierstrass elliptic functions (or Weierstrass P-functions, voiced "p-functions") are elliptic functions which, unlike the Jacobi elliptic functions, have a second-order ...