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The set R union {infty}, obtained by adjoining one improper element to the set R of real numbers, is the set of projectively extended real numbers. Although notation is not ...

A quaternion Kähler manifold is a Riemannian manifold of dimension 4n, n>=2, whose holonomy is, up to conjugacy, a subgroup of Sp(n)Sp(1)=Sp(n)×Sp(1)/Z_2, but is not a ...

When discussing a rotation, there are two possible conventions: rotation of the axes, and rotation of the object relative to fixed axes. In R^2, consider the matrix that ...

Rubik's Cube is a 3×3×3 cube in which the 26 subcubes on the outside are internally hinged in such a way that rotation (by a quarter turn in either direction or a half turn) ...

A simple directed graph is a directed graph having no multiple edges or graph loops (corresponding to a binary adjacency matrix with 0s on the diagonal). The number of simple ...

Let sopfr(n) be the sum of prime factors (with repetition) of a number n. For example, 20=2^2·5, so sopfr(20)=2+2+5=9. Then sopfr(n) for n=1, 2, ... is given by 0, 2, 3, 4, ...

The total number of contravariant and covariant indices of a tensor. The rank R of a tensor is independent of the number of dimensions N of the underlying space. An intuitive ...

An n-trapezohedron, also called an antidipyramid, antibipyramid, or deltohedron (not to be confused with a deltahedron), is a solid composed of interleaved symmetric ...

Turmites, also called turning machines, are 2-dimensional Turing machines in which the "tape" consists of a grid of spaces that can be written and erased by an active ...

There are several different definitions of the term "unital" used throughout various branches of mathematics. In geometric combinatorics, a block design of the form (q^3+1, ...