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

The prime signature of a positive integer n is a sorted list of nonzero exponents a_i in the prime factorization n=p_1^(a_1)p_2^(a_2).... By definition, the prime signature ...

The regular octahedron, often simply called "the" octahedron, is the Platonic solid with six polyhedron vertices, 12 polyhedron edges, and eight equivalent equilateral ...

Consider the sum (1) where the x_js are nonnegative and the denominators are positive. Shapiro (1954) asked if f_n(x_1,x_2,...,x_n)>=1/2n (2) for all n. It turns out ...

A Smarandache-Wellin number that is prime is known as a Smarandache-Wellin prime. Concatenations of the first n=1, 2, 4, 128, 174, 342, 435, 1429 (OEIS A046035; Ibstedt 1998, ...

A solvable Lie group is a Lie group G which is connected and whose Lie algebra g is a solvable Lie algebra. That is, the Lie algebra commutator series ...

A determinant used to determine in which coordinate systems the Helmholtz differential equation is separable (Morse and Feshbach 1953). A determinant S=|Phi_(mn)|=|Phi_(11) ...

The stellated truncated hexahedron (Maeder 1997), also called the quasitruncated hexahedron (Wenninger 1989, p. 144), is the uniform polyhedron with Maeder index 19 (Maeder ...

A square matrix with nonzero elements only on the diagonal and slots horizontally or vertically adjacent the diagonal (i.e., along the subdiagonal and superdiagonal), [a_(11) ...

A multivariate normal distribution in three variables. It has probability density function (1) where (2) The standardized trivariate normal distribution takes unit variances ...