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A free Abelian group is a group G with a subset which generates the group G with the only relation being ab=ba. That is, it has no group torsion. All such groups are a direct ...

"The" Jacobi identity is a relationship [A,[B,C]]+[B,[C,A]]+[C,[A,B]]=0,, (1) between three elements A, B, and C, where [A,B] is the commutator. The elements of a Lie algebra ...

A univariate function f(x) is said to be odd provided that f(-x)=-f(x). Geometrically, such functions are symmetric about the origin. Examples of odd functions include x, ...

The permutation tensor, also called the Levi-Civita tensor or isotropic tensor of rank 3 (Goldstein 1980, p. 172), is a pseudotensor which is antisymmetric under the ...

A prime factorization algorithm which can be implemented in a single-step or double-step form. In the single-step version, a prime factor p of a number n can be found if p-1 ...

A sphenic number is a positive integer n which is the product of exactly three distinct primes. The first few sphenic numbers are 30, 42, 66, 70, 78, 102, 105, 110, 114, ... ...

In the biconjugate gradient method, the residual vector r^((i)) can be regarded as the product of r^((0)) and an ith degree polynomial in A, i.e., r^((i))=P_i(A)r^((0)). (1) ...

The hypersine (n-dimensional sine function) is a function of a vertex angle of an n-dimensional parallelotope or simplex. If the content of the parallelotope is P and the ...

An unsolved problem in mathematics attributed to Lehmer (1933) that concerns the minimum Mahler measure M_1(P) for a univariate polynomial P(x) that is not a product of ...

product_(i)dp_idq_i, where p_i and q_i are momenta and positions of particles.