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The direct sum of modules A and B is the module A direct sum B={a direct sum b|a in A,b in B}, (1) where all algebraic operations are defined componentwise. In particular, ...

The monster group is the highest order sporadic group M. It has group order |M| = (1) = (2) where the divisors are precisely the 15 supersingular primes (Ogg 1980). The ...

A generalization of the factorial and double factorial, n! = n(n-1)(n-2)...2·1 (1) n!! = n(n-2)(n-4)... (2) n!!! = n(n-3)(n-6)..., (3) etc., where the products run through ...

A multivariate is a vector each of whose elements is a variate. The variates need not be independent, and if they are not, a correlation is said to exist between them. The ...

Multivariate analysis is the simultaneous statistical consideration of relationships among many measured properties of a given system (Gould 1996, p. 42).

NAND, also known as the Sheffer stroke, is a connective in logic equivalent to the composition NOT AND that yields true if any condition is false, and false if all conditions ...

NAND, also known as the Sheffer stroke, is a connective in logic equivalent to the composition NOT AND that yields true if any condition is false, and false if all conditions ...

A geometric construction, also called a verging construction, which allows the classical geometric construction rules to be bent in order to permit sliding of a marked ruler. ...

Samuel Pepys wrote Isaac Newton a long letter asking him to determine the probabilities for a set of dice rolls related to a wager he planned to make. Pepys asked which was ...

A vector space V with a ring structure and a vector norm such that for all v,W in V, ||vw||<=||v||||w||. If V has a multiplicative identity 1, it is also required that ...