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Let K be a number field with ring of integers R and let A be a nontrivial ideal of R. Then the ideal class of A, denoted [A], is the set of fractional ideals B such that ...

Conditions at an initial time t=t_0 from which a given set of mathematical equations or physical system evolves. A system with initial conditions specified is known as an ...

Let S={x_1,...,x_n} be a set of n distinct positive integers. Then the matrix [S]_n having the least common multiple LCM(x_i,x_j) of x_i and x_j as its i,jth entry is called ...

L=sigma/(sigma_B), where sigma is the variance in a set of s Lexis trials and sigma_B is the variance assuming Bernoulli trials. If L<1, the trials are said to be subnormal, ...

Pathological functions that are continuous but differentiable only on a set of points of measure zero are sometimes known as monsters of real analysis. Examples include the ...

A theorem in game theory which guarantees the existence of a set of mixed strategies for finite, noncooperative games of two or more players in which no player can improve ...

The set of nilpotent elements in a commutative ring is an ideal, and it is called the nilradical. Another equivalent description is that it is the intersection of the prime ...

An orthogonal array OA(k,s) is a k×s^2 array with entries taken from an s-set S having the property that in any two rows, each ordered pair of symbols from S occurs exactly ...

An analog of the determinant for number triangles defined as a signed sum indexed by set partitions of {1,...,n} into pairs of elements. The Pfaffian is the square root of ...

If f is analytic on a domain U, then a point z_0 on the boundary partialU is called regular if f extends to be an analytic function on an open set containing U and also the ...