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The inversion of a convolution equation, i.e., the solution for f of an equation of the form f*g=h+epsilon, given g and h, where epsilon is the noise and * denotes the ...

A function f(x) decreases on an interval I if f(b)<=f(a) for all b>a, where a,b in I. If f(b)<f(a) for all b>a, the function is said to be strictly decreasing. Conversely, a ...

A set partition of the rational numbers into two nonempty subsets S_1 and S_2 such that all members of S_1 are less than those of S_2 and such that S_1 has no greatest ...

The Dedekind psi-function is defined by the divisor product psi(n)=nproduct_(p|n)(1+1/p), (1) where the product is over the distinct prime factors of n, with the special case ...

A Dedekind ring is a commutative ring in which the following hold. 1. It is a Noetherian ring and a integral domain. 2. It is the set of algebraic integers in its field of ...

The determination of the number of monotone Boolean functions of n variables (equivalent to the number of antichains on the n-set {1,2,...,n}) is called Dedekind's problem, ...

A metatheorem in mathematical logic also known under the name "conditional proof." It states that if the sentential formula B can be derived from the set of sentential ...

Given binomial coefficient (N; k), write N-k+i=a_ib_i, for 1<=i<=k, where b_i contains only those prime factors >k. Then the number of i for which b_i=1 (i.e., for which all ...

Numbers which are not perfect and for which s(N)=sigma(N)-N<N, or equivalently sigma(n)<2n, where sigma(N) is the divisor function. Deficient numbers are sometimes called ...

A limiting case in which a class of object changes its nature so as to belong to another, usually simpler, class. For example, the point is a degenerate case of the circle as ...