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If A and B are commutative unit rings, and A is a subring of B, then A is called integrally closed in B if every element of B which is integral over A belongs to A; in other ...

In univariate interpolation, an interpolant is a function L=L(x) which agrees with a particular function f at a set of known points x_0,x_1,x_2,...,x_n and which is used to ...

An element admitting a multiplicative or additive inverse. In most cases, the choice between these two options is clear from the context, as, for example, in a monoid, where ...

The (lower) irredundance number ir(G) of a graph G is the minimum size of a maximal irredundant set of vertices in G. The upper irredundance number is defined as the maximum ...

Let R[z]>0, 0<=alpha,beta<=1, and Lambda(alpha,beta,z)=sum_(r=0)^infty[lambda((r+alpha)z-ibeta)+lambda((r+1-alpha)z+ibeta)], (1) where lambda(x) = -ln(1-e^(-2pix)) (2) = ...

If, after constructing a difference table, no clear pattern emerges, turn the paper through an angle of 60 degrees and compute a new table. If necessary, repeat the process. ...

A relation connecting the values of a meromorphic function inside a disk with its boundary values on the circumference and with its zeros and poles (Jensen 1899, Levin 1980). ...

For every k>=1, let C_k be the set of composite numbers n>k such that if 1<a<n, GCD(a,n)=1 (where GCD is the greatest common divisor), then a^(n-k)=1 (mod n). Special cases ...

The signature s(K) of a knot K can be defined using the skein relationship s(unknot)=0 (1) s(K_+)-s(K_-) in {0,2}, (2) and 4|s(K)<->del (K)(2i)>0, (3) where del (K) is the ...

The mathematical study of knots. Knot theory considers questions such as the following: 1. Given a tangled loop of string, is it really knotted or can it, with enough ...