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A measure lambda is absolutely continuous with respect to another measure mu if lambda(E)=0 for every set with mu(E)=0. This makes sense as long as mu is a positive measure, ...

Given a number field K, a Galois extension field L, and prime ideals p of K and P of L unramified over p, there exists a unique element sigma=((L/K),P) of the Galois group ...

A number n is called a barrier of a number-theoretic function f(m) if, for all m<n, m+f(m)<=n. Neither the totient function phi(n) nor the divisor function sigma(n) has a ...

A CW-complex is a homotopy-theoretic generalization of the notion of a simplicial complex. A CW-complex is any space X which can be built by starting off with a discrete ...

A composite knot is a knot that is not a prime knot. Schubert (1949) showed that every knot can be uniquely decomposed (up to the order in which the decomposition is ...

The ratio C of the largest to smallest singular value in the singular value decomposition of a matrix. The base-b logarithm of C is an estimate of how many base-b digits are ...

A cryptographic hash function is most commonly one of the following: a one-way hash function, a collision-free hash function, a trapdoor one-way hash function, or a function ...

The partial order width of a set P is equal to the minimum number of chains needed to cover P. Equivalently, if a set P of ab+1 elements is partially ordered, then P contains ...

A Dyck path is a staircase walk from (0,0) to (n,n) that lies strictly below (but may touch) the diagonal y=x. The number of Dyck paths of order n is given by the Catalan ...

Consider a point P inside a reference triangle DeltaABC, construct line segments AP, BP, and CP. The Ehrmann congruent squares point is the unique point P such that three ...