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A fundamental result of de Rham cohomology is that the kth de Rham cohomology vector space of a manifold M is canonically isomorphic to the Alexander-Spanier cohomology ...

A number that is "close" to (but not equal to) zero may be called an almost zero. In contrast, a number or expression that is equal to zero is said to be identically zero. ...

Let {A_n}_(n=0)^infty be a sequence of events occurring with a certain probability distribution, and let A be the event consisting of the occurrence of a finite number of ...

A class number formula is a finite series giving exactly the class number of a ring. For a ring of quadratic integers, the class number is denoted h(d), where d is the ...

The concatenation of two strings a and b is the string ab formed by joining a and b. Thus the concatenation of the strings "book" and "case" is the string "bookcase". The ...

The closed cyclic self-intersecting hexagon formed by joining the adjacent antiparallels in the construction of the cosine circle. The sides of this hexagon have the property ...

A diminished polyhedron is a polyhedron in which one or more groups of associated faces (such as those comprising the top of a pyramid or cupola in the case of a Johnson ...

If, for n and d integers, the ratio n/d is itself an integer, then d is said to divide n. This relationship is written d|n, read "d divides n." In this case, n is also said ...

There are two similar but distinct concepts related to equidecomposability: "equidecomposable" and "equidecomposable by dissection." The difference is in that the pieces ...

A special case of the Artin L-function for the polynomial x^2+1. It is given by L(s)=product_(p odd prime)1/(1-chi^-(p)p^(-s)), (1) where chi^-(p) = {1 for p=1 (mod 4); -1 ...