Search Results for ""

The blow-up lemma essentially says that regular pairs in Szemerédi's regularity lemma behave like complete bipartite graphs from the point of view of embedding bounded degree ...

A theorem about (or providing an equivalent definition of) compact sets, originally due to Georg Cantor. Given a decreasing sequence of bounded nonempty closed sets C_1 ...

The functions describing the horizontal and vertical positions of a point on a circle as a function of angle (cosine and sine) and those functions derived from them: cotx = ...

The second-order ordinary differential equation xy^('')+(c-x)y^'-ay=0, sometimes also called Kummer's differential equation (Slater 1960, p. 2; Zwillinger 1997, p. 124). It ...

An integral obtained by contour integration. The particular path in the complex plane used to compute the integral is called a contour. As a result of a truly amazing ...

C_3 is the unique group of group order 3. It is both Abelian and cyclic. Examples include the point groups C_3, C_(3v), and C_(3h) and the integers under addition modulo 3 ...

C_5 is the unique group of group order 5, which is Abelian. Examples include the point group C_5 and the integers mod 5 under addition (Z_5). No modulo multiplication group ...

C_7 is the cyclic group that is the unique group of group order 7. Examples include the point group C_7 and the integers modulo 7 under addition (Z_7). No modulo ...

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 ...

A polynomial Z_G(q,v) in two variables for abstract graphs. A graph with one graph vertex has Z=q. Adding a graph vertex not attached by any graph edges multiplies the Z by ...