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The inverse limit of a family of R-modules is the dual notion of a direct limit and is characterized by the following mapping property. For a directed set I and a family of ...

Let S_n be the sum of n random variates X_i with a Bernoulli distribution with P(X_i=1)=p_i. Then sum_(k=0)^infty|P(S_n=k)-(e^(-lambda)lambda^k)/(k!)|<2sum_(i=1)^np_i^2, ...

The Moscow-Soicher graph is a weakly regular graph on 672 vertices with parameters (nu,k,lambda,mu)=(672,110,28,(0,18)). It is distance-regular but not distance-transitive ...

A diagram lemma also known as 3×3 lemma. According to its most general statement, the commutative diagram illustrated above with exact rows and columns can be completed by ...

Numerical differentiation is the process of finding the numerical value of a derivative of a given function at a given point. In general, numerical differentiation is more ...

An operator A:f^((n))(I)|->f(I) assigns to every function f in f^((n))(I) a function A(f) in f(I). It is therefore a mapping between two function spaces. If the range is on ...

A system of curvilinear coordinates. There are several different conventions for the orientation and designation of these coordinates. Arfken (1970) defines coordinates ...

The index of a permutation p is defined as the sum of all subscripts j such that p_j>p_(j+1), for 1<=j<=n. MacMahon (1960) proved that the number of permutations of size n ...

Any entire analytic function whose range omits two points must be a constant function. Of course, an entire function that omits a single point from its range need not be a ...

A separating family is a set of subsets in which each pair of adjacent elements are found separated, each in one of two disjoint subsets. The 26 letters of the alphabet can ...