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If a is an arbitrary integer relatively prime to n and g is a primitive root of n, then there exists among the numbers 0, 1, 2, ..., phi(n)-1, where phi(n) is the totient ...

Discrete Mathematics

C_2×C_4 is one of the three Abelian groups of group order 8 (the other two being non-Abelian). Examples include the modulo multiplication groups M_(15), M_(16), M_(20), and ...

Let S be a semigroup and alpha a positive real-valued function on S such that alpha(st)<=alpha(s)alpha(t) (s,t in S). If l^1(S,alpha) is the set of all complex-valued ...

The set of left cosets of a subgroup H of a topological group G forms a topological space. Its topology is defined by the quotient topology from pi:G->G/H. Namely, the open ...

The continuous Fourier transform is defined as f(nu) = F_t[f(t)](nu) (1) = int_(-infty)^inftyf(t)e^(-2piinut)dt. (2) Now consider generalization to the case of a discrete ...

The discrete uniform distribution is also known as the "equally likely outcomes" distribution. Letting a set S have N elements, each of them having the same probability, then ...

The term discrete percolation is used to describe models of percolation theory whose media are discrete sets like sets of regular lattice points (e.g., bond percolation and ...

A family composed of countably many discrete families.

The group of an elliptic curve which has been transformed to the form y^2=x^3+ax+b is the set of K-rational points, including the single point at infinity. The group law ...