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Eisenstein's irreducibility criterion is a sufficient condition assuring that an integer polynomial p(x) is irreducible in the polynomial ring Q[x]. The polynomial ...

An elliptic fixed point of a differential equation is a fixed point for which the stability matrix has purely imaginary eigenvalues lambda_+/-=+/-iomega (for omega>0). An ...

In real and functional analysis, equicontinuity is a concept which extends the notion of uniform continuity from a single function to collection of functions. Given ...

A functor between categories of groups or modules is called exact if it preserves the exactness of sequences, or equivalently, if it transforms short exact sequences into ...

Given a field F and an extension field K superset= F, if alpha in K is an algebraic element over F, the minimal polynomial of alpha over F is the unique monic irreducible ...

For any real alpha and beta such that beta>alpha, let p(alpha)!=0 and p(beta)!=0 be real polynomials of degree n, and v(x) denote the number of sign changes in the sequence ...

Let G be a group and S be a topological G-set. Then a closed subset F of S is called a fundamental domain of G in S if S is the union of conjugates of F, i.e., S= union _(g ...

In his monumental treatise Disquisitiones Arithmeticae, Gauss conjectured that the class number h(-d) of an imaginary quadratic field with binary quadratic form discriminant ...

f(x) approx t_n(x)=sum_(k=0)^(2n)f_kzeta_k(x), where t_n(x) is a trigonometric polynomial of degree n such that t_n(x_k)=f_k for k=0, ..., 2n, and ...

The polynomials G_n(x;a,b) given by the associated Sheffer sequence with f(t)=e^(at)(e^(bt)-1), (1) where b!=0. The inverse function (and therefore generating function) ...