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A perfect field is a field F such that every algebraic extension is separable. Any field in field characteristic zero, such as the rationals or the p-adics, or any finite ...

A^*(x)=sum_(lambda_n<=x)^'a_n=1/(2pii)int_(c-iinfty)^(c+iinfty)f(s)(e^(sx))/sds, where f(s)=suma_ne^(-lambda_ns).

The first and second Pöschl-Teller differential equations are given by y^('')-{a^2[(kappa(kappa-1))/(sin^2(ax))+(lambda(lambda-1))/(cos^2(ax))]-b^2}y=0 and ...

A pointed space is a topological space X together with a choice of a basepoint x in X. The notation for a pointed space is (X,x). Maps between two pointed spaces must take ...

The l^infty-polynomial norm defined for a polynomial P=a_kx^k+...+a_1x+a_0 by ||P||_infty=max_(k)|a_k|. Note that some authors (especially in the area of Diophantine ...

A positive measure is a measure which is a function from the measurable sets of a measure space to the nonnegative real numbers. Sometimes, this is what is meant by measure, ...

An extension A subset B of a group, ring, module, field, etc., such that A!=B.

An algebraic structure whose elements consist of selected homeomorphisms between open subsets of a space, with the composition of two transformations defined on the largest ...

A power series containing fractional exponents (Davenport et al. 1993, p. 91) and logarithms, where the logarithms may be multiply nested, e.g., lnlnx.

A commutative unit ring having only finitely many maximal ideals.