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If a real algebraic curve has no singularities except nodes and cusps, bitangents, and inflection points, then n+2tau_2^'+iota^'=m+2delta_2^'+kappa^', where n is the order, ...

Any finite semigroup is a divisor for an alternating wreath product of finite groups and semigroups.

A submodule L of a module M such that for any other nonzero submodule K of M, the intersection L intersection K is not the zero module. L is also called an essential ...

Suppose that {f_n} is a sequence of measurable functions, that f_n->f pointwise almost everywhere as n->infty, and that |f_n|<=g for all n, where g is integrable. Then f is ...

A method of displaying simple statistical parameters including hinges, the statistical median, and upper and lower values.

A link invariant is a function from the set of all links to any other set such that the function does not change as the link is changed (up to isotopy). In other words, a ...

A local extremum, also called a relative extremum, is a local minimum or local maximum.

A branch point whose neighborhood of values wrap around an infinite number of times as their complex arguments are varied. The point z=0 under the function lnz is therefore a ...

The logarithmic integral (in the "American" convention; Abramowitz and Stegun 1972; Edwards 2001, p. 26), is defined for real x as li(x) = {int_0^x(dt)/(lnt) for 0<x<1; ...

The two integrals involving Bessel functions of the first kind given by (alpha^2-beta^2)intxJ_n(alphax)J_n(betax)dx ...