Residue

From Wikipedia, the free encyclopedia

A residue in normal English speech is a product, usually unwanted, left behind by any process.

• In mathematics:
  • Residue (complex analysis), a complex number which describes the behavior of line integrals of a meromorphic function around a singularity
  • In modular arithmetic, the residue of an integer n to base b is the remainder r after the largest multiple mb of b no greater than n has been subtracted from n. (If n < 0, one adds multiples of b just sufficient to make the result non-negative.) The residues modulo (to the base) b form a ring. Sometimes "residue" is shorthand for "quadratic residue".
  • In a locally ringed space (X, O_X), the residue of a section f in O_X(U) at a point p of X is the reduction of the germ of f at p modulo the unique maximal ideal of the stalk of O_X at p. When O_X is a sheaf of functions on X, the residue of a section f at a point p is the value f(p).
• In general chemistry, a residue is what is left behind by a reaction.
• Residue (chemistry), a portion of a larger molecule
• In petroleum refining the residue comprises the heavier fractions that fail to vaporize. It can be used as fuel oil or cracked to produce lighter fractions. The volume and degree of cracking carried out is determined by the price difference between the light and heavy fractions and the cost of the cracking process.
• Crop residue