Residue
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A residue, broadly, is anything left behind by a reaction or other process.
- In complex analysis, the residue is 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.
- In a locally ringed space (X, OX), the residue of a section f in OX(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 OX at p. When OX is a sheaf of functions on X, the residue of a section f at a point p is the value f(p).
- In chemistry, a residue refers to a portion of a larger molecule; for example in biochemistry and molecular biology, a residue refers to a specific monomer within the polymeric chain of a polysaccharide, protein or nucleic acid. For example one might say, "The histidine residue is considered to be basic due to its imidazole ring." Note that a residue is different from a moiety, which, in the above example would consistute the imidazole ring or "the imidazole moiety". Note also the origin of this usage: during the process by which monomeric building blocks (e.g. amino acids) are strung together into a polymeric chain (e.g. a protein), some material (typically adding up to one molecule of water) is discarded from each building block, and only a "residue" of the building block ends up in the finished product.
- In refining petroleum by distilling residue is the heavier fractions that fail to vaporize. They can be used as fuel oil or cracked to produce lighter fractions. The volume and degree of cracking depends on the price difference between the light and heavy fractions.
- Crop residue
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