Residue

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A residue, broadly, is anything left behind by a reaction or event.

• In complex analysis, the residue is a complex number which describes the behavior of path 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 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 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".

• 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.

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