Information about Residues
A residue in normal English speech is a product, usually unwanted, left behind by any process.
- In mathematics:
- 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 general chemistry, a residue is what is left behind by a reaction.
- In chemistry a portion of a larger molecule is often called a residue. See residue (chemistry).
- 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
Complex analysis, traditionally known as the theory of functions of a complex variable, is the branch of mathematics investigating functions of complex numbers. It is useful in many branches of mathematics, including number theory and applied mathematics.
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In complex analysis, the residue is a complex number which describes the behavior of line integrals of a meromorphic function around a singularity. Residues can be computed quite easily and, once known, allow the determination of more complicated path integrals via the residue
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In mathematics, a complex number is a number of the form
where a and b are real numbers, and i is the imaginary unit, with the property i ² = −1.
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where a and b are real numbers, and i is the imaginary unit, with the property i ² = −1.
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In mathematics, a line integral (sometimes called a path integral) is an integral where the function to be integrated is evaluated along a curve. Various different line integrals are in use. In the case of a closed curve it is also called a contour integral.
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In complex analysis, a meromorphic function on an open subset D of the complex plane is a function that is holomorphic on all D except a set of isolated points, which are poles for the function.
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In mathematics, a singularity is in general a point at which a given mathematical object is not defined, or a point of an exceptional set where it fails to be well-behaved in some particular way, such as differentiability.
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Modular arithmetic (sometimes called modulo arithmetic, or clock arithmetic) is a system of arithmetic for integers, where numbers "wrap around" after they reach a certain value — the modulus.
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In mathematics, a ring is an algebraic structure in which addition and multiplication are defined and have properties listed below. The branch of abstract algebra which studies rings is called ring theory.
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In mathematics, a ringed space is, intuitively speaking, a space together with a collection of commutative rings, the elements of which are "functions" on each open set of the space.
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chemical reaction is a process that results in the interconversion of chemical substances.[1] The substance or substances initially involved in a chemical reaction are called reactants.
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molecule is defined as a sufficiently stable electrically neutral group of at least two atoms in a definite arrangement held together by strong chemical bonds.[1][2] In organic chemistry and biochemistry, the term molecule
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In chemistry, residue refers to a portion of a larger molecule, such as a methyl group.
In biochemistry and molecular biology, a residue refers to a specific monomer within the polymeric chain of a polysaccharide, protein or nucleic acid.
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In biochemistry and molecular biology, a residue refers to a specific monomer within the polymeric chain of a polysaccharide, protein or nucleic acid.
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Petroleum (Latin Petroleum derived from Greek πέτρα (Latin petra) - rock + έλαιον (Latin oleum) - oil) or crude oil
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oil refinery is an industrial process plant where crude oil is processed and refined into more useful petroleum products, such as gasoline, diesel fuel, asphalt base, heating oil, kerosene, and liquefied petroleum gas.
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Fractional distillation is the separation of a mixture into its component parts, or fractions, such as in separating chemical compounds by their boiling point by heating them to a temperature at which several fractions of the compound will evaporate.
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Fuel oil is a fraction obtained from petroleum distillation, either as a distillate or a residue. Broadly speaking, fuel oil is any liquid petroleum product that is burned in a furnace or boiler for the generation of heat or used in an engine for the generation of power, except
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cracking is the process whereby complex organic molecules such as kerogens or heavy hydrocarbons are broken down into simpler molecules (e.g. light hydrocarbons) by the breaking of carbon-carbon bonds in the precursors.
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There are two types of agricultural crop residues. Field residues are materials left in an agricultural field or orchard after the crop has been harvested. These residues include stalks and stubble (stems), leaves, and seed pods.
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