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Physical world and mathematics

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Degree of a polynomial

The degree of a polynomial, or polynomial degree, is the largest exponent with a nonzero coefficient among its terms, naming it linear, quadratic, cubic, and so on.

Degree of branching

The degree of branching is a dimensionless measure of how closely a hyperbranched polymer approaches the fully branched structure of a dendrimer, from 0 to 1.

Degree of coherence

The degree of coherence is a normalized correlation measure of how strongly a light field's phase and amplitude at two space-time points relate; its magnitude gives interference fringe visibility.

Degree of esterification

The degree of esterification (DE), also called the degree of methylesterification, is the percentage of pectin's carboxyl groups that are esterified; above 50% is high-methoxyl pectin.

Degree of hydrolysis

Degree of hydrolysis (DH) measures how far a hydrolysis reaction has proceeded: the percentage of acetate groups converted in poly(vinyl alcohol), or of peptide bonds cleaved in protein hydrolysates.

Degree of polarization

The degree of polarization (DOP) is a dimensionless measure, between 0 and 1, of how completely a beam of light is polarized, computed from the Stokes parameters.

Degree of polymerization

The degree of polymerization, or polymerization degree, is the number of monomeric units in a polymer chain, almost always reported as an average tied to molar mass.

Degree of reduction

The degree of reduction (γ), also called degree of reductance, is a stoichiometric quantity expressing the available electrons per gram atom of carbon, used in electron balances for microbial growth.

Degree of substitution

Degree of substitution is a measure in carbohydrate chemistry of the average number of hydroxyl groups replaced per polysaccharide repeating unit, ranging from 0 to 3 for cellulose and starch.

Degree of unsaturation

The degree of unsaturation, also called the index of hydrogen deficiency or double bond equivalent, counts the total rings and π bonds in an organic molecule.

Degree spectrum

A degree spectrum is the set of Turing degrees that compute isomorphic copies of a mathematical structure, introduced by Linda Jean Richter in computable structure theory.

Degree symbol

The degree symbol (°), also called the degree sign, is a typographic mark after a numeral indicating degrees of temperature (30.2 °C) or plane angle (90°).

Degrees of freedom (mechanics)

In mechanics, the degrees of freedom of a system are the number of independent parameters needed to specify its configuration, with a free point particle having three.

Degrees of freedom (physics and chemistry)

A degree of freedom in physics and chemistry is one independent way a system can move, store energy, or vary, such as a molecule's translation, rotation, or vibration.

Degrees of freedom (statistics)

Degrees of freedom in statistics is the number of independent pieces of information available to estimate a quantity, typically the number of observations minus the number of estimated parameters.

Dehalogenation

Dehalogenation is any chemical reaction that removes halogen atoms such as chlorine, bromine, or iodine from a molecule, used in organic synthesis and environmental cleanup of chlorinated pollutants.

Dehalogenative cross-coupling

Dehalogenative cross-coupling is a class of metal-catalyzed reactions in which a halogen atom on an organic molecule acts as a removable handle, replaced by a new substituent to build more complex molecules.

Dehn surgery

Dehn surgery is a construction in 3-manifold topology that removes a solid torus and reglues it along a slope p/q, yielding every closed orientable 3-manifold.

Dehn–Sommerville equations

The Dehn–Sommerville equations are linear relations among the face numbers of simplicial or simple polytopes, found by Max Dehn in 1905 and Sommerville in 1927.

Dehydration reaction

A dehydration reaction is a chemical reaction that combines two functional groups with the loss of a molecule of water, most often converting an alcohol to an alkene.

Dehydroacetic acid

Dehydroacetic acid is a pyrone derivative used mainly as a preservative against yeasts and molds in cosmetics, food, and pharmaceuticals; its sodium salt is the more water-soluble form.

Dehydroalanine

Dehydroalanine (Dha) is a non-proteinogenic unsaturated amino acid that occurs in peptide antibiotics such as nisin, forms during food processing, and serves in chemical biology as a tag for protein modification.

Dehydroamino acid

A dehydroamino acid is a noncanonical amino acid with a double bond between the α- and β-carbons, occurring in peptide natural products such as nisin.

Dehydroascorbic acid

Dehydroascorbic acid, or dehydroascorbate (DHA), is the two-electron oxidation product of vitamin C that cells take up through glucose transporters and recycle back to ascorbate.

Dehydroepiandrosterone sulfate

Dehydroepiandrosterone sulfate (DHEA-S, DHEAS) is the sulfate ester of the steroid DHEA, made almost entirely by the adrenal cortex and the most abundant steroid in blood.

Dehydrogenation

Dehydrogenation is a chemical reaction that removes hydrogen from a molecule; industrially, propane dehydrogenation produces about 10% of the world's propylene using chromium or platinum catalysts.

Dehydrogenation of amine-boranes

Dehydrogenation of amine-boranes is the release of dihydrogen from amine-borane adducts such as ammonia-borane, studied for hydrogen storage because these bench-stable compounds carry high hydrogen content.

Dehydrogenative coupling

Dehydrogenative coupling, also known as cross-dehydrogenative coupling, is a bond-forming chemical reaction that joins C–H bonds directly without prefunctionalized partners, pioneered by Zhiping Li and Chao-Jun Li in 2004.

Dehydrohalogenation

Dehydrohalogenation is an elimination reaction in which a base removes hydrogen and a halogen from adjacent carbons, forming an alkene or, from dihalides, an alkyne.

Deimos (moon)

Deimos, also known as Mars II, is the smaller and outer moon of Mars, discovered by Asaph Hall in 1877 and named for the Greek personification of flight.