Physical world and mathematics

Reduced density matrix

A reduced density matrix describes the state of a quantum subsystem of a larger system, obtained by the partial trace, and is the standard tool for quantifying entanglement.

Reduced mass

Reduced mass is the effective mass μ = m₁m₂/(m₁+m₂), always smaller than either body, that reduces a two-body problem to one-body motion; it enters atomic spectra and rotational spectroscopy.

Reduced ring

A reduced ring is a ring containing no nonzero nilpotent elements, so x squared equaling zero forces x to be zero; examples include every integral domain and Boolean ring.

Reduced shear

Reduced shear, g = γ/(1−κ), is the quantity actually measured in weak gravitational lensing, since galaxy ellipticities respond to it rather than to the shear alone.

Reduced word

A reduced word, also called a reduced expression, is a shortest expression for an element of a Coxeter group as a product of simple reflections, with its common length the element's length.

Reduced-rank regression (RRR) is a multivariate statistical method that models many correlated responses as linear functions of predictors through a low-rank coefficient matrix, used in econometrics, biology, and neuroscience.

Reducing agent

A reducing agent, also called a reduction agent or reductant, is a chemical species that donates electrons to another in a redox reaction, reducing it while being oxidized itself.

Reducing emissions from deforestation and forest degradation (REDD+)

REDD+ is a UNFCCC framework under which developing countries receive results-based payments for verified emission reductions from reducing deforestation and forest degradation, plus conservation and sustainable management of forests.

Reducing sugar

A reducing sugar is a carbohydrate containing an aldehyde or hemiacetal group that acts as a reducing agent, such as glucose, fructose, lactose, and maltose; sucrose is nonreducing.

Reduction of nitro compounds

Reduction of nitro compounds, also known as nitro group reduction, converts organic nitro groups into amines by hydrogenation or metal-acid methods, the standard industrial route from nitroarenes to anilines.

Reduction of thermodynamics to statistical mechanics

The reduction of thermodynamics to statistical mechanics asks whether thermodynamic laws and concepts like temperature and entropy can be recovered from statistical mechanics, the canonical case study in intertheoretic reduction.

Reduction potential

Reduction potential, also called redox potential or oxidation-reduction potential, measures a species' tendency to gain electrons, expressed in volts relative to the standard hydrogen electrode at 0 V.

Reductionism

Reductionism is the philosophical position that the entities or explanations of one domain can be accounted for in terms of a more fundamental one, such as biology reducing to physics.

Reductive amination

Reductive amination, also known as the reductive amination reaction, converts an aldehyde or ketone into an amine through an imine intermediate that is then reduced.

Oct 22, 2026

Reductive coupling

Reductive coupling is a class of transition-metal-catalyzed carbon–carbon bond-forming reactions joining two π-components, such as an alkyne and an aldehyde, using a stoichiometric reducing agent.

Reductive cross-coupling

Reductive cross-coupling, also called cross-electrophile coupling (XEC), forms carbon–carbon bonds between two electrophiles, such as aryl and alkyl halides, using a reductant instead of an organometallic reagent.

Reductive dechlorination

Reductive dechlorination is a chemical reaction that removes chlorine atoms from chlorinated organic molecules by reduction, used to destroy chlorinated solvents and PCBs in environmental remediation.

Reductive dehalogenation of halo ketones

Reductive dehalogenation of halo ketones is the removal of a halogen atom from an α-halo ketone by a reducing agent, giving the parent ketone or a metal enolate.

Reductive group

A reductive group, or reductive algebraic group, is an algebraic group whose unipotent radical is trivial; examples include GL, SL, SO, and Sp, central to the Langlands program.

Reductone

A reductone is a compound containing an enediol group stabilized by an adjacent carbonyl, giving strong reducing power and acidity; ascorbic acid (vitamin C) is the best known member, and reductones form in the Maillard reaction.

Redundancy (engineering)

Redundancy in engineering is the use of more than one independent means to do a job, so one failure does not stop the system; the gain requires independent failures.

Redundancy analysis

Redundancy analysis (RDA), also called reduced-rank regression, is a constrained ordination method introduced by C. R. Rao in 1964 that relates response variables to explanatory variables through regression followed by PCA.

Reeb vector field

A Reeb vector field is the unique vector field associated to a contact form on an odd-dimensional manifold, defined by α(R) = 1 and ιR dα = 0.

Reed Timmer

Reed Timmer is an American extreme meteorologist and storm chaser known for driving armored vehicles into tornadoes and starring in the Discovery Channel series Storm Chasers.

Reed–Muller code

Reed–Muller codes are a family of linear error-correcting codes whose codewords are evaluations of multivariate polynomials over finite fields, introduced in 1954 by David E. Muller.

Reed–Solomon error correction

Reed–Solomon error correction is a family of error-correcting codes, introduced by Irving Reed and Gustave Solomon in 1960, used in QR codes, CDs, and spacecraft.

Reeds–Shepp curve

A Reeds–Shepp curve is the shortest path between two oriented points in the plane for a car-like vehicle with a minimum turning radius that can drive both forwards and backwards.

Reference conditions (Water Framework Directive)

Reference conditions under the EU Water Framework Directive are the near-natural values for surface water quality elements, serving as the benchmark for classifying high ecological status.

Reference electrode

A reference electrode is an electrode that maintains a virtually invariant potential in electrochemical measurements; the saturated calomel and silver/silver chloride electrodes are the most common laboratory types.