Reduction

 ( Mathematics Disambiguation Pages ) 

Reduction, reduced, or reduce may refer to:

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Science and technology

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Chemistry

• Reduction (chemistry), part of a reduction-oxidation (redox) reaction in which atoms have their oxidation state changed.
• Organic redox reaction, a redox reaction that takes place with organic compounds
• Ore reduction: see smelting

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Computing and algorithms

• Reduction (complexity), a transformation of one problem into another problem
• Reduction (recursion theory), given sets A and B of natural numbers, is it possible to effectively convert a method for deciding membership in B into a method for deciding membership in A?
• Bit Rate Reduction, an audio compression method
• Data reduction, simplifying data in order to facilitate analysis
• Graph reduction, an efficient version of non-strict evaluation
• L-reduction, a transformation of optimization problems which keeps the approximability features
• Partial order reduction, a technique for reducing the size of the state-space to be searched by a model checking algorithm
• Strength reduction, a compiler optimization where a function of some systematically changing variable is calculated more efficiently by using previous values of the function
• Reduce (computer algebra system), a general-purpose computer algebra system geared towards applications in physics
• Reduce (higher-order function), in functional programming, a family of higher-order functions that process a data structure in some order and build up a return value
• Reduced instruction set computing, a CPU design philosophy favoring an instruction set reduced in size and complexity of addressing, to simplify implementation, instruction level parallelism, and compiling

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Pure mathematics and statistics

• Reducible as the opposite of irreducible (mathematics)
• Reduction (mathematics), the rewriting of an expression into a simpler form
• Beta reduction, the rewriting of an expression from lambda calculus into a simpler form
• Dimension reduction, the process of reducing the number of random variables under consideration
• Lattice reduction, given an integer lattice basis as input, to find a basis with short, nearly orthogonal vectors
• Subject reduction or preservation, a rewrite of an expression that does not change its type
• Reduction of order, a technique for solving second-order ordinary differential equations
• Reduction of the structure group, for a $G$-bundle $B$ and a map $H\; \backslash to\; G$ an $H$-bundle $B\_H$ such that the pushout $B\_H\; \backslash times\_H\; G$ is isomorphic to $B$
• Reduction system, reduction strategy, the application of rewriting systems to eliminate reducible expressions
• Reduced form, in statistics, an equation which relates the endogenous variable X to all the available exogenous variables, both those included in the regression of interest (W) and the instruments (Z)
• Reduced homology, a minor modification made to homology theory in algebraic topology, designed to make a point have all its homology groups zero
• Reduced product, a construction that generalizes both direct product and ultraproduct
• Reduced residue system, a set of φ(n) integers such that each integer is relatively prime to n and no two are congruent modulo n
• Reduced ring, a ring with no non-zero nilpotent elements
• Reduced row echelon form, a certain reduced row echelon form of a matrix which completely and uniquely determines its row space
• Reduced word, in a free group, a word with no adjacent generator-inverse pairs
• Variance reduction, a procedure used to increase the precision of the estimates that can be obtained for a given number of iterations

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Medicine

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Medical procedures

• Lung volume reduction surgery, a treatment for chronic obstructive pulmonary disease
• Selective reduction (or fetal reduction), the practice of reducing the number of fetuses in a multifetal pregnancy
• Reduction (orthopedic surgery), a medical procedure to restore a fracture or dislocation to the correct alignment
• Ventricular reduction, a type of operation in cardiac surgery
• Cosmetic surgery:
• Breast reduction
• Jaw reduction

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Other uses in medicine

• Weight loss
• In epidemiology:
• Relative risk reduction, the absolute risk reduction by the control event rate
• Absolute risk reduction, the decrease in risk of a given activity or treatment in relation to a control activity or treatment
• Urea reduction ratio (URR), a dimensionless number used to quantify hemodialysis treatment adequacy

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Physics

• Dimensional reduction, the limit of a compactified theory where the size of the compact dimension goes to zero
• Reduction criterion, in quantum information theory, a necessary condition a mixed state must satisfy in order for it to be separable
• Reduced mass, the "effective" inertial mass appearing in the two-body problem of Newtonian mechanics
• Reduced properties (pressure, temperature, or volume) of a fluid, defined based on the fluid's critical point

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Other uses in science and technology

• Lithic reduction, in Stone Age toolmaking, to detach lithic flakes from a lump of tool stone
• Noise reduction, in acoustic or signal processing
• Reduction drive, a mechanical device to shift rotational speed

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Arts and media

• Reducing (film), a 1931 American film
• Reduction (music), music arranged for smaller resources (piano) for easier analysis or performance

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Linguistics

• Accent reduction, modifying one's foreign accent towards that of a native speaker
• Vowel reduction, any change in vowel quality perceived as "weakening"
• Vowel reduction in English
• Relaxed pronunciation, slurring of syllables of common words
• Definite article reduction, use of vowel-less forms of the English definite article in Northern England

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Philosophy

• Reductionism, a range of philosophical systems
• Reductio ad absurdum, a form of argument in which a proposition is disproven by following its implications to an absurd consequence
• Eidetic reduction, a technique in the study of essences in phenomenology whose goal is to identify the basic components of phenomena
• Intertheoretic reduction, in philosophy of science, one theory makes predictions that perfectly or almost perfectly match the predictions of a second theory

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Settlements

• Reductions, settlements in Spanish America intended to control and Christianize Indians
• Indian reductions in the Andes, settlements in the Andes to control and Christianize Indians

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Other uses

• Reduction (cooking), the process of thickening or intensifying the flavor of a liquid mixture such as a soup, sauce, wine, or juice by evaporation
• Reduction (military), the siege and capture of a fortified place
• Reduction (Sweden), a return to the Crown of fiefs that had been granted to the Swedish nobility
• Reduce (waste), practices of minimizing waste
• Reduction, Pennsylvania, unincorporated community, United States
• Reduction in rank, in military law
• Reduction to practice, in United States patent law, the embodiment of the concept of an invention
• Ego reduction, predicated on the use of Sigmund Freud's concept of the ego
• Reductions, resettlement of indigenous peoples during the Spanish colonization of the Americas

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See also

• Prevention (disambiguation)
• Risk reduction (disambiguation)

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