Reduction in rank

Reduction, reduced, or reduce may refer to:

Science and technology

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

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

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 $H \to G$ an $H$-bundle $B_H$ such that the pushout $B_H \times_H G$ 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

Medicine

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

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

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

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

Arts and media

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

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

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

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

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

See also

* Prevention (disambiguation)
* Risk reduction (disambiguation)

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Mathematics disambiguation pages