Reduction


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Related to Reduction: reduction formula, Reduction reaction

reduction,

in chemistry: see oxidation and reductionoxidation and reduction,
complementary chemical reactions characterized by the loss or gain, respectively, of one or more electrons by an atom or molecule. Originally the term oxidation
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.

Reduction

 

(1) A supplemental musical notation for piano, first violin, or accordion that gives the primary melodies played by other instruments, showing the entrances of whole sections or solo instruments. Reductions are used extensively in adaptations or transcriptions of orchestral works for smaller combinations of instruments. They allow such orchestral works to be performed without a score or a conductor, since several instruments’ parts can be played on one instrument.

(2) An abridged score of shorter works (marches, dances, song transcriptions) for bands. All the parts are written on three or four musical staffs and are left untransposed, even for those instruments in keys other than C.


Reduction

 

the restoration of a previous state or the breakdown of the complex into a simpler form. In various branches of science and technology, “reduction” refers to processes that result in a decrease in the dimensions or a simplification of the structure of an object. It can also refer to a weakening of the tension or force and sometimes to the complete disappearance of an object.


Reduction

 

in biology, a decrease in the size or a simplification of the structure of an organ; reduction often refers to a loss of inherent organic functions in the course of the individual development of an organism (ontogeny) or the historical development of an organism (phylogeny). The complete disappearance of an organ or of tissue is sometimes called reduction.


Reduction

 

the confiscation of crown lands that had been acquired by the feudal aristocracy, carried out by the monarchy in a number of European states in the 16th and 17th centuries.

Reduction was carried out on the largest scale and acquired its greatest significance in the second half of the 17th century in Sweden, where it was done to strengthen absolutism. Partial reduction was decided on by the Riksdag in 1655, during the reign of Charles X. Extensive reduction was carried out under Charles XI, whose policies were supported by the nobility with small landholdings, the burghers, and the richer peasants; the process was initiated in 1680 and was basically concluded by 1700. As a result of this policy, the extent of large-scale land-holding by the Swedish nobility, both in Sweden and in its dependent territories, was reduced approximately by one-half as compared to the first half of the 17th century.

In Poland, the decision to carry out a reduction (egzekucja, rewindykacja) of crown lands distributed after 1504 was taken at the sejm of 1562–63 at the insistence of the nobility. Reduction in Poland represented one stage in the struggle within the ruling class for the redistribution of landholdings.


Reduction

 

in linguistics, a weakening of vowel sounds in unstressed position. In quantitative reduction, vowel length is decreased. In qualitative reduction, distinct articulation is lost, resulting in a change in the way the vowel is formed and a neutralization of phonemic opposition. In Russian, the degree of reduction depends on the position of the vowel relative to word stress, as in zolotoi (“golden”), which can be represented phonetically as [zəlʌtój]. Sometimes the term “reduction” is used to refer to any change from a fuller form of a linguistic element (sound, word, sentence) to a shorter form. The term “reduced” sometimes refers to all reduced sounds, positional variants and independent phonemes alike.


Reduction

 

a methodological tool that plays an important role in logic, mathematics, and other deductive sciences.

Reduction involves a transformation of given data (problems, propositions) into the form most convenient from a certain standpoint, for example, a form that is logically simpler and more easily analyzed. Reduction of one problem to another plays a dual role: on the one hand, the solution of the second problem is applicable to the first problem, and on the other hand, the impossibility of solving the first problem—at least with certain specified methods—means that the second problem is also unsolvable by the same methods. Reduction can thus be used to derive from a positive (negative) solution of one problem a positive (negative) solution of an entire class of problems. The term “reduction” is also used in a natural sense to refer to inferences, methods of proof (such as reductio ad absurdum), concepts, conceptions, and theories.

In astronomy and geodesy, the term “reduction” is used to refer to the reduction of observations and measurements from one frame of reference to another through the introduction of corrections needed to account for the influence of various factors; these corrections are themselves often referred to as reductions. For example, the position of a star observed at a given moment differs from the position as given in star catalogs because of precession, nutation, and the star’s proper motion. Astronomical observations made at different moments of time are therefore corrected, or reduced, to a single epoch. Geodetic measurements made at some point of the earth’s surface are reduced by means of computations to a neighboring point or the corresponding point of the reference ellipsoid.


Reduction

 

the relative magnitude of deformation imparted to a billet during forging operations, such as drawing, upsetting, or extrusion. Reduction is characterized by the reduction coefficient, which is defined as the ratio of the initial and final crosssectional area of the deformed billet or as the corresponding ratio of the billet’s initial and final length and height. The coefficient also depends on the shape of the die faces (flat, notched, or composite), the temperature, and the rate of deformation. The reduction coefficient may be 10 or more, in which case the coarsegrained cast structure of the original ingot acquires a clearly expressed fibrous structure. This ensures that the metal has uniform properties and high-quality mechanical characteristics in the longitudinal direction.

reduction

[ri′dək·shən]
(analytical chemistry)
Preparation of one or more subsamples from a sample of material that is to be analyzed chemically.
(chemistry)
Reaction of hydrogen with another substance.
Chemical reaction in which an element gains an electron (has a decrease in positive valence).
(computer science)
Any process by which data are condensed, such as changing the encoding to eliminate redundancy, extracting significant details from the data and eliminating the rest, or choosing every second or third out of the totality of available points.
(geology)
The lowering of a land surface by erosion.
(navigation)
The process of substituting for an observed value one derived therefrom, as the calculation of the corresponding meridian altitude from an observation of a celestial body near the meridian, or the derivation from a celestial observation of the information needed for establishing a line of position.

reduction

Maths
a. the process of converting a fraction into its decimal form
b. the process of dividing out the common factors in the numerator and denominator of a fraction; cancellation

reduction

(Or "contraction") The process of transforming an expression according to certain reduction rules. The most important forms are beta reduction (application of a lambda abstraction to one or more argument expressions) and delta reduction (application of a mathematical function to the required number of arguments).

An evaluation strategy (or reduction strategy), determines which part of an expression (which redex) to reduce first. There are many such strategies.

See graph reduction, string reduction, normal order reduction, applicative order reduction, parallel reduction, alpha conversion, beta conversion, delta conversion, eta conversion.
References in classic literature ?
Furthermore, when the expense of the maintenance of armed guards over the pest-house, day and night, throughout the years, is considered, Walter Merritt Emory could have saved many thousands of dollars to the tax-payers of the city and county of San Francisco, which thousands of dollars, had they been spent otherwise, could have been diverted to the reduction of the notorious crowding in school-rooms, to purer milk for the babies of the poor, or to an increase of breathing-space in the park system for the people of the stifling ghetto.
By this system of taxation, each individual tax-payer pays less in reality, while the State receives more, and consumers profit by a vast reduction in the price of things which the State releases from its perpetual and harassing interference.
Those persons who study writing as an art are probably the only persons who can measure the vast distance which separates a conception as it exists in the mind from the reduction of that conception to form and shape in words.
That they came at all times and seasons--that they dined there one day, supped the next, dined again on the next, and were constantly to and fro on all--that they made parties to visit public places, and met by accident at lounges--that upon all these occasions Miss Nickleby was exposed to the constant and unremitting persecution of Sir Mulberry Hawk, who now began to feel his character, even in the estimation of his two dependants, involved in the successful reduction of her pride--that she had no intervals of peace or rest, except at those hours when she could sit in her solitary room, and weep over the trials of the day--all these were consequences naturally flowing from the well-laid plans of Sir Mulberry, and their able execution by the auxiliaries, Pyke and Pluck.
This state of the eyes is probably due to gradual reduction from disuse, but aided perhaps by natural selection.
Few smelting-furnaces are now at work in any part of Chile; it is found more profitable, on account of the extreme scarcity of firewood, and from the Chilian method of reduction being so unskilful, to ship the ore for Swansea.
But this reduction of art to strict order and decorum, it should be clear, was quite in accord with the whole spirit of the time.
We know when spring is coming by the reduction in his figure.
A surplusage given to one part is paid out of a reduction from another part of the same creature.
We only know in part how to reduce physiology to chemistry, but we know enough to make it likely that the reduction is possible.
He felt so mirthful that, contrary to his rules, he made a reduction in his terms to the haggling lady, and gave up catching moths, finally deciding that next winter he must have the furniture covered with velvet, like Sigonin's.
Raffles wrote, as he had telegraphed, from Bremen; and I gathered that the personal use of some little influence with the authorities there had resulted in a material reduction in our fares.