Inversion

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Related to Inversions: temperature inversions

inversion

1. Chem
a. the conversion of a dextrorotatory solution of sucrose into a laevorotatory solution of glucose and fructose by hydrolysis
b. any similar reaction in which the optical properties of the reactants are opposite to those of the products
2. Music
a. the process or result of transposing the notes of a chord (esp a triad) such that the root, originally in the bass, is placed in an upper part. When the bass note is the third of the triad, the resulting chord is the first inversion; when it is the fifth, the resulting chord is the second inversion
b. (in counterpoint) the modification of a melody or part in which all ascending intervals are replaced by corresponding descending intervals and vice versa
c. the modification of an interval in which the higher note becomes the lower or the lower one the higher
3. Pathol abnormal positioning of an organ or part, as in being upside down or turned inside out
4. Psychiatry
a. the adoption of the role or characteristics of the opposite sex
b. another word for homosexuality
5. Meteorol an abnormal condition in which the layer of air next to the earth's surface is cooler than an overlying layer
6. Computing an operation by which each digit of a binary number is changed to the alternative digit, as 10110 to 01001
7. Genetics a type of chromosomal mutation in which a section of a chromosome, and hence the order of its genes, is reversed
8. Logic the process of deriving the inverse of a categorial proposition
9. Maths a transformation that takes a point P to a point Pʹ such that OP?OPʹ = a2, where a is a constant and P and Pʹ lie on a straight line through a fixed point O and on the same side of it

Inversion

 

in chemistry. (1) A change in the conformation of a cyclic molecule as a result of which the orientation of the substituent with respect to the ring changes. For example, methylcyclohexane exists in the form of an equilibrium mixture of two conformations, form II predominating (see Figure 1).

The frequency of inversion depends on the nature of the substituents and on temperature.

(2) The conversion of the configuration of a molecule containing a trivalent “pyramidal” atom (for example, nitrogen or arsenic) into the mirror image. Thus, for a molecule with a trivalent atom, forms I and II are the optical antipodes:

where a, b, and c are different atoms or groups of atoms. The energy barrier for inversion is usually low and depends on the temperature and the nature of a, b, and c. For the carbon atom (a “tetrahedral” atom), the term “configuration reversal” is usually used.

(3) The inversion of sugar is the hydrolysis of a saccharose (such as beet sugar) accompanied by a change in the direction of rotation of the plane of a polarized beam of light by a sugar solution.

B. L. DIATKIN


Inversion

 

(1) In geometry, inversion with respect to a given circle of radius R with a center O is a transformation (see Figure 1) in which a point P is converted to a point P ′ (in Figure 1 the points Pand P ′ are given with numerical subscripts), which lies on a radial line OP at a distance OP ′ = R2/OP from the center O; the number R2 is called the inversion factor. Upon inversion, straight lines and circles become straight lines and circles, and circles, for example, may become straight lines and vice versa. Inversion in space with reference to a sphere is defined similarly. The transformation of an inversion has numerous applications in geometry (the interpretation of Lobachevskii’s geometry, the theory of geometric constructions) and in the theory of mechanisms—so-called inversors.

Figure 1

(2) In combinatorial analysis, inversion is the disruption of the normal sequence of two elements in a permutation regardless of whether these two terms stand together or are separated from each other by some other elements, for example, in the permutation eacbd the terms a and e, c and e, b and e, d and e, and b and c form an inversion if abcde is considered to be the normal order.


Inversion

 

a change in the usual word order in a sentence. Inversion is generally used to accentuate the rearranged element in the sentence and to give the entire sentence special meaning. In languages with fixed word order, inversion has a grammatical function—for example, to form interrogative sentences in Russian, English, and French. It is one of the aspects of the actual division of a sentence—for example, Russian Videl ia otsa (“Saw I Father”) and German Den Sohn liebt die Mutter (literally, “The son [accusative] loves the mother [nominative],” that is, “The mother loves the son”).

Frequently, inverted forms that are not accepted in everyday speech are used in poetry. For example, A. S. Pushkin: Minutnykh zhizni vpechatlenii / Ne sokhranit dusha moia (roughly, “The fleeting impressions of life/ My soul does not retain”) and Pod vecher, osen ‘iu nenastnoi, / V dalekikh deva shla mestakh (roughly, “Toward evening, in rainy autumn, / In far-off places a maiden walked”).

inversion

[in′vər·zhən]
(chemistry)
Change of a compound into an isomeric form.
(communications)
The process of scrambling speech for secrecy by beating the voice signal with a fixed, higher audio frequency and using only the difference frequencies.
(crystallography)
A change from one crystal polymorph to another. Also known as transformation.
(electricity)
The solution of certain problems in electrostatics through the use of the transformation in Kelvin's inversion theorem.
(genetics)
A type of chromosomal rearrangement in which two breaks take place in a chromosome and the orientation of the fragment between breaks rotates 180° before rejoining.
(geology)
Development of inverted relief through which anticlines are transformed into valleys and synclines are changed into mountains.
The occupancy by a lava flow of a ravine or valley that occurred in the side of a volcano.
A diagenetic process in which unstable minerals are converted to a more stable form without a change in chemical composition.
(mathematics)
Given a point O lying in a plane or in space, a mapping of the plane or of space, excluding the point O, into itself in which every point is mapped into its inverse point with respect to a circle or sphere centered at O.
The interchange of two adjacent members of a sequence.
(mechanical engineering)
The conversion of basic four-bar linkages to special motion linkages, such as parallelogram linkage, slider-crank mechanism, and slow-motion mechanism by successively holding fast, as ground link, members of a specific linkage (as drag link).
(medicine)
The act or process of turning inward or upside down.
(meteorology)
A departure from the usual decrease or increase with altitude of the value of an atmospheric property, most commonly temperature.
(optics)
The formation of an inverted image by an optical system.
(physics)
The simultaneous reflection of all three directions in space, so that each coordinate is replaced by the negative of itself. Also known as space inversion.
(solid-state physics)
The production of a layer at the surface of a semiconductor which is of opposite type from that of the bulk of the semiconductor, usually as the result of an applied electric field.
(thermodynamics)
A reversal of the usual direction of a variation or process, such as the change in sign of the expansion coefficient of water at 4°C, or a change in sign in the Joule-Thomson coefficient at a certain temperature.

inversion

inversionclick for a larger image
In meteorology, a departure from the usual decrease or increase with altitude of the value of an atmospheric property. Also, the layer through which this departure occurs, called the inversion layer, or the lowest altitude at which the departure is found (i.e., the base of the inversion). This term almost always means a temperature inversion and an increase in temperature with height. It is one of the causes for the formation of smog. The presence of an inversion creates a very stable atmosphere; when it occurs at the surface it leads to very little mixing and a trapping of pollutants in the lower atmosphere.
References in periodicals archive ?
Our calculations show that the number of inversion sequences avoiding the pattern 120 is given by:
It is easy to check that the mapping sending such a tree T to the inversion sequence e, where [e.sub.i] is the parent of i in T, is a bijection between these trees and [I.sub.n] (000).
The results are very similar around the 2006:Q1 and the 2006:Q3 to 2007:Q2 inversions. The forecasters predicted inversions for 2006:Q3 and 2007:Q1 to 2007:Q4 when making 2-quarter-ahead forecasts, and they predicted inversions for 2007:Q1, 2008:Q1, and 2008:Q2 when making 4-quarter-ahead forecasts.
To see why professional forecasters missed the onset of all three yield curve inversions, I examined their forecasts of 1-year and 10-year Treasury interest rates separately.
Given the procedural assumptions made in this study, only inversions lasting longer periods of time are considered (positive SHUM gradient in daily averages) as well as those of appropriate strength (Section 2).
[18], who used data from 5 different sets of reanalysis data and compared them with weather balloon surveys in order to show the occurrence of inversions in polar areas, mostly in the winter season, and the low base of these inversions.
The bottom line is that there has been a surge of inversions in the past decade, (18) the deals have grown in size, (19) and the tactics have become cleverer.
Democrats and Republicans agree that inversions need to be curbed but disagree on what needs to be done.
For example, uncertainty in an event location negatively affects the source mechanism inversion and may project into a false fault plane or spurious non-shear components may be obtained.
The inversion of full-waveforms is not as common as in earthquake seismology because the reservoir models generally do not allow modeling the full waveforms at high frequencies--in microseismic monitoring, the signal strength usually peaks at frequencies in the band 20-40 Hz for surface monitoring and typically waveforms with peak frequencies 100 Hz and higher are used in borehole monitoring (Duncan and Eisner, 2010).
By Lemma 2 we need to utilize the additional data [theta]([t.sub.i]) measured at [x.sub.0] for i = 1,2, ...; however, in concrete computations, we find that the numerical inversions can also be performed only employing a few of the additional data.
The tax consequences of inversions are complicated because they are taxable events.