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Examples of inversion of circles A to J with respect to the red circle at O. Circles A to F, which pass through O, map to straight lines. Circles G to J, which do not, map to other circles. The reference circle and line L map to themselves. Circles intersect their inverses, if any, on the reference circle.
An inversion is a chromosome rearrangement in which a segment of a chromosome becomes inverted within its original position. An inversion occurs when a chromosome undergoes a two breaks within the chromosomal arm, and the segment between the two breaks inserts itself in the opposite direction in the same chromosome arm.
Balanoglossus, an example of a Hemichordata, represents an "evolutionary link" between invertebrates and vertebrates. In addition to the simple observation that the dorsoventral axes of protostomes and chordates appear to be inverted with respect to each other, molecular biology provides some support for the inversion hypothesis.
Inversion in a point, or point reflection, a kind of isometric (distance-preserving) transformation in a Euclidean space; Inversion transformation, a conformal transformation (one which preserves angles of intersection) Method of inversion, the image of a harmonic function in a sphere (or plane); see Method of image charges
The point O in this construction is called the center of inversion, the circle the circle of inversion, and k the radius of inversion. An inversion applied twice is the identity transformation, so the inverse of an inverse curve with respect to the same circle is the original curve.
Pyramidal inversion in nitrogen and amines is known as nitrogen inversion. [8] It is a rapid oscillation of the nitrogen atom and substituents, the nitrogen "moving" through the plane formed by the substituents (although the substituents also move - in the other direction); [ 9 ] the molecule passing through a planar transition state . [ 10 ]
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A population inversion (N 2 > N 1) has thus been achieved between level 1 and 2, and optical amplification at the frequency ν 21 can be obtained. Because at least half the population of atoms must be excited from the ground state to obtain a population inversion, the laser medium must be very strongly pumped.