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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.
Applying this transformation twice on a 4-vector gives a transformation of the same form. The new symmetry of 'inversion' is given by the 3-tensor . This symmetry becomes Poincaré symmetry if we set = When = the second condition requires that is an orthogonal matrix. This transformation is 1-1 meaning that each point is mapped to a unique ...
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.
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In structural geology, inversion or basin inversion relates to the relative uplift of a sedimentary basin or similar structure [example needed] as a result of crustal shortening. This normally excludes uplift developed in the footwalls of later extensional faults , or uplift caused by mantle plumes .