Involution

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involution

[‚in·və′lü·shən]
(biology)
A turning or rolling in.
(embryology)
Gastrulation by ingrowth of blastomeres around the dorsal lip.
(mathematics)
Any transformation that is its own inverse.
In particular, a correspondence between the points on a line that is its own inverse, given algebraically by x ′ = (ax + b)/(cx-a), where a 2+ bc ≠ 0.
A correspondence between the lines passing through a given point on a plane such that corresponding lines pass through corresponding points of an involution of points on a line.
(medicine)
The retrogressive change to their normal condition that organs undergo after fulfilling their functional purposes, as the uterus after pregnancy.
The period of regression or the processes of decline or decay which occur in the human constitution after middle life.

Involution

 

(raising to a power), an algebraic operation consisting in repeating a quantity a n number of times:

The number a is the base of the power, n is the exponent, and an is the power. For example, 3x3x3x3 = 34 = 81. The second power of a number is called its square and the third power, its cube.


Involution

 

(regression), in biology, a reduction or loss, in the process of evolution, of certain organs, and a simplification of their organization and functions (for example, various degrees of intestinal reduction in certain parasitic worms and arthropods). Degenerative changes in protozoans and bacteria caused by unfavorable conditions in the habitat are also called involutional. In medicine, the term sometimes refers to atrophy of organs and tissues, such as in aging.

References in periodicals archive ?
2]) are 3412-avoiding involutions, so c([beta]) = (1 [?
Let F be a set of involutions with no fixed points.
b) There exists an r-admissible involution [iota] of [Z.
After parturition, suitable approach is proposed to administer oxytocin for three days followed by prostaglandins for three days for better expulsion of placenta and its shreds with speedy and early uterine involution.
not equal to] 2, D a division k-algebra with center K = k([square root of (a)]) and involution J of second kind, non-trivial on K and h a non-degenerate hermitian form of rank n with respect to J and with values in D.
To be precise, one of the orbits of the involution is missing.
3 (InvolutionJumper) Input: G = (X) and an involution x [member of] G.
Indeed, the file-toggle operations (in which one performs piecewise-linear toggling at all x e P belonging to the ith file of [n - A] x [A], with 1 [less than or equal to] i [less than or equal to] n; see 6) can be shown to correspond respectively to the n Bender- Knuth involutions on the Young tableau, whose composition gives [[pi].
Then h is a bijective involution (that is hoh = id) of D onto D.
Suppose that Levi subgroups L and H contain the same maximal torus T of G, and let a be a Chevalley-Weyl involution of G with respect to T in the sense that [sigma](t) = [t.
The topics include the isotopy of links, most knots are wild, infinite cyclic coverings, some curious involutions of spheres, two complexes that are homeomorphic but combinatorially distinct, uses of the fundamental group, and a unique decomposition theorem for three-manifolds.
n,j] denotes the number of involutions on [n] = {1, 2, .