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convolution|kɒnvəˈljuːʃən|
[n. of action f. L. convolūt-, ppl. stem of convolvĕre to roll together: see convolve.]
1. The action of folding (obs.), coiling, twisting, or winding together; the condition of being coiled or convoluted.
1597J. King Jonas (1618) 375 A conuolution or folding vp together. 1674Grew Anat. Plants iii. ii. vi. (1682) 137 The Claspers of a Vine..have also a Motion of Convolution. 1678Cudworth Intell. Syst. (1837) I. 152 Where, after many convolutions and evolutions..they chanced..to settle. 1730Thomson Autumn 837 Toss'd wide around, O'er the calm sky, in convolution swift. 1835Lindley Introd. Bot. (1848) I. 393 If the convolution is imperfect..the ovules are partially naked.
2. A fold, twist, turn, winding, sinuosity (of anything rolled or coiled up, or of a coiled form).
1545T. Raynalde Byrth Mankynde 26 It hath many conuolucyons, as wormes lyeng together haue. 1667Boyle Orig. Formes & Qual., To cast it self into such grand..convolutions as the Cartesians call Vortices. 1682T. Gibson Anat. (1697) 375 Full of windings, like the convolutions of the guts. 1774Goldsm. Nat. Hist. (1776) VII. 5 The center round which every succeeding convolution of the shell is formed. 1871Tyndall Fragm. Sc. (ed. 6) II. xvi. 439 Each additional convolution..adds its electro-motive force to that of all the others. 1873Black Pr. Thule vi. 89 The curious convolutions of this rugged coast.
3. Anat. Each of the sinuous folds or windings of the surface of the cerebral hemispheres in man and the higher animals.
1615Crooke Body of Man 449 The convolutions of the Brain. 1804Abernethy Surg. Obs. 203 Upon the surface of the convolutions of the cerebrum. 1880Bastian Brain 279 In the lowest Quadrupeds there are no convolutions.
4. Math. An integral function of two or more given functions f1, f2,{ddd}, fn of the type ∫{ddd}∫f1(u1)f2(u2 - u1){ddd}fn(x-un - 1)du1du2{ddd}dun-1 ; an analogous summation.
1934Amer. Jrnl. Math. LVI. 662 Bernoulli convolutions. 1935Trans. Amer. Math. Soc. XXXVIII. 48 Distribution functions and their convolutions (‘Faltungen’). 1947Duke Math. Jrnl. XIV. 236 The convolution of two positive functions is positive. 1963G. F. Simmons Introd. Topol. & Mod. Analysis xii. 305 Let G = {ob}{ddd}, -2, -1, 0, 1, 2,{ddd}{cb} be the additive group of integers... The linear operations are defined pointwise,..and the convolution of f and g..by (f*g)(n) = {Summ}∞m= -∞f(n-m)g(m). 1968P. A. P. Moran Introd. Probability Theory vi. 265 The operation of a convolution..has many of the properties of multiplication but there is not a complete analogy,..since ‘division’ is not always possible... The class of all distributions is made into a semi-group (but not a group) by the operation of convolution. 1979Nature 1 Mar. 27/1 The procedure we have implemented involves a direct synthesis of a ‘dirty’ map which is the convolution of the true brightness distribution with the response function of a point source. |