convolutionn.

/kɒnvəˈljuːʃən/

Etymology: noun of action < Latin convolūt-, participial stem of convolvĕre to roll together: see convolve v.

1. The action of folding (obsolete), coiling, twisting, or winding together; the condition of being coiled or convoluted.

ΘΚΠ

the world > movement > motion in specific manner > writhing or twisting movement > [noun]

throwingOE

wringinga1375

twining1398

wrenching1398

wresting1398

writhing?a1400

wrying1566

wreathing1571

convolution1597

twinding1602

contortion1611

distorquement1628

distortion1718

twisting1725

quirling1754

circumgyration1843

the world > space > relative position > folding or folded condition > [noun] > action of folding

reduplication?a1425

foldingc1440

pranking1440

replication1538

convolution1597

rolling1601

fold1609

doubling1634

foldure1823

1597 Bp. J. King Lect. Ionas xxviii. 376 A convolution or folding it vppe togither.

1675 N. Grew Compar. Anat. Trunks ii. vi. 73 The Claspers of a Vine..have also a motion of Convolution.

1678 R. Cudworth True Intellect. Syst. Universe i. ii. 98 Where after many Convolutions and Evolutions..they chanced..to settle.

1730 J. Thomson Autumn in Seasons 164 Tost wide around, O'er the calm sky, in convolution swift.

1835 J. Lindley 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).

ΘΚΠ

the world > space > shape > curvature > coil > [noun]

rundlec1300

waif1513

enwrapping1543

convolution1545

entrail?a1549

wreath1555

roundness1572

spire1572

rolling1576

enfold1578

infold1578

obvolution1578

gyre1590

whorl1592

enfoldment1593

twine1600

turn1625

volume1646

volution1752

swirl1786

coil1805

swirling1825

convolute1846

whirl1862

enfolding1873

snaking1888

1545 T. Raynald in tr. E. Roesslin Byrth of Mankynde i. sig. G.iv It hath many conuolucyons as wormes lyeng together haue.

1667 R. Boyle Origine Formes & Qualities (ed. 2) To cast it self into such grand..convolutions as the Cartesians call Vortices.

1682 T. Gibson Anat. (1697) 375 Full of windings, like the convolutions of the guts.

1774 O. Goldsmith Hist. Earth VII. 5 The center round which every succeeding convolution of the shell is formed.

1871 J. Tyndall Fragm. Sci. (ed. 6) II. xvi. 439 Each additional convolution..adds its electro-motive force to that of all the others.

1873 W. Black Princess of Thule vi. 89 The curious convolutions of this rugged coast.

3. Anatomy. Each of the sinuous folds or windings of the surface of the cerebral hemispheres in humans and the higher animals.

ΘΚΠ

the world > life > the body > nervous system > cerebrospinal axis > brain > parts of brain > [noun] > cerebrum > hemisphere > convolutions and parts

circumvolution1578

convolution1615

crotchet1678

gyrus1842

subgyre1889

suboperculum1889

1615 H. Crooke Μικροκοσμογραϕια 449 The convolutions of the Brain.

1804 J. Abernethy Surg. Observ. 203 Upon the surface of the convolutions of the cerebrum.

1880 H. C. Bastian Brain 279 In the lowest Quadrupeds there are no convolutions.

4. Mathematics. An integral function of two or more given functions f₁, f₂,…, f_n of the type ∫…∫f₁(u₁)f₂(u₂ − u₁)…f_n(x−u_{n − 1})du₁du₂…du_n−1; an analogous summation.

ΘΚΠ

the world > relative properties > number > calculus > [noun] > integral calculus > integration or integrability > integral

fluent1706

integral1728

gamma function1834

surface integral1867

Riemann integral1894

Cauchy's integral1898

Lebesgue integral1905

Stieltjes integral1914

convolution1934

1934 Amer. Jrnl. Math. 56 662 Bernoulli convolutions.

1935 Trans. Amer. Math. Soc. 38 48 Distribution functions and their convolutions (‘Faltungen’).

1947 Duke Math. Jrnl. 14 236 The convolution of two positive functions is positive.

1963 G. F. Simmons Introd. Topol. xii. 305 Let G = {…, −2, −1, 0, 1, 2,…} be the additive group of integers... The linear operations are defined pointwise,..and the convolution of f and g..by (f*g)(n) = ∑∞m=−∞f(n−m)g(m).

1968 P. 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.

1979 Nature 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.

This entry has not yet been fully updated (first published 1893; most recently modified version published online June 2020).

单词	convolution
释义	convolutionn. /kɒnvəˈljuːʃən/ Etymology: noun of action < Latin convolūt-, participial stem of convolvĕre to roll together: see convolve v. 1. The action of folding (obsolete), coiling, twisting, or winding together; the condition of being coiled or convoluted. ΘΚΠ the world > movement > motion in specific manner > writhing or twisting movement > [noun] throwingOE wringinga1375 twining1398 wrenching1398 wresting1398 writhing?a1400 wrying1566 wreathing1571 convolution1597 twinding1602 contortion1611 distorquement1628 distortion1718 twisting1725 quirling1754 circumgyration1843 the world > space > relative position > folding or folded condition > [noun] > action of folding reduplication?a1425 foldingc1440 pranking1440 replication1538 convolution1597 rolling1601 fold1609 doubling1634 foldure1823 1597 Bp. J. King Lect. Ionas xxviii. 376 A convolution or folding it vppe togither. 1675 N. Grew Compar. Anat. Trunks ii. vi. 73 The Claspers of a Vine..have also a motion of Convolution. 1678 R. Cudworth True Intellect. Syst. Universe i. ii. 98 Where after many Convolutions and Evolutions..they chanced..to settle. 1730 J. Thomson Autumn in Seasons 164 Tost wide around, O'er the calm sky, in convolution swift. 1835 J. Lindley 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). ΘΚΠ the world > space > shape > curvature > coil > [noun] rundlec1300 waif1513 enwrapping1543 convolution1545 entrail?a1549 wreath1555 roundness1572 spire1572 rolling1576 enfold1578 infold1578 obvolution1578 gyre1590 whorl1592 enfoldment1593 twine1600 turn1625 volume1646 volution1752 swirl1786 coil1805 swirling1825 convolute1846 whirl1862 enfolding1873 snaking1888 1545 T. Raynald in tr. E. Roesslin Byrth of Mankynde i. sig. G.iv It hath many conuolucyons as wormes lyeng together haue. 1667 R. Boyle Origine Formes & Qualities (ed. 2) To cast it self into such grand..convolutions as the Cartesians call Vortices. 1682 T. Gibson Anat. (1697) 375 Full of windings, like the convolutions of the guts. 1774 O. Goldsmith Hist. Earth VII. 5 The center round which every succeeding convolution of the shell is formed. 1871 J. Tyndall Fragm. Sci. (ed. 6) II. xvi. 439 Each additional convolution..adds its electro-motive force to that of all the others. 1873 W. Black Princess of Thule vi. 89 The curious convolutions of this rugged coast. 3. Anatomy. Each of the sinuous folds or windings of the surface of the cerebral hemispheres in humans and the higher animals. ΘΚΠ the world > life > the body > nervous system > cerebrospinal axis > brain > parts of brain > [noun] > cerebrum > hemisphere > convolutions and parts circumvolution1578 convolution1615 crotchet1678 gyrus1842 subgyre1889 suboperculum1889 1615 H. Crooke Μικροκοσμογραϕια 449 The convolutions of the Brain. 1804 J. Abernethy Surg. Observ. 203 Upon the surface of the convolutions of the cerebrum. 1880 H. C. Bastian Brain 279 In the lowest Quadrupeds there are no convolutions. 4. Mathematics. An integral function of two or more given functions f₁, f₂,…, f_n of the type ∫…∫f₁(u₁)f₂(u₂ − u₁)…f_n(x−u_{n − 1})du₁du₂…du_n−1; an analogous summation. ΘΚΠ the world > relative properties > number > calculus > [noun] > integral calculus > integration or integrability > integral fluent1706 integral1728 gamma function1834 surface integral1867 Riemann integral1894 Cauchy's integral1898 Lebesgue integral1905 Stieltjes integral1914 convolution1934 1934 Amer. Jrnl. Math. 56 662 Bernoulli convolutions. 1935 Trans. Amer. Math. Soc. 38 48 Distribution functions and their convolutions (‘Faltungen’). 1947 Duke Math. Jrnl. 14 236 The convolution of two positive functions is positive. 1963 G. F. Simmons Introd. Topol. xii. 305 Let G = {…, −2, −1, 0, 1, 2,…} be the additive group of integers... The linear operations are defined pointwise,..and the convolution of f and g..by (fg)(n) = ∑∞m=−∞f(n−m)g(m). 1968 P. 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. 1979 Nature 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. This entry has not yet been fully updated (first published 1893; most recently modified version published online June 2020). < n.1545
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