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单词 bernoulli
释义

Bernoullin.

/bəˈnuːli/
Etymology: < Bernoulli, the name of a Swiss family which in the 17th and 18th centuries contained several eminent mathematicians and scientists.
Applied to various principles, theorems, etc., formulated by members of the Bernoulli family (see quots.). Bernoulli's formula and Bernoulli's theorem in hydrodynamics were proposed by Daniel Bernoulli (1700–1782); Bernoulli's numbers and Bernoulli's theorem in statistics were proposed by Jacob (also known as James) Bernoulli (1654–1705).
ΘΚΠ
the world > relative properties > number > mathematics > [adjective] > characterized by theories of or approaches to
physico-mathematical1660
analytical1694
Bernoulli1749
analytic1761
Boolean1851
Sturmian1853
Bernoullian1876
Fermatian1887
Grassmannian1894
number-theoretic1899
Cantor1902
Cantorian1912
Tauberian1913
Thiessen1923
intuitionist1926
metamathematical1926
finitist1931
number-theoretical1936
finitistic1937
proof-theoretic1940
formalistic1941
Gödelian1942
constructivist1943
constructivistic1944
game-theoretical1946
game-theoretic1950
finitary1952
perturbation-theoretic1964
perturbation-theoretical1968
constructive1979
the world > relative properties > number > mathematics > [noun] > mathematical enquiry > proposition > theorem > specific theorem
pons asinorum1718
Fermat's theorem1845
Bernoulli's theorem1865
Fermat's last theorem1865
Fourier's theorem1880
remainder theorem1886
Stokes' theorem1893
Jordan('s) (curve) theorem1900
Waring's theorem1920
Gödel's theorem1933
maximin1953
incompleteness theorem1955
Schwarz inequality1955
1749 J. Stirling Differential Method 94 The first series is not extended to those cases in which the first ordinate touches the curve, nor does Bernoulli's series extend to those cases wherein the last ordinate touches the curve.
1842 A. De Morgan Differential & Integral Calculus xiii. 247 The values of U, U′, &c. are called the numbers of Bernoulli; and though they do not follow a visibly regular law, yet the connexion between them is simple.
1842 A. De Morgan Differential & Integral Calculus xiii. 248 The development of tan x by Bernoulli's numbers.
1865 I. Todhunter Math. Theory Probability vii. 71 In the fourth part of the Ars Conjectandi is the enunciation and investigation of what we now call Bernoulli's theorem.
1865 I. Todhunter Math. Theory Probability xi. 226 Let x denote the age expressed in years; let ξ denote the number who survive at that age out of a given number who were born; let s denote the number of these survivors who have not had the small-pox... Daniel Bernoulli's formula then gives the value of s.
1875 Encycl. Brit. I. 114/1 The basis of Bernouilli's [sic] Theory of Pipes.
1920 L. Bairstow Appl. Aerodynamics vi. 281 The simple form of Bernoulli's equation developed in the chapter on fluid motion may be applied separately to the two parts of streamlines which are separated by the actuator disc.
1922 R. Glazebrook Dict. Appl. Physics I. 26/2 Bernoulli's theorem. Along any stream line in a liquid subject only to gravity p + gρz + ½ρv2 = constant, p being the pressure at a point at a depth z below the plane of reference, ρ the density, and v the velocity.

Derivatives

Berˈnoullian adj.
ΘΚΠ
the world > relative properties > number > mathematics > [adjective] > characterized by theories of or approaches to
physico-mathematical1660
analytical1694
Bernoulli1749
analytic1761
Boolean1851
Sturmian1853
Bernoullian1876
Fermatian1887
Grassmannian1894
number-theoretic1899
Cantor1902
Cantorian1912
Tauberian1913
Thiessen1923
intuitionist1926
metamathematical1926
finitist1931
number-theoretical1936
finitistic1937
proof-theoretic1940
formalistic1941
Gödelian1942
constructivist1943
constructivistic1944
game-theoretical1946
game-theoretic1950
finitary1952
perturbation-theoretic1964
perturbation-theoretical1968
constructive1979
1876 Messenger Math. VI. 49 Bernoullian and Eulerian numbers.
1888 Encycl. Brit. XXIII. 14/1 Bernoullian numbers.
1937 Mind 46 488 The least rigid of these suggested conditions is that the series must be ‘Bernoullian’.
This entry has not yet been fully updated (first published 1972; most recently modified version published online December 2018).
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n.1749
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