单词 | bernoulli |
释义 | Bernoullin. 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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