| 单词 | schwarz inequality |
| 释义 | > as lemmasSchwarz inequality Used attributively and in the possessive to designate the various forms of the theorem which states that the square of the sum of a set of products of two quantities cannot exceed the sum of the squares of the first terms multiplied by the sum of the squares of the second terms. Chiefly in Schwarz inequality. ΘΚΠ 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 1955 M. Loève Probability Theory ix. 156 Hölder's inequality with r = s = 2, is called the Schwarz inequality: E2 | XY | ≤ E | X | 2.E | Y |2. 1962 W. B. Thompson Introd. Plasma Physics viii. 222 This makes use of the Schwartz inequality ∫f2dx∫g2dx ≥ [∫fgdx]2. 1964 McCord & Moroney Introd. Probability Theory ix. 155 Let X1 and X2 be any two jointly distributed random variables which have finite, positive variances... If a and b are any real constants deduce that [E(X1 − a)(X2 − b)]2 ≤ [E(X1 − a)2][E(X2 − b)2], which is a form of Schwarz's inequality. 1965 E. M. Patterson & D. E. Rutherford Elem. Abstr. Algebra v. 176 In a unitary space ‖a‖ ‖b‖ ≥ |a·b|... The inequality is known as Schwartz's inequality. 1975 Karlin & Taylor First Course Stochastic Processes (ed. 2) ix. 452 E[|YZ|] ≤ √(E[Y2]E[Z2]) = ‖Y‖ ‖Z‖. This is known as Schwartz' inequality. < as lemmas |
| 随便看 |
英语词典包含1132095条英英释义在线翻译词条，基本涵盖了全部常用单词的英英翻译及用法，是英语学习的有利工具。