| 释义 |
▪ I. extremal, a.|ɛkˈstriːməl|
[f. extreme n. + -al; in sense 2 re-formed on extremum, perh. influenced by next.]
†1. Farthest from the middle of a line or area; outermost. Obs.
1432–50tr. Higden (Rolls) III. 211 And if the wire be distreynede in to thre equalites, and the seide instrumente be putte under the oon extremalle diuision other departenge, the longer parte of the wyre ytowchede yeldethe diapente. 1447O. Bokenham Hooly Wummen (1938) l. 6903 The extremal marchys of hys regyoun.
2. Math. Of or pertaining to extreme qualities or configurations, or highest or lowest values.
1939Nature 4 Mar. 358/1 There seems to be no objection to extremal laws of the local type; but those of the integral type make our modern mind uneasy. 1957Kendall & Buckland Dict. Statistical Terms 104 Extremal quotient, the ratio of the absolute value of the largest observation to the smallest observation in a sample. 1966Mathematical Rev. XXXI. 17/1 Turán's original theorem on extremal problems in graph theory.
▪ II. extremal, n. Math.|ɛkˈstriːməl|
[ad. G. extremale (A. Kneser Lehrb. der Variationsrechnung (1900) ii. 24), prob. f. G. extremum extremum.]
A function y(x) or its graphical representation that is a solution of the Euler–Lagrange equation and so makes an integral ∫f(x, y, dy/dx)dx along an arc of the curve a maximum or a minimum; also applied to a surface the integral over which is a maximum or a minimum. Also attrib. or as adj.
1901Ann. Mathematics 2nd Ser. II. 108 Any function y of x..which, at all interior points of an interval (x′, x{pp}) throughout which it is considered satisfies Lagrange's equation..is called an extremal. 1904O. Bolza Lect. Calculus Variations i. 27 Every solution of Euler's equation (curve as well as function) is called, according to Kneser, an extremal. 1950C. Fox Introd. Calculus Variations iii. 69 Surfaces for which I is stationary will be referred to as extremals. Ibid., An extremal surface. 1962L. A. Pars Introd. Calculus Variations i. 18 In the early history of the subject it was often assumed that if there is a unique extremal through A and B the problem is solved. Ibid. ii. 43 An extremal arc. |