extremaln.

/ɛkˈstriːməl/

Etymology: < German extremale (A. Kneser Lehrb. der Variationsrechnung (1900) ii. 24), probably < German extremum extremum n.

Mathematics.

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 attributive or as adj.

ΚΠ

1901 Ann. Math. 2 108 Any function y of x..which, at all interior points of an interval (x′, x″) throughout which it is considered satisfies Lagrange's equation..is called an extremal.

1904 O. Bolza Lect. Calculus Variations i. 27 Every solution of Euler's equation (curve as well as function) is called, according to Kneser, an extremal.

1950 C. Fox Introd. Calculus Variations iii. 69 Surfaces for which I is stationary will be referred to as extremals.

1950 C. Fox Introd. Calculus Variations iii. 69 An extremal surface.

1962 L. 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.

1962 L. A. Pars Introd. Calculus Variations ii. 43 An extremal arc.

This entry has not yet been fully updated (first published 1933; most recently modified version published online December 2018).

extremaladj.

/ɛkˈstriːməl/

Etymology: < extreme n. + -al suffix¹; in sense 2 re-formed on extrem- (in extremum n.), perhaps influenced by extreme adj.

†1. Farthest from the middle of a line or area; outermost. Obsolete.

ΘΚΠ

the world > space > relative position > condition of being external > [adjective] > outermost

utmostc950

outmosta1382

outerestc1392

uttermost1398

extremal1447

utteresta1492

extreme1503

uppermost1548

outermost1587

outwardmost1598

extimate1659

1447 O. Bokenham Lives of Saints (Arun.) (1938) l. 6903 The extremal marchys of hys regyoun.

?a1475 (?a1425) tr. R. Higden Polychron. (Harl. 2261) (1871) 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.

2. Mathematics. Of or pertaining to extreme qualities or configurations, or highest or lowest values.

ΘΚΠ

the world > relative properties > number > mathematics > [adjective] > relating to mathematical property

simple1570

dissevered1605

periodicala1690

irreductible1753

analytical1799

analytic1800

compound1806

well-conditioned1843

one-valued1884

non-empty1905

well-behaved1912

minimax1917

irredundant1925

non-linear1930

constructive1938

extremal1939

max-min1949

meta-analytic1968

meta-analytic1978

1939 Nature 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.

1957 M. G. Kendall & W. R. Buckland Dict. Statist. Terms 104 Extremal quotient, the ratio of the absolute value of the largest observation to the smallest observation in a sample.

1966 Math. Rev. 31 17/1 Turán's original theorem on extremal problems in graph theory.

This entry has not yet been fully updated (first published 1972; most recently modified version published online December 2021).

单词	extremal
释义	extremaln. /ɛkˈstriːməl/ Etymology: < German extremale (A. Kneser Lehrb. der Variationsrechnung (1900) ii. 24), probably < German extremum extremum n. Mathematics. 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 attributive or as adj. ΚΠ 1901 Ann. Math. 2 108 Any function y of x..which, at all interior points of an interval (x′, x″) throughout which it is considered satisfies Lagrange's equation..is called an extremal. 1904 O. Bolza Lect. Calculus Variations i. 27 Every solution of Euler's equation (curve as well as function) is called, according to Kneser, an extremal. 1950 C. Fox Introd. Calculus Variations iii. 69 Surfaces for which I is stationary will be referred to as extremals. 1950 C. Fox Introd. Calculus Variations iii. 69 An extremal surface. 1962 L. 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. 1962 L. A. Pars Introd. Calculus Variations ii. 43 An extremal arc. This entry has not yet been fully updated (first published 1933; most recently modified version published online December 2018). extremaladj. /ɛkˈstriːməl/ Etymology: < extreme n. + -al suffix¹; in sense 2 re-formed on extrem- (in extremum n.), perhaps influenced by extreme adj. †1. Farthest from the middle of a line or area; outermost. Obsolete. ΘΚΠ the world > space > relative position > condition of being external > [adjective] > outermost utmostc950 outmosta1382 outerestc1392 uttermost1398 extremal1447 utteresta1492 extreme1503 uppermost1548 outermost1587 outwardmost1598 extimate1659 1447 O. Bokenham Lives of Saints (Arun.) (1938) l. 6903 The extremal marchys of hys regyoun. ?a1475 (?a1425) tr. R. Higden Polychron. (Harl. 2261) (1871) 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. 2. Mathematics. Of or pertaining to extreme qualities or configurations, or highest or lowest values. ΘΚΠ the world > relative properties > number > mathematics > [adjective] > relating to mathematical property simple1570 dissevered1605 periodicala1690 irreductible1753 analytical1799 analytic1800 compound1806 well-conditioned1843 one-valued1884 non-empty1905 well-behaved1912 minimax1917 irredundant1925 non-linear1930 constructive1938 extremal1939 max-min1949 meta-analytic1968 meta-analytic1978 1939 Nature 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. 1957 M. G. Kendall & W. R. Buckland Dict. Statist. Terms 104 Extremal quotient, the ratio of the absolute value of the largest observation to the smallest observation in a sample. 1966 Math. Rev. 31 17/1 Turán's original theorem on extremal problems in graph theory. This entry has not yet been fully updated (first published 1972; most recently modified version published online December 2021). < n.1901adj.1447
随便看	uncompellable uncompelled uncompelling uncompellingly uncompensable uncompensated uncompetence uncompetent uncompetible uncompetitive uncompetitiveness uncompetitivenesses uncomplacent uncomplained uncomplaining uncomplainingly uncomplainingness uncomplaisance uncomplaisant uncomplaisantly uncomplemental uncomplete uncompleted uncompletely uncomplex