| 释义 |
▪ I. convex, a. and n.|ˈkɒnvɛks|
[ad. L. convexus vaulted, arched, rounded, app. an old pa. pple. (= convectus) of convehĕre to carry or bring together (because in forming an arch the extremities of the surface are brought together): in Lat. convexus was sometimes used to include concavus: see B. 1 c. By Milton stressed conˈvex, which is not infrequent with later poets.
For a possible early use see convers.]
A. adj.
1. Curved like the outside of a circle or sphere; having a curvature that bulges toward the point of observation; the reverse of concave.
1571Digges Pantom. Pref. A ij, Manyfolde superficies, playne Conuex and Concaue. 1594Blundevil Exerc. iii. i. (ed. 7) 271 The upper part of such a Vault is sayd to be Convex and the inward part Concave. 1614Bp. Hall Recoll. Treat. 695 The convexe or out-bowed side of a vessell. 1706Lond. Gaz. No. 4292/3 Letters-Patents for the Convex-Lamps. 1794Sullivan View Nat. I. 459 Flint breaks with smooth surfaces, one of which is convex, the other concave. 1853Herschel Pop. Lect. Sc. v. §13 (1873) 191 The earth's surface is..less convex—that is, flatter—as we approach its poles on all sides from the equator. 1879A. R. Wallace Austral. ix. 195 Its coast being concave instead of convex, and, therefore less open to the cool sea.
b. esp. of glasses, lenses, mirrors, etc. of this shape used for optical purposes.
1571,1662[see concave a. 2 b]. 1751Chambers Cycl. s.v., A convex mirrour represents its images smaller than the objects. 1822J. Imison Sc. & Art I. 237 When parallel rays..fall upon a double convex lens, they will be refracted. 1833N. Arnott Physics (ed. 5) II. i. 130 The light is made by a convex glass or lens to converge to one point or focus. 1869Tyndall Notes on Light §104. 16 All the foci, and all the images of a convex mirror are virtual.
2. Comb., as convex-concave.
1840Carlyle Heroes (1858) 263 No twisted, poor convex-concave mirror, reflecting all objects with its own convexities and concavities.
B. n. [elliptical use of the adj.]
†1. A convex surface or body; a vault, arch, hemisphere, etc. as viewed from without. Obs.
1626Bacon Sylva §222 Flat against Flat, and Convex against Convex. 1659T. Pecke Parnassi Puerp. 160 The sublime convex of the Quirine Hils. 1727De Foe Hist. Appar. (1840) 56 He has apparently posted an army of ministering Spirits..round this convex, this globe the earth. 1796Morse Amer. Geog. I. 56 A spherical convex nearly as round as the globe itself.
b. The convex part of anything.
1703Moxon Mech. Exerc. 208 The middle of the Convex of the Hook. 1816Keatinge Trav. II. 262 Placed on the convex of a piece of timber.
c. By the poets often applied to the vault of the sky or heavens, hell, etc. Cf. L. convexum, -a.
1627May Lucan ix. (1631) 1 And takes Up to the convexe of the sky his flight. 1667Milton P.L. ii. 434 This huge convex of Fire..immures us round Ninefold. Ibid. vii. 266 In circuit to the uttermost convex Of this great Round. 1700Prior Carmen Seculare 514 Through the large Convex of the Azure Sky. a1740Tickell (J.), Half heav'n's convex glitters with the flame.
2. A convex glass or lens.
1705Berkeley Common-pl. Bk. Wks. IV. 480 Qu. if blind would think things diminish'd by convexes. 1708J. Phillips Cyder (R.), The polish'd glass, whose small convex Enlarges to ten millions of degrees The mite.
3. A card prepared for cheating by being cut slightly convex along two edges.
1873[see concave n. 4].
Add:[A.] [1.] c. Math. Of a plane figure, a solid, a set (of points), etc.: containing the straight line segment joining any two points in the set. Of a function: having a graph which forms the lower boundary of a convex set. Of a linear combination of quantities: having coefficients which are non-negative and which total 1. Also applied to other entities in analogous senses. Cf. *concave a. 2 c.
1858Q. Jrnl. Pure & Appl. Math. II. 340 Every number n answers to a simple polygon of n + 2 sides: that is, a polygon in which no side cuts another side. The simple polygon may be either convex, or with some angles re-entrant. [1905J. L. W. V. Jensen in Nyt Tidsskrift for Matematik XVI b. 49 (heading) Om konvekse funktioner og uligheder imellem middelværdier.] 1915Proc. London Math. Soc. XIV. 269 Log M(r) is a convex function of log r. 1930Proc. Nat. Acad. Sci. XVI. 240 (heading) Combinatory topology of convex regions. 1951E. W. Barankin in J. Neyman Proc. 2nd Berkeley Symp. Math., Statistics & Probability 167 (heading) Conditional expectation and convex functions. 1959G. & R. C. James Math. Dict. 234/2 A convex linear combination of quantities xi(i= 1, 2,...,n ) is an expression.. {Summ}n1λixi , where {Summ}n1λi = 1 and each λi is a non-negative real number. 1965Ann. Math. Statistics XXXVI. 703 (heading) Peakedness of distributions of convex combinations. 1974Adby & Dempster Introd. Optimization Methods i. 10 More formally, a function of a single argument is convex if for all x and y and all numbers λ between 0 and 1, f(λx + (1 - λ)y) ≤ λf(x) + (1 - λ)f(y). 1980A. J. Jones Game Theory ii. 109 A continuous game is called convex if for each fixed x, 0≤x≤1, P (x, y) is a convex function of y.
3. Special collocations (in Math.): convex envelope = convex hull.
1964A. P. & W. Robertson Topological Vector Spaces i. 45 Each xi{elem}A is a convex set containing A called the *convex envelope of A.
convex hull, the smallest convex set which contains a given set.
1951E. W. Barankin in J. Neyman Proc. 2nd Berkeley Symp. Math., Statistics & Probability 168 The *convex hull of a set in {scrE}k is the smallest convex set containing the given set. 1965Biometrika LII. 331 (heading) The convex hull of a random set of points.
convex programming, any of various procedures for finding the minimum value of a convex function subject to specified constraints.
1963Austral. Jrnl. Statistics V. 14 (heading) An algorithm for *convex programming.
▪ II. convex, v. rare.
[f. prec. The stress varies.]
1. intr. To bow or bend convexly; to present a convex side to or toward.
1805Ld. Collingwood in A. Duncan Nelson (1806) 263 It formed a crescent, convexing to leeward. 1853Sir H. Douglas Mil. Bridges 148 The island..convexing, towards Entzersdorf and Essling, in a large, regular curve.
2. trans. To make convex; to bow or bend (anything) outwards.
1865Carlyle Fredk. Gt. xv. ix, Must be imperceptibly convexed a little. |