| 释义 |
linear, a. and n.|ˈlɪnɪə(r)|
[ad. L. līneāris, f. līnea line. Cf. F. linéaire.]
A. adj.
1. Of or pertaining to a line or lines. linear perspective: that branch of perspective which is concerned with the apparent form, magnitude, and position of visual objects, as distinguished from aerial perspective (see aerial 4).
1656in Blount Glossogr. 1841W. Spalding Italy & It. Isl. I. 192 When backgrounds were introduced, they were ill-executed, the linear-perspective being nowhere accurately observed. 1865Pall Mall G. 11 Nov. 9 That linear hardness which never appears in nature. 1869J. Martineau Ess. II. 63 The general rules of linear perspective. 1878Gurney Crystallogr. 29 This difference between models and crystals must be remembered. The former have linear symmetry.
2. a. Consisting of lines; involving the use of lines.
1840Lardner Geom. ix. 93 The..extent of space included within the linear boundaries of any figure is called its area. 1884Ruskin Pleas. Eng. 21 The Celts developing peculiar gifts in linear design, but wholly incapable of drawing animals and figures. 1900Contemp. Rev. Dec. 796 Two systems of writing, pictographic and linear, did, indeed, exist in the early Aegean world.
fig.1830Carlyle Misc. (1857) II. 172 Narrative is linear, Action is solid.
b. Linear A, the earlier of two related forms of writing discovered at Knossos in Crete by Sir A. J. Evans between 1894 and 1901; Linear B, the later form, found also on the mainland of Greece, and now shown to be a syllabary imperfectly adapted to the writing of Mycenæan Greek.
[1902–3A. J. Evans in Ann. Brit. School at Athens IX. 52 This early system of linear script—which may be conveniently termed Class A as opposed to Class B of the latest Palace Period at Knossos—had a wide extension in the island.] 1907R. M. Burrows Discoveries Crete vi. 84 The linear writing of class A is now in regular use. Ibid. 92 The hoard of clay tablets..shows that its linear writing, called by Mr. Evans Class B, is more advanced. 1909A. J. Evans Scripta Minoa I. i. v. 31 Documents belonging to the Linear Class A only occur in this particular stratum... In deposits clearly belonging to the remodelled building the inscribed documents all belonged to Class B. Ibid. 35 Common to both the linear scripts A and B. Ibid. 36 The system of numerals..of the Linear Class B. 1948A. E. Kober in Amer. Jrnl. Archaeol. LII. 89 Inscriptions of Linear A have been found at several sites. 1950E. L. Bennett in Ibid. LIV. 81/1 Translations of and commentary upon additional Linear-B tablets from Knossos. Ibid. 204/1 The Linear A flourished in the rest of Crete.., and the Linear B at Knossos only. Ibid. 218/2 The Linear A ideogram L85 appears to have..the same form. Ibid. 219/1 The shapes of four other signs of Linear A..are reflected in the Linear B signs. 1952J. L. Myres Evans' Scripta Minoa II. 1 In this new ‘Linear A’ script about one-third of the signs are derived from linearized hieroglyphs. Ibid. 2 It was doubtless..local unconformity that provoked the drastic reform of the ‘Linear B’ script at Knossos. 1953Ventris & Chadwick in Jrnl. Hellenic Stud. LXXIII. 84 Evans believed that Linear B..was an administrative revision of Linear A, designed to express the same ‘Aegean’ language. 1966C. H. Gordon Evidence for Minoan Lang. ix. 32 The Linear A and B texts overlap in time. 1972Sci. Amer. Oct. 37/1 The Cretan system of writing, which we call Linear A, was crude but it was adequate for keeping rough accounts.
c. Mus. = horizontal a. 4.
1944W. Apel Harvard Dict. Mus. 409/1 Linear counterpoint, a term introduced by E. Kurth..in order to emphasize the ‘linear’, i.e., horizontal aspect of counterpoint... The term is also used..for what the Germans call rücksichtsloser (reckless) Kontrapunkt, i.e., the modern type of counterpoint which pays little attention to harmonic combination and euphony. 1955[see horizontal a. 4]. 1958A. Jacobs New Dict. Mus. 211 Linear counterpoint, term—senseless, because all counterpoint is a matter of lines—sometimes used for a type of 20th-century counterpoint (e.g. Stravinsky's) held to be musically valid through the value of the separate lines themselves. 1959Listener 8 Jan. 80/2 In the slow movement the orchestral texture begins in linear style, spare and canonic. 1962Ibid. 18 Jan. 147/1 Linear and rhythmic techniques suggested by medieval music. Ibid. 147/2 A conscious employment of linear and metrical ‘series’ derived from Indian ragas and talas.
3. a. Having the direction of a line; extended in a line or in length; spec. in Math. and Phys. involving measurement in one dimension only; capable of being represented by a straight line on a graph (in Cartesian co-ordinates); involving or possessing the property that a change in one quantity is accompanied by or corresponds to a directly proportional change in a related one. linear equation, an equation of the first degree. linear numbers, linear problem (see quot. 1706).
1706Phillips (ed. Kersey), Linear Numbers, are those that have relation to Length only: For Example, such as represent one Side of a plane Figure; and if the Figure be a Square, the Linear Number is call'd a Root. Ibid., Linear Problem (in Mathem.), such a Problem as can be solved Geometrically, by the Intersection..of two Right⁓lines. 1799J. Wood Elem. Optics iv. (1811) 83 This line is called the diameter, or linear aperture of the lens. 1806Hutton Course Math. I. 340 Similar Prisms and Cylinders are to each other, as the Cubes of their Altitudes, or of any other Like Linear Dimensions. 1812–16Playfair Nat. Phil. (1819) I. 201 The superficial breadth of the stream, expressed in linear inches. 1816tr. Lacroix's Diff. & Int. Calculus 326 We call it from thence, a linear equation of the first order. 1830Lyell Princ. Geol. I. 314 Active volcanic vents..arranged in a linear direction. 1831Brewster Optics xli. 336 The linear magnifying power is the number of times an object is magnified in length. 1867Denison Astron. without Math. 71 The resistance does diminish the actual or linear speed. 1872Nicholson Palæont. 44 It is possible to arrange the animals of any one sub-kingdom in something like a linear series. 1882Minchin Unipl. Kinemat. 6 A point P moves in a circle with constant linear velocity. Ibid. 123 So that (ξ, η) are also linear functions of (ξ′, η′); and if the first satisfy a linear equation..so must the second. 1910Encycl. Brit. IX. 146/2 The limiting tension beyond which the above law of proportionality [between tension and extension] fails to hold is often called the ‘limit of linear elasticity’. 1940Chambers's Techn. Dict. 503/1 Linear amplification, amplification in which the output current or voltage is strictly proportional to the input voltage. 1941Proc. R. Soc. A. CLXXVII. 382 The disintegration of boron by slow neutrons has been investigated using an ionization chamber filled with boron trichloride in conjunction with a linear amplifier. 1942Electronic Engin. XIV. 711/1 The conversion must be accomplished in a linear manner, i.e., the amplitude change is directly proportional to the frequency change. 1962D. F. Shaw Introd. Electronics vii. 126 The preservation of the shape is a unique property of the sine wave and..is a feature which it possesses for all linear circuits. Ibid. viii. 147 A circuit is linear if the individual components behave in such a manner that the amplitude of the current through each component is directly proportional to the amplitude of the applied voltage and the relationship between the phases of the voltage and current is independent of the current and voltage magnitude. 1973Physics Bull. Oct. 606/1 A linearizer circuit is used to ensure a true linear relationship between conveyor load and indicated reading.
b. Educ. Designating or pertaining to programmed learning aimed at step-by-step progress in which the material is broken down into small steps each of which must elicit a correct response before the next one is presented; freq. contrasted with branching methods.
For linear programming in a different sense see 7.
1958B. F. Skinner in Science 24 Oct. 974/2 A first step is to define the field. A second is to collect technical terms, facts, laws, principles, and cases. These must then be arranged in a plausible developmental order—linear if possible, branching if necessary. 1961Barron's Nat. Business & Financial Weekly 30 Oct. 14/2 We are disciples of neither Crowder nor Skinner. Our programs will make use of either branching or linear techniques, depending on which seems best suited to the subject matter. 1962A. A. Lumsdaine in J. E. Coulson Programmed Learning 135, I believe that linear programs should almost invariably be constructed first, even if branching is later to be introduced. 1964Times Rev. Industry Feb. 100/2 A novel feature is the method it uses—the linear (non-branching) technique of programmed learning. 1969G. Kent Blackboard to Computer viii. 109 The basis of linear programming is that the subject matter to be understood is always presented to the student in small quantities. 1970W. K. Richmond Concept Educ. Technol. iii. 103 That the majority of linear programmes are inordinately dull is, of course, a charge which will be strenuously denied by anyone who has laboured to produce one. Ibid., This aseptic dullness is explained by the linear programmer's dependence upon a bird-brained psychology.
4. a. Resembling a line; very narrow in proportion to its length, and of uniform breadth.
1642H. More Song of Soul ii. i. ii. 42 [The Soul] Girds the swoln earth with linear list. 1828Stark Elem. Nat. Hist. I. 362 Body gray brown, with transverse linear whitish stripes. 1853G. Bird Urin. Deposits (ed. 3) 357 Minute linear bodies hardly so long as the diameter of a blood⁓corpuscle. 1854Brewster More Worlds xi. 178 These linear nebulæ, which Sir John Herschel thinks are flat ellipsoids seen edgewise. 1885Watson & Burbury Math. Th. Electr. & Magn. I. 218 A conductor, two of whose dimensions are very small compared with the third, as for instance a wire, is called a linear conductor. 1923C. R. Stockard in Amer. Jrnl. Anat. XXXI. iii. 278 The two groups into which almost all ordinary persons fall more or less exactly may..be termed the Linear Type and the Lateral Type. The linear type is the faster growing high metabolizing thin but not necessarily tall group, while the lateral type is slower in maturing and is stocky and rounder in form. 1932Field Archæol. (Ordnance Survey) 30 This term ‘Linear Earthwork’ is used to describe earthworks like Wansdyke..and the numerous Grim's Dykes... They consist of a bank and ditch and may be of any length from a few yards..to 10 miles. 1959Jrnl. Soc. Archit. Historians XVIII. 40/1 Soria..customarily described his Linear City as a vertebrate animal. 1964M. Argyle Psychol. & Social Probl. v. 62 Fewer of the delinquents are of linear (thin and bony) physique. 1966Guardian 5 Apr. 2/6 A new linear city of half a million people..near Inverness..is the ambition of Professor Robert Grieve.
b. spec. Bot. and Zool. Like a thread, elongated.
1753Chambers Cycl. Supp. s.v. Leaf, Linear Leaf, one the two sides of which run almost parallel to one another. 1777Robson Brit. Flora 15 Linear, everywhere of the same breadth, though sometimes narrowing at the extremities only. 1787Fam. Plants I. 2 Anther linear..Stigma linear. 1828Stark Elem. Nat. Hist. II. 89 Shell equivalve..; hinge, linear, without teeth. 1851Richardson Geol. (1855) 180 Verticillate fringes of linear leaves growing round the joints. 1851Woodward Mollusca 106 Muricidæ... Lingual ribbon long, linear. 1870Hooker Stud. Flora 225 Campanula rotundifolia,..lower cauline leaves lanceolate, upper narrow linear quite entire. 1874Coues Birds N.W. 430 Two narrowly linear feathers. 1880Gray Struct. Bot. iii. §4. (ed. 6) 95 Linear, when leaf-blades are narrow, several times longer than wide, and of about the same breadth throughout.
c. Having a (more or less) plain outline; not indented or notched; also said of the outline.
1796C. Marshall Garden. xii. (1813) 139 A tree may be regular without being linear. 1797Encycl. Brit. (ed. 3) III. 444/1 A Margin..entire, linear without the least dent or notch.
5. Surg. linear extraction (of cataract): see quot. 1890. linear rectotomy: the operation of dividing a strictured urethra through the rectum.
1874G. Lawson Dis. Eye 127 Linear Extraction of Cataract. 1878T. Bryant Pract. Surg. I. 724 M. Verneuil has advocated the operation of ‘linear rectotomy’ for the cure of stricture. 1890Billings Nat. Med. Dict., Linear extraction, methods of cataract extraction in which the corneal incision approaches to a plane passing through the centre of curvature of the globe.
6. Comb. chiefly Bot.
a. Signifying ‘linear and{ddd}’, ‘between linear and{ddd}’, as linear-acute, linear-attenuate, linear-awled, linear-elliptical, linear-elongate, linear-ensate, linear-filiform, linear-lanceolate, linear-ligulate, linear-oblong, linear-obovate, linear-setaceous, linear-spathulate, linear-subulate adjs.; also linear-leaved, linear-shaped adjs.
1847W. E. Steele Field Bot. 9 Hawkweed,..bracts *linear-attenuate.
a1794Sir W. Jones in Asiat. Res. (1795) IV. 269 Leaves *linear-awled, pointed, opposite.
1881–2W. S. Kent Man. Infusoria II. 786 Body..*linear-elliptical.
1836Loudon Encycl. Plants Gloss., *Linear-ensate, long sword-shaped.
1845Lindley Sch. Bot. iv. (1858) 42, 1. A[lsine] rubra. Leaves *linear-filiform, mucronate, some⁓what fleshy.
1793Martyn Lang. Bot., Lineari-lanceolatum, *linear-lanceolate.
1825Greenhouse Comp. II. 20 Pharnaceum lineare, *linear-leaved Pharnaceum.
1870Hooker Stud. Flora 373 Potamogeton... Leaves..*linear⁓ligulate.
1839Johnston in Proc. Berw. Nat. Club I. No. 7. 205 Teeth transverse, *linear-oblong. 1870Hooker Stud. Flora 312 Rumex conglomeratus,..inner fruiting sepals linear-oblong.
1845Florist's Jrnl. 89 Styphelia tubiflora... Leaves which are sometimes *linear-obovate.
1847W. E. Steele Field Bot. 21 Scales of receptacle *linear-setaceous.
1845Darwin Voy. Nat. vii. (1879) 126 The view would resemble that of a great lake, if it were not for the *linear⁓shaped islets.
1870Hooker Stud. Flora 130 Saxifraga Andrewsii... Leaves *linear-spathulate.
1793Martyn Lang. Bot., Lineari-subulatum, *linear-subulate.
b. In quasi-Latin form, as lineari-elongate, lineari-laciniose, lineari-oblong adjs.
1871W. A. Leighton Lichen-flora 9 Spores 8, oblong or lineari-elongate or cylindrical. Ibid. 12 Spores 8, colourless, lineari-oblong or subfusiform. Ibid. 18 Fuscous-black, lineari-laciniose, laciniæ ligulate.
7. Special collocations: linear accelerator (see accelerator e); linear motor, a motor (esp. an induction motor) which produces motion directly in a straight line (as opposed to rotary motion); linear programming, a mathematical technique for maximizing or minimizing a linear function (such as output or cost) of several variables (such as resources) when these are required to satisfy a set of linear equations and inequalities; (see also 3 b above).
1957E. R. Laithwaite in Proc. Inst. Electr. Engin. CIV. a. 461/1 [The word ‘linear’ has already been used in connection with particle accelerators, but as there is little likelihood of confusion between these devices and electric motors, there appears to be no objection to the use of the word for the latter.] Ibid., The use of *linear motors as liquid-metal pumps is examined. 1966Listener 13 Oct. 535/3 British Rail were the first to support Laithwaite's work on the linear motor, and suggested to him in 1960 its possible application to rail traction. 1973Sci. Amer. Oct. 21/1 The evolution of electromagnetic flight is inextricably linked to the problem of propulsion. Two types of ‘linear motor’ are being studied for this application. One is called the linear induction motor, the other the linear synchronous motor.
1949G. B. Dantzig in Econometrica XVII. 203 It is our purpose now to discuss the kinds of restrictions that fit naturally into *linear programming. 1953Cooper & Henderson in W. W. Cooper et al. Introd. Linear Programming i. 1 Linear programming is concerned with the problem of planning a complex of interdependent activities in the best possible (optimal) fashion. 1966A. Battersby Math. in Managem. iv. 85 Transporting coal to power stations or gasworks, allocating cash to local branches, formulating foods and drawing up a maintenance schedule: these are all areas in which linear programming is at work today. 1967E. Duckworth in Wills & Yearsley Handbk. Managem. Technol. vi. 110 When the optimum order quantities have been decided, problems may occur in scheduling these through factories in the optimum manner... Quite complex methods of the linear programming or queueing theory type may be needed. 1971Sci. Amer. Feb. 84/2 Among the intended tasks for illiac iv is linear programming, a mathematical technique for allocating the use of limited resources to maximize or minimize a specified objective. Ibid. 85/2 In order to apply linear programming to an entire economic sector one must incur considerable expense in gathering the data to be used in the model.
†B. n. A linear equation. Obs.
1684T. Baker Geometr. Key title-p., Of linears, qvadratics, cubics, biqvadratics; And the finding of all their Roots.
Add:[A.] [3.] c. Of causation, evolution, time, etc.: progressing in a single direction by regular steps or stages, sequential.
1948E. Whittaker Space & Spirit xxxix. 126 In the argument as usually presented..all chains of causation are simple linear sequences. 1954A. P. Usher Hist. Mech. Inventions (ed. 2) ii. 30 The cultures of antiquity do not fit the patterns of the linear sequences of social and economic evolution developed by the German Historical Schools. 1972R. D. Walshe in G. W. Turner Good Austral. Eng. xi. 228 The McLuhan thesis that..‘linear thinking’..had been rendered obsolete by the new ‘in-depth’, ‘all-at-once’ thinking of the electronic media. 1979P. Matthiessen Snow Leopard i. 60 The Australian aborigines..distinguish between linear time and a ‘Great Time’ of dreams, myths, and heroes, in which all is present in this moment. 1983P. Lively Perfect Happiness viii. 112 Time, that should be linear, had become formless. 1992Forum Mod. Lang. Stud. Jan. 22 It is impossible to over-emphasise the importance of the poet's decision to keep the inexorable linear flow of time intact on each occasion when a-temporality is alluded to.
d. Linguistics. Of phonological, morphological, or syntactic elements or their ordering: consisting of a series arranged sequentially; spec. (in Generative Grammar) of a surface structure.
1955N. Chomsky Theory of Linguistic Struct. (microfilm, Mass. Inst. Technol.) vi. 235 The linear grammar is a sequence of conversion statements S1,.., Sn where each Si is of the form ‘Xi→Yi’. 1959W. Baskin tr. F. de Saussure's Course in Gen. Linguistics ii. v. 123 In discourse..words acquire relations based on the linear nature of language because they are chained together. 1968J. Lyons Introd. Theoret. Linguistics vi. 209 We..adopted the view that all sentences had a simple linear structure. 1969Canad. Jrnl. Ling. XV. 25 It was speculated..that the reason that languages had embedding transformations..was to ‘linearize’ or spread out in linear form the deeply embedded concoctions which the human mind can produce. 1982Ibid. XXVII. 74 Werth observes that it is possible to eliminate linear order in the base... If there is no linear order in the base, then grammatical relations must be marked in the base. 1991Applied Linguistics XII. 189 It is based ultimately on a pre-Chomskyan linear model of language production.
[7.] linear algebra Math., a finite-dimensional vector space, with multiplication defined and distributive over addition, in which (λa)b = λ(ab) = a(λb) for any scalar λ of the associated field and any vectors a and b ; also, the branch of algebra which deals with the properties of these entities, esp. of vector spaces over the real or complex numbers.
1870B. Peirce in Amer. Jrnl. Math. (1881) IV. 107 An algebra in which every expression is reducible to the form of an algebraic sum of terms, each of which consists of a single letter with a quantitative coefficient, is called a *linear algebra. 1945E. T. Bell Devel. Math. (ed. 2) x. 231 The introduction of general methods into linear algebra, beginning in the first decade of the twentieth century, prepared that vast field of mathematics..for partial arithmetization in the second and third decades. 1965Patterson & Rutherford Elem. Abstr. Algebra v. 187 The set of all m × m matrices over a field F forms a linear algebra of dimension m2. 1975I. Stewart Concepts Mod. Math. xv. 227 A proper understanding of linear algebra requires a synthesis of three points of view: (i) the underlying geometrical motivation, (ii) the abstract algebraic formulation, (iii) the matrix-theoretic technique. 1986C. W. Norman Undergraduate Algebra p. vii, Many of the problems which linear algebra sets out to solve are dealt with in a practical way by the row-reduction algorithm in Chapter 8.
linear search Computing, a search in which items stored in a file are examined sequentially.
1968Communications Assoc. Computing Machinery XI. 36/1 It has been noticed..that the *linear search process itself produces clustering and is therefore intrinsically slow. 1970Ibid. XIII. 103/2 The simplest search is the linear search in which the search progresses by a multiple of an increment m, e.g. k + 1m, k + 2m,.., etc. 1987Austral. Personal Computer Aug. 224/1 Linear search takes, on average, N/2 operations to find an item and N operations to discover that an item is not on the list. |