| 释义 |
scalar, a. and n.|ˈskeɪlə(r), formerly ˈskeɪlɑː(r)|
[ad. L. scālār-is, f. scāla ladder, scale n.3]
A. adj.
1. Resembling a ladder; Bot. = scalariform.
1656Blount Glossogr., Scalar, Scalary, leaning one way, ladderwise, not bolt up right. 1880Linn. Soc. Jrnl. XV. 92 Spire rather high, scalar.
2. Math. Of the nature of a scalar (see B).
1846W. R. Hamilton in Phil. Mag. XXIX. 26 The algebraically real part may receive, according to the question in which it occurs, all values contained on the one scale of progression of numbers from negative to positive infinity; we shall call it therefore the scalar part, or simply the scalar of the quaternion, and shall form its symbol by prefixing, to the symbol of the quaternion, the characteristic Scal., or simply S. 1853Hamilton in Phil. Mag. Ser. iv. V. 322 The two values of the vector ρ, which answer to the two values of the scalar coefficient x. 1853― Elem. Quaternions ii. i. (1866) 175 The Scalar (or Scalar Part) of a Quaternion. Ibid. iii. iii. 721 The scalar equation of the polar of the latter point. 1873Maxwell Electr. & Magn. I. 9 Scalar quantities do not involve direction. 1911Encycl. Brit. XXVII. 962/2 The mass of a body, the pressure of a gas, the charge of an electrified conductor, are instances of scalar magnitudes. 1932R. Gans Vector Analysis ii. 58 Let W..be a scalar..property of a field, and let it be regarded as a function of the position and of the time. 1964N. N. Hancock Matrix Analysis Electr. Machinery ii. 18 A ‘scalar’ matrix is a diagonal matrix in which all the elements on the principal diagonal are equal.
3. Of or pertaining to a musical scale (scale n.3 4).
1928G. Cooke Theory of Music ii. 18 One cannot..over-emphasise the importance of these groups of notes in the theoretic study of scalar development. Ibid. vi. 77 The variety inherent in modulation and scalar variety. 1946R. Blesh Shining Trumpets ii. 25 The basic material is recast in its scalar compass and its tonal intervals. 1959M. T. Williams Art of Jazz (1960) xi. 106 Sliding tones peculiar to the scalar and harmonic structure. 1966New Statesman 11 Feb. 204/1 The integration of triadic and scalar elements within a serial or non-tonal field.
4. Of or pertaining to a graduated scale (scale n.3 9).
1959G. D. Mitchell Sociology 130 Very often there is an identity of functional and scalar status. 1974G. Leech Semantics ii. 21 A selection from indefinitely many possible scales, which in any case would only provide for associative meaning in so far as it is explicable in scalar terms.
B. n.
1. Math. In quaternions, a real number. More widely, a quantity having magnitude but no direction, and representable by a single real number.
1846[see sense A. 2]. 1853Hamilton Elem. Quaternions i. ii. (1866) 10 The..quotient..obtained by the division of two parallel vectors by another, including zero as a limit, may also be called a Scalar; because it can always be found..by the comparison of positions upon one common scale (or axis)... Such Scalars are..simply the Reals..of Algebra. Ibid. 11 The combination, ‘Scalar plus Vector,’ is a Quaternion. 1882Minchin Unipl. Kinemat. 260 The result of the operation ∇2 on any scalar is purely a scalar. 1903[see non-directional a. (n.)]. 1932R. Gans Vector Analysis i. 2 We shall denote scalars by ordinary type and vectors by heavy type. 1965Patterson & Rutherford Elem. Abstr. Algebra v. 145 By a scalar we shall mean an entity determined by a single real number and by a vector we shall mean an entity determined by both a positive real number, measuring magnitude, and a direction in space.
2. attrib. (some of the following may be regarded as collocations of the adj.): scalar field, a map from a space to the real line (see quot. 1932); scalar function, a function whose value is a scalar; scalar multiplication, multiplication of a vector by a scalar to give another vector; scalar product = inner product s.v. inner a. (n.2) 1 k; scalar triple product, a scalar function of three three-vectors ((a1, a2, a3), (b1, b2, b3), (c1, c2, c3)) which can be calculated as (a1, b2, c3 + b1 c2 a3 + c1 a2 b3 - a1 c2 b3 - b1 a2 c3 - c1 b2 a3), being the volume of the parallelepiped which has the three vectors as three coincident edges.
1932R. Gans Vector Analysis i. 1 The field is called a *scalar field or a vector field according as the quantity associated with the field is a scalar or a vector. 1959M. R. Spiegel Vector Analysis i. 3 The temperature at any point within or on the earth's surface at a certain time defines a scalar field. 1974G. Reece tr. Hund's Hist. Quantum Theory xv. 207 It was therefore a major advance when Pauli and Victor Weisskopf developed the quantum theory of a scalar field.
1956A. A. Townsend Struct. Turbulent Shear Flow iii. 35 The double-correlation function depends only on a single *scalar function. 1972A. G. Howson Handbk. Terms Algebra & Anal. xxvi. 126 Functions such as f are often referred to as vector-valued functions and are denoted by symbols printed in bold type so as to distinguish them from real-valued or scalar functions.
1901Gibbs & Wilson Vector Analysis i. 13 The laws which govern addition, subtraction, and *scalar multiplication of vectors are identical with those governing these operations in ordinary scalar algebra. 1968A. P. Armit Advanced Level Vectors ii. 25 (heading) Scalar multiplication of a vector..in terms of cartesian components.
1878*Scalar product [see vector n. 2]. 1932R. Gans Vector Analysis i. 17 By the scalar product of two vectors A and B we mean a scalar of magnitude equal to the product of the absolute values and the cosine of the angle between the vectors. 1941,1968Scalar product [see inner a. (n.2) 1 k].
1901Gibbs & Wilson Vector Analysis ii. 68 The second triple product is the scalar product of two vectors, of which one is itself a vector product, as A · (B × C) or (A × B) · C. This sort of product has a scalar value and consequently is often called the *scalar triple product. 1959M. R. Spiegel Vector Analysis ii. 17 The product A · (B × C) is sometimes called the scalar triple product or box product and may be denoted by [ABC]. 1964E. Œ. Wolstenholme Elem. Vectors ii. 38 If a, b, c are three vectors, any pair of them may be multiplied vectorially to form a new vector d, the third of the original vectors may then be multiplied by d, either scalarly to form what is known as a scalar triple product, or vectorially to form..the vector triple product.
▸ scalar implicature n. Linguistics (of a gradable term or construction) an implicature that no stronger value can truthfully be used; the use of a relatively lower-valued term to implicate that no higher value is true.
1972L. R. Horn On Semantic Properties of Logical Operators in Eng. (Ph.D. diss., UCLA) 96 Both John and Bill didn't go (just one of them)... Notice that the implicit continuation we have filled in above is simply a *scalar implicature: not all implicates not none, i.e. some. 1985Language 61 771 The negative quality which Cutler attributes to this example does not result from FR [sc. fall-rise intonation], but rather from the scalar implicature which A is entitled to infer from B's response—i.e., that the higher value good is false or unknown to B. 1999Jrnl. Aesthetics & Art Crit. 57 379/2 If a narrator described two characters as ‘engaged’ then, in accordance with the phenomenon of what linguists call scalar implicature, the reader can assume as a fictional fact that these two characters are not already married, even though the narrator does not explicitly say so. |
