| 释义 |
exponential, a. and n.|ɛkspəʊˈnɛnʃəl|
[f. prec. + -ial.]
A. adj.
1. That has the function of setting forth or exhibiting. rare.
1730–6in Bailey (folio). 1809–10Coleridge Friend (1818) III. 185 Where the hypothesis is an exponential image..of an idea.
2. a. Math. Involving the unknown quantity or variable as an exponent, or as part of an exponent. So exponential equation, exponential function, exponential quantity, etc.
exponential curve, one expressed by an exponential equation. † e. calculus: see quot. 1796. e. series, the infinite series 1 + x + ½x2 + 1/6x3 etc. e. theorem, the theorem that the value of ex (the ‘exponential’, or Napierian antilogarithm, of x) is expressed by this series.
1704J. Harris Lex. Techn. II. s.v., Exponential curves are such as partake both of the nature of Algebraick and Transcendent ones. 1715Phil. Trans. XXIX. 212 These Equations he now calls Exponential. 1739Anderson in Rigaud Corr. Sci. Men (1841) I. 342 The exponential equation xx = d. 1784Phil. Trans. LXXIV. 401 P is either an algebraical, exponential, or fluential fluxion of X. 1796Hutton Math. Dict., Exponential Calculus the method of differencing or finding the fluxions of Exponential quantities, and of summing up those differences or finding their fluents. 1881Maxwell Electr. & Magn. I. 221 We call the exponential quantity..the hyperbolic cosine of β.
b. exponential horn, a loudspeaker horn in which the diameter and the transverse cross-sectional area increase exponentially with the distance from the diaphragm. Hence exponential-horned adj.
1927Wireless World 16 Nov. 664 Whereas a conical horn increases in diameter by a constant additive factor per unit of length, the exponential horn increases its diameter by a constant multiple per unit of length. 1954K. Amis Lucky Jim viii. 87 The rondo of some boring piano concerto Welch had once insisted on playing him on his complicated exponential-horned gramophone. 1962A. Nisbett Technique Sound Studio 269 A flared (exponential) horn is provided to improve coupling.
c. exponential pile or exponential reactor, a small, subcritical section of a reactor lattice with a neutron source at one end, used to obtain information about the full-sized critical reactor.
1945H. D. Smyth Gen. Acct. Devel. Atomic Energy Mil. Purposes vi. 58 By this time [sc. 1942] it was known that the neutron density decreased exponentially with increasing distance from the neutron source (hence the name often used for experiments of this type, ‘exponential pile’). 1963F. A. Valente Man. Exper. Reactor Physics viii. 262 In principle, exponential piles have the same structure and composition as the potential or proposed reactor of which they are supposed to be a copy and for which they are supposed to obtain design information by experiment.
B. n. Math. An exponential quantity or function; spec. the Napierian base e raised to the power denoted by the variable; the Napierian antilogarithm of the variable.
1784Waring in Phil. Trans. LXXIV. 395 When the terms are exponentials of superior orders. 1833Sir W. R. Hamilton in R. P. Graves Life II. 58 My extension of Herschel's theorem for the development of functions of exponentials. 1885Athenæum 11 July 52/1 The discussion of logarithms and exponentials by means of the properties of the logarithmic spiral.
Add:[A.] [2.] d. exponential time, an amount of time expressible as an exponential whose exponent is an increasing function of the size of a given problem whose solution is required. Cf. *polynomial a. 3.
1972SIAM Jrnl. Computing I. 281 It has been shown..that any language in NP is ‘polynomially reducible’ to various languages accepted by deterministic linear bounded automata and hence by deterministic Turing machines operating in exponential time. 1979Page & Wilson Introd. Computational Combinatorics vi. 155 This theoretical result suggests that problems in the class NP are likely to require exponential time on a real computer. 1985Purdom & Brown Analysis of Algorithms i. 3 Exponential time algorithms (such as those that use time 2n or en) are suitable only for small problems, even when the fastest computers are used. |