| 释义 |
invariant, a. and n.|ɪnˈvɛərɪənt|
[f. in-3 + variant.]
A. adj.
a. Unvarying, invariable.
1874Lewes Probl. Life & Mind I. 95 Each cause is invariant; it is only the phenomena that are variable. 1957G. E. Hutchinson Treat. Limnol. I. ix. 634 The relatively invariant climatic conditions of the equatorial regions. 1964M. Argyle Psychol. & Social Probl. i. 14 These so-called ‘first-order factors’ are not a satisfactory final solution, since they will reflect the numbers of tests of different kinds which have been used, and fail to yield a stable or ‘invariant’ set of factors. 1966[see sense B. 2 below]. 1973Sci. Amer. Feb. 26/1 The locations of nerve cells, the trajectories of nerve fibers and the spatial arrays of synaptic connections are invariant in all individuals of the same species. This invariance is termed neuronal specificity.
b. Physical Chem. Having no degrees of freedom (see freedom 10 b).
1899R. A. Lehfeldt Text-bk. Physical Chem. v. 208 Such systems may conveniently be called invariant, univariant, divariant, &c., according as they possess no, one, two, &c., degrees of freedom. 1923A. C. D. Rivett Phase Rule i. 25 When F = o the system is said to be invariant, since none of its variables may be altered at will without destroying the system in the sense of altering the number of coexisting phases. 1971F. A. Bettelheim Exper. Physical Chem. xxvii. 259 Phase diagrams of ternary systems that are plotted on a triple co-ordinate graph have two important features: an invariant point, O, and the solubility curves.
c. Math. and Physics. Unchanged by a specified transformation or operation. Const. under.
1908H. Hilton Introd. Theory Groups of Finite Order v. 62 If every element of a group G transforms an element g of G into itself, so that g is permutable with every element of G, g is called a normal, self-conjugate, or invariant element of G... Similarly, if every element of G transforms a subgroup H into itself, H is called a normal, self-conjugate, or invariant subgroup of G. 1914L. Silberstein Theory of Relativity iv. 111 The principle of relativity excludes all such laws as are not invariant with respect to the Lorentz transformation. 1919A. N. Whitehead Enquiry Princ. Nat. Knowl. 39 They [sc. Newton's equations] are invariant for the spatio-temporal transformations from one such set to another within the Newtonian group. 1941Birkhoff & MacLane Survey Mod. Algebra vi. 153 A subgroup S of a group G is normal (in G) if and only if it is invariant under all inner automorphisms of G (i.e., contains with any element all its conjugates). 1955W. Pauli Niels Bohr 34 The theory is invariant with respect to space or time reflection separately. 1968[see covariant B].
B. n. Math.
1. a. A function of the coefficients of a quantic such that, if the quantic be linearly transformed, the same function of the new coefficients is equal to the first function multiplied by some power of the modulus of transformation. Also attrib.
1851Sylvester in Philos. Mag. Nov., The remaining coefficients are the two well-known hyperdeterminants, or, as I propose henceforth to call them, the two Invariants of the form ax4 + 4bx3y + 6cx2y2 + 4dxy3 + ey4. Ibid., If I (a, b,..l) = I (a′, b′,..l′), then I is defined to be an invariant of f. 1873H. Spencer Study Sociol. (1882) 223, I learn that the Theory of Invariants and the methods of investigation which have grown out of it constitute a step in mathematical progress larger than any made since the Differential Calculus. 1908J. E. Wright Invariants of Quadratic Differential Forms Pref., The aim of this tract is to give..an account of the invariant theory connected with a single quadratic differential form. 1940J. L. Coolidge Hist. Geom. Methods ii. ii. 156 The invariant idea, thus launched, was eagerly seized on, especially..by the great twin brethren, Cayley and Sylvester.
b. Any quantity or expression which is invariant under a specified transformation or operation.
1908H. Hilton Introd. Theory Groups of Finite Order vii. 99 An expression is an invariant of [a substitution-group] G if it is not altered when we perform on it every one of a set of substitutions which generate G. 1914L. Silberstein Theory of Relativity iv. 112 It may be expressed shortly by saying that x2 + y2 + z2 — c2t2..is a relativistic invariant. 1956E. M. Patterson Topology i. 11 Such entities are called topological invariants, because they are the same for all topologically equivalent spaces. 1959,1967[see covariant].
2. gen. An invariant property or feature.
1939Mind XLVIII. 39 There is a widespread view that the sole invariant of morals is their sociological function to secure the preservation and welfare of a social group. 1960E. Delavenay Introd. Machine Transl. iii. 28 In 1949 Weaver pointed out that..one discovers statistical invariants, as found in cryptography.., semantic invariants,..and logical invariants. 1966J. J. Katz Philos. of Lang. ii. 9 The study of language in general provides us with generalizations expressing the invariant features of language which we may particularize as the requirement that an empirically correct description of a natural language represents such invariants. |