| 释义 |
▪ I. tensor|ˈtɛnsə(r)|
[a. mod.L. tensor, agent-n. from tendĕre to stretch.]
1. Anat. Also tensor muscle. A muscle that stretches or tightens some part. Opp. to laxator.
In mod. use, distinguished from an extensor by not altering the direction of the part.
1704J. Harris Lex. Techn. I, Tensors, or Extensors, are those common Muscles that serve to extend the Toes, and have their Tendons inserted into all the lesser Toes. 1799Home in Phil. Trans. XC. 10 The combined action of the tensor and laxator muscles varying the degree of its [the membrana tympani] tension. 1808Barclay Muscular Motions 384 The biceps..being a flexor and supinator of the fore-arm, and at the same time a tensor of its fascia. 1879St. George's Hosp. Rep. IX. 591 The functions of the adductors and tensors are more delicate.
2. Math.
a. In Quaternions, a quantity expressing the ratio in which the length of a vector is increased.
1846W. R. Hamilton in Phil. Mag. XXIX. 27 Since the square of a scalar is always positive, while the square of a vector is always negative, the algebraical excess of the former over the latter square is always a positive number; if then we make (TQ)2 = (SQ)2 - (VQ)2, and if we suppose TQ to be always a real and positive or absolute number, which we may call the tensor of the quaternion Q, we shall not thereby diminish the generality of that quaternion. This tensor is what was called in former articles the modulus. 1853― Elem. Quaternions ii. i. (1866) 108 The former element of the complex relation..between..two lines or vectors [viz. their relative length], is..represented by a simple ratio.., or by a number expressing that ratio. Note, This number, which we shall..call the tensor of the quotient,..may always be equated..to a positive scalar. 1886W. S. Aldis Solid Geom. xiv. (ed. 4) 235 Since the operation denoted by a quarternion consists of two parts, one of rotating OA into the position OB and the other of extending OA into the length OB, a quaternion may be..represented as the product of two factors,..the versor..and..the tensor of the quaternion.
b. An abstract entity represented by an array of components that are functions of co-ordinates such that, under a transformation of co-ordinates, the new components are related to the transformation and to the original components in a definite way. [This sense is due to W. Voigt (Die Fund. Physik. Eigenschaften der Krystalle (1898) p. vi).]
1916Monthly Notices R. Astron. Soc. LXXVI. 701 In the four-dimensional time-space we consider tensors of different orders. The tensor of order zero is a pure number (scalar), the tensor of the first order is a vector, which has 4 components, the tensor of the second order has 16 components, and so on. Ibid. 702 If once we have expressed the laws of nature in the form of linear relations between tensors, they will be invariant for all transformations. Thus with the aid of the calculus of tensors Einstein has succeeded in satisfying the postulate of general relativity. 1934Nature 20 Oct. 612 The theory of tensors, so important in physics and geometry on account of their property of vanishing in every co-ordinate system if they vanish in one, was created by Ricci (1887) and his pupil Levi-Civita, although the name tensor was not introduced by them. 1943Jrnl. London Math. Soc. XVIII. 109 The study of the particular class of invariants known as tensors goes back to the work of Riemann and Christoffel on quadratic differential forms. 1953C.-T. Wang Applied Elasticity i. 1 Stress is called a tensor, because in addition to its magnitude, direction, and sense, which define a vector, it depends on another vector, which represents the surface upon which it acts. 1970G. K. Woodgate Elem. Atomic Struct. iii. 50 The operator in eqn. (3.95) is a component of a second-rank tensor, the atomic electric quadrupole moment. 1974G. Reece tr. Hund's Hist. Quantum Theory xv. 211 ψ and χ were scalars, spinors, vectors or tensors.
c. attrib. and Comb., as tensor algebra, tensor analysis, tensor calculus, tensor product; tensor field, a field for which a tensor is defined at each point; tensor force, a force between two bodies that has to be expressed as a tensor rather than a vector, esp. a non-central force between sub-atomic particles; tensor-twist, in Clifford's biquaternions, a twist multiplied by a tensor.
1922Tensor algebra [see tensor analysis below]. 1936Electr. Engin. LV. 1214/1 The object of this paper is to apply tensor algebra to the solution of the circuits of multi-winding transformers. 1971C. W. Curtis in Powell & Higman Finite Simple Groups iii. 142 Form a vector space M with basis X, and let {scrF}x be the tensor algebra over M.
1922H. L. Brose tr. Weyl's Space–Time–Matter i. 58 Tensor analysis tells us how, by differentiating with respect to the space co-ordinates, a new tensor can be derived from the old one in a manner entirely independent of the co-ordinate system. This method, like tensor algebra, is of extreme simplicity. 1939G. Kron Tensor Analysis of Networks p. xvi, Tensor analysis may be considered as an extension and generalization of vector analysis from three- to n-dimensional spaces and from Euclidean to non-Euclidean spaces. 1976Sci. Amer. Aug. 98/2 Einstein's ideas were cast in a language very different from even non-Euclidean geometry, called the absolute differential calculus... Einstein used it and changed its name to tensor analysis. 1977D. Bagley Enemy xxxiii. 266 This joker is using Hamiltonian quaternions!.. No one..has used Hamiltonian quaternions since 1915 when tensor analysis was invented.
1922H. L. Brose tr. Weyl's Space–Time–Matter i. 53 The study of tensor-calculus is, without doubt, attended by conceptual difficulties—over and above the apprehension inspired by indices. 1944G. B. Shaw Everybody's Political What's What? ii. 22 Experts in the tensor calculus. 1981Sci. Amer. July 95/1 Tensor calculus..was essential to Einstein's formulation of his general theory of relativity.
1922H. L. Brose tr. Weyl's Space–Time–Matter i. 61 An important example of a tensor field is offered by the stresses occurring in an elastic body. 1934R. C. Tolman Relativity, Thermodynamics, & Cosmol. 36 Tensor fields may..be constructed, in which a value of the field tensor is associated with each point in the continuum.
1948Physical Rev. LXXII. 987/1 The result of the present calculation and that of the proton–neutron scattering, which includes the tensor forces, show that the difference among the three potentials is quite pronounced at these high energies. 1972Physics Bull. June 349/2 The noncentral force causing the anomalies mentioned above is called the tensor force, and it results from a neutron–protonspin–spin interaction.
1964A. P. & W. Robertson Topological Vector Spaces vii. 141 It is essential to form the completion of the tensor product under the correct topology. 1971E. C. Dade in Powell & Higman Finite Simple Groups viii. 252 The tensor product..is again a finite-dimensional vector space over F.
Hence tenˈsorial a.
1934[see anti-1 2 d]. 1968C. G. Kuper Introd. Theory Superconductivity iv. 58 Since..Pippard's experimental data..do not support the idea of a tensorial anisotropy, these equations have not proved useful.
▪ II. tensor, tensur, -ure
var. ff. tenser Obs. |