| 释义 |
Laplacian, a. and n.|laˈplasɪən|
Also Laplacean (rare in the physical sciences).
[f. Laplace + -ian.]
A. adj. Of or pertaining to Laplace; originating with Laplace.
1836Rep. Brit. Assoc. Adv. Sci. 1835 27 M. Poisson, indeed, carries much further than Laplace himself the Laplacian views of molecular action. 1852Cambr. & Dublin Math. Jrnl. VII. 127 The class of partial differential equations to which the Laplacian equation belongs. 1881Maxwell Electr. & Magn. I. 117 When we have to specify a distribution [of electricity] which is at once irrotational and solenoidal, we shall call it a Laplacian distribution; Laplace having pointed out some of the most important properties of such a distribution. 1908Westm. Gaz. 21 Feb. 2/1 According to the Laplacian hypothesis no ‘month’ can be shorter than the corresponding day [of the parent planet]. 1911J. Ward Realm of Ends i. 15 Laplace, brushing aside freewill as a palpable illusion, proclaimed the implicit omniscience of the mechanical theory. [Note] It was reserved for Clerk Maxwell to point out clearly the inevitable limitation of the Laplacean data. 1920S. Alexander Space, Time, & Deity II. 328 The famous puzzle of the Laplacean calculator is full of confusions but contains a truth. A person who knows the whole state of the universe at any moment can calculate, so it urges, the whole future. 1929V. Bush Operational Circuit Analysis x. 184 f(ω)/ω = ∫∞0 e-ωλA(λ)dλ. .. In an expression of this sort f(ω)/ω is called the Laplacian transform of A. 1936P. M. Morse Vibration & Sound v. 136 Writing the wave equation as ∇2η = (∂2η/∂t2)/c2 where the symbol ∇2 is called the Laplacian operator, or simply the Laplacian. It stands for the operation of finding the bulginess of the surface at some point. 1962Simpson & Richards Physical Princ. Junction Transistors 468 In these [equations] ∇, ∇., and ∇2 are symbols for the gradient, divergence, and Laplacian operators. 1971I. G. Gass et al. Understanding Earth iii. 64/2 The planets have only 0·1% of the mass of the solar system, but 98% of..the energy of angular momentum. From the Laplacian hypothesis [of their origin] the Sun would be expected to have much more angular momentum. 1972J. Rawls Theory of Justice §28. 171 They must follow what some may have called the Laplacean rule for choice under uncertainty. The possibilities are identified in some natural way and each assigned the same likelihood.
B. n. The Laplacian operator, i.e. the differential operator ∇2 (‘del squared’) that occurs in Laplace's equation.
1935Pauling & Wilson Introd. Quantum Mech. iv. 85 This [Schrödinger] equation is often written as -h2 / 8π2 {Summ}Ni = 1 1 / mi ∇i2Ψ + VΨ = - h / 2πi ∂Ψ / ∂t , in which ∇ i2 is the Laplace operator or Laplacian for the ith particle. 1936P. M. Morse Vibration & Sound vii. 232 We can write the wave equation as ∇2p = (∂2p/∂t2)/c2... The operator ∇2 is called the Laplace operator, or the Laplacian: it measures the concentration of a quantity (or, rather, the negative of the concentration). The value of ∇2p at a point is proportional to the difference between the average pressure near a point and the pressure right at the point. 1962Corson & Lorrain Introd. Electromagn. Fields i. 17 The product ∇. ∇f is commonly abbreviated to ∇2f, and the operator ∇2 is called the Laplacian. |