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51.
A. I. Bril' V. P. Kabashnikov N. V. Kuz'mina Yu. V. Khodyko 《Journal of Applied Spectroscopy》1991,55(3):934-939
Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 55, No. 3, pp. 478–484, September, 1991. 相似文献
52.
A fast-frequency modulated (FM) diode laser has been optically narrowed using the technique of resonant optical feedback, to provide linewidths in each FM mode of ≈ 200 kHz peak-to-peak. With a drive frequency of 50 MHz and modulation index of 0.2, the FM laser has been used for the first time to obtain Doppler-free FM spectra of the Rb D1 line at 795 nm. The potential use of this system for laser frequency stabilisation is discussed. 相似文献
53.
A. P. Prudnikov Yu. A. Brychkov O. I. Marichev 《Journal of Mathematical Sciences》1991,54(6):1239-1341
Translated from Itogi Nauki i Tekhniki, Seriya Matematicheskii Analiz, Vol. 27, pp. 3–146, 1989. 相似文献
54.
Summary Considered here are model equations for weakly nonlinear and dispersive long waves, which feature general forms of dispersion and pure power nonlinearity. Two variants of such equations are introduced, one of Korteweg-de Vries type and one of regularized long-wave type. It is proven that solutions of the pure initial-value problem for these two types of model equations are the same, to within the order of accuracy attributable to either, on the long time scale during which nonlinear and dispersive effects may accumulate to make an order-one relative difference to the wave profiles.This research was supported in part by the National Science Foundation. A considerable portion of the project was completed while the first author was resident at the Institute for Mathematics and Its Applications, University of Minnesota. 相似文献
55.
W. Richard Strark 《Mathematical Logic Quarterly》1989,35(4):311-320
56.
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58.
When solving large complex optimization problems, the user is faced with three major problems. These are (i) the cost in human time in obtaining accurate expressions for the derivatives involved; (ii) the need to store second derivative information; and (iii), of lessening importance, the time taken to solve the problem on the computer. For many problems, a significant part of the latter can be attributed to solving Newton-like equations. In the algorithm described, the equations are solved using a conjugate direction method that only needs the Hessian at the current point when it is multiplied by a trial vector. In this paper, we present a method that finds this product using automatic differentiation while only requiring vector storage. The method takes advantage of any sparsity in the Hessian matrix and computes exact derivatives. It avoids the complexity of symbolic differentiation, the inaccuracy of numerical differentiation, the labor of finding analytic derivatives, and the need for matrix store. When far from a minimum, an accurate solution to the Newton equations is not justified, so an approximate solution is obtained by using a version of Dembo and Steihaug's truncated Newton algorithm (Ref. 1).This paper was presented at the SIAM National Meeting, Boston, Massachusetts, 1986. 相似文献
59.
P. M. Gandini A. Zucco 《Abhandlungen aus dem Mathematischen Seminar der Universit?t Hamburg》1989,59(1):15-21
Some well-known theorems on typical properties of real-valued continuous functions defined on [0, 1] are improved using the
notion of porosity. 相似文献
60.