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121.
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
122.
William J. Reed 《Natural Resource Modeling》1989,3(4):463-480
It is assumed that the probability of destruction of a biological asset by natural hazards can be reduced through investment in protection. Specifically a model, in which the hazard rate depends on both the age of the asset and the accumulated invested protection capital, is assumed. The protection capital depreciates through time and its effectiveness in reducing the hazard rate is subject to diminishing returns. It is shown how the investment schedule to maximize the expected net present value of the asset can be determined using the methods of deterministic optimal control, with the survival probability regarded as a state variable. The optimal investment pattern involves “bang-bang-singular” control. A numerical scheme for determining jointly the optimal investment policy and the optimal harvest (or replacement) age is outlined and a numerical example involving forest fire protection is given. 相似文献
123.
The singular-perturbation expansion of the plasma cold-fluid equations for crossed fields in a planar geometry is presented. The general expansion is carried out to third order. Various instabilities that occur in the first, second, and third orders are discussed. 相似文献
124.
Partially supported by the general research fund at the University of Kansas 相似文献
125.
B. R. Harvey M. B. Lovett S. J. Boggis 《Journal of Radioanalytical and Nuclear Chemistry》1987,115(2):357-368
Selected experiences in the control of contamination and the threat it poses to the quality of analytical date are discussed in the context of the whole analytical process from collection of marine environmental samples, through handling and radiochemical separation, to the final interpretation of results. Examples include a demonstration of the contamination introduced during sediment core sectioning, contamination of sea water by a ship's pumping system, and the effect of filtration on the apparent partitioning of radionuclides between solid and liquid phases of sea water. 相似文献
126.
Lithium (10–150 ng ml?1) in wine is determined by atomic absorption spectrometry by direct nebulization and after digestion with mixed acids. The results of methods are similar. Thirty-four wines from various Spanish provinces are analysed. 相似文献
127.
128.
We study matter-wave solitons in Bose-Einstein condensates of ultracold gaseous atoms with spin degrees of freedom and present a class of exact solutions based on the inverse scattering method. The one-soliton solutions are classified with respect to the spin states. We analyze collisional effects between solitons in the same or different spin state(s), which reveals a very interesting possibility: we can manipulate the spin dynamics by controlling the parameters of colliding solitons. 相似文献
129.
The acoustic field inside a shell excited by a spatially inhomogeneous harmonic pressure field is studied. The shell is assumed
to have a finite length, a set of orthogonal stiffening ribs, two ends bounding the acoustic volume, and a sound-insulating
structure, which includes layers of sound-insulating material, resonant elements, and an interior panel. The shell is considered
to be orthotropic with boundary conditions corresponding to a free support. For the acoustic field in the closed volume, analytical
expressions are derived with allowance for the elastoacoustic interaction of the shell with the sound-insulating layers and
with the medium both inside the shell (with arbitrary impedance values at the ends) and outside it. These expressions are
used to investigate the effect of different types of resonant systems on the sound field inside the shell. 相似文献
130.
J.R. Cooper 《Journal of Molecular Spectroscopy》2006,239(1):51-58
The ν9 fundamental band of ethane occurs in the 12 μm region. It is the strongest band of ethane in a terrestrial window and is commonly used for the identification of ethane in the Jovian planets. The ν9 + ν4 − ν4 band occurs in the same region; neither can be analysed as an isolated band, since both are embedded in the torsional bath of the ground vibrational state. We report here two global fit models including data from both of these bands as well as the ν3 fundamental and the ν4, 2ν4 − ν4, and 3ν4 torsional transitions. The first is restricted to −5 ? KΔK ? 15 in the hot band and gives an excellent fit to the included data. Three resonant interactions are identified in this fit—a Coriolis interaction with two resonant cases between the ν9 torsional stack and that of the ground vibrational state (gs) and a resonant Fermi interaction between the ν3 fundamental and the gs. Hot band lines with KΔK < −5 are influenced by a fourth perturbation, with a crossing at −11 < KΔK < −10, which has been attributed to an interaction with the ν12 fundamental. A second fit, demonstrating a promising treatment of this interaction, is also presented. 相似文献