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61.
62.
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
63.
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
64.
65.
An efficient synthesis of isothiazolidines in good yields is described. 相似文献
66.
67.
D. Yu. Gladilov S. Yu. Nekhaevskii A. V. Ochkin 《Russian Journal of Physical Chemistry A, Focus on Chemistry》2006,80(12):1934-1939
Various methods for describing the distribution of water in the H2O-tributyl phosphate (TBP) system were considered. An equation for describing the deviations from the Henry law was proposed. A three-parameter equation for calculating the distribution of water in H2O-TBP-solvent systems was derived. It is based on the additive solubility model and allows for the dependence of the activity coefficients on the TBP concentration. Based on the published data, the parameters of the equation for a number of systems were calculated. 相似文献
68.
The occurrence and formation of black spots areas in PolyLED devices has been studied by time-of-flight SIMS (TOFSIMS). The composition, shape and position of the black spots is visualised by three-dimensional (3D)-TOFSIMS depth-profiling. It has been established that the formation of non-emissive spots is due to the growth of aluminium oxide clusters at the AlBa/polymer interface. Electron injection in the black spots is lost by the resulting local increase of the resistivity of the cathode. 相似文献
69.
In this work, the natural convection in a concentric annulus between a cold outer square cylinder and a heated inner circular cylinder is simulated using the differential quadrature (DQ) method. The vorticity‐stream function formulation is used as the governing equation, and the coordinate transformation technique is introduced in the DQ computation. It is shown in this paper that the outer square boundary can be approximated by a super elliptic function. As a result, the coordinate transformation from the physical domain to the computational domain is set up by an analytical expression, and all the geometrical parameters can be computed exactly. Numerical results for Rayleigh numbers range from 104 to 106 and aspect ratios between 1.67 and 5.0 are presented, which are in a good agreement with available data in the literature. It is found that both the aspect ratio and the Rayleigh number are critical to the patterns of flow and thermal fields. The present study suggests that a critical aspect ratio may exist at high Rayleigh number to distinguish the flow and thermal patterns. Copyright © 2002 John Wiley & Sons, Ltd. 相似文献
70.
Gábor Dörnyei Marietta Bárczai-Beke Gábor Blaskó Péter Péchy Csaba Szántay 《Tetrahedron letters》1982,23(28):2913-2916
Regioselective demethylation of 3,4-dihydropapaveraldine (a) at 7 and 3' positions affords a properly substituted diphenolic key intermidiate (d) for the synthesis of reticuline and N-norreticuline. 相似文献