In this work, we propose a class of numerical schemes for solving semilinear Hamilton–Jacobi–Bellman–Isaacs (HJBI) boundary value problems which arise naturally from exit time problems of diffusion processes with controlled drift. We exploit policy iteration to reduce the semilinear problem into a sequence of linear Dirichlet problems, which are subsequently approximated by a multilayer feedforward neural network ansatz. We establish that the numerical solutions converge globally in the \(H^2\)-norm and further demonstrate that this convergence is superlinear, by interpreting the algorithm as an inexact Newton iteration for the HJBI equation. Moreover, we construct the optimal feedback controls from the numerical value functions and deduce convergence. The numerical schemes and convergence results are then extended to oblique derivative boundary conditions. Numerical experiments on the stochastic Zermelo navigation problem are presented to illustrate the theoretical results and to demonstrate the effectiveness of the method.
A new rotational band has been observed in 167Lu by 152Sm (19F,4n)reaction at the HI-13 tandem accelerator of CIAE in Beijing. The high spin transition energies of the new band are almost
identical to the triaxial superdeformed bands recently discovered in 163Lu and 165Lu. This new band is predicted as a triaxial superdeformed band by total routhian surface calculations.
Received: 6 October 1997 相似文献
Cell suspension cultures of Lithospermum erythrorhizon produced a large amount of lithospermic acid B, a caffeic acid tetramer, as well as shikonin derivatives (each ca. 10% of dry wt.) when cultured in shikonin production medium M-9. Various culture factors for increasing the production of lithospermic acid B were investigated. Lithospermic acid B production was inhibited by 2, 4-D or NH4+, whereas it was stimulated by Cu2+. These regulatory patterns were similar to those for the production of shikonin derivatives in these cell cultures, suggestive of close relations and similar metabolic regulation between the production of these compounds. Cultivation under light illumination, however, showed that these metabolisms were independently regulated. In particular, blue light showed a stimulatory effect on lithospermic acid B production, while shikonin production was strongly inhibited, indicative of an effective condition for lithospermic acid B production. 相似文献
The synthesis of 2-naphthyl 2′-dibenzothienyl ether, 1-(1′-naphthyl)-2-(4″-acridinyl)ethane and a series of naphthylethyldibenzothiophenes is reported. 相似文献
The four acridinecarbaldehydes, namely, acridine-1-carbaldehyde, acridine-2-carbaldehyde, acridine-3-carbaldehyde, and acridine-4-carbaldehyde have been synthesized for the first time. 相似文献
Various asymmetric or cyclic ester derivatives of the phosphonic acid moiety in the calcium antagonist fostedil (KB-944) were synthesized. The coronary vasodilator activity of these compounds was assessed by Langendorff's method. Among them, the ethyl isopropyl ester 12 showed the most potent activity, which was comparable to that of fostedil. 相似文献
Nine analogs based on a structure of Tyr-D-Arg-Phe-X (X = alkylamides or alkylhydrazide containing electron-withdrawing atoms or groups) were newly synthesized and their biological properties were examined by the opioid receptor binding properties of mu-, delta- and kappa-receptors, guinea-pig ileum (GPI) assay and analgesic activity in the tail pinch test after subcutaneous administration in mice. Analogs with X = NHCF2CF3, Sar-ol, or NH(CH2)2CN showed potent activities in the GPI and analgesic assays and high affinity for mu-receptor. An analog with X = taurinamide was found to possess 4-fold higher mu-receptor selectivity than that of [D-Ala2, MePhe4, Gly-ol5]enkephalin (DAGO). The receptor binding properties of previously reported analogs [Chem. Pharm. Bull., 33, 1528 (1985); ibid., 33, 4865 (1985); ibid., 36, 4834 (1988)] were also examined for overall discussion of the structure-activity relationships of this series of tripeptide amides. 相似文献
Amphiphilic block copolymers, i.e., poly(methyl methacrylate)-b-poly(2-dimethylethylammoniumethyl methacrylate), were synthesized by the reaction between two prepolymers. Carboxyl-terminated poly(methyl methacrylate) and hydroxyl-terminated poly(2-dimethylaminoethyl methacrylate) were prepared by radical polymerization of the corresponding monomers in the presence of thioglycolic acid and 2-mercaptoethanol as a chain transfer agent, respectively. Two condensation methods, i.e., DCC and the acid chloride method, were used for the reactions of these prepolymers. The subsequent quarternization produced the amphiphilic block copolymers. Surface property of poly(methyl methacrylate) films containing this amphiphilic block copolymer was examined by measuring contact angles for water. The addition of only 0.5 wt% of the block copolymer was sufficient to make poly(methyl methacrylate) surfaces hydrophilic. The block copolymer formed a polymeric micelle in acetone–water mixed solvent. 相似文献