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.
Methacrylic esters, represented by methyl methacrylate (MMA), are widely used as commodity chemicals. Here, the one-pot synthesis of methacrylic esters from acetone, a haloform and alcohols in the presence of an organic base is described. Using DBU as the organic base for the reaction of acetone, chloroform and methanol in acetonitrile afforded MMA in 66 % yield. When the solvent was replaced by benzonitrile, the product MMA was successfully purified by distillation. Applicability of this process to various alcohols was also investigated to show ethyl, phenyl, CF3CH2, and n-C6F13CH2CH2 esters were obtained in moderate yields. The use of bromoform instead of chloroform resulted in the improvement of the yield, for example, methyl and n-C6F13CH2CH2 esters up to 81 and 70 %, respectively. The reaction with deuterated starting materials acetone-d6 and MeOH-d4, with DBU in acetonitrile afforded deuterated MMA (MMA-d8) in 70 % yield. 相似文献
The trend in magnetic recording media is towards higher frequencies and larger storage capacities. Base film technology has developed in a manner analogous to corresponding demands on particulate and thin-film media, i.e. in the direction to reduced thickness, smoother surfaces, and very high uniformity. Key elements for the success of polyester films as substrates for all kinds of flexible media are new concepts for pigmentation and surface design. Future digital video recording systems and thin-film media will require new substrates with higher mechanical strength and thermal stability. Trends in base film development including dual-surface films and alternative polymer substrates are discussed. 相似文献
Several investigations on the extraction of dioxins from soil and fly ash with supercritical fluid have been reported; however, few of them describe the influence of components on the extraction. We extracted dioxins from eight samples with different values of organic carbon content and surface area with supercritical CO(2) at a temperature of 463 K, a pressure of 40 MPa, and using 10% toluene as an entrainer. We researched the influence of the characteristics of soil and fly ash on supercritical CO(2) extraction of dioxins. The results revealed that the extraction efficiencies of PCDD/DFs and PCBs were high for all soil samples, while that of fly ash samples decreased with the increase in organic carbon content and surface area. The extraction efficiencies of dioxins from four standard samples, activated carbon, humic acid, alumina, and florisil, were also examined. The results revealed that the extraction efficiencies were strongly influenced by activated carbon like components present in the samples. 相似文献
In this paper, a silicon-based integrated optic pressure sensor using an intermodal interference between the fundamental TM-like and TE-like modes is described. The sensor consists of a micromachined rectangular diaphragm and a straight polystyrene optical waveguide passing over the diaphragm. Its sensitivity is theoretically known to be strongly dependent on the position of the waveguide over the diaphragm. To experimentally investigate such dependence, we fabricated a sensor with a 1.2 mm ×10 mm ×20 μm diaphragm, over which waveguides were placed at 50 μm intervals. The measured phase sensitivity was 98 mrad/kPa for the waveguide nearest to the diaphragm edge. The measurement was also carried out for the other waveguides. As theoretically expected, the largest sensitivity was obtained for the waveguide nearest to the edge. 相似文献
Summary In [6], we introduced and investigated the notions of strong β-I-open sets and strong β-I-continuous functions in ideal topological spaces. In this paper, we investigate further their important properties. 相似文献