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.
ABSTRACTNano-polycrystalline diamond (NPD) with various grain sizes has been synthesized from glassy carbon at pressures 15–25?GPa and temperatures 1700–2300°C using multianvil apparatus. The minimum temperature for the synthesis of pure NPD, below which a small amount of compressed graphite was formed, significantly increased with pressure from ~1700°C at 15?GPa to ~1900°C at 25?GPa. The NPD having grain sizes less than ~50?nm was synthesized at temperatures below ~2000°C at 15?GPa and ~2300°C at 25?GPa, above which significant grain growth was observed. The grain size of NPD decreases with increasing pressure and decreasing temperature, and the pure NPD with grain sizes less than 10?nm is obtained in a limited temperature range around 1800–2000°C, depending on pressure. The pure NPD from glassy carbon is highly transparent and exhibits a granular nano-texture, whose grain size is tunable by selecting adequate pressure and temperature conditions. 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
Phosphonic acid analogues of acylcarnitine were prepared in an optically active form expecting CPT I inhibitory activities. The synthetic methodology was based on catalytic asymmetric dihydroxylation of β,γ-unsaturated phosphonates and subsequent regioselective amination via the cyclic sulfates. 相似文献
Linear and nonlinear optical properties of racemic (±)2-(α-methylbenzylamino)-5-nitropyridine ((±)MBANP) single crystals have been comprehensively investigated and compared with those of the enantiomorph (–)2-(α-methylbenzylamino)-5-nitropyridine ((–)MBANP) crystals. (±)MBANP crystal exhibits very high chemical and physical stability, but relatively small nonlinear optical coefficients (d31 = 6.8 pm/V, d32 = 4.7 pm/V, d33 = 0.84 pm/V). A comparison between the nonlinear optical coefficients of (±)MBANP and (–)MBANP demonstrates the validity of the oriented-gas model in molecular crystals that neglects all the contributions from intermolecular interaction. 相似文献
An optical fiber multi-function device consisting of a single gradient-index-rod lens and a multi-facet blazed reflection
grating is proposed to simultaneously realize functions of wavelength demultiplexing and optical signal distribution in a
multimode optical fiber transmission system. We analyzed the demultiplexing characteristics and the tolerance of optical components
using the ray trace method. This device can realize not only low loss optical signal distribution but also offers improved
demultiplexing characteristics in comparison with the previously proposed demultiplexer-multiposition switch. The following
characteristics are expected from the design using commercially available optical components: a working band of 0.64–0.88
μm, channel separation of 34–36 nm, 3 dB bandwidth of 27–28 nm, channel cross-talk of less than - 40 dB and minimum excess
insertion loss of 0.9–2.1 dB. 相似文献