A Neural Network-Based Policy Iteration Algorithm with Global $$H^2$$ -Superlinear Convergence for Stochastic Games on Domains

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.

     

Substrates for flexible magnetic recording media: The role of base films for modern performance requirements

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.     

Synthesis and refractive‐index control of fluoropolymers by the polyaddition of bis(epoxide)s and triazine di(aryl ether)s

The polyaddition of fluorine‐containing bis(epoxide)s and fluorine‐containing triazine di(aryl ether)s were examined to give the corresponding fluorine‐containing poly(cyanurate)s. It was observed that the synthesized fluoropolymers had good thermal stabilities and good film‐forming properties. The glass transition temperatures (T_g's) and refractive‐indices (n_D's) of synthesized polymers were determined by differential scanning calorimetry and ellipsometry, respectively, and it was found that the values of T_g's and n_D's were supported by their fluorine containing ratios and skeletons. © 2007 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 45: 4421–4429, 2007     

Changes in the near-edge X-ray absorption fine structure spectra of long-chain diacetylene derivatives through photopolymerization in Langmuir–Blodgett films

Photopolymerization of cadmium 10,12-pentacosadiynoate (CdDA) in Langmuir–Blodgett (LB) films, with the molecular packing well arranged by moderate preannealing, was investigated with near-edge X-ray absorption fine structure (NEXAFS) spectroscopy. Greenish films of polydiacetylene with an absorption wavelength of 705 nm were obtained through the photopolymerization of preannealed monomer LB films, and this resulted in an extended π-conjugate system based on the well-ordered monomer in a two-dimensional arrangement. The electronic structures of the polydiacetylenes were found to be correlated to the variation of the molecular arrangements in the films from the changes in the NEXAFS spectra through photopolymerization in the LB films. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 2329–2336, 2004     

New approaches to liquid interfaces through changes in the refractive index and nonlinear susceptibility utilizing ultrashort laser pulses.

Molecules in inhomogeneous liquid environments, such as air/liquid, liquid/liquid, solid/liquid interfaces interact with each other specifically, and sometimes form characteristic structures and emerge unique properties. Here, we introduce two newly developed spectroscopic techniques, the total-internal-reflection ultrafast transient lens method (TIR-UTL) and second harmonic generation-coherent vibrational spectroscopy (SHG-CVS), to investigate the characteristic behaviors of molecules in such inhomogeneous environments. TIR-UTL probes the refractive-index change with sub-picosecond resolution and provides information on ultrafast changes in the population, density, and thermal properties, such as temperature increase and energy transfer from the solute molecules to the surrounding solvent molecules. On the other hand, SHG-CVS probes nonlinear susceptibility changes at the interfacial areas, and is expected to provide spectroscopic information on the low-frequency vibrational modes that reflect the corrective motion of the molecules in such an inhomogeneous environment. These new approaches are based on pump-probe techniques utilizing (ultra) short laser pulses. They are expected to provide further information on inhomogeneous environments from the viewpoints of solute-solvent interactions, changes in the molecular orientation, and the corrective motion of molecules at liquid interfaces.     

A simple and sensitive method for the determination of hydroxylamine in fresh-water samples using hypochlorite followed by gas chromatography.

A new and simple method for the determination of hydroxylamine in environmental water, such as fresh rivers and lakes using hypochlorite, followed by its gas choromatographic detection, has been developed. A glass vial filled with sample water was sealed by a butyl-rubber stopper and aluminum cap without head-space, and then sodium hypochlorite solution was injected into the vial through a syringe to convert hydroxylamine to nitrous oxide. The head-space in the glass vial was prepared with 99.9% grade N2 using a gas-tight syringe. After the glass vial was shaken for a few minutes, nitrous oxide in the gas-phase was measured by a gas chromatograph with an electron-capture detector. The dissolved nitrous oxide in the liquid-phase was calculated according to the solubility formula. The proposed method was applied to the analysis of fresh-water samples taken from Iu river and Hii river, flowing into brackish Lakes Nakaumi and Shinji, respectively.     

Linear and Nonlinear Optical Properties Of Racemic (±)2-(α-Methylbenzylamino)-5-Nitropyridine Single Crystals

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.     

Sub-critical crack growth rate of soda-lime-silicate glass and less brittle glass as a function of fictive temperature

Sub-critical crack growth rates of soda-lime-silicate glass and less brittle glass with different fictive temperatures were compared using the DCDC method under both dry and humid atmospheres in order to investigate the origin of the unique mechanical features of the less brittle glass developed by Ito and his collaborators. In both dry and humid atmospheres, the crack velocity of the soda-lime-silicate glass was slower than that of the less brittle glass. For both glasses, the glass sample with higher fictive temperature showed a slower crack growth rate under both dry and humid atmospheres. These observations can be explained by the tendency for the plastic flow at the crack tip; the soda-lime-silicate glass is expected to show easier plastic flow under tension than the less brittle glass, and also the samples with higher fictive temperatures are expected to show easier plastic flow, leading to greater fracture toughness, K_IC, and slower crack growth rate.