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.

     

Computational Analysis Reveals a Critical Point Mutation in the N-Terminal Region of the Signaling Lymphocytic Activation Molecule Responsible for the Cross-Species Infection with Canine Distemper Virus

Infection of hosts by morbilliviruses is facilitated by the interaction between viral hemagglutinin (H-protein) and the signaling lymphocytic activation molecule (SLAM). Recently, the functional importance of the n-terminal region of human SLAM as a measles virus receptor was demonstrated. However, the functional roles of this region in the infection process by other morbilliviruses and host range determination remain unknown, partly because this region is highly flexible, which has hampered accurate structure determination of this region by X-ray crystallography. In this study, we analyzed the interaction between the H-protein from canine distemper virus (CDV-H) and SLAMs by a computational chemistry approach. Molecular dynamics simulations and fragment molecular orbital analysis demonstrated that the unique His28 in the N-terminal region of SLAM from Macaca is a key determinant that enables the formation of a stable interaction with CDV-H, providing a basis for CDV infection in Macaca. The computational chemistry approach presented should enable the determination of molecular interactions involving regions of proteins that are difficult to predict from crystal structures because of their high flexibility.     

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 characterization of molybdenum incorporated mesoporous aluminophosphate

A synthesis of molybdenum incorporated mesoporous aluminophosphate with long-chain n-alkylamine as template material had been prepared under non-aqueous condition. These materials were extensively characterized by using X-ray diffraction (XRD), nitrogen sorption isotherms, nuclear magnetic resonance of ²⁷Al and ³¹P (NMR), inductive coupled plasma (ICP), electron spin resonance (ESR), Fourier transform infrared (FTIR) and thermogravimetric-differential thermal analysis (TG-DTA). Morphology of the materials had been observed by using transmission electron microscope (TEM) that revealed the mesoporous materials possessed wormhole-like structures. Alkaline solvent extraction using n-butylamine/ethanol had been efficiently removed the n-alkylamine from the mesoporous samples which yielded BET surface areas around 550-730 m²/g. BJH analysis showed a narrow pore size distribution which increased with increasing of the carbon chain length of alkylamine (template). Valence state and coordination of the molybdenum in the obtained samples were investigated by using ESR and FTIR where it was found that Mo⁴⁺ and Mo⁶⁺ molybdenum species existed in the molybdenum incorporated mesoporous aluminophosphate in tetrahedral coordination.     

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     

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.