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.

     

D3h‐Symmetric Porphyrin‐Based Rigid Macrocyclic Ligands for Multicofacial Multinuclear Complexes in a One‐Nanometer‐Sized Cavity

The one‐step synthesis of D_3h‐symmetric cyclic porphyrin trimers 1 composed of three 2,2′‐[4,4′‐bis(methoxycarbonyl)]bipyridyl moieties and three porphyrinatozinc moieties was achieved from a nickel‐mediated reductive coupling of meso‐5,15‐bis(6‐chloro‐4‐methoxycarbonylpyrid‐2‐yl)porphyrinatozinc. Although cyclic trimers 1 were obtained as a mixture that included other cyclic and acyclic porphyrin oligomers, an extremely specific separation was observed only for cyclic trimers 1 when using columns of silica gel modified with pyrenylethyl, cyanopropyl, and other groups. Structural analysis of cyclic trimers 1 was carried out by means of NMR spectroscopy and X‐ray crystallography. Treatment of an η³‐allylpalladium complex with a cyclic trimer gave a tris(palladium) complex containing three η³‐allylpalladium groups inside the space, which indicated that the bipyridyl moieties inside the ring could work as bidentate metalloligands.     

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.     

Positive photosensitive polyimides with cyclobutane structure

A new family of positive photosensitive polyimide (PPI) systems composed of solvent soluble polyimides (Pls) with cyclobutane (CBDA) structures and diazonaphthoquinone compounds (DNQ) has been prepared. Heat and catalytic imidizations were carried out to obtain CBDA Pls; the former was better than the latter in controlling the molecular weight of the Pl. The ? OH groups in the Pls were easily acetylated during catalytic imidization, so ? COOH groups were selected as weak acidic groups in the Pls. The ? COOH groups were also effective in giving the Pls an alkaline solubility. Therefore, Pls having ? COOH groups were superior to those having ? OH groups for PPI systems. The photosensitive properties of various PPl systems containing ? COOH were found to vary with the fraction of ? COOH groups in the Pls, the content of DNQ in the systems, and the molecular weight of the Pls.     

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