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.

     

Regulation of lithospermic acid B and shikonin production in Lithospermum erythrorhizon cell suspension cultures

Cell suspension cultures of Lithospermum erythrorhizon produced a large amount of lithospermic acid B, a caffeic acid tetramer, as well as shikonin derivatives (each ca. 10% of dry wt.) when cultured in shikonin production medium M-9. Various culture factors for increasing the production of lithospermic acid B were investigated. Lithospermic acid B production was inhibited by 2, 4-D or NH4+, whereas it was stimulated by Cu2+. These regulatory patterns were similar to those for the production of shikonin derivatives in these cell cultures, suggestive of close relations and similar metabolic regulation between the production of these compounds. Cultivation under light illumination, however, showed that these metabolisms were independently regulated. In particular, blue light showed a stimulatory effect on lithospermic acid B production, while shikonin production was strongly inhibited, indicative of an effective condition for lithospermic acid B production.     

Synthesis of bridged heteroaromatic compounds as reference standards for coal degradation products

The synthesis of 2-naphthyl 2′-dibenzothienyl ether, 1-(1′-naphthyl)-2-(4″-acridinyl)ethane and a series of naphthylethyldibenzothiophenes is reported.     

Syntheses of 1-, 2-, 3- and 4-acridinecarbaldehydes

The four acridinecarbaldehydes, namely, acridine-1-carbaldehyde, acridine-2-carbaldehyde, acridine-3-carbaldehyde, and acridine-4-carbaldehyde have been synthesized for the first time.     

Addition reactions of cyclooctatetraene with 1,3-diphenylisobenzofuran the benzene ring as dienophile in a [4+2] cycloaddition reaction

Addition reactions of cyclooctatetraene with 1,3-diphenylisobenzofuran resulted in the formation of three 1:1 cycloadducts, 1, 2, and 3, and a 1:2 cycloadduct, 4. Single crystal x-ray analysis established 3 to be a cage compound formed by an unprecedented [4+2] cycloaddition reaction of 1 in which the double bond of the benzene moiety acted as the dienophile.     

Sulfur nitride in organic chemistry. 9. The reaction of tetrasulfur tetranitride with benzyl ketones. Preparation of 3,4-disubstituted-1,2,5-thiadiazoles

The reaction of tetrasulfur tetranitride ( 1 ) with various aryl and alkyl benzyl ketones ( 2a-o ), oxindole ( 11 ), benzyl α-pyridyl ketone ( 12 ) and α-phenacylpyridine ( 13 ) afforded the corresponding 1,2,5-thiadiazoles ( 3a-n, 11 and 14 ). The scope and limitations of the above reaction were investigated and the evidences suggesting the radical anion mechanism are presented.     

Isolation and structure determination of six glucocerebrosides from the starfish Luidia maculata

Two new glucocerebrosides, luidiacerebroside A (2) and B (6), were isolated from the cerebroside molecular species obtained from the less polar fraction of the CHCl3/MeOH extract of the starfish Luidia maculata using HPLC. Four known cerebrosides, CE-2b (1), astrocerebroside B (3), acanthacerebroside B (4), and CE-3-2 (5) have also been isolated and characterized. The structures of these cerebrosides were determined on the basis of chemical and spectroscopic evidence. Mass spectrometry of dimethyl disulfide derivatives was useful for the determination of the double-bond position in the long-chain base.     

Time-dependent fluctuations in infrared vsCH2 frequencies in acyl chain membranes of Acholeplasma laidlawii cells

We measured FT-IR spectra of intact Acholeplasma laidlawii cells grown at 37 °C on palmitic acid (C16:0) or on binary palmitic acid-d31/oleic acid (C16:0-d31/C18:1(9)) at an initial mole ratio of 2:3, which have been previously reported to produce significant fluctuations in CH₂ symmetric stretching (ν_sCH₂) and CD₂ asymmetric stretching (ν_aCD₂) frequencies (Biochim. Biophys. Acta 1279 (1996) 49). Time courses for acyl chain ν_sCH₂ and ν_aCD₂ frequencies determined from fourth derivative spectra are presented. Fluctuations were detected with the C16:0 enriched cells at temperatures above 40 °C as well as with the cells enriched in 2:3 C16:0-d₃₁/C18:1(9). These observations at temperatures above 40 °C for the C16:0 enriched cells were not in agreement with the conclusion in the previous work by Moore et al. Our results have suggested that the 2850 cm⁻¹ ν_sCH₂ band comprises two components arising from trans and gauche conformations, and that the fluctuations in ν_sCH₂ frequency are caused by random temporal changes in the relative intensities of these two components.     

Technical study for SPECT of the head using slant hole collimator

The performance of a 160 keV slant hole collimator (160 keV SH) was compared with that of a 140 keV high resolution collimator (140 keV HR) for SPECT imaging of the head using 99mTc. The minimum radius of revolution was reduced from about 23 cm to 13 cm using 160 keV SH. Relative sensitivity of the 160 keV SH was 108% of that of the 140 keV HR. Compared with SPECT using 140 keV HR, 160 keV SH SPECT yielded approximately a 15% increase in resolution. The 160 keV SH SPECT images of phantom were superior in resolution and contrast to that of 140 keV HR SPECT. We concluded that high quality SPECT images of the head can be obtained from rotating gamma cameras equipped with slant hole collimators.     

Synthesis of Acid-Resistant P-Quinone Monoketals and Thermally Stable 4,4-Dialkoxycyclohexa-2,5-Dien-1-OLS

Preparation and high resistance to acid hydrolysis of sterically hindered p-quinone monoketals 1a, 1b and 1c are described. Thermal stability of ketal alcohols 2a and 2b derived from 1a and 1c, respectively, is also mentioned.