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.

     

Silicon-Based Integrated Optic Pressure Sensor Using Intermodal Interference between TM-Like and TE-Like Modes

In this paper, a silicon-based integrated optic pressure sensor using an intermodal interference between the fundamental TM-like and TE-like modes is described. The sensor consists of a micromachined rectangular diaphragm and a straight polystyrene optical waveguide passing over the diaphragm. Its sensitivity is theoretically known to be strongly dependent on the position of the waveguide over the diaphragm. To experimentally investigate such dependence, we fabricated a sensor with a 1.2 mm ×10 mm ×20 μm diaphragm, over which waveguides were placed at 50 μm intervals. The measured phase sensitivity was 98 mrad/kPa for the waveguide nearest to the diaphragm edge. The measurement was also carried out for the other waveguides. As theoretically expected, the largest sensitivity was obtained for the waveguide nearest to the edge.     

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.     

Stability of porphyrin-calix[4]arene complexes analyzed by electrospray ionization mass spectrometry

The stability of some porphyrin-calix[4]arene sodium-ion complexes were determined by a collision-activated decomposition (CAD) method utilizing electrospray ionization mass spectrometry (ESI-MS). Comparing the values of E(1/2), the collision energy at which the relative intensity of the complex ion is 0.5, we found that the porphyrin-calix[4]arene complex with the higher value of E(1/2) corresponded to that with the larger association constant (Kass), as measured by 1H-NMR in CDCl3. Both our ESI-MS and NMR studies proved that the number of hydrogen bonds and the rigidity of the calix[4]arene stabilized the complex. The ESI-MS technique could be successful in screening the binding affinity in host-guest systems with a small amount of sample.     

Evaluation of thallium-201 myocardial emission computed tomography based on a comparison with postmortem findings

The correlative study of myocardial perfusion assessed by 201Tl myocardial ECT with the pathological finding of the heart was performed in 10 autopsied cases with mean age of 77 years old (range: 60-90 y). In 6 cases with myocardial infarction (MI) 7 perfusion defects were observed, that was, 3 in anteroseptal wall, 1 in anterolateral wall and 3 in posterior wall on the images of SPECT. Seven MIs were also found in postmortem examination. Six MIs were observed at autopsy corresponding to perfusion defect on SPECT images. In one myocardial perfusion defect at inferoposterior portion on SPECT, a non-transmural MI was found at anteroseptum. In one case with valvular disease a false positive result was obtained at posterior wall where neither myocardial necrosis nor fibrosis was observed at autopsy. This case had aortic stenosis due to bicuspid aortic valve by autopsy. The ventricle was divided into 16 segments in each of 4 short axial images to evaluate extent of MI. SPECT for extent of MI showed sensitivity of 81.9%, specificity of 96.0% and diagnostic accuracy of 92.5%. False negative segment was apt to be observed at the surrounding of non-transmural MI or basal half of left ventricle (LV) with transmural MI, while false positive segment was at posterior portion of basal half of LV. It was concluded that myocardial ECT was useful for evaluation of the site and extent of MI.     

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.