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.
Fluorescence correlation spectroscopy (FCS) has been widely used to investigate molecular diffusion behavior in various samples. The use of the maximum entropy method (MEM) for FCS data analysis provides a unique means to determine multiple distinct diffusion coefficients without a priori assumption of their number. Comparison of the MEM-based FCS method (MEM-FCS) with another method will reveal its utility and advantage as an analytical tool to investigate diffusion dynamics. Herein, we measured diffusion of fluorescent probes doped into nanostructured thin films using MEM-FCS, and validated the results with single molecule tracking (SMT) data. The efficacy of the MEM code employed was first demonstrated by analyzing simulated FCS data for systems incorporating one and two diffusion modes with broadly distributed diffusion coefficients. The MEM analysis accurately afforded the number of distinct diffusion modes and their mean diffusion coefficients. These results contrasted with those obtained by fitting the simulated data to conventional two-component and anomalous diffusion models, which yielded inaccurate estimates of the diffusion coefficients. Subsequently, the MEM analysis was applied to FCS data acquired from hydrophilic dye molecules incorporated into microphase-separated polystyrene-block-poly(ethylene oxide) (PS-b-PEO) thin films characterized under a water-saturated N2 atmosphere. The MEM analysis revealed distinct fast and slow diffusion components attributable to molecules diffusing on the film surface and inside the film, respectively. SMT studies of the same materials yielded trajectories for mobile molecules that appear to follow the curved PEO microdomains. Diffusion coefficients obtained from the SMT data were consistent with those obtained for the slow diffusion component detected by MEM-FCS. These results highlight the utility of MEM-FCS and SMT for gaining complementary information on molecular diffusion processes in heterogeneous material systems.
The first dimesitylboryl substitution of aryl halides with a silylborane bearing a dimesitylboryl group in the presence of alkali‐metal alkoxides is described. The reactions of aryl bromides or iodides with Ph2MeSi?BMes2 and Na(OtBu) afforded the desired aryl dimesitylboranes in good to high yields and with high borylation/silylation ratios. Selective reaction of the sterically less‐hindered C?Br bond of dibromoarenes provided monoborylated products. This reaction was used to rapidly construct a D‐π‐A aryl dimesityl borane with a non‐symmetrical biphenyl spacer. 相似文献
The electronic and molecular structures of 9,10‐diamino‐substituted anthracenes with different N‐substituents have been re‐examined. In particular, different N‐substituents influence both the electronic and molecular structures of the oxidized species of 9,10‐diaminoanthracenes. The anthrylene moiety of 9,10‐bis(N,N‐di(p‐anisyl)amino)anthracene retains its planarity during the course of two successive one‐electron oxidations, whereas 9,10‐bis(N,N‐dimethylamino)anthracene and 9,10‐bis(N‐p‐anisyl‐N‐methylamino)anthracene undergo a substantial structural change to a butterfly‐like structure through a two‐electron oxidation process. The structural changes observed for the oxidized states are ascribed to significant differences in the frontier molecular orbitals of the above‐mentioned three kinds of 9,10‐diaminoanthracenes due to different extents of mixing between the amine‐localized and anthrylene‐localized orbitals. 相似文献
Aryl‐substituted 1,1,4,4‐tetracyano‐1,3‐butadienes (FcTCBDs) and bis(1,1,4,4‐tetracyanobutadiene)s (bis‐FcTCBDs), possessing a ferrocenyl group on each terminal, were prepared by the reaction of a variety of alkynes with tetracyanoethylene (TCNE) in a [2+2] cycloaddition reaction, followed by retro‐electrocyclization of the initially formed [2+2] cycloadducts (i.e., cyclobutene derivatives). The characteristic intramolecular charge transfer (ICT) between the donor (ferrocene) and acceptor (TCBD) moieties were investigated by using UV/Vis spectroscopy. The redox behaviors of FcTCBDs and bis‐FcTCBDs were examined by cyclic voltammetry (CV) and differential pulse voltammetry (DPV), which revealed their properties of multi‐electron transfer depending on the number of ferrocene and TCBD moieties. Moreover, significant color changes were observed by visible spectroscopy under the electrochemical reduction conditions. 相似文献
The regioselective anti-carboindation of ynamides by using InBr3 and silylated nucleophiles was developed to synthesize (Z)-β-(carbonylamino)alkenylindiums. The X-ray crystallographic analysis of an alkenylindium suggested that the reaction proceeded in an anti-addition fashion. In contrast to reported syn-carbometalations of ynamides by using organometallics, a cooperation of InBr3 and silylated nucleophiles to ynamides achieved an anti-addition, which was supported by DFT calculations. The scope of substrates included various ynamides and silylated nucleophiles, such as silyl ketene acetals and silyl ketene imines. The transformation of synthesized alkenylindiums by iodination, radical coupling, and Pd-catalyzed cross-coupling successfully afforded trisubstituted enamines with high regio- and stereoselectivities. 相似文献
An artificial tongue that detects astringent components for a comprehensive evaluation of taste has not been established to date. Herein, we first propose fluorescent polythiophene (PT) derivatives ( S1 – S3 ) modified with 3-pyridinium boronic acid as supramolecular chemosensors for wine components including astringent procyanidin C1. After numerous attempts for the synthetic conditions, more than 95 mol % of the PT unit was modified with the pyridinium boronic acid moiety. To evaluate the PT derivatives as chemosensors of the artificial tongue, qualitative and quantitative analyses were performed with four types of wine components (i.e., sweet, sour, bitter, and astringent tastes) in combination with pattern recognition models. Notably, procyanidin C1 in the actual wine sample was successfully detected in a quantitative manner. In other words, we have established an authentic artificial tongue using PT based supramolecular chemosensors. 相似文献