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.
A tertiary hydroxy group α to a carboxyl moiety comprises a key structural motif in many bioactive substances. With the herein presented metal‐free rearrangement of imides triggered by hypervalent λ3‐iodane, an easy and selective way to gain access to such a compound class, namely α,α‐disubstituted‐α‐hydroxy carboxylamides, was established. Their additional methylene bromide side chain constitutes a useful handle for rapid diversification, as demonstrated by a series of further functionalizations. Moreover, the in situ formation of an iodine(III) species under the reaction conditions was proven. Our findings clearly corroborate that hypervalent λ3‐benziodoxolones are involved in these organocatalytic reactions. 相似文献
Despite the development of targeted therapies in cancer, the problem of multidrug resistance (MDR) is still unsolved. Most patients with metastatic cancer die from MDR. Transmembrane efflux pumps as the main cause of MDR have been addressed by developed inhibitors, but early inhibitors of the most prominent and longest known efflux pump P-glycoprotein (P-gp) were disappointing. Those inhibitors have been used without knowledge about the expression of P-gp by the treated tumor. Therefore the use of inhibitors of transmembrane efflux pumps in clinical settings is reconsidered as a promising strategy in the case of the respective efflux pump expression. We discovered novel symmetric inhibitors of the symmetric efflux pump MRP4 encoded by the ABCC4 gene. MRP4 is involved in many kinds of cancer with resistance to anticancer drugs. All compounds showed better activities than the best known MRP4 inhibitor MK571 in an MRP4-overexpressing cell line assay, and the activities could be related to the various substitution patterns of aromatic residues within the symmetric molecular framework. One of the best compounds was demonstrated to overcome the MRP4-mediated resistance in the cell line model to restore the anticancer drug sensitivity as a proof of concept. 相似文献
By tuning the length and rigidity of the spacer of bis(biurea) ligands L, three structural motifs of the A2L3 complexes (A represents anion, here orthophosphate PO43?), namely helicate, mesocate, and mono‐bridged motif, have been assembled by coordination of the ligand to phosphate anion. Crystal structure analysis indicated that in the three complexes, each of the phosphate ions is coordinated by twelve hydrogen bonds from six surrounding urea groups. The anion coordination properties in solution have also been studied. The results further demonstrate the coordination behavior of phosphate ion, which shows strong tendency for coordination saturation and geometrical preference, thus allowing for the assembly of novel anion coordination‐based structures as in transition‐metal complexes. 相似文献
We apply a majorizing measure theorem of Talagrand to obtain uniform bounds for sums of random variables satisfying increment conditions of the type considered in Gál-Koksma Theorems. We give some applications.
Using sofic systems, modifications of the self-similar sets of Hutchinson are defined as solutions of systems of fixed-point equations. Their Hausdorff dimension is determined. 相似文献
We study correlations in the exclusive reaction at rest with complete reconstruction of the kinematics for each event. The inclusive distribution is fairly flat at small
invariant mass of the pion pair while a small enhancement in the double differential distribution is observed for small invariant
masses of both pion pairs. Dynamical models with resonances in the final state are shown to be consistent with the data while
the stochastic HBT mechanism is not supported by the present findings.
Received: 26 February 2002 / Revised version: 22 July 2002 / Published online: 30 August 2002 相似文献
We show how the Hopf algebra of rooted trees encodes the combinatorics of Epstein-Glaser renormalization and coordinate space renormalization in general. In particular, we prove that the Epstein-Glaser time-ordered products can be obtained from the Hopf algebra by suitable Feynman rules, mapping trees to operator-valued distributions. Twisting the antipode with a renormalization map formally solves the Epstein-Glaser recursion and provides local counterterms due to the Hochschild 1-closedness of the grafting operator B+.submitted 29/03/04, accepted 01/06/04 相似文献
Under a very moderate assumption on the Fourier coefficients of a periodic function, we show the convergence almost everywhere of the sequence of averages of its associated Riemann sums. The structure of the set of averages is analyzed by proving a spectral regularization type inequality, which allows to control the corresponding Littlewood-Paley square function. 相似文献