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.

     

一类非线性Schr(o)dinger方程的守恒差分法与Fourier谱方法

考察了一类带导数项的非线性Schrodinger方程的周期边值问题，提出了一种守恒的差分格式，在空间方向上采用Fourier谱方法，证明了格式的稳定性和收敛性．数值试验得到了与理论分析一致的结果．     

小肽修饰的PAMAM树枝状化合物的生物活性

合成了甘氨酸 (Gly) 天冬氨酸 (Asp)组成的肽链Gly Asp、Gly Asp Gly Asp、Gly Asp (Gly Asp) 2 .分别将天冬氨酸及上述合成的肽链引入到聚酰胺 胺型树枝状化合物 (PAMAM)的表面 .对所得化合物进行了分子模拟 ,结果表明Gly Asp (Gly Asp) 2 肽链在PAMAM表面可形成接近于 β sheet的构象 .由实验得知 ,经Asp、Gly Asp、Gly Asp Gly Asp、Gly Asp (Gly Asp) 2 修饰的PAMAM树枝状化合物对抗坏血酸还原FeⅢ 细胞色素C(cytc)的反应有干扰作用 ,导致该反应速率下降 .这说明所合成的化合物与cytc有较好的结合能力 .特别是Gly Asp (Gly Asp) 2 修饰的PAMAM ,其与cytc的结合常数为 1 6ⅹ 1 0 5.     

Ionization potentials,electron affinities,electronegativities, and hardnesses of fractional charged atoms from the density-functional theory

The electron-correlation and self-interaction corrected generalized exchange local-spin-density functional theory with the Gopinathan, Whitehead, and Bogdanovic Fermi-hole parameters has been employed to give self-consistent field calculations for the quark atoms, the first- and second-order positive ions, and the first- and second-order negative ions of the quark atoms with fractional nuclear charges $ Z = N \pm \frac{1}{3} $ and $ Z = N \pm \frac{2}{3} $. A special technique to obtain the converged second-order negative ions is discussed. The first and second ionization potentials and electron affinities are calculated by the differences of the total energies between the ionized and nonionized systems and compared with the empirical inter-extrapolation results. The agreement between the present calculations and the inter-extrapolated results is excellent for the ionization potentials and reasonably good for the electron affinities of the quark atoms. Finally, the calculated ionization potentials and electron affinities are used in obtaining the electronegativities and hardnesses for these quark atoms.     

Progress on the application of electrochemiluminescence biosensor based on nanomaterials

In this review, we check out the number of published literature in the field of ECL biosensors trends during nearly a decade, and compare the research status of four different types of biosensors; summarize the application forms of nanomaterials in ECL biosensor. We have an overview of the building patterns and application example of the four main types of biosensors in the paper.     

“鱼”乐圈大揭秘

This article introduces the relationship between chemistry and fish farming, fish selling, and fish food. The nitrogen cycle process in fish ponds is introduced to explain the fish farming. "Yufuling" is used as the entry point to fish selling to connect food safety with chemistry. Fishy smell is explained from a chemical perspective for fish food. This paper aims at making a scientific explanation of life phenomena, deepening the consciousness of chemical life, helping people establish a correct view of chemical science, and inspiring youth to learn to use the knowledge that they have learned to explain life phenomena. This paper also tries to show the youth that life cannot be separated from chemistry, and chemistry cannot be separated from life.     

脊髓小脑变性疾病病人血清铜,锌,铝,铁含量的研究

脊髓小脑变性疾病（ＳＣＤ）的病因可能与遗传、神经生化紊乱、感染、微量元素平衡障碍及自由基损伤等因素有关，其中微量元素平衡障碍的研究具有重要意义。检测了ＳＣＤ中发病率较高的橄榄桥小脑萎缩症（ＯＰＣＡ）及晚发性小脑皮质萎缩症（ＬＣＣＡ）病人１５例血清中铜、锌、铝、铁等微量元素含量。发现病人比对照组铜明显降低，Ｐ〈０．０１；锌明显降低，Ｐ〈０．０１；铝明显升高，Ｐ〈０．０１；铁无明显差别。     

Simultaneous quantification of budesonide and its two metabolites, 6beta-hydroxybudesonide and 16alpha-hydroxyprednisolone,in human plasma by liquid chromatography negative electrospray ionization tandem mass spectrometry

A sensitive, rapid and selective liquid chromatography negative electrospray ionization tandem mass spectrometry [LC-(-)ESI-MS-MS] method has been developed and validated for the simultaneous quantification of budesonide (BUD) and its major metabolites, 6beta-hydroxybudesonide (OH-BUD) and 16alpha-hydroxyprednisolone (OH-PRED) in human plasma. The method was validated over a linear range from 0.1 to 10 ng/mL for all three analytes using a solid-phase extraction procedure with 9-fluoro-hydrocortisone as the internal standard. The between-day and within-day coefficients of variation for all compounds were < or =20% at the concentrations of lower limit of quantification and < or =15% at other quality control concentrations. The utility of this assay was demonstrated by monitoring BUD, OH-BUD and OH-PRED plasma concentrations in one healthy subject for 24 h following a 3 mg oral dose of budesonide, administered as a pH modified release capsule (Budenofalk) to healthy volunteers.     

Synthesis of chiral γ-lactones via a RuPHOX-Ru catalyzed asymmetric hydrogenation of aroylacrylic acids

An asymmetric hydrogenation of aroylacrylic acids catalyzed by RuPHOX-Ru catalyst has been developed, affording the corresponding chiral γ-lactones in high yields and with up to 93% ee. The methodology has the advantage of utilizing easily accessible substrates and has therefore expand the scope of the resulting chiral γ-lactones. Furthermore, high catalytic efficiency was achieved in that the reduction of both the CC and CO double bonds was achieved in one step. The current work provides an alternative and convenient pathway for the synthesis of a wide range of chiral γ-lactones.     

流向强迫振荡圆柱绕流的涡脱落模态分析

通过求解采用ALE方法描述的运动坐标系Navier-Stokes方程组,分析均匀来流下雷诺 数为150的静止和流向振荡的圆柱绕流. 主要研究了强迫振荡频率和较大振幅比 (A/D=0.3-1.2)对圆柱升力、阻力变化特性以及涡脱落模态的影响. 研究表 明,流向振荡圆柱绕流存在多种涡脱落模态,如对称S以及反对称A-I, A-III, A-IV等多种形式;比较研究结果,拓展了各模态下对应的锁定区域,并将其分为5个 子区;A-I模态中圆柱受力较以前所知更复杂;通过分析计算结果,发现最大加速度 比Af_{c}^{2}/Df_{s0}^{2}可能是涡脱落模态(尤其是对称S模态)最有效的控制参数.