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．     

The polar ionosphere at Zhongshan station on May 11, 1999, the day the solar wind almost disappeared

The solar wind almost disappeared on May 11, 1999: the solar wind plasma density and dynamic pressure were less than 1cm⁻³ and 0.1 nPa respectively, while the interplanetary magnetic field was northward. The polar ionospheric data observed by the multi-instruments at Zhongshan Station in Antarctica on such special event day was compared with those of the control day (May 14). It was shown that geomagnetic activity was very quiet on May 11 at Zhongshan. The magnetic pulsation, which usually occurred at about magnetic noon, did not appear. The ionosphere was steady and stratified, and the F₂ layer spread very little. The critical frequency of day-side F₂ layer, f₀F₂, was larger than that of control day, and the peak of f₀F₂ appeared 2 hours earlier. The ionospheric drift velocity was less than usual. There were intensive auroral E_s appearing at magnetic noon. All this indicates that the polar ionosphere was extremely quiet and geomagnetic field was much more dipolar on May 11. There were some signatures of auroral substorm before midnight, such as the negative deviation of the geomagnetic H component, accompanied with auroral E_s and weak Pc3 pulsation.

     

A finite model property for RMImin

It is proved that the variety of relevant disjunction lattices has the finite embeddability property. It follows that Avron's relevance logic RMI _min has a strong form of the finite model property, so it has a solvable deducibility problem. This strengthens Avron's result that RMI _min is decidable. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

不同入射角度下强流脉冲电子束能量沉积剖面和束流传输系数模拟计算

 强流脉冲电子束在材料中的能量沉积剖面、能量沉积系数和束流传输系数受其入射角的影响很大，理论计算了0.5~2.0MeV的电子束以不同的入射角在Al材料中的能量沉积剖面和能量沉积系数，并且还计算了0.4~1.4MeV电子束以不同入射角穿透不同厚度C靶的束流传输系数。计算结果表明，随着入射角的增大，靶材表面层单位质量中沉积的能量增大，电子在靶材料中穿透深度减小，能量沉积系数减小，相应的束流传输系数也减小；能量为0.5~2.0MeV的电子束当入射角在60°~70°时在材料表面层单位质量中沉积的能量较大。     

In situ observation of NaBi(WO4)2 dendrite growth and the study on microstructure of solidification

The dendrite growth process of transparent NaBi(WO₄)₂ with small prandtl and high melting point was studied by using the in-situ observation system. According to the dynamic images and detailed information, there are two kinds of restriction effect on the dendrite growth, the competition between arms and branches and the convection in the melt. The dendrite growth rate was time dependent, and the rate of arm growth reached the maximum 5.8 mm/s in the diffusive-advective region and rapidly decreased in the diffusive-convective region. The growth rate of branch had the same change trends as the arm’s. Based on the EPMA-EDS data of solidification structure of quenched NaBi(WO₄)₂ melt, it was found that there were component differences from stoichiometric concentration in the melt near the interface during the growth process. Supported by the National Natural Science Foundation of China (Grant No. 50331040) and the Innovation Funds from Shanghai Institute of Ceramics, Chinese Academy of Sciences (Grant No. SCX0623)     

Q-正则Loewner空间中的拟对称映射

本文在Q-正则Loewner空间中用环模不等式刻划了拟对称映射.另外,在 Q-维Ahlfors-David正则空间中建立了拟对称映射作用下的Grotzsch-Teichmuller型 模不等式,它是通过伸张系数的积分平均来表示.     

采用Authorware 5制作现代光学实验多媒体课件

我们采用目前最流行的多媒体制作软件Authorware 5开发工具，把现代光学实验原理，公式推导，实验内容，步骤等字材料，以及用CCD采集的干涉图像，优美的背景音乐及解说词等多种数学信息，制作成多媒体课件，可直接用于远程教育，有较大的实用价值。     

锰(Ⅱ)-高碘酸钾-灿烂绿体系测定水中痕量锰

在 HAc- Na Ac环境中 ,锰 ( )对于高碘酸钾氧化灿烂绿的反应具有很强的催化作用。据此 ,建立了催化动力学光度法测定痕量锰 ( )的新方法。该方法的检出限为 2 .2 2× 10 -11g/ m L ,测定线性范围为0 .1— 12 ng/ m L。直接用于环境水样中锰的测定 ,获得满意的结果     

Spectroscopic evidence for triplet excitation energy transfer among carotenoids in the LH2 complex from photosynthetic bacterium <Emphasis Type="Italic">Rhodopseudomonas palustris</Emphasis>

The LH2 complex from Rhodopsudomonas (Rps.) palustris is unique in the heterogeneous carotenoid compositions. The dynamics of triplet excited state Carotenoids (³Car* has been investigated by means of sub-microsecond time-resolved absorption spectroscopy both at physiological temperature (295 K) and at cryogenic temperature (77K). Broad and asymmetric T _n ←T ₁ transient absorption was observed at room temperature following the photo-excitation of Car at 532 nm, which suggests the contribution from various carotenoid compositions having different numbers of conjugated C=C double bonds (N_c=c). The triplet absorption bands of different carotenoids, which superimposed at room temperature, could be clearly distinguished upon decreasing the temperature down to 77 K. At room temperature the shorter-wavelength side of the main T_n04T₁ absorption band decayed rapidly to reach a spectral equilibration with a characteristic time constant of ∽1 μs, the same spectral dynamics, however, was not observed at 77 K. The aforementioned spectral dynamics can be explained in terms of the triplet-excitation transfer among heterogeneous carotenoid compositions. Global spectral analysis was applied to the time-resolved spectra at room temperature, which revealed two spectral components peaked at 545 and 565 nm, and assignable to the T_n04 T₁ absorption of Cars with Nc=c=11 and Nc=c=13, respectively. Surprisingly, the decay time constant of a shorter-conjugated Car, i.e. 0.72 ώs (aerobic) and 1.36 ώs (anaerobic), is smaller than that of a longer-conjugated Car, i.e. 2.12 us (aerobic) and 3.75 ώs (anaerobic), which is contradictory to the general rule of carotenoids and relative polyenes. The results are explained in terms of triplet-excitation transfer among different types of Cars. It is postulated that two Cars with different conjugation lengths coexist in an α, β-subunit in the LH2 complex.