On a poisson reduction for Gel'fand-Zakharevich manifolds

We formulate and discuss a reduction theorem for Poisson pencils associated with a class of integrable systems, defined on bi-Hamiltonian manifolds, recently studied by Gel'fand and Zakharevich. The reduction procedure is suggested by the bi-Hamiltonian approach to the separation of variables problem.     

A priori tests of a stochastic mode reduction strategy

Several a priori tests of a systematic stochastic mode reduction procedure recently devised by the authors [Proc. Natl. Acad. Sci. 96 (1999) 14687; Commun. Pure Appl. Math. 54 (2001) 891] are developed here. In this procedure, reduced stochastic equations for a smaller collections of resolved variables are derived systematically for complex nonlinear systems with many degrees of freedom and a large collection of unresolved variables. While the above approach is mathematically rigorous in the limit when the ratio of correlation times between the resolved and the unresolved variables is arbitrary small, it is shown here on a systematic hierarchy of models that this ratio can be surprisingly big. Typically, the systematic reduced stochastic modeling yields quantitatively realistic dynamics for ratios as large as 1/2. The examples studied here vary from instructive stochastic triad models to prototype complex systems with many degrees of freedom utilizing the truncated Burgers–Hopf equations as a nonlinear heat bath. Systematic quantitative tests for the stochastic modeling procedure are developed here which involve the stationary distribution and the two-time correlations for the second and fourth moments including the resolved variables and the energy in the resolved variables. In an important illustrative example presented here, the nonlinear original system involves 102 degrees of freedom and the reduced stochastic model predicted by the theory for two resolved variables involves both nonlinear interaction and multiplicative noises. Even for large value of the correlation time ratio of the order of 1/2, the reduced stochastic model with two degrees of freedom captures the essentially nonlinear and non-Gaussian statistics of the original nonlinear systems with 102 modes extremely well. Furthermore, it is shown here that the standard regression fitting of the second-order correlations alone fails to reproduce the nonlinear stochastic dynamics in this example.     

一维核废料污染问题的一个二阶格式

利用降价法研究了多孔介质中一维核废料污染问题，此模型由一非线性抛物－椭圆耦合偏微分方程组的初边值问题来描述，对此问题给出了一个关于时间和空间均具有二阶精度的差分格式，并进行了理论分析。     

The entropy of Garfinkle-Horne dilaton black hole due to arbitrary spin fields

Using the membrane model which is based on brick wall model, we calculated the free energy and entropy of Garfinkle-Horne dilatonic black hole due to arbitrary spin fields. The result shows that the entropy of scalar field and the entropy of Fermionic field have similar formulas. There is only a coefficient between them.     

宽带膜厚实时监控过程中膜层折射率的确定方法

为了准确计算出镀膜过程中每层膜的折射率，介绍了实时监控过程中确定膜层折射率的2种方法：一种是由实测的透射比光谱直接反算出膜层的折射率；另一种是用最小二乘法的优化算法实时拟合折射率。试验结果表明：在线反算适合单点监控，所得折射率误差小于2%。然而在实际镀膜过程中,由于宽带内膜层参数误差较大,一般大于25%。为此，采用最小二乘法拟合，即在整个宽光谱范围内采集每个波长点的信息，所得结果误差很小，一般都在2％～5%之间,有时可达到10%,在很大程度上提高了实际镀膜时膜厚监控的精度。     

Reductions of interval nonlinear programming problem

A general nonlinear programming problem with interval functions is considered. Two reductions of this problem to the deterministic nonlinear programming problem are proposed, and illustrative examples are discussed.     

Indirect Oxidation of Organic Substances by Intermediates of the Oxygen Reduction

Results of two urgent and practically important directions of research on the indirect oxidation of organic compounds by highly reactive intermediates generated electrochemically from oxygen (HO₂ ^–, HO₂ ^·, HO^·) are considered and orderly arranged. The studies in question are the indirect synthesis and mineralization of organic toxicants in waste water.     

Polyaniline/12-phosphotungstic acid/V<Subscript>2</Subscript>O<Subscript>5</Subscript> nanocomposite and its platinum analog as oxygen reduction electrocatalysts

A guest-host nanocomposite based on electroconducting polyaniline doped with 12-phosphotungstic acid and V₂O₅ as well as its bifunctional analog containing not more than 5 mass% nanosized platinum were obtained. A study was carried out on the structure of these nanocomposites, their redox characteristics, and electrocatalytic activity in the reduction of oxygen. These nanocomposites were found to display catalytic properties in the electrochemical reduction of oxygen, while the presence of even a slight amount of nanosized platinum in the bifunctional composite leads to a significant increase in its electrocatalytic activity. __________ Translated from Teoreticheskaya i éksperimental’naya Khimiya, Vol. 43, No. 5, pp. 307–314, September–October, 2007.     

厚度对非极性聚合物薄膜驻极体电荷储存及电荷动态特性的影响

以Du Pont公司的商用Teflon FEP A型薄膜为例，通过热脉冲技术、等温表面电位衰减测量和开路热刺激放电电流谱分析等实验结果，讨论了经常温和高温电晕充电后样品厚度对薄膜驻极体的沉积电荷密度、薄膜驻极体的内电场、体电导率以及电荷储存稳定性的影响.通过热脉冲技术组合电导率温度曲线的测量，研究了在不同温度条件下样品厚度对沉积电荷层的平均电荷重心移动的影响.结果表明：在充电参数一定的条件下，随着膜厚的降低，储存电荷密度上升，但电荷稳定性有所下降.因此，合理地调控薄膜厚度，可以有效地优化驻极体的电荷储存能 关键词： 厚度 驻极体 电荷储存能力 电荷稳定性     

Baker＇s Yeast Mediated Reduction of Optically Active Diketone

Baker‘s yeast mediated reduction of optically active diketone is described. The two keto groups are efficiently differentiated and the ee value of the recovered material is considerably raised. It affords highly optically active key intermediates efficiently for the synthesis of natural polyhydroxylated agarofuran products.