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21.
Gregorio Falqui 《Reports on Mathematical Physics》2002,50(3):395
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. 相似文献
22.
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. 相似文献
23.
High temperature oxidation of metals leads to residual stresses both in the metal and in the growing oxide. In this work, the evolution of this residual stresses is theoretically predicted in the growing oxide layers. The origin of these stresses is based on a microstructural model. Using experimental results providing from the oxidation kinetics, and an analysis proposed to describe the growth strain occurring in the thin layers, a set of equations is established allowing determining the stresses evolution with oxidation time. Then, the model is compared with experimental results obtained on both α-Fe and phosphated α-Fe, oxidised at different temperatures. Numerical data are extracted from experiments either with an asymptotic formulation or with an inverse method. These two methods give good agreement with experiments and allow extracting the model parameters. 相似文献
24.
L. T. Ashchepkov 《Computational Mathematics and Mathematical Physics》2006,46(7):1168-1175
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. 相似文献
25.
LIN Chang ZHANG Xiu-Lian 《理论物理通讯》2005,44(2):247-251
The nonlinear dust acoustic waves in two-dimensional dust plasma with dust charge variation is analytically investigated by using the formally variable separation approach. New analytical solutions for the governing equation of this system have been obtained for dust acoustic waves in a dust plasma for the first time. We derive exact analytical expressions for the general case of the nonlinear dust acoustic waves in two-dimensional dust plasma with dust charge variation. 相似文献
26.
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. 相似文献
27.
Ya. I. Kurys’ N. S. Netyaga V. G. Koshechko V. D. Pokhodenko 《Theoretical and Experimental Chemistry》2007,43(5):334-342
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. 相似文献
28.
Guy Bayada 《Journal of Mathematical Analysis and Applications》2003,282(1):212-231
The asymptotic behaviour of a Stokes flow with Tresca free boundary friction conditions when one dimension of the fluid domain tends to zero is studied. A specific Reynolds equation associated with variational inequalities is obtained and uniqueness is proved. 相似文献
29.
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. 相似文献
30.
XiangBaoMENG HuiLI QingLI ZhongJunLI 《中国化学快报》2004,15(7):777-778
An unusual reductive ring-opening reaction of phthalimide with sodium hydride in anhydrous DMF was observed for the first time. The presumed mechanism was described in detail. 相似文献