Simple global reduction technique based on decomposition approach

Large and complex (nonlinear) models of chemical kinetics are one of the major obstacles in simulations of reacting flows. In the present work a new approach for an automatic reduction of chemical kinetics models, the so-called Global Quasi-Linearization (GQL) method is presented. The method is similar to the ILDM and CSP approaches in the sense that it is based on a decomposition into fast/slow motions and on slow invariant manifolds, but has a global character which allows us to overcome difficulties with the application of slow invariant manifolds and significantly simplifies the construction procedure for approximation of the slow invariant system manifold. The method is implemented within the standard ILDM method and applied to a number of model examples and to a meaningful combustion chemistry model.     

A note on gradient Einstein-type manifolds

In this note, we show that a nontrivial, compact, degenerate or nondegenerate, gradient Einstein-type manifold of constant scalar curvature is isometric to the standard sphere with a well defined potential function. Moreover, under some geometric assumptions the noncompact case is also treated. In this case, the main result is that a homogeneous, proper, noncompact, nondegenerate, gradient Einstein-type manifold is an Einstein manifold.     

一阶格点系统的不变测度与Liouville型方程

该文讨论一阶格点系统的解在相空间中的概率分布问题.作者先证明该格点系统的解算子生成的过程存在拉回吸引子,然后证明拉回吸引子上存在唯一的Borel不变概率测度,且该不变测度满足Liouville型方程.     

Cellular homology of real flag manifolds

Let ${\mathbb{F}}_{\Theta }=G∕P_{\Theta }$ be a generalized flag manifold, where $G$ is a real non-compact semi-simple Lie group and $P_{\Theta }$ a parabolic subgroup. A classical result says the Schubert cells, which are the closure of the Bruhat cells, endow ${\mathbb{F}}_{\Theta }$ with a cellular CW structure. In this paper we exhibit explicit parametrizations of the Schubert cells by closed balls (cubes) in ${\mathbb{R}}^n$ and use them to compute the boundary operator $\partial$ for the cellular homology. We recover the result obtained by Kocherlakota [1995], in the setting of Morse Homology, that the coefficients of $\partial$ are 0 or $\pm 2$ (so that ${\mathbb{Z}}_2$-homology is freely generated by the cells). In particular, the formula given here is more refined in the sense that the ambiguity of signals in the Morse–Witten complex is solved.     

Invariant pseudo-Kähler metrics on generalized flag manifolds

It is well known that a pseudo-Kähler structure is one of the natural generalizations of a Kähler structure. In this paper, we consider signatures of invariant pseudo-Kähler metrics on generalized flag manifolds from the viewpoint of T-root systems.