Stably and almost complex structures on bounded flag manifolds

We study the enumeration problem of stably complex structures on bounded flag manifolds arising from omniorientations, and determine those induced by almost complex structures. We also enumerate the stably complex structures on these manifolds which bound, therefore representing zero in the complex cobordism ring .

     

On complex and noncommutative tori

The ``noncommutative geometry' of complex algebraic curves is studied. As a first step, we clarify a morphism between elliptic curves, or complex tori, and -algebras , or noncommutative tori. The main result says that under the morphism, isomorphic elliptic curves map to the Morita equivalent noncommutative tori. Our approach is based on the rigidity of the length spectra of Riemann surfaces.

     

Dominating sets in triangulations on surfaces

Let G be a graph and let S?V(G). We say that S is dominating in G if each vertex of G is in S or adjacent to a vertex in S. We show that every triangulation on the torus and the Klein bottle with n vertices has a dominating set of cardinality at most $\frac{n}{3}Let G be a graph and let S?V(G). We say that S is dominating in G if each vertex of G is in S or adjacent to a vertex in S. We show that every triangulation on the torus and the Klein bottle with n vertices has a dominating set of cardinality at most $\frac{n}{3}$. Moreover, we show that the same conclusion holds for a triangulation on any non‐spherical surface with sufficiently large representativity. These results generalize that for plane triangulations proved by Matheson and Tarjan (European J Combin 17 (1996), 565–568), and solve a conjecture by Plummer (Private Communication). © 2009 Wiley Periodicals, Inc. J Graph Theory 63: 17–30, 2010     

A characterization of the Clifford torus

In this paper, we prove that an -dimensional closed minimal hypersurface with Ricci curvature of a unit sphere is isometric to a Clifford torus if , where is the squared norm of the second fundamental form of .

     

Equivalence Bimodule between Spherical Noncommutative Tori

Let n _i ,m _j > 1. In [5], the sperical noncommutative torus was defined by twisting in by a totally skew multiplier p on for T ^pd a pd-homogeneous C*-algebra over . It is shown that is strongly Morita equivalent to . This work is supported by Grant No. 1999-2-102-001-3 from the interdisciplinary research program year of the KOSEF     

Integrals polynomial in velocity for two-degrees-of-freedom dynamical systems whose configuration space is a torus

We consider dynamical systems with two degrees of freedom whose configuration space is a torus and which admit first integrals polynomial in velocity. We obtain constructive criteria for the existence of conditional linear and quadratic integrals on the two-dimensional torus. Moreover, we show that under some additional conditions the degree of an irreducible integral of the geodesic flow on the torus does not exceed 2.Translated fromMatematicheskie Zametki, Vol. 64, No. 1, pp. 37–44, July, 1998.The author wishes to express his thanks to V. V. Kozlov for his interest and his help in this work.This research was supported by the Russian Foundation for Basic Research under grant No. 96-01-00747.     

非对易torus上的新孤子解

利用在非对易可积torus(环)上的算子都有约化矩阵这一特点, 孤子解的求解问题可以化为求满足代数方程Q(M)=0的有限维矩阵解问题. 本文研究了当 矩阵M不可对角化时的情形, 分析这种情形,得到当势函数V(\phi)具有三阶以上的极值点时, 有限维矩阵方程V′(M)=0存在不可对角化的矩阵解. 研究了这种解的一般形式, 并通过kq表象, 构造了非对易整环上以上述矩阵解为约化矩阵 的新孤子解. 根据这种构造方法, 可以得到非对易orbifold上的新孤子解.     

Normal Form for Families of Hamiltonian Systems

We consider perturbations of integrable Hamiltonian systems in the neighborhood of normally parabolic invariant tori. Using the techniques of KAM-theory we prove that there exists a canonical transformation that puts the Hamiltonian in normal form up to a remainder of weighted order 2d ＋ 1. And some dynamical consequences are obtained.     

The question of the realizability of the Landau scenario for the development of turbulence

We suggest a phenomenological model for the development of turbulence in the form of the nonlinear Klein-Gordon equation perturbed by nonconservative disturbances. Combining analytic and numerical methods, we establish that the transition to turbulence in this equation can follow both the Landau and the Landau-Sell scenarios. As is known, the first scenario is related to a cascade of bifurcations of stable invariant tori of increasing dimensions. The other scenario is related to a chaotic attractor whose Lyapunov dimension increases indefinitely under variation of a certain control parameter. __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 158, No. 2, pp. 292–311, February, 2009.     

保持n-形式系统的Lie对称群约化及应用

本文考虑保持ｎ－形式（面积、体积的高维推广概念）的ｎ维向量场,应用Ｌｉｅ群方法对其约化问题进行了系统性研究,得到了下列结果,第一,如何保持ｎ－ｇａａａ的ｎ维向量场具有一个单参数保持ｎ－形式的空间对称群,则可具体地构造出一个与向量场无关变换,便得原向量场约化掉一维,并且该约化向量场保持相应的（ｎ－１）形式,特别ｎ＝３时可直接得到「１」中的重要结果,第二,上述ｎ维向量场如果具有一个ｒ参数保持ｎ－ｇａａ