A descent principle for the Dirac-dual-Dirac method

Let G be a torsion-free discrete group with a finite-dimensional classifying space BG. We show that G has a dual-Dirac morphism if and only if a certain coarse (co-)assembly map is an isomorphism. Hence the existence of a dual-Dirac morphism for such groups is a metric, that is, coarse, invariant. We get results for groups with torsion as well.     

关于区间上的Lorenz映射

本文引进了变换ζ．首先，用比文［４］简捷的方法证明了Ｌｏｒｅｎｚ映射的Ｓａｒｋｏｖｓｋｉ定理并更正了文［４］中的一个错误，还得到了扩张的Ｌｏｒｅｎｚ映射中周期点的存在性与其扩张常数之间的关系．其次，证明了Ｌｏｒｅｎｚ映射与其在变换ζ的像具有相等的捏制行列式．此外，给出了广义的Ｌｏｒｅｎｚ映射的周期点的存在性适合Ｓａｒｋｏｖｓｋｉ序关系的一个充分条件     

Spatio-temporal symmetries and bifurcations via bi-orthogonal decompositions

Summary A tool for analyzing spatio-temporal complex physical phenomena was recently proposed by the authors, Aubry et al. [5]. This tool consists in decomposing a spatially and temporally evolving signal into orthogonal temporal modes (temporal “structures”) and orthogonal spatial modes (spatial “structures”) which are coupled. This allows the introduction of a temporal configuration space and a spatial one which are related to each other by an isomorphism. In this paper, we show how such a tool can be used to analyze space-time bifurcations, that is, qualitative changes in both space and time as a parameter varies. The Hopf bifurcation and various spatio-temporal symmetry related bifurcations, such as bifurcations to traveling waves, are studied in detail. In particular, it is shown that symmetry-breaking bifurcations can be detected by analyzing the temporal and spatial eigenspaces of the decomposition which then lose their degeneracy, namely their invariance under the symmetry. Furthermore, we show how an extension of the theory to “quasi-symmetries” permits the treatment of nondegenerate signals and leads to an exponentially decreasing law of the energy spectrum. Examples extracted from numerically obtained solutions of the Kuramoto-Sivashinsky equation, a coupled map lattice, and fully developed turbulence are given to illustrate the theory.     

随机性参数自适应的混沌同步

对两个不同参数的混沌系统进行随机性参数自适应控制，选取合适的控制律和反馈系数，导致其同步.以Henon映射为例进行数值模拟，结果表明，由于控制周期和反馈系数的随机变化，具有一定的实用意义. 关键词： Henon映射 混沌同步 随机性自适应控制     

从复流形到对称空间的多重调和映射

本文首先证明了从复流形到对称空间的多重调和映射空间与扩张提升空间之间在相差一规范变换下存在一一对应,并给出确定的环路群在扩张提升空间的作用,因而也给出多重调和映射空间上的作用.其次,利用环路群及其代数的Iwasawa分解给出从Cn到对称空间的有限型的多重调和映射不同于文[1]中的刻划.     

Remarks on a Noble''''s Theorem

Noble proved the following Theorem: If A (?) X with a nonisolated point and B (?) Y, then A × B is bounded in X×Y if and only if the projection map π : X × Y → X is a z-map with respect to A × B and A, A is bounded in X and B is bounded in Y. In this note, we give two examples showing the necessary and sufficient conditions of Noble's theorem are not right.     

Even the first iterate of a Markov operator is contracting in anL 2 norm

A weightedL ₂ norm is introduced in which Markov operators, e.g., associated with noisy maps, are contracting provided the kernel (i.e., the transitional distribution) is smooth enough. This results in strong relaxational properties of noisy maps. Similar to this norm, integral functionals appear useful when studying spatiotemporal chaos and random fields.     

嗜麦芽假单胞菌质粒pSH1的限制图谱及km~r标记的克隆

对嗜麦芽假单胞菌Ｐ２菌株（ＰｓｅｕｄｏｍｏｎａｓｍａｌｔｏｏｈｉｌｉａＰ２）的质粒ｐＳＨ１进行了限制酶切分析，确定了ＢｇｌⅡ、ＥｃｏＲⅠ、ＰｓｔⅠ、ＸｂａⅠ、ＢａｍＨⅠ、ＢｇｌⅠ、及ＰｖｕⅡ共７种限制性内切酶在ｐＳＨ１、质粒上的切割位点，前４种酶均为单一切点；后３种依次为２、７、５个切点．通过双酶切和部分酶切的方法绘制了ｐＳＨ１质粒的限制酶切图谱．将ｐＧＰ１－２质粒上的卡那霉素抗性基因（ｋｍｒ）片段插入ｐＳＨ１，获得了重组质粒ｐＳＨ２．ｐＳＨ２是由ｐＧＰ１－２质粒上大小为２．９０ｋｂ的ＤＮＡ片段（含ｋｍｒ）和ｇｈＨ１经ＢａｍＨⅠ－ＰｓｔⅠ双酶切产生５．７０ｋｂ大片段组成，它能够重新转化到喀麦芽假单胞菌受体（ｋｍｒ）中，其ｋｍｒ标记能够得到稳定的表达．     

广义Taylor映射与Hénon映射具有混沌条件的改进

本文进一步讨论了近年来动力系统中关于对具有混沌现象的Taylor映射,Henon映射等函数所做的研究,并着重分析了所讨论函数的参数.     

3维双曲空间中曲面的双曲Gauss映照和法Gauss映照

本文导出了3维双曲空间中曲面的双曲Gauss映照和法Gauss映照的关系,发现了一般的曲面由双曲Gauss映照和平均曲率函数唯一确定,并证明了双曲Gauss映照所满足的二阶线性椭圆方程,给出了两种形式的关于双曲Gauss映照的三阶非线性偏微分方程(组)的一个解.