De Rham and Infinitesimal Cohomology in Kapranov's Model for Non commutative Algebraic Geometry

The title refers to the nilcommutative or NC-schemes introduced by M. Kapranov in Noncommutative Geometry Based on Commutator Expansions, J. Reine Angew. Math 505 (1998) 73–118. The latter are noncommutative nilpotent thickenings of commutative schemes. We also consider the parallel theory of nil-Poisson or NP-schemes, which are nilpotent thickenings of commutative schemes in the category of Poisson schemes. We study several variants of de Rham cohomology for NC- and NP-schemes. The variants include nilcommutative and nil-Poisson versions of the de Rham complex as well as of the cohomology of the infinitesimal site introduced by Grothendieck in Crystals and the de Rham Cohomology of Schemes, Dix exposés sur la cohomologie des schémas, Masson, Paris (1968), pp. 306–358. It turns out that each of these noncommutative variants admits a kind of Hodge decomposition which allows one to express the cohomology groups of a noncommutative scheme Y as a sum of copies of the usual (de Rham, infinitesimal) cohomology groups of the underlying commutative scheme X (Theorems 6.1, 6.4, 6.7). As a byproduct we obtain new proofs for classical results of Grothendieck (Corollary 6.2) and of Feigin and Tsygan (Corollary 6.8) on the relation between de Rham and infinitesimal cohomology and between the latter and periodic cyclic homology.     

R13中混合型曲面保主曲率等距变形

本文研究了Minkowski空间R₁³曲面的等距变形问题.建立了R₁³中曲面的共形、等距等概念.推广了O.Bonnet和S.S.Chern关于欧氏空间的结论.对R₁³出现的新情况——曲面的中曲率梯度类光作了一定探讨,得出的主要结果为:非平坦的、允许保主曲率等距变形的曲面一定不是W-曲面.     

横观各向同性多孔超弹性矩形板的单向拉伸

利用横观各向同性超弹性材料的广义neo-Hookean应变能函数研究了含有多个微孔的超弹性矩形板在单向拉伸作用下的有限变形和受力分析.给出了含有某种对称性分布的多个微孔的矩形板的变形模式,通过求解该变形模式满足的微分方程,将它用两个参数表示出来.可应用最小势能原理导出变分近似解,从而得到矩形板的变形和应力分布的解析解.分析了板中微孔的增长及微孔边缘应力的分布情况,讨论了板的各向异性程度及微孔的大小和孔间距离的影响,得到了单个、三个及五个微孔板中微孔的增长变形和孔边应力分布的一些基本规律规律,并进行了相互比较.     

一类混杂动态系统的能控性（I）——基本结果

首次将时滞现象引入到线性切换系统的模型中，研究含有时滞线性切换系统的能控性及其判定条件．全部工作由三部分组成，第I部分首先，提出含时滞的线性切换系统的数学模型，并介绍切换系统的基本概念——切换序列．其次，引入列空间、循环不变子空间和广义循环不变子空间等基本几何概念，给出一些有关概念的基本性质，特别是分离引理．然后以一个基本引理的形式揭式某一积分方程的解集与广义循环不变子空间之间的联系，这个引理将在能控性的判定中起关键作用．这些概念和引理都将作为以后展开能控性分析所必需的研究工具．     

一类混杂动态系统的能控性(Ⅲ)——含多时滞的情形

首次将时滞现象引入到线性切换系统的模型中,研究含有时滞线性切换系统的能控性及其判定条件。全部工作由三部分组成。第Ⅲ部分,主要研究含多时滞的线性切换系统的能控性及其判定规则。首先给出周期型系统的单周能控性和多周期能控性的定义和充要条件,其次给出非周期系统的能控性的定义和充要条件。最后,研究时滞大小不一致的情形,指出能控性与时滞大小无关。     

On Gouvêa's conjecture in the unobstructed case

In this article, for a residual modular representation defined over an arbitrary finite field, Gouvêa's conjecture which says that the universal deformation ring is isomorphic to a certain Hecke algebra is proven in the unobstructed case.     

离焦散斑技术研究Kirchhoff板在动载作用期的弯曲

本文使用动态离焦散斑技术,测试板的动态弯曲获得成功。并推导了Kirchhoff板动态变形的有关分析,提出了由最大斜率确定材料常数的思想。显然,这是同离焦散斑方法所测数据直接相关的处理手法。     

Classes Caractéristiques de Fibrés Feuilletés, Holomorphes ou Algébriques

Résumé L'objet de cet article est de montrer comment laK-théorie multiplicative peut être utilisée pour définir de nouvelles classes caractéristiques secondaires de fibrés vectoriels munis de structures supplémentaires, dans des contextes géométriques variés. On y développe des exemples reliés à des travaux antérieurs divers.

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The purpose of this paper is to show how multiplicativeK-theory may be used to define new secondary characteristic classes for vector bundles with additional structures, in various geometrical contexts. Many examples are developed which are related to previous works.

     

Cyclic reduction and FACR methods for piecewise hermite bicubic orthogonal spline collocation

Cyclic reduction and Fourier analysis-cyclic reduction (FACR) methods are presented for the solution of the linear systems which arise when orthogonal spline collocation with piecewise Hermite bicubics is applied to boundary value problems for certain separable partial differential equations on a rectangle. On anN×N uniform partition, the cyclic reduction and Fourier analysis-cyclic reduction methods requireO(N ²log₂ N) andO(N ²log₂log₂ N) arithmetic operations, respectively.     

Note on the optimal transportation of distributions

We extend our work on the optimal mapping of distributions in three directions: (a) we consider any set-valued mapping, not just diffeomorphisms; (b) we distinguish between weak and strong optimality, and identify strong optimality with cyclic monotonicity; and (c) we prove that, under some restrictions, a weakly optimal mapping has the subgradient property.