Nondegenerate cohomology pairing for transitive Lie algebroids,characterization

The Evens-Lu-Weinstein representation (Q _A , D) for a Lie algebroid A on a manifold M is studied in the transitive case. To consider at the same time non-oriented manifolds as well, this representation is slightly modified to (Q _A ^or , D^or) by tensoring by orientation flat line bundle, Q _A ^or =Q_A⊗or (M) and D ^or=D⊗∂ _A ^or . It is shown that the induced cohomology pairing is nondegenerate and that the representation (Q _A ^or , D^or) is the unique (up to isomorphy) line representation for which the top group of compactly supported cohomology is nontrivial. In the case of trivial Lie algebroid A=TM the theorem reduce to the following: the orientation flat bundle (or (M), ∂ _A ^or ) is the unique (up to isomorphy) flat line bundle (ξ, ∇) for which the twisted de Rham complex of compactly supported differential forms on M with values in ξ possesses the nontrivial cohomology group in the top dimension. Finally it is obtained the characterization of transitive Lie algebroids for which the Lie algebroid cohomology with trivial coefficients (or with coefficients in the orientation flat line bundle) gives Poincaré duality. In proofs of these theorems for Lie algebroids it is used the Hochschild-Serre spectral sequence and it is shown the general fact concerning pairings between graded filtered differential ℝ-vector spaces: assuming that the second terms live in the finite rectangular, nondegeneration of the pairing for the second terms (which can be infinite dimensional) implies the same for cohomology spaces.     

Legendre rational approximation on the whole line

The Legendre rational approximation is investigated. Some approximation results are established, which form the mathematical foundation of a new spectral method on the whole line. A model problem is considered. Numerical results show the efficiency of this new approach.     

发射光谱法测定ITO透明导电膜的Sn／In

本文采用运动电极，火花激发，讨论了膜样品分析中标样和分析样品的一致性，介绍了选用多个样品叠加摄谱对ＩＴＯ膜中Ｓｎ／Ｉｎ浓度比的测量。结果表明分析方法的精密度和准确度满足分析要求。     

Analysis of a new BEM‐FEM coupling for two‐dimensional fluid‐solid interaction

In this work we present a new numerical method, based on a coupling of finite and boundary elements, to solve a fluid‐solid interaction problem in the plane. The discrete method uses classical Lagrange finite elements adapted to curved boundaries for the field variable and spectral approximation of the unknowns on the artificial boundary. We provide error estimates for this Galerkin scheme and propose a full discretization based on elementary quadrature formulae, showing that the perturbation due to numerical integration preserves the optimal rate of convergence. We also suggest an iterative method to solve the complicated linear systems arising from this type of schemes. © 2005 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2005     

球面稳定同伦群中的一族新元素及h_0b_1~2在π_*V(1)中的收敛性

对连通有限型谱x,y,存在着Adams谱序列(ASS){Es,tr,dr}满足(1)dr:Es,tr→Es r,t r-1r 是谱序列的微分,(2)Es,t2≌Exts,tA(H*(X),H*(Y)),(3)并且收敛到[∑t-sY,X]p.当X是球谱S, Moore谱M,Toda-Smith谱V(1)时,(πt-sX)p分别为S,M,v(1)的稳定同伦群.本文通过Adams 谱序列,发现了球谱S的稳定同伦群中的一族非零元素γth0b21及Toda-Smith谱V(1)的稳定同伦群中的非零元素h0b21.在利用Adams谱序列求解同伦群的过程中,需要计算有关Exts,tA(H*X,H*Y) 的结果.利用谱的上纤维序列导出的Ext群的正合序列和May谱序列,得出Exts,tA(H*X,H*Y)的某些结果.本文令p≥7为奇素数,q=2(p-1).     

On a Constrained Approximate Controllability Problem for the Heat Equation: Addendum

In this note, we clarify a technical point of Ref. 1, devoted to studying a constrained approximate controllability for the heat equation.     

弱非线性复合体中的高阶非线性响应

利用谱表示理论和微扰展开法，从理论上给出了适合于一般微结构复合体系的有效非线性响 应的一般表示式，并结合有效媒质近似（EMA），在弱非线性条件下研究了由三阶非线性组 分（体积分数为p）和线性组分构成的非线性复合体系的有效非线性响应，讨论了复合 体系的有效介电常数ε～e=εe+χe|E0|2+ηe|E0| 4中的有效三次非线性响应χe和有效高次非线性响应ηe与体积分数p和 退极化因子L之间的关系，分析了非线性组分的介电常数为复数情形时体系的有效高阶非线 性响应，从理论上说明了组分的高次非线性响应对整个复合体系的有效介电常数的影响.  关键词： 非线性复合介质 有效非线性响应 谱表示理论     

Inverse spectral problems for Sturm-Liouville operators with singular potentials. Part III: Reconstruction by three spectra

We solve the inverse spectral problem of recovering the singular potential from W⁻¹₂(0,1) of a Sturm-Liouville operator by its spectra on the three intervals [0,1], [0,a], and [a,1] for some a∈(0,1). Necessary and sufficient conditions on the spectral data are derived, and uniqueness of the solution is analyzed.     

Parameter Estimation for Stochastic Parabolic Equations: Asymptotic Properties of a Two-Dimensional Projection-Based Estimator

A two-dimensional parameter is estimated from the observations of a random field defined on a compact manifold by a stochastic parabolic equation. Unlike the previous works on the subject, the equation is not necessarily diagonalizable, and no assumptions are made about the eigenfunctions of the operators in the equation. The estimator is based on certain finite-dimensional projections of the observed random field, and the asymptotic properties of the estimator are studied as the dimension of the projection is increased while the observation time is fixed. Simple conditions are found for the consistency and asymptotic normality of the estimator. An application to a problem in oceanography is discussed.     

气固两相圆柱绕流的直接数值模拟

本文运用谱元方法对气固两相圆柱绕流进行了直接数值模拟。在获得高精度计算流场信息基础上,进行颗粒扩散运动的研究。通过研究颗粒大小对颗粒扩散运动的影响来刻画气固两相圆柱绕流的物理特征。研究时发现,由于圆柱尾流独特的涡结构特征,颗粒在流场中心轴线附近区域的扩散机理主要是决定于吸力作用,该作用会驱使小颗粒卷吸进入圆柱尾部近壁区,甚至与圆柱后壁发生碰撞,这种扩散机理与混合层中颗粒扩散机理明显不同。