积域上一类奇异积分算子的L~p有界性

本文证明,对于Ω∈(1)∩L(log~+L)~2(S~(n-1)×S~(m-1)),h(r,s)∈L~∞(R_+~1×R_+~1)和P_(N_1),P_(N_2)∈(2),带粗糙核的奇异积分算子为L~p有界。     

A Petrov-Galerkin method for equal width equation

The equal width equation is solved numerically by Petrov-Galerkin method using linear hat function and quadratic B-spline function as trial and test functions respectively. Product approximation has been used in this method. A linear stability analysis of the scheme is shown to be conditionally stable. Test problems including the single soliton and the interaction of solitons are used to validate the suggested method, which is found to be accurate and efficient. The Maxwellian initial condition pulse and the development of an undular bore are also studied.     

Riesz transform on locally symmetric spaces and Riemannian manifolds with a spectral gap

In this paper we study the Riesz transform on complete and connected Riemannian manifolds M with a certain spectral gap in the L² spectrum of the Laplacian. We show that on such manifolds the Riesz transform is Lp bounded for all p∈(1,∞). This generalizes a result by Mandouvalos and Marias and extends a result by Auscher, Coulhon, Duong, and Hofmann to the case where zero is an isolated point of the L² spectrum of the Laplacian.     

内积在溶液浓度测定中的应用

提出内积的溶液浓度测定方法。该方法计算已知浓度溶液透光率曲线与0号溶液（浓度最低的溶液）透光率曲线的内积ρ,确定溶液的ρ-C曲线,然后测定未知溶液的透光率曲线,计算其与0号溶液透光率曲线的内积,并利用已建立好的ρ-C曲线进行插值以估计溶液浓度。由于该方法利用了透光率曲线的全部信息,因此对溶液浓度的估计精度较高。对K2Cr2O7溶液浓度的测定实验结果表明,该方法对溶液浓度的估计相对误差小于1.00%。     

Sobolev spaces with variable exponents on Riemannian manifolds

In this article we study variable exponent Sobolev spaces on Riemannian manifolds. The spaces are examined in the case of compact manifolds. Continuous and compact embeddings are discussed. The paper contains an example of the application of the theory to elliptic equations on compact manifolds.     

图胞映射的一种改进方法

通过引入新的概念，提出了图胞映射动力系统中瞬态胞的新的分类方法，基于新的分类方法研究了动力系统中不变流形的胞映射逼近问题；并结合计算机的计算速度与内存特点，建立了完成上述压缩分类的有效算法.通过对典型算例Henon映射的应用分析，证实了该方法的有效性.     

Integrated Density of States for Ergodic Random Schrödinger Operators on Manifolds

We consider the Riemannian universal covering of a compact manifold M = X/ and assume that is amenable. We show the existence of a (nonrandom) integrated density of states for an ergodic random family of Schrödinger operators on X.     

The Index of Cusp Operators on Manifolds with Corners

We recall a Fredholm criterion for fully elliptic cusp(pseudo)differential operators on a compact manifold with corners ofarbitrary codimension, acting on suitable Sobolev spaces. Then we give aformula for the index in terms of regularized `trace' functionalssimilar to the residue trace of Wodzicki and Guillemin.     

Rozansky–Witten invariants via Atiyah classes

Recently, L. Rozansky and E. Witten associated to any hyper-Kähler manifold X a system of weights (numbers, one for each trivalent graph) and used them to construct invariants of topological 3-manifolds. We give a simple cohomological definition of these weights in terms of the Atiyah class of X (the obstruction to the existence of a holomorphic connection). We show that the analogy between the tensor of curvature of a hyper-Kähler metric and the tensor of structure constants of a Lie algebra observed by Rozansky and Witten, holds in fact for any complex manifold, if we work at the level of cohomology and for any Kähler manifold, if we work at the level of Dolbeault cochains. As an outcome of our considerations, we give a formula for Rozansky–Witten classes using any Kähler metric on a holomorphic symplectic manifold.