Line integrals and Green's formula on time scales

In this paper we study curves parametrized by a time scale parameter, introduce line delta and nabla integrals along time scale curves, and obtain an analog of Green's formula in the time scale setting.     

Congratulations to Professor K. Itô

In this paper we describe a story how a Moscow mathematician solved an important problem in ergodic theory using It? multiple stochastic integrals.     

Boundary convergence of vector-valued pseudocontinuable functions

In the first part of the paper we discuss a multi-dimensional analogue of the well-known construction by D. Clark that allows one to study families of spectral measures of perturbations of the model contraction. In the second part we present extensions of the relevant results on the boundary behavior of pseudocontinuable functions. We show that, although the most direct analogue of the scalar theorem on the existence of boundary values for pseudocontinuable functions with respect to Clark measures fails in the non-scalar situation, suitable vector-valued versions of such results can be found.     

分数次积分算子的交换子在齐型空间上的弱型估计

本文研究分数次积分交换子,其中Kα(x,y)=d(x,y)α-1,m∈N且b(x)∈BMO(X,μ),证明了Iα,bm是从Orlicz空间L(log L)m(X)到弱Lq(X)空间的映照．同时还证明了分数次极大算子交换子Mα,bm也有类似性质．     

Boundedness of Marcinkiewicz integrals and their commutators in H~1(R~n×R~m)

The authors establish the boundedness of Marcinkiewicz integrals from the Hardy space H1(Rn×Rm) to the Lebesgue space L1(Rn×Rm) and their commutators with Lipschitz functions from the Hardy space H1(Rn×Rm) to the Lebesgue space Lq(Rn×Rm) for some q>1     

Mixed radial-angular integrability for rough maximal singular integrals and Marcinkiewicz integrals with mixed homogeneity

This paper is devoted to studying maximal singular integrals and Marcinkiewicz integrals with rough kernels in a mixed homogeneity setting. Assuming that the kernels satisfy certain rather weak size conditions, the boundedness of such operators on the mixed radial-angular spaces are established, respectively. Meanwhile, the corresponding vector-valued versions are also given.     

Weighted isoperimetric inequalities in warped product manifolds

We prove some sharp isoperimetric type inequalities in warped product manifolds, or more generally, multiply warped product manifolds. We also relate them to inequalities involving the higher order mean-curvature integrals. Applications include some sharp eigenvalue estimates, Pólya-Szegö inequality, Faber-Krahn inequality, Sobolev inequality and some sharp geometric inequalities in some warped product spaces.     

含界面裂纹的不可压缩双金属胶接件的解析变分－守恒积分解法

本文根据平面问题的复变函数理论推导了含界面裂纹双金属胶接件满足微分方程、开裂界面边界条件与未开裂界面连续条件的应力与位移本征函数展开式，并建立了不可压缩双金属界面裂纹的复合型守恒积分及其与应力强度因子之关系，进而利用分区广义变分原理满足其余边界条件确定包含应力强度因子在内的展开式系数，得到守恒积分并求出应力强度因子．数值计算表明，沿不同回路的在恒积分具有很好的守恒性而且由这两种方法所得应力强度因子具有很好的一致性．     

正交各向异性位势问题边界元法中几乎奇异积分的解析算法

几乎奇异积分的计算困难阻碍了边界元法的工程应用。本文针对二维正交各向异性位势问题边界元法中近边界点的几乎奇异积分,采用分部积分法,导出一种直接的解析计算公式。该解析公式可以精确计算线性单元上的几乎奇异积分。对二次单元,可将其细分为几个线性元,采用该解析公式近似计算其边界积分。当内点离当前积分单元较远时,仍保持常规高斯数值积分模式;而当内点离其较近时,因常规高斯积分结果失效,则采用该解析积分取代高斯数值积分。数值算例证明了该算法的有效性和精确性。二次元计算结果比线性元计算结果更精确。