基于小波与重调和方程的扩散去噪模型的研究

在图像处理过程中, 为了在图像去噪时更好地保留图像的角点、尖峰和窄边缘, 利用重调和方程的应力平衡性及其高阶偏导数的局部极大值, 构建新算子, 建立重调和扩散模型. 考虑到若图像中的噪声很强, 则会在处理后的图像上留下一些孤立的斑点, 且图像的纹理是在较大范围上具有的统计特性, 而新建模型只能保留局部细节, 图像大范围上的信息没有得到很好保留, 故对上述新建模型做进一步改进, 采用小波变换提取图像的高频部分, 对这部分运用应力平衡性构建新算子, 从局部上较稳定地控制图像的细节信息, 建立波域重调和扩散模型. 分析与仿真结果表明, 该模型与Perona-Mailik模型相比较保留了更多的图像信息, 有效地增强了图像的边缘, 同时很好地保持了图像的角点、尖峰、和窄边缘, 是一个理想的模型.     

Energy-Momentum Properties and the Spin of Short-Lived Particles

The space–time translation property of a stable particle is characterized by a time-like Lorentz vector (E, _k ). We show in this contribution that unstable particles are, in addition, characterized by a space-like Lorentz 4-vector of uncertainties, or spreads, ( E, k). This is true for unstable states created in formation-, in production-, and in decay-experiments. The space-like nature of the spread vector causes a nonzero momentum spread to be present in all Lorentz frames so that there is no Lorentz frame in which the unstable particle is entirely at rest. With the space-like spreadvector ( E, k) in addition to the time-like (E, _k ), also the rotation property of an unstable particle is affected, and unstable states have an uncertainty in their spin. This means neighboring spin states are occupied in addition to the original spin. Experiments are discussed that show a principal limitation of the accuracy of spin measurement from finite lifetimes. Wave functions for unstable particles are discussed, and we show in the example of a short-lived spin-0 state that the appearance of a spin neighbor in the amplitude is proportional to the inverse lifetime.     

An ALE approach to mechano‐chemical processes in fluid–structure interactions

Mathematical modeling and simulation of fluid–structure interaction problems are in the focus of research already for a longer period. However, taking into account also chemical reactions, leading to structural changes, including changes of mechanical properties of the solid phase, is rather new but for many applications is highly important area. This paper formulates a model system for reactive flow and transport in a vessel system, the penetration of chemical substances into the solid wall. Inside the wall, reactions take place that lead to changes of volume and of the mechanical properties of the wall. Numerical algorithms are developed and used to simulate the dynamics of such a mechano‐chemical fluid–structure interaction problem. As a proof of concept scenario, plaque formation in blood vessels is chosen. The arbitrary Lagrangian Eulerian approach (ALE) is chosen to solve the systems numerically. Temporal discretization of the fully coupled monolithic model is accomplished by backward Euler scheme and spatial discretization by stabilized finite elements. The numerical approach is verified by numerical tests, and effective methods to maintain mesh qualities under large deformations are described. For realistic system parameters, the simulations show that the plaque formation in blood vessel is a long‐time effect. The time scale of the formation is in the simulation of comparable order as in reality. Copyright © 2016 John Wiley & Sons, Ltd.     

Constructing center-stable tori

We show that certain derived-from-Anosov diffeomorphisms on the 2-torus may be realized as the dynamics on a center-stable or center-unstable torus of a 3-dimensional strongly partially hyperbolic system. We also construct examples of center-stable and center-unstable tori in higher dimensions.     

关于伪脐子流形的一些性质

对于局部对称黎曼流形中的伪脐点子流形给出了一个积分不等式，推广了CHEN Bang-yan的一个相应的结果。对于局部对称伪黎曼流形中的类空伪脐子流形，给出了关于第二基本形式长度平方与平均曲率之间的一个结论。     

局部对称Lorentz流形中的2-调和类空子流形

研究局部对称Lorentz流行中的2-调和类空子流形，得到2-调和等距浸入的平均曲率为零的充分条件，紧致超曲面以及常平均曲率超曲面的全测地性质。     

A New Boundary Element Method for the Biharmonic Equation with Dirichlet Boundary Conditions

We consider a scalar boundary integral formulation for the biharmonic equation based on the Almansi representation. This formulation was derived by the first author in an earlier paper. Our aim here is to prove the ellipticity of the integral operator and hence establish convergence of and error bounds for Galerkin boundary element methods. The theory applies both in two and three dimensions, but only for star-shaped domains. Numerical results in two dimensions confirm our analysis.     

关于复射影空间中紧.致极小子流形的特征值

本文在推广Yang, P.C.和Yau, S.T.关于球面中紧致极小子流形的特征值不等式的基础上,得到了复射影空间中紧致极小子流形的某些特征值不等式.     

Local conjugacy theorem, rank theorems in advanced calculus and a generalized principle for constructing Banach manifolds

Applications of locally fine property for operators are further developed. LetE andF be Banach spaces andF:U(x ₀)⊂E→F be C¹ nonlinear map, whereU (x ₀) is an open set containing pointx ₀∈E. With the locally fine property for Frechet derivativesf′(x) and generalized rank theorem forf′(x), a local conjugacy theorem, i. e. a characteristic condition forf being conjugate tof′(x ₀) near x₀,is proved. This theorem gives a complete answer to the local conjugacy problem. Consequently, several rank theorems in advanced calculus are established, including a theorem for C¹ Fredholm map which has been so far unknown. Also with this property the concept of regular value is extended, which gives rise to a generalized principle for constructing Banach submanifolds.