Regeneration of surface roughness by the Langevin equation using stochastic analysis on AFM image of a carbon fiber

A new method was developed using AFM images of a fiber surface to regenerate the surface roughness in 3D geometry, such as the cylindrical shape of a “model” fiber. The Langevin equation was used to derive the fluctuations of a carbon fiber surface image. The equation contains two quantities, D⁽¹⁾ (h) and D⁽²⁾ (h) which in physics represent drift and diffusion coefficients. Knowing this coefficient and adding a proper noise function, a similar surface of larger dimension with the same statistical properties of the initial data was created. The generated surface was mapped into cylindrical coordinates, then a mesh generated. The resulting reconstructed surface, input over the geometry of a cylindrical shape, can be implemented for finite element analysis of a single fiber surrounded by matrix and generalized to a many fiber model.     

Effect of annealing on the nanoscratch behavior of multilayer Si0.8Ge0.2/Si films

In this study, we examined the nanoscratch behavior of annealed multilayered silicon-germanium (SiGe) films comprising alternating sublayers (Si) deposited using an ultrahigh-vacuum chemical vapor deposition (UHV/CVD) system. Annealing consisted of ex situ thermal treatment in a furnace system. We used a nanoscratch technique to investigate the nanotribological behavior of the SiGe films and atomic force microscopy (AFM) to observe deformation phenomena. Our AFM morphological studies of the SiGe films revealed that pile-up phenomena occurred on both sides of each scratch. The scratched surfaces of the SiGe films that had been subjected to various annealing conditions exhibited significantly different features, it is conjectured that cracking dominates in the case of SiGe films while ploughing dominates during the scratching process. We obtained higher coefficients of friction (μ) when the ramped force was set at 6000 μN, rather than 2000 μN, suggesting that annealing of SiGe films leads to higher shear resistance; annealing treatment not only produced misfit dislocations in the form of a significantly wavy sliding surface but also promoted scratching resistance.     

Direct observation of surface and internal phase-separated structure of the active layer buried in organic photovoltaic cells

A phase-separated structure of the active layer, of variable thickness, buried in organic thin film solar cells (OTSC) was directly observed by scanning force microscopy (SFM) with the aid of a surface and interface cutting analysis system (SAICAS). This deals with SFM observation to both the surface and the internal regions of the OTSCs, leading to discussion about the formation of the overlayer in the active layer.     

Stochastic Maximum Principle for Forward-Backward Regime Switching Jump Diffusion Systems and Applications to Finance

The authors prove a sufficient stochastic maximum principle for the optimal control of a forward-backward Markov regime switching jump diffusion system and show its connection to dynamic programming principle. The result is applied to a cash flow valuation problem with terminal wealth constraint in a financial market. An explicit optimal strategy is obtained in this example.     

Stability of the Equilibrium to the Boltzmann Equation with Large Potential Force

The Boltzmann equation with external potential force exists a unique equilibrium—local Maxwellian. The author constructs the nonlinear stability of the equilibrium when the initial datum is a small perturbation of the local Maxwellian in the whole space R~3. Compared with the previous result [Ukai, S., Yang, T. and Zhao, H.-J.,Global solutions to the Boltzmann equation with external forces, Anal. Appl.(Singap.), 3,2005, 157–193], no smallness condition on the Sobolev norm H~1 of the potential is needed in our arguments. The proof is based on the entropy-energy inequality and the L~2-L~∞ estimates.     

Radial symmetry for systems of fractional Laplacian

In this paper, we consider systems of fractional Laplacian equations in Rnwith nonlinear terms satisfying some quite general structural conditions. These systems were categorized critical and subcritical cases. We show that there is no positive solution in the subcritical cases, and we classify all positive solutions ui in the critical cases by using a direct method of moving planes introduced in Chen-Li-Li [11] and some new maximum principles in Li-Wu-Xu [27].     

Graphs in which some and every maximum matching is uniquely restricted

A matching M in a graph G is uniquely restricted if there is no matching in G that is distinct from M but covers the same vertices as M. Solving a problem posed by Golumbic, Hirst, and Lewenstein, we characterize the graphs in which some maximum matching is uniquely restricted. Solving a problem posed by Levit and Mandrescu, we characterize the graphs in which every maximum matching is uniquely restricted. Both our characterizations lead to efficient recognition algorithms for the corresponding graphs.     

Discretization error for the maximum of a Gaussian field

The paper considers the difference between (a) the true maximum of a Gaussian field on a square and (b) its maximum on a regular grid. This difference is called the discretization error. A kind of Slepian model is used to study the behavior of the field around the location of the maximum. We show that the normalized discretization error can be bounded by a quantity that converges to a uniform variable, depending on the Hessian matrix at the point of the maximum. The bound is applied to simulated and real data (satellite positioning data).     

一类零膨胀广义线性模型极大似然估计的相合性与渐近正态性

讨论了响应变量为单参数指数族且在零点处膨胀的广义线性模型的大样本性质,对其参数进行了极大似然估计,给出了一些正则条件.基于所提出的正则条件,证明了模型参数极大似然估计的相合性与渐近正态性.     

Submanifolds in Cauchy Riemann Geometry

In this paper I would like to make a report on the results about hypersurfaces in the Heisenberg group and invariant curves and surfaces in CR geometry. The results are contained in the papers [8, 9, 16] and [14]. Besides, I would also report on the results about the strong maximum principle for a class of mean curvature type operators in [10].