Optimal design of a multilayer diffractive optical element for dual wavebands

A method for optimal design of a multilayer diffractive optical element (MLDOE) for dual-wide-waveband optical systems is presented with consideration of polychromatic integral diffraction efficiency (PIDE) and the weight factors of PIDE for each waveband. The design process and simulation of a MLDOE in mid-wave and long-wave IR are described, and the comparison of diffraction efficiency of the MLDOEs for different design wavelength pairs determined by different methods is given. This method can make the design process more rational and more reasonable and can give a better design result than that with the conventional design method.     

Preparation and electrochemistry of one-dimensional nanostructured MnO2/PPy composite for electrochemical capacitor

One-dimensional nanostructured manganese dioxide/polypyrrole (MnO₂/PPy) composite was prepared by in situ chemical oxidation polymerization of pyrrole in the host of inorganic matrix of MnO₂, using complex of methyl orange (MO)/FeCl₃ as a reactive self-degraded soft-template. The morphology and structure of the composite were characterized by infrared spectroscopy (IR) X-ray diffraction (XRD), scanning electron microscopy (SEM) and transmission electron microscopy (TEM). The results show that the MnO₂/PPy composite consists of α-MnO₂ and PPy with nanotube-like structure. Electrochemical properties of the composite demonstrated the material showed good electrochemical reversibility after 500 charge-discharge cycles in the potential range of −0.4 to 0.6 V, the tube-like nanocomposite has the potential application in electrochemical capacitor.     

Convergence to nonlinear diffusion waves for solutions of Euler equations with time-depending damping

In this paper, we are concerned with the asymptotic behavior of solutions to the system of Euler equations with time-depending damping, in particular, include the constant coefficient damping. We rigorously prove that the solutions time-asymptotically converge to the diffusion wave whose profile is self-similar solution to the corresponding parabolic equation, which justifies Darcy's law. Compared with previous results about Euler equations with constant coefficient damping obtained by Hsiao and Liu (1992) [2], and Nishihara (1996) [9], we obtain a general result when the initial perturbation belongs to the same space, i.e. $H^3(\mathbb{R})\times H^2(\mathbb{R})$. Our proof is based on the classical energy method.     

Global viscosity solutions for eikonal equations on class A Lorentzian 2-tori

On the Abelian cover \(({\mathbb {R}}^{2},g)\) of a class A Lorentzian 2-torus \(({\mathbb {T}}^{2},g)\), we showed the existence of global viscosity solutions to the eikonal equation

$$\begin{aligned} g(\nabla u,\nabla u)=-1 \end{aligned}$$

associated to those homologies in the interior of the stable time cone. Some other related dynamical properties are also considered. As an application of the main results, we study the differentiability of the unit sphere of the stable time separation associated to the class A Lorentzian 2-torus.

     

Robust Nonparametric Function Estimation for Errors-in-variables Models

This paper discusses robust nonparametric estimators of location regression function for errorsin-variables model with de-convolution kernel.The local constant smoother is used for the estimation of the nonparametric function,and the local linear smoother is proposed to deal with the boundary problem,as well as to improve the local constant smoother.We establish the asymptotic properties of the estimator,the influence function of the statistical functional and the breakdown point.A simulation study is carried out to demonstrate robust performance of the proposed estimator.The motorcycle data is presented to illustrate the application of the robust estimator further.     

A second-order space–time accurate scheme for nonlinear diffusion equation with general capacity term

A fully implicit finite difference (FIFD) scheme with second-order space–time accuracy is studied for a nonlinear diffusion equation with general capacity term. A new reasoning procedure is introduced to overcome difficulties caused by the nonlinearity of the capacity term and the diffusion operator in the theoretical analysis. The existence of the FIFD solution is investigated at first which plays an important role in the analysis. It is established by choosing a new test function to bound the solution and its temporal and spatial difference quotients in suitable norms in the fixed point arguments, which is different from the traditional way. Based on these bounds, other fundamental properties of the scheme are rigorously analyzed consequently. It shows that the scheme is uniquely solvable, unconditionally stable, and convergent with second-order space–time accuracy in L^∞(L²) and L^∞(H¹) norms. The theoretical analysis adapts to both one- and multidimensional problems, and can be extended to schemes with first-order time accuracy. Numerical tests are provided to verify the theoretical results and highlight the high accuracy of the second-order space–time accurate scheme. The reasoning techniques can be extended to a broad family of discrete schemes for nonlinear problems with capacity terms.     

离散分红下障碍期权的间接级数展开定价方法

人们投资股票市场的最大动力,除了从股票本身的升值中获利,还包括收益分红.提出了带有离散分红的障碍期权的一种新型的近似方法,以向上敲出看涨障碍期权为例,固定分红的次数,通过泰勒级数展开得到关于关键变量的仿射函数,给出了一个只带有一维积分的定价公式,提高了计算速度.该方法还可以用于回望期权等其它衍生品的定价,对在市场上进行期权交易有一定指导意义.     

Asymptotics of convolution with the semi-regular-variation tail and its application to risk

In this paper, according to a certain criterion, we divide the exponential distribution class into some subclasses. One of them is closely related to the regular-variation-tailed distribution class, and is called the semi-regular-variation-tailed distribution class. The new class possesses several nice properties, although distributions in it are not convolution equivalent. We give the precise tail asymptotic expression of convolutions of these distributions, and prove that the class is closed under convolution. In addition, we do not need to require the corresponding random variables to be identically distributed. Finally, we apply these results to a discrete time risk model with stochastic returns, and obtain the precise asymptotic estimation of the finite time ruin probability.     

Empirical likelihood for median regression model with designed censoring variables

We propose a new and simple estimating equation for the parameters in median regression models with designed censoring variables, and then apply the empirical log likelihood ratio statistic to construct confidence region for the parameters. The empirical log likelihood ratio statistic is shown to have a standard chi-square distribution, which makes this method easy to implement. At the same time, another empirical log likelihood ratio statistic is proposed based on an existing estimating equation and the limiting distribution of the empirical likelihood ratio statistic is shown to be a sum of weighted chi-square distributions. We compare the performance of the empirical likelihood confidence region based on the new estimating equation, with that based on the existing estimating equation and a normal approximation method by simulation studies.     

Silica-coated CdTe quantum dots functionalized with thiols for bioconjugation to IgG proteins

Quantum dots (QDs) have been increasingly used in biolabeling recently as their advantages over molecular fluorophores have become clear. For bioapplications QDs must be water-soluble and buffer stable, making their synthesis challenging and time-consuming. A simple aqueous synthesis of silica-capped, highly fluorescent CdTe quantum dots has been developed. CdTe QDs are advantageous as the emission can be tuned to the near-infrared where tissue absorption is at a minimum, while the silica shell can prevent the leakage of toxic Cd(2+) and provide a surface for easy conjugation to biomolecules such as proteins. The presence of a silica shell of 2-5 nm in thickness has been confirmed by transmission electron microscopy and atomic force microscopy measurements. Photoluminescence studies show that the silica shell results in greatly increased photostability in Tris-borate-ethylenediaminetetraacetate and phosphate-buffered saline buffers. To further improve their biocompatibility, the silica-capped QDs have been functionalized with poly(ethylene glycol) and thiol-terminated biolinkers. Through the use of these linkers, antibody proteins were successfully conjugated as confirmed by agarose gel electrophoresis. Streptavidin-maleimide and biotinylated polystyrene microbeads confirmed the bioactivity and conjugation specificity of the thiolated QDs. These functionalized, silica-capped QDs are ideal labels, easily synthesized, robust, safe, and readily conjugated to biomolecules while maintaining bioactivity. They are potentially useful for a number of applications in biolabeling and imaging.