On the expected discounted penalty function for risk process with tax

In this paper we consider the generalized Cramér-Lundberg risk model including tax payments. We investigate how tax payments affect the behavior of a Cramér-Lundberg surplus process by defining an expected discounted penalty function at ruin. We derive an explicit expression for this function by solving a differential equation. Consequently, the explicit formulas for the discounted probability density function of the surplus immediately before ruin and the discounted joint probability density function of the surplus immediately before ruin and the deficit at ruin are obtained. We also give explicit expressions for the function for exponential claims.     

Pathwise Estimation of Stochastic Differential Equations with Unbounded Delay and Its Application to Stochastic Pantograph Equations

The existence and uniqueness of the global solution of stochastic differential equations with discrete variable delay is investigated in this paper, and the pathwise estimation is also done by using Lyapunov function method and exponential martingale inequality. The results can be used not only in the case of bounded delay but also in the case of unbounded delay. As the applications, this paper considers the pathwise estimation of solutions of stochastic pantograph equations.     

The synthesis, structure, and electrochemical properties of a novel rods-shaped Li6V10O28 for lithium-ion batteries

Rods-shaped Li₆V₁₀O₂₈ powders were synthesized by rheological phase reaction. The ratio of the Li/V of the product sintered at 600 °C for 8 h was characterized by inductively coupled plasma. The structure, composite, and morphology of the product have been investigated by X-ray diffraction, scan electron microscope, transmission electron microscopy, and X-ray photoelectron spectrometry, respectively. After charge–discharge test using the product as the cathode material of lithium-ion batteries, the product calcined at 600 °C for 8 h exhibited an initial high discharge specific capacity of 212.4 mAh/g at a rate of 1.0 mA/cm² in a potential range of 2.0 and 4.4 V, and its stabilized capacity still remained 167.7 mAh/g after 30 cycles, which indicates that the rods-shaped Li₆V₁₀O₂₈ are promising cathode materials in lithium-ion batteries.     

胶体水相法制备高量子产率及高稳定性的水溶性ZnSe量子点

采用简便的胶体水相法制备了高荧光强度且稳定性良好的ZnSe量子点(ZnSe QDs),克服了以往水相合成法稳定性差、量子产率低等缺陷。优化后的最佳合成条件为:以还原型L-谷胱甘肽作为稳定剂,L-谷胱甘肽∶Se2-∶Zn2+摩尔比为5∶1∶5,介质pH 10.5,反应温度在90~100℃之间。且合成后不需要采取任何光照后处理,ZnSe QDs的量子产率(QYs)即可高达50.1%,放置3个月后荧光强度基本不变,水溶性优良。用紫外-可见分光光度法(UV-Vis)、荧光分光光度法(FL)、透射电子显微镜(TEM)等分析检测手段,对得到的ZnSe QDs的性能进行表征。合成的量子点在300 nm激发下发蓝紫色荧光(370 nm),其优良的光化学特性将有利于其在光热器件的制造及化学生物领域的应用。     

红外辐射在水雾中衰减计算的修正方法研究

水雾系统对红外光谱有着强烈的衰减作用,因此在军事目标的各种制导对抗中被予以高度的关注.以Mie散射理论为基础,分析了粒子对红外光潜前向散射的聚集特性,定义了近前向散射比,并确定了在应用朗伯比尔定律时需修正的粒子尺度和散射半角的范围.通过大量计算发现,单独将粒子尺度和散射半角的乘积作为独立变量计算的视消光系数不够精确.在中远红外波段,前向散射附近的小角度内散射强度积分与粒子尺度和散射角都成正比,若红外波长为定值,则与粒子半径成正比.最后根据前向散射规律给出了两个不单独以x·θ为变量的经验计算公式,使得对水雾消光的修正计算更加简便精确.     

Global decaying solution to dissipative nonlinear evolution equations with ellipticity

We establish the global existence and decaying results for the Cauchy problem of nonlinear evolution equations:

(E)     

A sufficient descent LS conjugate gradient method for unconstrained optimization problems

In this paper, we make a modification to the Liu-Storey (LS) conjugate gradient method and propose a descent LS method. The method can generate sufficient descent directions for the objective function. This property is independent of the line search used. We prove that the modified LS method is globally convergent with the strong Wolfe line search. The numerical results show that the proposed descent LS method is efficient for the unconstrained problems in the CUTEr library.     

Asymptotic behavior of the empirical conditional value-at-risk

We study asymptotic behavior of the empirical conditional value-at-risk (CVaR). In particular, the Berry–Essen bound, the law of iterated logarithm, the moderate deviation principle and the large deviation principle for the empirical CVaR are obtained. We also give some numerical examples.     

Riemann boundary value problems and reflection of shock for the Chaplygin gas

In this paper,we study two-dimensional Riemann boundary value problems of Euler system for the isentropic and irrotational Chaplygin gas with initial data being two constant states given in two sectors respectively,where one sector is a quadrant and the other one has an acute vertex angle.We prove that the Riemann boundary value problem admits a global self-similar solution,if either the initial states are close,or the smaller sector is also near a quadrant.Our result can be applied to solving the problem of shock reflection by a ramp.     

Cryopreservation of in vitro grown shoot tips of Diospyros kaki thunb. using different methods

The objective of this study was to compare the potential of different cryopreservation strategies for in vitro shoot tips of Diospyros kaki Thunb. The treatments consisted of three different cryopreservation methods: vitrification, droplet-vitrification and modified droplet-vitrification. The following variables were assessed: cold acclimation, sucrose concentration in the preculture medium and PVS2 treatment time. A higher average survival level was obtained using the modified droplet-vitrification method compared to the other two methods.