Inelastic mean free path of low‐energy electrons in condensed media: beyond the standard models

The most established approach for ‘practical’ calculations of the inelastic mean free path (IMFP) of low‐energy electrons (~10 eV to ~10 keV) is based on optical‐data models of the dielectric function. Despite nearly four decades of efforts, the IMFP of low‐energy electrons is often not known with the desired accuracy. A universal conclusion is that the predictions of the most popular models are in rather fair agreement above a few hundred electron volts but exhibit considerable differences at lower energies. However, this is the energy range where their two main approximations, namely, the random‐phase approximation (RPA) and the Born approximation, may be invalid. After a short overview of the most popular optical‐data models, we present an approach to include exchange and correlation (XC) effects in IMFP calculations, thus going beyond the RPA and Born approximation. The key element is the so‐called many‐body local‐field correction (LFC). XC effects among the screening electrons are included using a time‐dependent local‐density approximation for the LFC. Additional XC effects related to the incident and struck electrons are included through the vertex correction calculated using a screened‐Hubbard formula for the LFC. The results presented for liquid water reveal that XC may increase the IMFP by 15–45% from its Born–RPA value, yielding much better agreement with available experimental data. The present work provides a manageable, yet rigorous, approach to improve upon the standard models for IMFP calculations, through the inclusion of XC effects at both the level of screening and the level of interaction. Copyright © 2015 John Wiley & Sons, Ltd.     

Inelastic scattering and energy loss of swift electron beams in biologically relevant materials

The inelastic mean free path and the stopping power of swift electrons in relevant biomaterials, such as liquid water, DNA, protein, lipid, carotene, sugar, and ice are calculated in the framework of the dielectric formalism. The Mermin Energy Loss Function – Generalized Oscillator Strength model is used to determine the energy loss function of these materials for arbitrary energy and momentum transfer using electron energy‐loss spectroscopy data as input. To ensure the consistency of the model, efforts are made so that both the Kramers–Kronig and f‐sum rules are fulfilled to better than 2%. Our findings indicate sizeable differences in the inelastic mean free path and stopping power among these biomaterials for low‐energy electrons. For example, at 100‐eV electron energy, the inelastic mean free path in protein is 25% smaller than for water and around 10% smaller than for the other biomaterials. The stopping power values of protein, DNA, and sugar are rather similar but 20% larger than for water. Taking into account these results, we conclude that electron interactions with living tissues at the nanometric scale cannot be reliably described using only liquid water as the surrogate of the biological target. Copyright © 2016 John Wiley & Sons, Ltd.     

Mean‐square stability of the backward Euler–Maruyama method for neutral stochastic delay differential equations with jumps

This paper is mainly considered whether the mean‐square stability of neutral stochastic delay differential equations (NSDDEs) with jumps is shared with that of the backward Euler–Maruyama method. Under the one‐sided Lipschitz condition and the linear growth condition, the trivial solution of NSDDEs with jumps is proved to be mean‐square stable by using the functional comparison principle and the Barbalat's lemma. It is shown that the backward Euler–Maruyama method can reproduce the mean‐square stability of the trivial solution under the same conditions. The implicit backward Euler–Maruyama method shows better characteristic than the explicit Euler–Maruyama method for the reason that it works without the linear growth condition on the drift coefficient. Compared with some existing results, our results do not need to add extra condition on the neutral part. The conclusions can be applied to NSDDEs and SDDEs with jumps. The effectiveness of the theoretical results is illustrated by an example. Copyright © 2016 John Wiley & Sons, Ltd.     

左截断右删失数据分位差估计及其渐近性质

我们研究了左截断右删失数据分位差,基于左截断右删失数据乘积限构造了分位差的经验估计,同时克服经验估计的非光滑性,提出了分位数差的核光滑估计.利用经验过程理论推导出这两个估计的渐近偏差和渐近方差,并且在左截断右删失数据下研究了这两个分位差的大样本性质,获得分位差估计的相合性和渐近正态性.同时给出计算模拟以验证光滑分位差估计的表现,在均方损失的意义下模拟结果表明光滑估计比经验估计具有更好的性质.     

关于Van Der Corput不等式双参数推广的改进

梳理了有关Van Der Corput不等式的研究成果与方法,并对Van Der Corput不等式的双参数推广作了进一步改进,建立了更强的推广式,它优于现有的相关结论.     

Random points in halfspheres

A random spherical polytope P_n in a spherically convex set as considered here is the spherical convex hull of n independent, uniformly distributed random points in K. The behaviour of P_n for a spherically convex set K contained in an open halfsphere is quite similar to that of a similarly generated random convex polytope in a Euclidean space, but the case when K is a halfsphere is different. This is what we investigate here, establishing the asymptotic behaviour, as n tends to infinity, of the expectation of several characteristics of P_n, such as facet and vertex number, volume and surface area. For the Hausdorff distance from the halfsphere, we obtain also some almost sure asymptotic estimates. © 2016 Wiley Periodicals, Inc. Random Struct. Alg., 50, 3–22, 2017     

A strategy based on mean reverting property of markets and applications to foreign exchange trading with trailing stops

We propose a strategy for automated trading, outline theoretical justification of the profitability of this strategy, and overview the backtesting results in application to foreign currencies trading. The proposed methodology relies on the assumption that processes reflecting the dynamics of currency exchange rates are in a certain sense similar to the class of Ornstein–Uhlenbeck processes and exhibit the mean reverting property. In order to describe the quantitative characteristics of the projected return of the strategy, we derive the explicit expression for the running maximum of the Ornstein–Uhlenbeck process stopped at maximum drawdown and look at the correspondence between derived characteristics and the observed ones. Copyright © 2017 John Wiley & Sons, Ltd.     

Mean inequalities in certain Banach function spaces

Boundedness of the Hardy operator and its adjoint is characterized between Banach function spaces Xq and Lp. By applying a limiting procedure, corresponding boundedness of the geometric mean operator is also derived.     

一个包含Smarandache函数的复合函数

对任意正整数n,著名的Smarandache函数S(n)定义为最小的正整数m使得n|m!,或者S(n)=min{m∶n|m!,m∈N}.而函数Z(n)定义为最小的正整数k使得n≤k(k 1)/2,即就是Z(n)=min{k:n≤k(k 1)/2}.本文的主要目的是利用初等及解析方法研究复合函数S(Z(n))的均值,并给出一个较强的渐近公式.     

一个新的算术函数及其均值

对任意正整数n,我们定义算术函数(Ω)(n)为(Ω)(1)=0,当n＞1,且n=pα11·pα22…pαkk为n的标准分解式时,定义(Ω)(n)=α1p1 α2p2 … αkpk.显然这个函数是可加函数.即就是对任意正整数m及n有(Ω)(m·n)=(Ω)(m) (Ω)(n).本文主要目的是利用初等方法研究函数(Ω)(n)的算术性质,并给出一个较强的均值公式及有趣的恒等式.