Limit theorems for random walks

We consider a random walk $S_{\tau }$ which is obtained from the simple random walk $S$ by a discrete time version of Bochner’s subordination. We prove that under certain conditions on the subordinator $\tau$ appropriately scaled random walk $S_{\tau }$ converges in the Skorohod space to the symmetric $\alpha$-stable process $B^{\alpha }$. We also prove asymptotic formula for the transition function of $S_{\tau }$ similar to the Pólya’s asymptotic formula for $B^{\alpha }$.     

基于在线HHT和SVM的汽油机轻微漏气故障识别方法

针对汽油机轻微漏气故障会被闭环反馈控制所掩盖,提出了一种基于在线希尔伯特变换(Hilbert-Huang Transform,HHT)和支持向量机(Support vector machine,SVM)的两阶段微小故障识别方法(Online HHT-SVM,OHS).第一阶段在嵌入式两滑动时间窗内通过HHT对发动机空燃比数据流进行在线时频分析,以实时获取空燃比发生异常的时刻;第二阶段通过SVM对异常时刻的数据流故障模式进行离线识别.根据氧传感器信号特征,对经验模态分解(Empirical mode decomposition,EMD)算法进行了改进,并从理论上进行了证明.基于两款发动机的实际运行数据验证了该方法的有效性.     

具有缺失数据的Eichhorn模型

为了解决在Eichhorn乘法扰动模型中存在的项目无回答问题,对敏感变量总体均值在辅助变量总体均值已知与未知条件下提出了比率插补方法.理论比较和数值模拟得出的结果表明提出的插补方法比传统的方法效率更高.     

Indefinite integrals involving complete elliptic integrals of the third kind

A method developed recently for obtaining indefinite integrals of functions obeying inhomogeneous second-order linear differential equations has been applied to obtain integrals with respect to the modulus of the complete elliptic integral of the third kind. A formula is derived which gives an integral involving the complete integral of the third kind for every known integral for the complete elliptic integral of the second kind. The formula requires only differentiation and can therefore be applied for any such integral, and it is applied here to almost all such integrals given in the literature. Some additional integrals are derived using the recurrence relations for the complete elliptic integrals. This gives a total of 27 integrals for the complete integral of the third kind, including the single integral given in the literature. Some typographical errors in a previous related paper are corrected.     

Sharper asset ranking from total drawdown durations

The total duration of drawdowns is shown to provide a moment-free, unbiased, efficient and robust estimator of Sharpe ratios both for Gaussian and heavy-tailed price returns. We then use this quantity to infer an analytic expression of the bias of moment-based Sharpe ratio estimators as a function of the return distribution tail exponent. The heterogeneity of tail exponents at any given time among assets implies that our new method yields significantly different asset rankings than those of moment-based methods, especially in periods large volatility. This is fully confirmed by using 20 years of historical data on 3449 liquid US equities.     

New upper bounds for online strip packing

In this paper, we consider the online strip packing problem, in which a list of online rectangles has to be packed without overlap or rotation into one or more strips of width 1 and infinite height so as to minimize the required height of the packing. By analyzing a two-phase shelf algorithm, we derive a new upper bound 6.4786 on the competitive ratio for online one strip packing. This result improves the best known upper bound of 6.6623. We also extend this algorithm to online multiple strips packing and present some numeric upper bounds on their competitive ratios which are better than the previous bounds.     

Insights into stretching ratio and velocity slip on MHD rotating flow of Maxwell nanofluid over a stretching sheet: Semi-analytical technique OHAM

Main core part of the research is to develop a novel mathematical model of MHD-Maxwell nanofluid over a stretching and shrinking surface. The stretching ratio, velocity slip and convective boundary conditions are also incorporated. The PDE's with associative boundary conditions are deduced into coupled highly non-linear ODE's by utilizing suitable transformations. The deduced dimensionless sets of Ordinary differential equations are solved by Optimal-Homotopy Analysis Method (OHAM). Behavior of pertinent parameters on the velocity, temperature and concentration fields as well as important aspects skin friction, Nusselt number and Sherwood number are recorded in Table 2. Outcomes declared that role of stretching ratio plays a prominent role in stretching surfaces its clearly recorded in Table 1(a & b).     

MPKin-YSTR: Interpretation of Y chromosome STR haplotypes for missing persons cases

Y chromosome Short Tandem Repeat (STR) haplotypes have been used in assisting forensic investigations primarily for identification and male lineage determination. The current SWGDAM interpretation guidelines for Y-STR typing provide helpful guidance on those purposes but do not address the issue of kinship analysis with Y-STR haplotypes. Because of the high mutation rate of Y-STRs, there are complex missing person cases in which inconsistent Y-STR haplotypes between true paternal lineage relatives will arise and cases with two or more male references in the same lineage and yet differ in their haplotypes. Therefore, more useful methods are needed for interpreting the Y-STR haplotype data. Computational methods and interpretation guidelines have been developed specifically addressing this issue, either using a mismatch-based counting method or a pedigree likelihood ratio method. In this study, a software program, MPKin-YSTR, was developed by implementing those more sophisticated methods. This software should be able to improve the interpretation of complex cases with Y-STR haplotype evidence. Thus, more biological evidence will be interpreted, which in turn will result in more investigation leads to help solve crimes.     

常见炸药的稳定同位素比值分析方法研究进展

炸药的深度比对与溯源对于爆炸案事件的侦破具有重大意义,以不同地域来源的原料或不同生产工艺生产的炸药,其组成元素的稳定同位素比值具有差异,因而稳定同位素比值可作为炸药深度比对与溯源的重要指标。稳定同位素比值质谱法(IRMS)作为一种高精度的稳定同位素比值测量手段,已逐渐发展成熟,与元素分析仪、气相色谱仪、液相色谱仪等仪器联用,在食品安全、环境保护、法庭科学等领域应用广泛。IRMS在炸药比对与溯源上亦发挥了重要作用,自1975年IRMS被应用于区分不同国家生产的三硝基甲苯(TNT)以来,IRMS已成功用于多种炸药的分析。但目前尚未见有文献系统地总结常见炸药的稳定同位素比值分析研究进展。该文介绍了稳定同位素比值分析的相关原理、仪器组成及特点,分别总结了硝酸铵、黑火药、TNT、太恩、黑索金等常见炸药的稳定同位素比值分析方法,汇总了文献报道的不同国家生产的硝酸铵、黑火药、TNT等炸药的稳定同位素比值。文章就不同炸药的稳定同位素比值差异、炸药生产、存储过程中相关因素对同位素比值的影响,爆炸前后稳定同位素比值的变化情况等内容进行了分析。本文还指出了目前炸药的稳定同位素比值分析研究中存在的问题,对可能的解决办法进行了讨论,对未来的发展方向提出了建议。     

一种检测CO32-比率荧光探针的合成及其在细胞成像中的应用

本文设计开发了一种以2,6-二甲酰基对甲苯酚为母体的新型荧光探针HMI,可用于高效识别EtOH-H₂O (8/2, v/v, HEPES 10 mM, pH =7.4)体系中的CO_3^2-。HMI在660 nm处显示发射带,加入CO_3^2-后,在600 nm的等吸收点激发时,原来在660 nm处的荧光淬灭,而以540 nm为中心的新发射带荧光显着增加,为比率型荧光探针。HMI对CO_3^2-表现出高选择性且具有较强的抗干扰能力。此外,荧光探针HMI对CO_3^2-荧光响应的检测限较低,可达到3.938×10^_-6 M。更具有意义的是,HMI探针对CO_3^2-的检测能够在实际水样中起到很好的应用,而且细胞成像研究表明,HMI可用于活体MCF-7细胞中CO_3^2-的成像。