分数扩散模型的参数估计及其应用

研究分数扩散模型的参数估计及其应用问题.分数扩散模型是一类由分数Brownian运动驱动的随机微分方程.主要结果有:(1)利用二次变差方法给出模型中扩散系数的估计量,通过最小二乘法给出模型中漂移系数的估计量;(2)证明这些估计量的一致收敛性和渐近正态性;(3)利用MCMC方法对此估计量进行验证,并通过R软件将上述模型以及参数估计量应用到SHIBOR利率中进行实证研究.     

关于稳定矩阵分解定理的一个简单证明

一个矩阵称为稳定的,如果这个矩阵的特征值全包含在单位开圆盘内.利用Parker关于复方阵的分解定理给出了稳定矩阵分解定理的一个简单证明,并对奇异值全部严格小于1的矩阵给出了类似的结论.     

Estimates of densities for Lévy processes with lower intensity of large jumps

We obtain general lower estimates of transition densities of jump Lévy processes. We use them for processes with Lévy measures having bounded support, processes with exponentially decaying Lévy measures for large times and for processes with high intensity of small jumps for small times.     

Global stability of a multi‐group model with distributed delay and vaccination

A delayed multi‐group SVEIR epidemic model with vaccination and a general incidence function has been formulated and studied in this paper. Mathematical analysis shows that the basic reproduction number plays a key role in the dynamics of the model: the disease‐free equilibrium is globally asymptotically stable when , while the endemic equilibrium exists uniquely and is globally asymptotically stable when . For the proofs, we exploit a graph‐theoretical approach to the method of Lyapunov functionals. Our results show that distributed delay has no impact on the global stability of equilibria, and the results improve and generalize some known results. Copyright © 2016 John Wiley & Sons, Ltd.     

18O/16O-Encoding Strategy for Microscale Stereochemical Determination of Peptidic Natural Products

The demand for more efficient methods of establishing the undetermined stereochemistries of peptidic natural products continues unabated. A new method for microscale stereochemical determination was devised by integrating solid-phase synthesis, split-and-mix randomization, ¹⁸O/¹⁶O-encoding of d /l -configurations, tandem mass spectrometry, and biological evaluation. Here we applied gramicidin A as the molecule for a blind test. Gramicidin A and its 31 diastereomers were randomly prepared in microgram scale with ¹⁸O/¹⁶O-stereochemical encoding and subjected to MS/MS-structural determination and cytotoxicity assay. Only the parent gramicidin A was selected from among the 32 stereoisomers, validating the high reliability of the present strategy.     

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。     

Mean value formulas for classical solutions to uniformly parabolic equations in the divergence form with non-smooth coefficients

We prove surface and volume mean value formulas for classical solutions to uniformly parabolic equations in the divergence form with low regularity of the coefficients. We then use them to prove the parabolic strong maximum principle and the parabolic Harnack inequality. We emphasize that our results only rely on the classical theory, and our arguments follow the lines used in the original theory of harmonic functions. We provide two proofs relying on two different formulations of the divergence theorem, one stated for sets with almost C¹-boundary, the other stated for sets with finite perimeter.