Global dynamics for an age-structured epidemic model with media impact and incomplete vaccination

Some studies show that the efficacy of vaccines may decline and the vaccine-induced immunity wanes with time elapsed since vaccination (e.g., BCG, HBV vaccines). Meanwhile, the use of media can effectively contain the emerging epidemics. In our work, an SVEIR epidemic model with media impact, age-dependent vaccination and latency is proposed, where the efficacy of vaccines depends on the time since vaccination. Uniform persistence and the sharp threshold dynamics are established, that is, the vaccination reproduction number completely determines the global dynamics of the model system. Our main results established can be extended to the SVEIR model with the general nonlinear infectious force function of monotonicity and concavity.     

Optimal martingale measures for defaultable assets

We model a defaultable asset as solution to a stochastic differential equation driven by both a Brownian motion and the counting process martingale associated to the one-jump process. We discuss in this framework the minimal entropy martingale measure as well as the linear Esscher and the minimal martingale measure. In particular we deal with some rather delicate verification issues.     

Resolvable group divisible designs with block size four and index three

In this paper, we investigate the existence of resolvable group divisible designs (RGDDs) with block size four, group-type hⁿ and index three. The necessary conditions for the existence of such a design are n?4 and hn≡0. These necessary conditions are shown to be sufficient except for (h,n)∈{(2,4),(2,6)} and possibly excepting (h,n)=(2,54).     

Preference programming for robust portfolio modeling and project selection

In decision analysis, difficulties of obtaining complete information about model parameters make it advisable to seek robust solutions that perform reasonably well across the full range of feasible parameter values. In this paper, we develop the Robust Portfolio Modeling (RPM) methodology which extends Preference Programming methods into portfolio problems where a subset of project proposals are funded in view of multiple evaluation criteria. We also develop an algorithm for computing all non-dominated portfolios, subject to incomplete information about criterion weights and project-specific performance levels. Based on these portfolios, we propose a project-level index to convey (i) which projects are robust choices (in the sense that they would be recommended even if further information were to be obtained) and (ii) how continued activities in preference elicitation should be focused. The RPM methodology is illustrated with an application using real data on road pavement projects.     

American Options Exercise Boundary When the Volatility Changes Randomly

The American put option exercise boundary has been studied extensively as a function of time and the underlying asset price. In this paper we analyze its dependence on the volatility, since the Black and Scholes model is used in practice via the (varying) implied volatility parameter. We consider a stochastic volatility model for the underlying asset price. We provide an extension of the regularity results of the American put option price function and we prove that the optimal exercise boundary is a decreasing function of the current volatility process realization. Accepted 13 January 1998     

基于顺序注射分析的海水亚硝酸盐快速检测方法研究

为实现海水亚硝酸盐的快速检测,使测量过程更适用于在线监测,对前期已有的顺序注射分析技术进行了优化,结合自主研制的Z型高灵敏度液芯波导样品池和多适应环管器,基于分光光度检测方法,在不完全显色反应的基础上,建立了一种海水亚硝酸盐快速全自动检测方法。进样技术中高精度注射泵与多通道选择阀配合,顺序吸入样品和试剂至储液盘管后,再反推至混合盘管,期间发生不完全显色反应,并最终由注射泵将显色混合溶液缓推过Z型液芯波导样品池,同步流动检测溶液吸光度变化,结合朗伯比尔定律最终获取待测亚硝酸盐溶液浓度。为达到稳定且快速分析的目的,分析了测量方法中几个关键参数,如不完全显色反应时间、检测时流速和盐度对测量结果的影响,寻求最佳的技术及参数组合。不完全显色反应研究结果表明,在10~60 s显色时间范围内,吸光度检测结果的相对标准误差（RSD）均不超过1.64%,说明10~60 s的显色时间对本方法无影响,因此选择10s作为快速检测方法的显色反应时间。通过对不同流速情况下样品检测结果的分析发现,流速过快会导致检测不稳定,过慢则不利于快速分析,选择吸光度测量较为稳定的10,11.6,13和15 μL·s-1四个流速,对测量结果的稳定性和重复性进行分析,结果表明,上述四个流速下的线性效果都很好,因此,选择最快的15 μL·s-1作为该方法的检测流速。为验证该方法对盐度的敏感性,以适应淡水和大范围海水为出发点,研究分析了0~35盐度范围内,三种不同浓度（150,250,350 μg·L-1）亚硝酸盐溶液的吸光度变化情况,得到的RSD分别为1.39%,2.03%和1.28%,证明盐度对本方法的吸光度测量基本无影响。对80,150和250 μg·L-1亚硝酸盐标准溶液平行测定11次得到的RSD分别为2.13%,1.07%和1.83%,说明本方法精密度较好。通过对空白样品进行10次平行样测量,计算得到本方法检出限为37 μg·L-1（约0.5 μmol·L-1）。为验证本方法的可信度,利用该快速检测方法和《海洋调查规范》标准测量方法对同一批次亚硝酸盐标准溶液制作标准曲线,二者的R2均大于0.999,对同一浓度样品两种方法得到的测量结果数据拟合线性回归方程为y=1.046 1x-0.005 7,R2=0.999 6,说明两种检测方法结果高度一致,更进一步验证了该研究快速测量方法的可行性和可靠性。亚硝酸盐快速检测方法测样速率高达50样·h-1,与传统的人工检测和流动注射分析方法相比,亚硝酸盐的测量耗时从十几分钟缩短到1 min左右,检测分析过程中样品和试剂消耗量极少,测量过程重复性好,整个测量过程全自动进行,操作更为简单智能,避免了人工介入带来的误差,使得基于分光光度的营养盐要素在线及原位检测系统更加小巧、快速和低耗,更适用于现场在线及长时间序列监测,具有很广的应用范围和较好的应用前景。     

The effect of initial spatial correlations on late time kinetics of bimolecular irreversible reactions

We study anomalous kinetics associated with incomplete mixing for a bimolecular irreversible kinetic reaction where the underlying transport of reactants is governed by a fractional dispersion equation. As has been previously shown, we demonstrate that at late times incomplete mixing effects dominate and the decay of reactants follows a fundamentally different scaling comparing to the idealized well mixed case. We do so in a fully analytical manner using moment equations. In particular the novel aspect of this work is that we focus on the role that the initial correlation structure of the distribution of reactants plays on the late time scalings. We focus on short range and long (power law) range correlations and demonstrate how long range correlations can give rise to different late time scalings than one would expect purely from the underlying transport model. For the short range correlations the late time scalings deviate from the well mixed t⁻¹$t^{-1}$ and scale like t^−1/2α$t^{-1/2\alpha }$, where 1<α≤2$1<\alpha \le 2$ is the fractional dispersion exponent, in agreement with previous studies. For the long range correlation case it scales like t^−β/2α$t^{-\beta /2\alpha }$, where 0<β<1$0<\beta <1$ is the power law correlation exponent.     

海水硝酸盐/亚硝酸盐原位快速测量仪

基于SIA顺序注射法以及分光光度原理研制了海水硝酸盐/亚硝酸盐原位快速测量仪。对最佳不完全显色反应时间以及硝酸盐镉铜柱还原速度进行了实验优化筛选,采用液芯波导替代比色皿作为样品池,在实现原位快速测量(测量时间可短至4 min)的同时也大大减少了样品量,缩小了仪器体积、 重量,降低了仪器功耗,提高其灵敏度(nmol·L-1),使其更适于原位测量。仪器具有良好的通用性和可扩展性,稍作调整,即可用于不同海域各种营养要素的剖面及定点测量。     

基于小波多通道特征级融合的彩色纹理图像分析

在不完全树型小波分解基础上将纹理和颜色特征进行融合,提出了适合彩色纹理图像分析的新的特征,它比单纯的灰度纹理特征或颜色特征具有更强的分类能力.同时还利用20类真实彩色自然纹理图像对塔式小波分解、不完全树型小波分解和小波包分解进行了多特征融合的分类比较,实验结果表明:不完全树型小波分解的特征级融合表现出良好的分类性能和抗噪能力.     

Precise and fast computation of a general incomplete elliptic integral of second kind by half and double argument transformations

We developed a method to compute simultaneously two associate incomplete elliptic integrals of the second kind, B(φ|m) and D(φ|m), by the half argument formulas of Jacobian elliptic functions and the double argument transformations of the integrals. The relative errors of the new method are sufficiently small as 5-10 machine epsilons. Meanwhile, the new method runs 3-6 times faster than that using Carlson’s R_D. As a result, it enables a precise and fast computation of arbitrary linear combination of the incomplete elliptic integrals of the first and the second kind, F(φ|m) and E(φ|m).