A HIV Infection Model with Periodic Multidrug Therapy

This paper investigates the effects of periodic drug treatment on a HIV infection model with two co-circulation populations of target cells. We first introduce the basic reproduction ratio for the model, and then show that the infection free equilibrium is globally asymptotically stable if R0 < 1, while the infection persists and there exists at least one positive periodic state when R0 > 1. Therefore, R0 serves as a threshold parameter for the infection. We then consider an optimization problem by shifting the phase of drug efficacy functions, which corresponds to change the dosage time of drugs in each time interval. It turns out that shifting the phase affect critically on the stability of the infection free steady state. Finally, exhaustive numerical simulations are carried out to support our theoretical analysis and explore the optimal phase shift.     

Residue integrals and Waring’s formulas for algebraic or even transcendental systems

The present article is focused on the study of a special class of systems of non-linear transcendental equations for which classical algebraic and symbolic methods are inapplicable. For the purpose of study of such systems we develop a method for computing residue integrals with integration over certain cycles. We describe conditions under which the mentioned residue integrals coincide with power sums of the inverses to the roots of a system of equations (i.e. multidimensional Waring’s formulas). Based on this, we develop an algorithm that computes such power sums without computing the roots. As an application of the suggested method, we consider a problem of finding sums of multi-variable number series.     

An instrumentation system to measure the loads acting on the tractor PTO bearing during rotary tillage

Application of rotary tillage has been increased due to less tillage passes required, reduced draft, and greater efficiency through reduction in wheel slippage. Early failure of the bearing of tractor power take-off (PTO) shaft was observed in tractors of power range 30–35 horsepower during rotary tillage. An instrumentation setup involving an extended octagonal ring transducer (EORT) was developed and installed at the bottom of the bearing to measure the axial load and the vertical component of the radial load. The horizontal component of radial load was measured by strain gauges. Based on measured loads, the bearing life was assessed. Independent variables were: operating depth, number of blades, gear setting, engine speed, and tyre size. The average axial and radial loads varied from 786–3869 N, and 134–430 N, respectively. However, bearing experienced very high peak loads during each trial. The peak axial and radial loads was recorded between 1081–7534 N and 566–1794 N, respectively. The estimated bearing life based on peak loads was 171.98–28341.39 h. Based on the findings, it may be concluded that the average loads were not sufficient to cause quick failure of PTO bearing, rather sudden peak loads might be the root cause of early failure.     

Distributionally robust profit opportunities

This paper expands the notion of robust profit opportunities in financial markets to incorporate distributional ambiguity using Wasserstein distance as the ambiguity measure. Financial markets with risky and risk-free assets are considered. The infinite dimensional primal problems are formulated, leading to their simpler finite dimensional dual problems. A principal motivating question is how distributional ambiguity helps or hurts the robustness of the profit opportunity. Towards answering this question, some theory is developed and computational experiments are conducted. Finally some open questions and suggestions for future research are discussed.     

Hecke特征值相邻极大值的均值估计

取f为权为偶数k的全模群Γ=SL(2,Z)的Hecke特征型.定义λ_sym^mf(n)为与f关联的m阶对称幂次L-函数的Dirichlet展开式的第n个正规化系数.本文中,我们给出了∑_n≤x max{|λ_sym^mf(n)|^2β,|λ_sym^mf(n+h)|^2β}的上下界,其中h为一个固定的正整数,β> 0为一个正数.     

基于参数设计的信噪比交叉效率评价方法

针对DEA交叉效率评价过程中没有考虑自评与互评效率的作用而主观赋予相同权重导致交叉效率评价值不准确的问题.文章基于参数设计的思想,依据试验设计中可控与不可控因素的作用机理区分自评权重和互评权重对所评价决策单元交叉效率的影响与作用,将其界定为可控与不可控因素的管理学属性,明确不同权重作用机理;引入信噪比作为衡量决策单元交叉效率评价时的性能指标,实施DEA交叉效率评价方法的改进,设计出DEA信噪比交叉效率集结方法,从而实现交叉效率的集结方式由单一考虑交叉效率波动的均值转化为综合考虑交叉效率波动情况(均值与方差),交叉效率评价值用信噪比交叉效率替代交叉效率平均值更具有统计学意义并可从管理学角度解释,评价结果也具有更高的可区分性;最后通过算例分析验证了交叉效率评价理论上的必要性和该方法的合理性与可行性,同时发现了交叉效率评价中存在CCR有效DMU序位超出了有效DMU范围现象,建议应实施同质DMU检验和评价值归一化.文章的研究也为提高DEA交叉效率测算的准确性提供一种新思路.     

基于高斯分布的在线采购机制设计及竞争分析

依附于互联网电子商务的在线采购拍卖交易, 对传统的贝叶斯离线拍卖理论提出新的挑战, 因为面对不同时间点的投标, 采购电商必须即可决策出是否中标以及购买价格。鉴于此, 对于诸如石油、煤、粮食等无限可分商品的电子采购, 本文基于投标具有高斯分布特征设计了一种激励相容的在线采购策略, 演绎出在线采购的数学模型, 利用Runge-Kutta数值算法, 通过Matlab编程求解出采购电商在线定价策略的需求曲线及其对应的竞争比, 最后, 利用数值模拟, 将在线采购机制策略与纯竞争分析得到的在线采购策略比较, 结果显示利用了高斯分布信息的在线采购策略的竞争性能由于利用了投标的统计信息而得到了提高。     

基于权益再融资与策略性债务支付的公司财务困境纾解研究

为了应对公司财务困境问题,在兼顾股东与债权人利益的基础上,采用激励相容理论,构建了基于权益再融资和策略性债务支付的公司定价模型,厘清了权益再融资、债务重组、财务困境及其伴生的再谈判之间的关系,据此提出了一种公司财务困境纾解方案。特别地,给出了策略性债务支付下进行权益再融资的可行性依据,并辅以再谈判手段及股东、债权人双方利益最大化目标,确定了最优重组边界及最优减记息票。分析结果表明:①将策略性债务支付置于财务困境之后、兼容权益再融资的综合方案,可在一定程度上避免策略性债务支付行为的投机性所导致的对公司定价的高估,产生了在一定条件下增加债务价值、放缓信用价差增长速度的效果;②权益再融资成本与信用价差之间呈现倒U型关系;③基于纳什均衡博弈的策略性债务支付减记息票不受流动性及权益再融资的影响,并可保证其处于公司的支付能力之内。     

单机上带有可变前瞻区间的分批在线排序问题

本文研究单台无界平行批处理机上带有可变前瞻区间的在线排序问题。工件按时在线到达,目标是最小化时间表长。在时刻$t$,在线算法能够预见到$（t,t+\Delta（t）]$内到达工件的信息,这里前瞻区间的长度$\Delta（t）=\beta p_{\max}（t）$并非定长,其中$p_{\max}（t）$表示在$t$时刻及之前到达工件的最大加工时长,$\beta\in（0,1）$是常数。本文对于工件加工时长的一般情形,给出了当 0<β≤1/6 时最好可能的在线算法;对于工件加工时长被限制在一个区间的情形,给出了当 0<β<1 时最好可能的在线算法。     

基于激光诱导击穿光谱对长白山黑猪肉部位分类

猪肉内部结构成分复杂,各部位的成分相似,分辨较为困难。结合激光诱导击穿光谱技术,通过光谱分析的方式提高分类精度。以5种不同部位的长白山黑猪肉（里脊肉、梅花肉、后腿肉、前腿肉、五花肉）作为待测样品,通过冷藏、切片等预处理方法,探究激光诱导击穿光谱技术鉴别猪肉脂肪与肌肉及其不同部位的可行性。首先通过采集猪肉脂肪样品与肌肉样品的LIBS谱线信息发现,猪肉中Mg,K,Fe,Cu,Ca和Na等元素较为丰富,并在脂肪样品光谱中发现C-N键,与肌肉样品LIBS谱线信息相比,脂肪样品受其内部水分、有机质成分影响致使其谱线信息背景和噪声信号干扰较大,二者谱线信息存在一定差异,说明LIBS可对脂肪组织与肌肉组织进行鉴别。通过对目标元素Ca,Na,Mg,K和Al其LIBS特征谱线强度进行检测,计算Mg/Ca,Al/Ca,Na/Ca和K/Ca比值,发现与Al/Ca和Mg/Ca相比,Na/Ca和K/Ca各部位元素比值分布差异明显,在此基础上,根据Na/Ca和K/Ca比值,计算猪肉各部位元素分布决策阈值[（1-α）=90%]。发现与Al/Ca和Mg/Ca比值相比,Na/Ca和K/Ca更能明显的反应出各部位元素分布的不同。其比值分布阈值基本可对猪肉各部位进行区分。以前腿肉与后腿肉为例,前腿肉Na/Ca和K/Ca比值分别分布在1.29～1.58和0.31～0.42,后腿肉Na/Ca和K/Ca比值分别分布在0.98～1.18和0.15～0.23。其元素比值分布无明显重叠。最后,为提高LIBS技术对猪肉不同组织分类的可靠性,将光谱元素强度比值数据与主成分分析法相结合,基本可以实现对猪肉各部位的分类,说明元素特征谱线强度比值在对猪肉各部位分类时具有一定的预测精度。该工作证明,使用激光诱导击穿光谱技术对猪肉进行分类识别等定性分析时具有一定可行性,有望适用于其他生物组织检测分析。