时间延迟扩散-波动分数阶微分方程有限差分方法

本文提出求解时间延迟扩散-波动分数阶微分方程有限差分方法，方程中对时间的一阶导函数用α阶（0 < α < 1） Caputo分数阶导数代替.文章中利用Lubich线性多步法对分数阶微分进行差分离散，且文章利用分段区间证明该方法是稳定的，且利用数值实验加以验证.     

具有固定时滞的经济周期模型的动态分析

在经济活动中,投资行为和资本存量存在一定的时滞效应,这会影响经济周期模型的动态行为,进而使得投资政策对经济的稳定调整复杂化.考虑到资本存量的预期时间以及投资时滞对经济活动的影响,采用Hopf分岔理论,研究具有固定时滞的经济周期模型的均衡点的稳定性以及形成经济周期的条件.研究发现,投资过程中的投资时滞,以及投资决策中对于资本存量的预测时间构成经济周期产生的诱因;同时可通过政府投资政策调整达到预期均衡目标,这对保持经济周期稳定及经济政策制定有一定的指导作用.     

Stability and bifurcations analysis of a competition model with piecewise constant arguments

In this paper, we investigate local and global asymptotic stability of a positive equilibrium point of system of differential equations where t ≥ 0, the parameters r₁, k₁, α₁, α₂, r₂, k₂, and d₁ are positive, and [t] denotes the integer part of t ∈ [0, ∞ ). x(t) and y(t) represent population density for related species. Sufficient conditions are obtained for the local and global stability of the positive equilibrium point of the corresponding difference system. We show through numerical simulations that periodic solutions arise through Neimark–Sacker bifurcation. Copyright © 2014 John Wiley & Sons, Ltd.     

一类非线性时滞网络控制系统的无源性分析

本文研究了一类非线性时滞网络控制系统的无源性问题.利用Lyapunov稳定性理论,结合线性矩阵不等式(LMI)技术,通过构造Lyapunov-Krasovskii泛函,在考虑两种不同时滞的情况下,获得了系统满足无源性的充分条件,最后通过仿真算例验证了结论的正确性和方法的有效性.     

Spectrochemical analysis using LIBS and ICP-OES techniques of herbal medicine (Tinnevelly Senna leaves) and its anti-cancerous/antibacterial applications

Tinnevelly senna leaves are being applied to cure many diseases especially in developing countries and sub-Saharan region due to many bioactive compounds such as sennosides, phenols, and flavonoids. The conventional methods to isolate and analyze plant extracts biomolecules are not very effective as well cost effective as they require hazardous chemical solvents and reagents, which are time-consuming processes. The major objective of the present study is to investigate the feasibility of the Laser induced breakdown spectroscopy (LIBS) technique for rapid, eco-friendly, and multi-elemental analysis of Senna leaves extracts and study their antibacterial and anticancer potentials. The elegant LIBS technique was applied as a qualitative and quantitative method for Senna leaves sample’s elemental analysis and their biological activities were measured by evaluating anti-cancer and anti-bacterial analysis. The quantitative analysis of Senna leaves extracts was done using the calibration-free laser-induced breakdown spectroscopy (CF-LIBS) algorithm showing their appreciable content of several nutrient elements, and the obtained results were in close conformity with these achieved by using the standard analytical ICP OES technique. We studied the bactericidal efficacy of the Senna leaves extract against Staphylococcus aureus (S. aureus) by AWD assays and morphogenesis by scanning electron microscopy (SEM) and the anticancer activity was also investigated where different concentrations of Senna leaves extract were tested on cancer cells (HCT-116 and HeLa) and normal cells (HEK-293) using the cell metabolic activity MTT assay and Propidium iodide (PI) staining. We have also calculated the inhibitory concentration (IC50) value for the various extracts concentrations (25 µg/ml, 50 µg/ml, 100 µg/ml, 150 µg/ml, 200 µg/ml, and 225 µg/ml). We have found that IC₅₀ value for HCT-116 cells were 13.5 µg/ml, 17.5 µg/ml, 21.5 µg/ml, 22.5 µg/ml, 26 µg/ml and 33.5 µg/ml and for HeLa cells 15.25 µg/ml, 21.25 µg/ml, 23.5 µg/ml, 262.5 µg/ml, 36.25 µg/ml, and 39.50 µg/ml. The bactericidal efficacy of the Senna leaves extract showed significant inhibition against Gram-positive bacterium. Both MTT and PI analysis showed that Senna leaves extract induced profound inhibition on HCT-116 growth and proliferation. Additionally, Senna leaves extract did not exert an inhibitory influence on normal (HEK-293), which is non-cancerous cells. We suggest that the extract specifically targets the cancerous cells, which could be highly beneficial for the development of future safe anticancer and antibacterial drugs using these extracts.     

Functional Differential Equations With Delay and Random Effects

The authors study the existence of mild solutions to a functional differential equation with delay and random effects. They use a random fixed point theorem with a stochastic domain. An example is included to illustrate their results.     

8×8APD阵列激光三维成像接收机研制

为了实现对目标的无扫描阵列激光三维成像并研究系统参数对三维成像距离分辨率的影响,研制了8×8 pixel激光三维成像接收机。接收机采用线性模式APD阵列,设计了模拟信号放大、阈值处理将回波光信号转换为数字信号后,利用FPGA设计实现64通道高精度阵列计时系统,实现了对目标的无扫描实时三维成像功能。首先对设计完成的三维成像接收机组成及成像原理进行了介绍,对三维成像接收机中APD探测器阵列信号的模拟处理和数字处理流程和实现方式进行了说明。随后分别对三维成像的核心FPGA计时系统及探测器整体进行了电子学测试和实验测试。测试结果表明,FPGA计时子系统的时间分辨率优于140 ps,三维成像系统整体距离分辨率在0.2 m左右。最后对分辨率的误差进行了分析,结果表明,激光回波强度波动是影响此接收机距离分辨率的最主要因素。     

生物柴油替代混合物化学动力学模型构建及路径分析

以癸酸甲酯(C₁₁H₂₂O₂)和正庚烷(nC₇H₁₆)作为生物柴油替代混合物,通过相对分子质量、低热值以及含氧量与实际生物柴油对比确定两种组分按摩尔比1：1混合,并在此基础上构建了一个由691种组分、3226个基元反应组成的生物柴油替代混合物的化学动力学机理. 在激波管条件下该机理计算的着火延迟与实验数据吻合很好;在发动机条件下该机理计算的缸内压力与实验值吻合很好,CO、未燃碳氢和NOx与实验结果趋势一致.此外,本文还对替代混合物的低温反应动力学过程进行了分析,结果表明癸酸甲酯脱氢产物主要为MD2J和MDMJ. MD2J在低温阶段的主要消耗途径除了加氧之外,还有与正庚烷基(C₇H₁₅-1)第一次加氧产物(C₇H₁₅O₂-3)进行交叉反应;发生分解反应生成MP2D及与氧发生脱氢反应生成MD2D. 另一种主要脱氢产物MDMJ在低温阶段的主要消耗途径为通过同分异构转化为MD2J和MD3J.     

时滞效应对弹性地基上梁主共振响应影响分析

本文研究了弹性地基上梁主共振响应的时滞效应．基于Hamilton原理,建立了时滞影响下弹性地基上梁的非线性运动微分方程,采用多尺度法,求得了时滞效应下主共振响应调制方程以及稳定性条件．通过数值算例,分析了时滞和调谐参数影响下主共振响应的峰值及幅频响应特性．结果表明,地基反力中的时滞效应对主共振响应影响较大,会导致共振域偏移,在一定区间内,响应幅值随时滞变化先减小再增大,呈现出周期性,并导致幅频曲线弯曲程度增大．     

An improved robust delay-dependent stability criterion for genetic regulatory networks with interval time delays

This paper proposes an improved robust delay-dependent criterion for stability of genetic regulatory networks with delays which vary in an interval. A modified Lyapunov-Krasovskii functional is used to derive a sufficient condition in terms of linear matrix inequalities (LMIs) which can be easily solved by various convex optimization algorithms. The derived stability criterion is less conservative than ones in the literature. A numerical example and simulation results show the effectiveness of the proposed method.