Periodic Solutions of Third-order Differential Equations with Finite Delay in Vector-valued Functional Spaces

In this paper, we study the well-posedness of the third-order differential equation with finite delay(P_3): αu'"(t) + u"(t) = Au(t) + Bu'(t) + Fut +f(t)(t ∈ T := [0,2π]) with periodic boundary conditions u(0) = u(2π), u'(0) = u"(2π),u"(0)=u"(2π) in periodic Lebesgue-Bochner spaces Lp(T;X) and periodic Besov spaces B_(p,q)~s(T;X), where A and B are closed linear operators on a Banach space X satisfying D(A) ∩ D(B) ≠ {0}, α≠ 0 is a fixed constant and F is a bounded linear operator from Lp([-2π, 0]; X)(resp. Bp,qs([-2π, 0]; X)) into X, ut is given by ut(s) = u(t + s) when s ∈ [-2π,0]. Necessary and sufficient conditions for the Lp-well-posedness(resp. B_(p,q)~s-well-posedness)of(P_3) are given in the above two function spaces. We also give concrete examples that our abstract results may be applied.     

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.     

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.     

关于一类二阶微分方程的振动性的注记

考虑一类具连续分布滞量的二阶非线性泛函微分方程,获得了该方程的所有解振动的充分条件.     

变时滞Hopfield神经网络的全局吸引性和全局指数稳定性

对一类具时滞的Hopfeild型神经网络模型,在非线性神经元激励函数只要求满足Lipschitz连续的条件下,利用推广的Halanay时延微分析不等式、Dini导数以及泛函微分析技术,给出了这类模型的平衡点全局指数稳定性和全局吸引性的充分条件,这些条件易于检验,且改进和推广了前人的结论.此外,此文给出了研究神经网络模型的全局吸引性的微分不等式比较方法.     

修理设备可更换且修理有延迟的两不同型部件并联可修系统

假定部件的寿命服从指数分布,其修理延迟时间和修理时间均服从一般分布,并且修理设备的寿命服从指数分布,其更换时间服从一般分布,利用马尔可夫更新过程理论和一种新的分解方法,研究了修理设备可更换且修理有延迟的两不同型部件并联可修系统,求得了系统和修理设备有关可靠性指标的一系列结果.