On the Artificial Equilibrium Points in a Generalized Restricted Problem of Three Bodies

The present article studies the stability conditions of central control artificial equilibrium generalized restricted problem of three bodies. It is generalized in the sense that here we have taken the larger primary body to be in shape of an oblate spheroid. The equilibrium points are sought by the application of the propellant for which it would just balance the gravitational forces. The launching flight of such a satellite is seen to be applicable for having arbitrary space stations for these different missions. Specialty of the result of the investigation lies in the fact that an arbitrary space station can be formed to attain any specified mission.

Strong Convergence of a General Iterative Algorithm for Mixed Equilibrium, Variational Inequality and Common Fixed Points Problems

The aim of this paper, is to introduce and study a general iterative algorithm concerning the new mappings which the sequences generated by our proposed scheme converge strongly to a common element of the set of solutions of a mixed equilibrium problem, the set of common fixed points of a finite family of nonexpansive mappings and the set of solutions of the variational inequality for a relaxed cocoercive mapping in a real Hilbert space. In addition, we obtain some applications by using this result. The results obtained in this paper generalize and refine some known results in the current literature.

Existence of Equilibrium Points in the R3BP with Variable Mass When the Smaller Primary is an Oblate Spheroid

The paper deals with the existence of equilibrium points in the restricted three-body problem when the smaller primary is an oblate spheroid and the infinitesimal body is of variable mass. Following the method of small parameters;the co-ordinates of collinear equilibrium points have been calculated, whereas the co-ordinates of triangular equilibrium points are established by classical method. On studying the surface of zero-velocity curves, it is found that the mass reduction factor has very minor effect on the location of the equilibrium points;whereas the oblateness parameter of the smaller primary has a significant role on the existence of equilibrium points.

Existence of Multiple Equilibrium Points in Global Attractor for the Strongly Damped Wave Equations

The aim of this paper is to study the long-term behavior of strongly damped wave equations with a Lyapunov function. Using the theory established by estimating the Z2 index of some sets and the idea of invariant sets of semi-flow,the properties of the global attractor for strongly damped wave equation are discussed. The existence of multiple equilibrium points in global attractor for strongly damped wave equations with critical growth of nonlinearity is obtained. And under some additional condition, the infinite dimension of the attractor is proven.

Artificial Equilibrium Points in the Low-Thrust Restricted Three-Body Problem When Both the Primaries Are Oblate Spheroids

This paper studies the existence and stability of the artificial equilibrium points (AEPs) in the low-thrust restricted three-body problem when both the primaries are oblate spheroids. The artificial equilibrium points (AEPs) are generated by canceling the gravitational and centrifugal forces with continuous low-thrust at a non-equilibrium point. Some graphical investigations are shown for the effects of the relative parameters which characterized the locations of the AEPs. Also, the numerical values of AEPs have been calculated. The positions of these AEPs will depend not only also on magnitude and directions of low-thrust acceleration. The linear stability of the AEPs has been investigated. We have determined the stability regions in the xy, xz and yz-planes and studied the effect of oblateness parameters A1(0A1?and ?A2(0A2<1) on the motion of the spacecraft. We have found that the stability regions reduce around both the primaries for the increasing values of oblateness of the primaries. Finally, we have plotted the zero velocity curves to determine the possible regions of motion of the spacecraft.

LiDAR点云结合EPS在1:10000 DLG要素更新中的应用

分析了常规手段更新1:10000 DLG要素的缺点与不足,在卫片更新的基础上,利用LiDAR点云分类后生成的DEM数据得到高程成果。并以最新的、分辨率优于1 m的卫星遥感影像为参照影像,叠加本底数据,利用各类专题资料,对相对应的专题数据进行更新。同时发现并标识变化区域:在地形未变化区域,通过参照影像,进行更新;在地形变化区域,通过无人机倾斜摄影建立立体模型,在EPS中通过立体测图得到平高成果。通过融合高程成果、平高成果、本底数据,完成1:10000 DLG要素更新。

一类含常数项的混沌系统在未知参数下的同步

研究了一个新的含有常数项的混沌系统在参数未知情况下的修正函数投影同步问题。对新的含有常数项的混沌系统从平衡点的稳定性、耗散性、poincare映射、功率谱及初值敏感性5个方面进行了特性分析。基于修正函数投影同步方法,设计了有效的控制输入及参数自适应律,根据Lyapunov函数稳定性定理从理论上证明修正函数投影同步误差系统在原点的渐近稳定性,从而实现了新混沌系统的修正函数投影同步控制。数值模拟仿真证明了同步方法的正确性,该同步方法可以应用于混沌保密通信的研究中。

EPS混凝土动态力学性能研究

借助霍普金森杆(SHPB)对不同粒径、不同含量的EPS混凝土的动态性能进行了研究。EPS混凝土具有明显的率效应;EPS混凝土在低应变率下表现出明显的三个不同的阶段:弹性区、平台区和致密区,随应变率的增加,这一特性逐渐消失;对于同样体积含量、粒径小的EPS混凝土表现出来的平台区更明显,在此分析了产生这种现象的物理机制;在高体积含量的EPS混凝土中,粒子尺寸效应逐渐消失;随应变率的增加,峰值应力后留有长长的"尾巴",主要是由于EPS颗粒的粘弹性特性。

并网逆变器LVRT同步稳定性分析及其优化策略

针对现有低电压穿越(LVRT)研究难以准确全面评估变流器同步运行能力的问题,首先结合LVRT特性和电网侧特性定量研究不同因素对准静态平衡点的影响,揭示系统准静态平衡点的存在条件。其次,分析LVRT特性对并网逆变器暂态稳定性和小信号稳定性的影响,明晰电网故障期间系统不仅存在暂态失步的风险,而且难以在准静态平衡点稳定运行。基于以上理论分析,提出一种提高并网逆变器LVRT同步运行能力的优化策略。该策略在LVRT期间根据电网运行状态自适应调整锁相环参数,不仅可降低系统暂态失步的风险,还可增强其小信号稳定裕度。最后,通过仿真和实验验证了理论分析的正确性和优化策略的有效性。

考虑具有营销努力的双渠道供应链动态均衡

营销努力是发现或研究潜在消费者需求的过程,营销努力可以使企业利润产生浮动。在此背景下,构建了考虑营销努力的双渠道供应链动态博弈模型,并分析了系统均衡点的稳定性条件。通过数值模拟的方法,研究了系统分岔图、以及共存吸引子的演化情况。研究结果表明,需求调整速度、消费者渠道偏好、制造商营销努力投入系数、制造商与零售商需求敏感系数等因素都对系统稳定性产生影响。较小的调整速度和中等程度的营销努力投入有利于供应链成员实现最优利润。同时,渠道偏好系数和营销努力程度需要保持在一定范围内,否则市场会失去稳定性并呈现混沌状态。

一类具有垂直传染的传染病模型的稳定性

基于动力系统的理论,讨论了一类具有垂直传染的传染病模型的稳定性.采用下一代矩阵法获得了基本再生数R0.当R0<1时,由Routh-Hurwitz判别法,得到了无病平衡点的局部渐近稳定性.通过构造Lyapunov函数,证明了系统在无病平衡点全局渐近稳定.当R0> 1时,地方病平衡点存在且唯一,借助Routh判据,得出了系统在地方病平衡点局部渐近稳定的条件,并通过构造Lyapunov函数,证明了系统在地方病平衡点全局渐近稳定.最后,用数值模拟验证了结论的合理性.

一类污水处理数学模型的定性分析

污水处理是环境保护的主要内容之一,通过机理分析为污水处理提供理论依据是非常重要的.基于经典微生物和底物的物料守恒的数学模型,通过计算该数学模型的雅可比矩阵,分析了模型平衡点的存在性和动力学性质,给出了模型平衡点稳定的充分性条件,用数值模拟的方法对分析结果进行了有效验证,从数学分析的角度对污水处理过程中参数的设置提出了一些建议,以提升污水处理效果,并用数值模拟验证建议的正确性.

基于EPS 2008及地面三维激光扫描点云数据进行断面线提取

基于EPS 2008软件平台进行二次开发,实现了对三维激光扫描点云数据进行断面数据提取,提出了基于三维激光扫描技术进行快速断面测量的作业流程、方法,并通过工程实例进行了验证,其验证结果表明采用三维激光扫描技术进行断面测量提高了工作效率,同时也很好地弥补了常规断面测量点位密度不足的问题,保证了断面测量精度,其方法可实施性强。

具有相互干扰和恐惧效应的捕食模型的稳定性

研究一类具有相互干扰和恐惧效应的Lotka-Volterra食饵-捕食模型,分析解的有界性和系统平衡点的存在性,并给出系统持续性的充分条件,通过Dulac判别法得出正平衡点是全局渐近稳定的,具有相互干扰和恐惧效应的食饵-捕食模型能长期共存并保持生态平衡。

高功率微波加热三维温度模型仿真与验证

微波加热不均匀性一直以来都是从事微波加热控制方向研究人员心目中的热点问题。根据微波加热装置的物理结构建立了炉内各层表面的温度静态差分模型结合实验以求得微波加热的实际功率。再基于传热学的有限差分法建立三维空间中的温度分布模型,利用MATLAB以及COMSOL仿真对比验证了模型的有效性。假定微波均匀加热求得被加热介质的平衡温度与不均匀加热时的温度进行比对以找出微波加热过程中介质的部分温升平衡点,最后互相比对找出最优点为控制对象进行专家PID(proportion-integral-derivative)微波加热。实验结果表明,该方法能较为精确地测量出被加热介质任何时刻的平衡温度,使得微波加热在工业生产上有着更加广泛的应用。

一类免疫应答模型的分支分析

主要研究一类病原体与中性粒细胞(PMNs)相互作用的免疫应答模型,详细分析了其正平衡点的存在条件和类型,并通过MATLAB软件包对所得到的结论进行了数值模拟。

一类先天免疫应答模型的稳定性分析

主要研究了一类关于病原体与中性粒细胞(PMNs)之间的相互作用的免疫应答模型.首先讨论了该模型边界平衡点的存在条件;其次,通过Poincare′变换与中心流形理论证明了该模型边界平衡点的全局渐近稳定性;最后,利用MATLAB软件包对得到的结论进行了适当的数值模拟.

Quasi-anti-parity–time-symmetric single-resonator micro-optical gyroscope with Kerr nonlinearity

Parity–time(PT) and quasi-anti-parity–time(quasi-APT) symmetric optical gyroscopes have been proposed recently which enhance Sagnac frequency splitting. However, the operation of gyroscopes at the exceptional point(EP) is challenging due to strict fabrication requirements and experimental uncertainties. We propose a new quasi-APT-symmetric micro-optical gyroscope which can be operated at the EP by easily shifting the Kerr nonlinearity. A single resonator is used as the core sensitive component of the quasi-APT-symmetric optical gyroscope to reduce the size, overcome the strict structural requirements and detect small rotation rates. Moreover, the proposed scheme also has an easy readout method for the frequency splitting. As a result, the device achieves a frequency splitting 10~5 times higher than that of a classical resonant optical gyroscope with the Earth's rotation. This proposal paves the way for a new and valuable method for the engineering of micro-optical gyroscopes.

考虑怀疑和辟谣机制的SEIMR谣言传播模型

考虑到复杂网络上的谣言传播可能会受到怀疑和辟谣等因素的影响,在SIR谣言传播模型中引入怀疑和辟谣机制,构建了一个新的SEIMR谣言传播模型。基于微分方程理论给出了模型在均匀网络上的传播动力学方程,并分析了该模型的无谣言平衡点和谣言盛行平衡点的存在性,利用下一代矩阵法计算了模型在无谣言平衡点处的基本再生数R_(0)。在此基础上,通过Routh-Hurwitz判据分析了模型在无谣言平衡点处和谣言盛行平衡点处的局部渐近稳定性,并利用Lyapunov稳定性理论证明了模型在无谣言平衡点处的全局渐近稳定性。仿真实验结果表明,怀疑和辟谣机制对谣言爆发规模、爆发时间以及持续时间具有重要影响。

基于一类新型激活函数的递归神经网络的多稳定性分析

本研究基于一类新型连续锯齿型激活函数研究了递归神经网络(Hopfield神经网络)的多稳定性。首先,通过区间剖分法、Brouwer不动点定理证明了基于该激活函数的n维神经网络模型至少具有7n个平衡点,并运用对角占优矩阵理论、局部稳定性判定定理等方法证明了其中4n个平衡点是局部指数稳定的,剩余的平衡点是不稳定的。其次,通过增加锯齿型激活函数的峰值点将激活函数推广到更一般的情况,得到了n维神经网络在含有k个峰值点的连续锯齿型激活函数中至少具有(2k+1)n个平衡点,其中(k+1)n个平衡点为局部稳定的。本研究设计的激活函数相较于现有的一些激活函数会产生更多的稳定平衡点,并且在增加峰值点的过程中不会增加神经网络的计算复杂度。最后,通过两个具体的数值算例验证了本研究结果的有效性。