双时滞非线性微分系统周期解的存在性与唯一性

应用Krasnoselskii不动点定理及Banach压缩映射原理,研究双时滞非线性中立型微分系统d/dtx(t)=A(t)x(t-τ(t))+d/dtQ(t,x(t-g(t)))+G(t,x(t),x(t-g(t)))+∫₍t-τ(t))^t D(t, s)F (x(s))ds.结合Floquet理论及基本解矩阵概念,得到了系统周期解存在性与唯一性的充分条件,所得结论推广了已有文献中的相应结果.     

将MATLAB融入大学物理课程教学的探索与研究

本文以教育部“使用信息技术工具改造‘普通物理学’课程”教改项目的实施为契机,通过在大学物理课程中引入计算机数值模拟软件MATLAB教学模式的改革,使用偶极子天线经典案例,加深学生对物理概念的理解,引导学生由被动学习向主动学习转变,激发学生学习兴趣,培养学生创新意识。在疫情常态化背景下,改革受到了学生的支持和欢迎,达到了很好的效果。     

共轭梯度法自适应空间滤波

直接矩阵求逆(DMI)方法的空间滤波器具有很快的收敛跟踪速度,因而受到广泛重视,但在寂静噪声很小且阵元数多于干扰数时,求解最佳权矢量的DKI算法是数值不稳定的,收敛性能显著恶化。本文首先分析了DMI算法数值不稳定的机理,然后结合副瓣对消及波束形成这两个空间滤波问题,针对其DMI方法的数值不稳定性,从多元函数的概念入手,引入了共轭梯度方法。由干该方法是一种运算量少的算法,同时由于它具有很好的数值稳定性,有效地解决了在求解最佳权矢量时的DMI算法数值不稳定的问题,本文最后给出了计算机模拟结果和比较。     

Periodic Solutions for Two Coupled Nonlinear-Partial Differential Equations

In this paper, by applying the Jacobi elliptic function expansion method, the periodic solutions for two coupled nonlinear partial differential equations are obtained.     

Entanglement in an anisotropic spin-1 Heisenberg chain

The entanglement in an anisotropic spin-1 Heisenberg chain with a uniform magnetic field is investigated. The ground-state entanglement will undergo two different kinds of transitions when the anisotropy \Delta and the amplitude of the magnetic field B are varied. The thermal entanglement of the nearest neighbour always declines when B increases no matter what the value of the anisotropy is. It is very interesting to note that the entanglement of the next-nearest neighbour can increase to a maximum at a certain magnetic field. Regardless of the boundary condition, the nearest-neighbour entanglement always decreases and approaches to a constant value when the size of the system is very large. The constant value of open boundary condition is much larger than that of periodic boundary condition.     

Vlasov辐射器反射特性研究

利用矩量法导出Vlasov辐射器端口处各种模式模系数（振幅）的计算方法,并利用此方法通过数值计算研究了斜切形Vlasov辐射器的反射特性,得到了辐射器端口反射系数和斜切角度及直径波长比之间的关系。结果表明斜切形辐射器具有很小的反射系数,并从反射特性上为辐射器结构参数的选择提供了依据。     

准TEM高温超导微带线电容等效电路模型及其分电容模型

本文根据高温超导厚膜和薄膜场和电流的分布特点,给出厚膜和薄膜准TEM微带线电容等效电路及分电容表达式.这些表达式的正确性通过三个例子证实.     

随机配对的食饵-捕食者模型

建立了食饵具有性别结构的食饵-捕食者模型,其中食饵两性的配对是随机的.结论表明:没有偏食的捕食不能改变食饵的性比,偏食可以改变食饵的性比;若食饵两性的出生率相等,任意的偏食都可以消除周期振荡;若食饵两性的出生率不相等,较大的偏食总能消除周期振荡,周期振荡的消除与否由偏食系数和食饵两性的出生率之比共同决定.     

同轴周期慢波结构色散特性的通用数值解法

 运用场匹配法和傅里叶级数理论,提出一种原则上可数值求解任意同轴周期慢波结构色散特性的方法,给出了同轴慢波结构TM_0n模的色散方程。基于该方法,编制了Matlab程序,给出了同轴波纹波导和同轴双波纹波导色散特性,以算例形式分析计算了同轴盘荷波导的色散特性。数值计算结果与多维全电磁模拟软件结果进行比较,证明了该数值算法的准确性和可靠性。     

HOMOTOPY PERTURBATION SOLUTION AND PERIODICITY ANALYSIS OF NONLINEAR VIBRATION OF THIN RECTANGULAR FUNCTIONALLY GRADED PLATES

In this paper nonlinear analysis of a thin rectangular functionally graded piate is formulated in terms of von-Karman＇s dynamic equations. Functionaily Graded Material （FGM） properties vary through the constant thickness of the plate at ambient temperature. By expansion of the solution as a series of mode functions, we reduce the governing equations of motion to a Duffing＇s equation. The homotopy perturbation solution of generated Duffing＇s equation is also obtained and compared with numerical solutions. The sufficient conditions for the existence of periodic oscillatory behavior of the plate are established by using Green＇s function and Schauder＇s fixed point theorem.