Banach空间四阶边值问题的拟上下解方法

通过构造拟上下解的单调迭代过程,在拟解对之间利用Sadvoskii不动点定理获得了Banach空间四阶边值问题解的存在性     

基于四阶累积量的波束域MUSIC方法

在非白噪声背景下,基于二阶统计量的高分辨方法性能较差.基于四阶累积量的高分辨方法能较好地抑制空间高斯噪声,但其运算量较大.为了解决这一矛盾,文章提出了一种基于四阶累积量的波束域MUSIC方法.仿真分析和实验结果表明,与阵元域四阶累积量MUSIC方法相比,论文所提方法降低了分辨门限,减小了估计偏差和均方根误差,同时减小了运算量.     

基于四阶累积量的时延估计新方法

针对无线电定位中的时延估计问题,考虑接收信号为窄带信号以及背景噪声为高斯分布的情况下,将四阶累积量的一维切片作为高阶统计量,结合希尔伯特变换,给出一种新的时延估计方法.该方法对相关峰值进行了锐化处理,提高了估计精度.与广义互相关法相比,该算法可有效抑制空间相关高斯噪声的影响,计算量小,易于实现.仿真结果表明了该方法的有效性.     

基于二次虚拟扩展的高分辨率波达方向估计方法

为进一步提高天线阵波达方向估计的分辨率,在四阶量多重信号分类方法的基础上,提出一种高分辨率的波达方向估计方法.利用阵列接收数据的四阶矩量进行虚拟阵列扩展,再利用阵列接收数据的共轭进行虚拟阵列扩展,实现二次虚拟扩展;将扩展后的阵列导向矢量和协方差矩阵用于波达方向估计,与原阵列导向矢量和协方差矩阵相比,相当于构造了更多的虚拟阵元,并扩展了阵列的孔径.仿真结果表明:与四阶量多重信号分类等波达方向估计方法相比,所提出的方法在波达方向估计中成功概率更高,均方误差更低,具有更高的分辨率.所提方法通过二次虚拟扩展,构造了更多的虚拟阵元,有效地提高了天线阵波达方向估计的分辨率.     

应用原对偶方法光滑向量的四阶算子分裂方法

高阶算子分裂方法在改善图像边缘阶梯化、提高计算效率等问题上有很好的作用,其主要思想是将四阶的偏微分方程分裂成两个二阶的偏微分方程分别求解,先进行向量光滑,然后再进行图像重构。相对于第一步的一般显式数值迭代方法,本文应用原对偶格式进行变量替换,应用拟牛顿进行向量光滑。数值结果表明,该方法很好地提高了信噪比,且视觉效果显著。     

一种宽带注入锁定三倍频器

文章提出了一种宽带注入锁定三倍频器。在传统注入方式基础上,倍频器采用了推-推差分对输入信号进行二倍频,并将产生的二次谐波通过变压器耦合至注入管的源极共模点,增强了注入管源极共模点二次谐波。由于注入电流是由注入信号与源极共模点二次谐波进行混频而产生,因此注入电流也被增强,从而增大了锁定范围。除此之外,三倍频采用了四阶谐振器,谐振阻抗的相位在过零点被平坦化,锁定范围进一步被增大。采用标准CMOS 65 nm工艺设计三倍频,芯片面积为720×670 μm²,1.2-V供电时的功耗为15.2 mW。0 dBm注入功率下三倍频的锁定范围为19.2~27.6 GHz,对应的基波抑制比大于25 dB,二次谐波抑制大于35 dB。注入锁定三倍频器可满足5G收发机中本振源的要求。     

He's homotopy perturbation method for fourth-order parabolic equations

In this paper, He's homotopy perturbation method is applied to fourth-order parabolic partial differential equations with variable coefficients to obtain the analytic solution. The method is tested on six examples, which reveal its effectiveness and simplicity.     

An asymptotic numerical method for fourth order singular perturbation problems with a discontinuous source term

Singularly perturbed two-point boundary-value problems (BVPs) for fourth-order ordinary differential equations (ODEs) with a small positive parameter multiplying the highest derivative with a discontinuous source term is considered. The given fourth-order BVP is transformed into a system of weakly coupled systems of two second-order ODEs, one without the parameter and the other with the parameter ? multiplying the highest derivative, and suitable boundary conditions. In this paper a computational method for solving this system is presented. In this method we first find the zero-order asymptotic approximation expansion of the solution of the weakly coupled system. Then the system is decoupled by replacing the first component of the solution by its zero-order asymptotic approximation expansion of the solution in the second equation. Then the second equation is solved by the numerical method, which is constructed for this problem and which involves an appropriate piecewise-uniform mesh.     

Sextic spline solution of variable coefficient fourth-order parabolic equations

We report new three-level implicit methods of O(k ²+h ⁴) and O(k ⁴+h ⁴) for the numerical solution of fourth-order non-homogeneous parabolic partial differential equation with variable coefficients. We use sextic spline in space and finite difference in time directions. Sextic spline function relations are derived by using off-step points. The linear stability of the presented method is investigated. We solve test problems numerically to validate the derived methods. Numerical comparison with other existence methods shows the superiority of our presented scheme.     

四阶非线性边值问题解的单调迭代方法

通过上下解的单调迭代方法,讨论了四阶常微分方程u(4)(t)=f(t,u,u′,u″,u),t∈[0,1],u(0)=u′(1)=u″(0)=u(1)=0,的边值问题,获得了解的存在性结果,推广了已有的结果.并用一实例,说明其应用.