An improved lower bound for the expected number of real zeros of a random algebraic polynomials

In this note we estimate the lower bound of the average number of real zeros of a random algebraic polynomials when the random coefficients are standard normal random variables     

Description of K-spaces by means of J-spaces and the reverse problem in the limiting real interpolation

We establish conditions under which K-spaces in the limiting real interpolation involving slowly varying functions can be described by means of J-spaces and we also solve the reverse problem. To this end, we prove several versions of the fundamental lemma of the real interpolation theory. We apply our results to obtain density theorems for the corresponding limiting interpolation spaces.     

Discrete Morse Flow for Yamabe Type Heat Flows

In this paper, we study the discrete Morse flow for either Yamabe type heat flow or nonlinear heat flow on a bounded regular domain in the whole space. We show that under suitable assumptions on the initial data $g$ one has a weak approximate discrete Morse flow for the Yamabe type heat flow on any time interval. This phenomenon is very different from the smooth Yamabe flow, where the finite time blow up may exist.     

基于USB总线的离散量接口设计与实现

为了满足航空电子仿真系统对离散量输入输出控制的需求,设计开发了一种基于USB总线的离散量输入输出接口。该接口采用USB芯片CH375完成板卡与主机数据通信,51单片机作为主控制器,CPLD实现地址译码和逻辑控制,光耦和继电器分别为输入和输出隔离器件,具有采集56路光耦输入信号和56路继电器输出信号的功能。论文详细探讨了系统总体设计、硬件实现、软件配置和工作流程,给出了系统硬件的框架结构、软件架构,详细讨论了系统的驱动软件开发。该接口满足不同仿真系统离散量输入输出的需要,具有稳定性高、可热插拔、通道数目可变的特点,在工程应用中收到了很好的效果。     

基于分段直线拟合的伪随机码相位测量法

针对目前PN码(Pseudo-Noise Code)相位测量抗干扰能力有限的问题,提出了一种新的PN码相位测量方法,该方法以PN码的相关函数为基础,以峰值点为分界点对相关峰曲线两侧分别做最小二乘直线拟合。然后求出两条直线的交点坐标,其中横坐标与零相偏参考值的差值就是PN码相位的估值。该方法与目前常用的最小二乘同步法和三点二次插值PN码相位测量法相比较,算法复杂度增加有限。通过仿真数据可以得出,新的PN码测量方法在信噪比较低的情况下能得到比最小二乘同步法和三点二次插值法更加稳定和精确的估值结果。     

Properties of analytic Morrey spaces and applications

In this note, we aim to study analytic Morrey spaces . We first give the canonical factorization for . Then by applying p‐Carleson measure, we prove an atomic decomposition theorem of . As an application of the decomposition theorem, the interpolation problem of is solved. Finally, we show the boundedness and compactness of Toeplitz operators on .     

基于改进教学优化算法的Hermite正交基神经网络混沌时间序列预测

针对传统预测模型对混沌时间序列预测精度低、收敛速度慢及模型结构复杂的问题, 提出了基于改进教学优化算法的Hermite正交基神经网络预测模型. 首先, 将自相关法和Cao方法相结合对混沌时间序列进行相空间重构, 以获得重构延迟时间向量; 其次, 以Hermite正交基函数为激励函数构成Hermite正交基神经网络, 作为预测模型; 最后, 将模型参数优化问题转化为多维空间上的函数优化问题, 利用改进教学优化算法对预测模型进行参数优化, 以建立预测模型并进行预测分析. 分别以Lorenz 系统和Liu系统为模型, 通过四阶Runge-Kutta法产生混沌时间序列作为仿真对象, 并进行单步及多步预测对比实验. 仿真结果表明, 与径向基函数神经网络、回声状态网络、最小二乘支持向量机及基于教学优化算法的Hermite正交基神经网络预测模型相比, 所提预测模型具有更高的预测精度、更快的收敛速度和更简单的模型结构, 验证了该模型的高效性, 便于推广和应用.     

The global wellposedness of the 3D heat-conducting viscous incompressible fluids with bounded density

We consider the global wellposedness of the inhomogeneous incompressible heat-conducting viscous fluids in three dimension space. We generalize the result of Fujita & Kato for Navier–Stokes to the heat-conducting inhomogeneous incompressible viscous fluids. The key point is that we get the global wellposedness under the assumption that the initial density has positive lower and upper bound and the initial temperature can be arbitrarily large.