复合跟踪微分器在电容式位移传感器中的应用

针对从含噪原始信号中提取位置以及速度信息,经典跟踪微分器存在不能很好兼顾相位滞后和噪声放大问题、参数多,调试复杂等不足.在跟踪微分器等效线性分析基础上,提出复合形式跟踪微分器,用于电容式位移传感器位置信号跟踪以及速度信号估计,通过MATLAB\SIMULINK仿真以及实验平台测试,结果表明:在跟踪频率1 Hz、幅值1含噪声正弦信号中,复合跟踪微分器能光滑逼近原始位置信号,且能有效进行速度估计,相较于经典跟踪微分器,复合跟踪微分器跟踪相位滞后小0.03 rad,能更好兼顾跟踪信号相位滞后及速度信号噪声放大.     

从三个角度考察柯西不等式

柯西不等式是高等数学中的重要不等式,它在解析几何、数学分析与高等代数这3门数学专业主干基础课程中均有渗透.从这3门课程的角度,分别给出柯西不等式的不同形式和证明过程,并简要地阐述它们的联系,最后做出小结.     

齐次核的Hilbert型多重级数不等式取最佳常数因子的等价条件及应用

利用实分析技巧和权函数方法, 讨论具有齐次核的多重级数Hilbert型不等式, 得到了其取最佳常数因子的充分必要条件, 并给出其应用.     

中立型分数阶微分控制系统能控性

研究一类分数阶中立型微分控制系统的能控性问题,对系统状态方程的分析,利用拉普拉斯变换通过基本控制系统的基础解给出了控制系统通解的表达式,并且通过构造格拉姆矩阵,研究了控制系统能控性的充分必要条件;最后通过举出一个格拉姆矩阵的计算举例来进行验证。     

Modeling eBay price using stochastic differential equations

Online auctions have become increasingly popular in recent years. There is a growing body of research on this topic, whereas modeling online auction price curves constitutes one of the most interesting problems. Most research treats price curves as deterministic functions, which ignores the random effects of external and internal factors. To account for the randomness, a more realistic model using stochastic differential equations is proposed in this paper. The online auction price is modeled by a stochastic differential equation in which the deterministic part is equivalent to the second‐order differential equation model proposed in Wang et al. (Journal of the American Statistical Association, 2008, 103, 1100–1118). The model also includes a component representing the measurement errors. Explicit expressions for the likelihood function are also obtained, from which statistical inference can be conducted. Forecast accuracy of the proposed model is compared with the ODE (ordinary differential equation) approach. Simulation results show that the proposed model performs better.     

IMPLICITIZATION OF PARTIAL DIFFERENTIAL RATIONAL PARAMETRIC EQUATIONS

In this paper, we propose algorithms for the following problems in the implicitization of a set of partial differential rational parametric equations P. （1）To find a characteristic set for the implicit prime ideal of P; （2） To find a canonical representation for the image of P; （3）To decide whether the parameters of P are independent, and if not, to re-parameterize P so that the new parametric equations have independent parameters; （4） To compute the inversion maps of P, and as a consequence, to decide whether P is proper.     

一类二阶非线性常微分方程解的长时间行为

讨论二阶非线性常微分方程:-x″ f(t,x,x′)x′ g(x)=h(t)解的整体行为,在适当的条件下此柯西问题的解具有二分性质.     

Banach空间中二阶Volterra型积分微分方程边值问题解的存在性

利用上、下解法在正规锥上证明了二阶非线性Volterra型积分微分方程边值问题解的存在性。     

n个Schrodinger算子积自伴域

本文讨论了由微分算式l=-d2/dt2 q(t)生成的具有某种边界条件的n个正则Schrodinger算子Li(i=1,…,n)的积Ln…L2L1自伴性问题,证明了积算子Lm…L2L1自伴的充分必要条件为=L*n 1-i(i=1,…,[n 1/2]).     

任意循环的卡诺循环分解的综合讨论

综合讨论了任意循环的两种卡诺循环分解法 ,指出不能采用“串联”分解法来证明任意循环效率的极限 ,但可用这两种分解法来证明克劳修斯等式和不等式 ,同时指出了一些文献在涉及该问题时所存在的不妥之处。