The Kalman condition for the boundary controllability of coupled parabolic systems. Bounds on biorthogonal families to complex matrix exponentials

This paper is devoted to prove the controllability to trajectories of a system of n one-dimensional parabolic equations when the control is exerted on a part of the boundary by means of m controls. We give a general Kalman condition (necessary and sufficient) and also present a construction and sharp estimates of a biorthogonal family in L²(0,T;C) to {tje−Λkt}.     

Near-field-smoothing of periodic chirped pulse with applied angular dispersion

Periodic chirped pulse (PCP) with applied angular dispersion has been approved to be an efficient beam smoothing method in inertial confinement fusion. In this paper, the propagation characteristics of dispersed PCP in near field is analyzed theoretically and calculated numerically, and the results indict dispersed PCP is a motion beam, which can be applied to improve beam uniformity in near field. An experiment is carried out to validate the near-field-intensity smoothing effect of PCP.     

Exponential smoothing — I

Some new insights and results for exponential smoothing with application to forecasting and parameter estimation. Multidimensional exponential smoothing is described by a Kalman filter model with a limiting stationary gain matrix.     

Local smoothing property and Strichartz inequality for Schrödinger equations with potentials superquadratic at infinity

We study smoothing properties for time-dependent Schrödinger equations , , with potentials which satisfy V(x)=O(|x|^m) at infinity, m?2. We show that the solution u(t,x) is 1/m times differentiable with respect to x at almost all , and explain that this is the result of the fact that the sojourn time of classical particles with energy λ in arbitrary compact set is less than CTλ^−1/m during [0,T] when λ is very large. We also show Strichartz's inequality with derivative loss for such potentials and give its application to nonlinear Schrödinger equations.     

Predictor-Corrector Smoothing Methods for Monotone LCP

In this paper, we analyze the global and local convergence properties of two predictor-corrector smoothing methods, which are based on the framework of the method in [1], for monotone linear complementarity problems (LCPs). The difference between the algorithm in [1] and our algorithms is that the neighborhood of smoothing central path in our paper is different to that in [1]. In addition, the difference between Algorithm 2.1 and the algorithm in [1] exists in the calculation of the predictor step. Comparing with the results in [1],the global and local convergence of the two methods can be obtained under very mild conditions. The global convergence of the two methods do not need the boundness of the inverse of the Jacobian. The superlinear convergence of Algorithm 2.1‘ is obtained under the assumption of nonsingularity of generalized Jacobian of Φ(x,y) at the limit point and Algorithm 2.1 obtains superlinear convergence under the assumption of strict complementarity at the solution. The efficiency of the two methods is tested by numerical experiments.     

Smoothing Properties and Approximation of Time Derivatives for Parabolic Equations: Variable Time Steps

We study smoothing properties and approximation of time derivatives for time discretization schemes with variable time steps for a homogeneous parabolic problem formulated as an abstract initial value problem in a Banach space. The time stepping methods are based on using rational approximations to the exponential function which are A()-stable for suitable (0,/2] with unit bounded maximum norm. First- and second-order approximations of time derivatives based on using difference quotients are considered. Smoothing properties are derived and error estimates are established under the so-called increasing quasi-quasiuniform assumption on the time steps.     

Adaptive Smoothing Method,Deterministically Computable Generalized Jacobians,and the Newton Method

In this note, we show that a well-known integral method, which was used by Mayne and Polak to compute an -subgradient, can be exploited to compute deterministically an element of the plenary hull of the Clarke generalized Jacobian of a locally Lipschitz mapping regardless of its structure. In particular, we show that, when a locally Lipschitz mapping is piecewise smooth, we are able to compute deterministically an element of the Clarke generalized Jacobian by the adaptive smoothing method. Consequently, we show that the Newton method based on the plenary hull of the Clarke generalized Jacobian can be implemented in a deterministic way for solving Lipschitz nonsmooth equations.     

光谱导数Kalman滤波同时测定苯酚-邻氯苯酚和2,4二氯苯酚

文中提出了一个新的、稳定的光谱导数Kalman滤波紫外分光光度法同时定量分析方法,并且成功地将其应用于极难分辨的苯酚-邻氯苯酚和2,4二氯苯酚三组分混合体系的同时测量.选择分析光谱导数的原因是其不仅包含着吸光度,还包括在指定波长位置变化趋向等更多的信息量,这样更利于在吸收峰重叠的位置捕捉有较大差异的信号.利用Kalman滤波可以解决由光谱导数而引起的噪声放大问题,也可以过滤源于实验的噪声以及来自传递模型误差.在260～290 nm区间测量了30组浓度各自在1～10 mg·L-1范围的苯酚-邻氯苯酚和2,4二氯苯酚标准混合溶液紫外吸收光谱图.利用分段延伸高次多项式回归模拟求导准确获得吸光度导数,并且利用偏最小二乘法将其制作成Kalman滤波标准工作系数矩阵.通过随机线性离散系统的Kalman滤波器最优平滑计算,对混合体系中的各组分进行定量分析.回收实验显示出,光谱导数Kalman滤波分析法应用于本实验的极难分辨的三组分体系,得到了非常高的回收率,并且在整个实验范围内光谱导数Kalman滤波分析法具有非常好的稳定性.     

Identification of a fault zone ahead of the tunnel excavation face using the extended Kalman filter

Simulation of mechanized tunneling and on-site excavation require very good knowledge of the geomechanical and material properties. Identification of the material must be fast and continuously performed during tunnel excavation for the best possible strategies for advancing the tunnel boring machine. We present in this work the use of the extended Kalman filter (EKF) for identification of the inclined fault zone ahead of the face. The EKF showed fast and stable convergence of the model parameters under study. In comparison with the particle swarm optimization technique applied to the same back analysis problem, faster convergence of the identified parameters as well as high robustness with respect to the choice of the initial parameter values have been observed.