Rough paths analysis of general Banach space-valued Wiener processes

In this article, we carry out a rough paths analysis for Banach space-valued Wiener processes. We show that most of the features of the classical Wiener process pertain to its rough path analog. To be more precise, the enhanced process has the same scaling properties and it satisfies a Fernique type theorem, a support theorem and a large deviation principle in the same Hölder topologies as the classical Wiener process does. Moreover, the canonical rough paths of finite dimensional approximating Wiener processes converge to the enhanced Wiener process. Finally, a new criterion for the existence of the enhanced Wiener process is provided which is based on compact embeddings. This criterion is particularly handy when analyzing Kunita flows by means of rough paths analysis which is the topic of a forthcoming article.     

Estimation of systems with statistically-constrained inputs

This paper discusses the estimation of a class of discrete-time linear stochastic systems with statistically-constrained unknown inputs (UI), which can represent an arbitrary combination of a class of un-modeled dynamics, random UI with unknown covariance matrix and deterministic UI. In filter design, an upper bound filter is explored to compute, recursively and adaptively, the upper bounds of covariance matrices of the state prediction error, innovation and state estimate error. Furthermore, the minimum upper bound filter (MUBF) is obtained via online scalar parameter convex optimization in pursuit of the minimum upper bounds. Two examples, a system with multiple piecewise UIs and a continuous stirred tank reactor (CSTR), are used to illustrate the proposed MUBF scheme and verify its performance.     

Reconstruction of cracks of different types from far‐field measurements

In this paper, we deal with the acoustic inverse scattering problem for reconstructing cracks of possibly different types from the far‐field map. The scattering problem models the diffraction of waves by thin two‐sided cylindrical screens. The cracks are characterized by their shapes, the type of boundary conditions and the boundary coefficients (surface impedance). We give explicit formulas of the indicator function of the probe method, which can be used to reconstruct the shape of the cracks, distinguish their types of boundary conditions, the two faces of each of them and reconstruct the possible material coefficients on them by using the far‐field map. To test the validity of these formulas, we present some numerical implementations for a single crack, which show the efficiency of the proposed method for suitably distributed surface impedances. The difficulties for numerically recovering the properties of the crack in the concave side as well as near the tips are presented and some explanations are given. Copyright © 2009 John Wiley & Sons, Ltd.     

结合滤子技术的牛顿折线法及其实现

成功将多维滤子技术应用到牛顿折线法,提出了多维滤子牛顿折线法.新算法增加了牛顿点以及信赖域的试探点被接收作为下一步迭代点的几率.在一定的假设条件下证明了算法的全局收敛性.数值试验表明,滤子牛顿折线法适合于求解等势线呈峡谷状的函数.     

二维正交小波滤波器的逼近

提出了一种二维正交小波滤波器逼近的方法,采用分步优化的方法来构造小波滤波器,最后通过实验给出低通的小波滤波器.     

枪支弹头痕迹自动对比方法研究

建立了枪支弹头痕迹的自动识别模型.解决了细微信息提取,误差校正,特征位置选取等问题.以11只枪,22颗子弹的三维数据作为测试数据,模型的最高识别率达到77%.     

Matrix inverse problem and its optimal approximation problem for R-skew symmetric matrices

Let R ∈ C^n×n be a nontrivial involution, i.e., R² = I and R ≠ ±I. A matrix A ∈ C^n×n is called R-skew symmetric if RAR = −A. The least-squares solutions of the matrix inverse problem for R-skew symmetric matrices with R∗ = R are firstly derived, then the solvability conditions and the solutions of the matrix inverse problem for R-skew symmetric matrices with R∗ = R are given. The solutions of the corresponding optimal approximation problem with R∗ = R for R-skew symmetric matrices are also derived. At last an algorithm for the optimal approximation problem is given. It can be seen that we extend our previous results [G.X. Huang, F. Yin, Matrix inverse problem and its optimal approximation problem for R-symmetric matrices, Appl. Math. Comput. 189 (2007) 482-489] and the results proposed by Zhou et al. [F.Z. Zhou, L. Zhang, X.Y. Hu, Least-square solutions for inverse problem of centrosymmetric matrices, Comput. Math. Appl. 45 (2003) 1581-1589].     

Integral representation of the W-weighted Drazin inverse for Hilbert space operators

This paper studies the integral representation of the W-weighted Drazin inverse for bounded linear operators between Hilbert spaces. By using operator matrix blocks, some integral representations of the W-weighted Drazin inverse for Hilbert space operators are established.     

The degree of subsequentiality of a subsequential filter

A space is called subsequential if it is a subspace of a sequential space. A free filter F on ω is called subsequential if the space ω∪{F} is subsequential. The purpose of this paper is to introduce the degree of subsequentiality of a subsequential filter in a similar way as it is done in the realm of sequential spaces. A method to produce subsequential filters with arbitrary subsequential degree is given.     

Intercomparison of Inversion Algorithms for Particle‐Sizing Using Mie Scattering

The applicability of different inversion algorithms to retrieve a size distribution of particles in air from light scattering is examined. The investigation is focused on an optical measurement setup with an elliptical mirror as the main optical element. In order to evaluate the capabilities of the individual inversion methods, light scattering by spherical particles is simulated in the size ranges of 0.1 – 10 μm and 0.05 – 1 μm. The distribution of the particle diameters is modeled with three different parametric functions, i.e., RRSB, logarithmic‐normal and a more specific distribution from an ultrasonic nebulizer. Different kinds of noise, e.g., additive and/or multiplicative, are applied in different levels to the simulated scattering measurement to include real physical measurement conditions. The convergence properties of the scattering simulation are investigated with respect to the number of size classes, and thus, information concerning the size resolution required to simulate a measurement for a given particle size distribution is obtained. Further parameters of interest are the minimum angular resolution of the measurements, the number of size classes of the retrieved particle size distribution and the measured polarization of the scattered light.