低阶煤热萃取物与瘦煤共炭化焦炭的微观结构及显微强度研究

以众唯瘦煤作为主炼焦煤,大同长焰煤萃取物作为添加剂,进行共炭化处理制备坩埚焦。利用偏光显微镜法定量研究焦炭光学显微组分,获得焦炭的各向异性指数(DRAS);采用XRD及分峰拟合的方法研究了焦炭的微晶粒径(L_c)、芳香缩合度(I_a)、石墨化度(g);利用Raman光谱结合分峰拟合的方法研究了焦炭中理想石墨微晶含量(I_g)。对所得焦炭的光学显微组分进行定量分析发现:大同长焰煤热解萃取产物的添加对共炭化焦炭的光学显微组分有显著的影响,利用偏光显微镜法计算出焦炭的DRAS与XRD和Raman计算的焦炭微晶参数呈现很好一致性。并且,焦炭的显微强度与其微观结构关联性极大。     

Learning and approximation by Gaussians on Riemannian manifolds

Learning function relations or understanding structures of data lying in manifolds embedded in huge dimensional Euclidean spaces is an important topic in learning theory. In this paper we study the approximation and learning by Gaussians of functions defined on a d-dimensional connected compact C ^∞ Riemannian submanifold of which is isometrically embedded. We show that the convolution with the Gaussian kernel with variance σ provides the uniform approximation order of O(σ ^s ) when the approximated function is Lipschitz s ∈(0, 1]. The uniform normal neighborhoods of a compact Riemannian manifold play a central role in deriving the approximation order. This approximation result is used to investigate the regression learning algorithm generated by the multi-kernel least square regularization scheme associated with Gaussian kernels with flexible variances. When the regression function is Lipschitz s, our learning rate is (log² m)/m) ^{s/(8 s + 4 d)} where m is the sample size. When the manifold dimension d is smaller than the dimension n of the underlying Euclidean space, this rate is much faster compared with those in the literature. By comparing approximation orders, we also show the essential difference between approximation schemes with flexible variances and those with a single variance. Supported partially by the Research Grants Council of Hong Kong [Project No. CityU 103405], City University of Hong Kong [Project No. 7001983], National Science Fund for Distinguished Young Scholars of China [Project No. 10529101], and National Basic Research Program of China [Project No. 973-2006CB303102].     

Preconditioning techniques for an image deblurring problem

In this paper, we consider the solution of a large linear system of equations, which is obtained from discretizing the Euler–Lagrange equations associated with the image deblurring problem. The coefficient matrix of this system is of the generalized saddle point form with high condition number. One of the blocks of this matrix has the block Toeplitz with Toeplitz block structure. This system can be efficiently solved using the minimal residual iteration method with preconditioners based on the fast Fourier transform. Eigenvalue bounds for the preconditioner matrix are obtained. Numerical results are presented. Copyright © 2016 John Wiley & Sons, Ltd.     

Analytical formula for two‐dimensional ring artefact suppression

Ring artefacts are the most disturbing artefacts when reconstructed volumes are segmented. A lot of effort has already been put into better X‐ray optics, scintillators and detectors in order to minimize the appearance of these artefacts. However, additional processing is often required after standard flat‐field correction. Several methods exist to suppress artefacts. One group of methods is based on minimization of the Tikhonov functional. An analytical formula for processing of a single sinogram was developed. In this paper a similar approach is used and a formula for processing two‐dimensional projections is found. Thus suppression of ring artefacts is organized as a two‐dimensional convolution of `averaged' projections with a given filter. Several approaches are discussed in order to find elements of the filter in a faster and accurate way. Examples of experimental datasets processed by the proposed method are considered.     

灰色系统模型病态矩阵的双正则化算法

灰色系统模型矩阵会存在病态问题.为消除其病态性,基于病态矩阵的双正则化方法,建立了正则化灰色系统模型中灰参数求解的表达式,给出了其导出方式;提出了正则参数α的选择原则.从而避免了灰参数求解过程中矩阵的病态问题.数值试验分析说明,灰色系统模型的双正则化算法是正确和适用的.     

An iterative Bregman regularization method for optimal control problems with inequality constraints

We study an iterative regularization method of optimal control problems with control constraints. The regularization method is based on generalized Bregman distances. We provide convergence results under a combination of a source condition and a regularity condition on the active sets. We do not assume attainability of the desired state. Furthermore, a priori regularization error estimates are obtained.     

Quasi-Reversibility Method for an Ill-Posed Nonhomogeneous Parabolic Problem

The quasi-reversibility method is considered for the non-homogeneous backward Cauchy problem u_t+Au = f(t), u(τ) = ? for 0≤t<τ, which is known to be an ill-posed problem. Here, A is a densely defined positive self-adjoint unbounded operator on a Hilbert space H with given data f∈L¹([0,τ],H) and ?∈H. Error analysis is considered when the data ?, f are exact and also when they are noisy. The results obtained generalize and simplify many of the results available in the literature.     

用于前向光散射颗粒粒度测量的基函数Tikhonov正则化算法

以前向光散射颗粒测试技术中的反演问题为研究对象,将颗粒粒径分布函数表示为一系列B-spline函数的线性组合以降低反演问题的病态性。模拟计算与实验表明:采用基函数形式的Tikhonov正则化方法可减少传统Tikhonov正则化反演带来的振荡,使其更加光顺。