A new approach for data editing and imputation

The editing-and-imputation problem concerns the question of finding errors in a record which does not satisfy a set of consistency rules. Once some potential errors have been localizated, it is also necessary to impute new values to the associated fields. The output dataset should consist of valid records and preserve similar statistical properties as the input dataset. Most of this work is usually done manually by statistical agencies, thus consuming a great deal of human resources. This paper presents a mathematical programming model to optimally solve the problem on surveys with categorical values and particular edits. We also describe a heuristic approach to deal with the more complex surveys. The heuristic procedure follows a combination of the widely-accepted hot-deck donor scheme and the multivariate regression analysis. It has been implemented in a graphical user interface running on standard personal computers, and has been tested on real-world surveys. This paper demonstrates the satisfactory performance of our automatic procedure.     

On Finite Element Approximations to a Shape Gradient Flow in Shape Optimization of Elliptic Problems

Shape gradient flows are widely used in numerical shape optimization algorithms. We investigate the accuracy and effectiveness of approximate shape gradients flows for shape optimization of elliptic problems. We present convergence analysis with a priori error estimates for finite element approximations of shape gradient flows associated with a distributed or boundary expression of Eulerian derivative. Numerical examples are presented to verify theory and show that using the volume expression is effective for shape optimization with Dirichlet and Neumann boundary conditions.     

A deep neural network-based method for solving obstacle problems

In this paper, we propose a method based on deep neural networks to solve obstacle problems. By introducing penalty terms, we reformulate the obstacle problem as a minimization optimization problem and utilize a deep neural network to approximate its solution. The convergence analysis is established by decomposing the error into three parts: approximation error, statistical error and optimization error. The approximate error is bounded by the depth and width of the network, the statistical error is estimated by the number of samples, and the optimization error is reflected in the empirical loss term. Due to its unsupervised and meshless advantages, the proposed method has wide applicability. Numerical experiments illustrate the effectiveness and robustness of the proposed method and verify the theoretical proof.     

纳米自组装γ-Al_2O_3孔隙结构的核磁共振表征

纳米自组装γ-Al_2O_3具有两种纳米级孔道,可作为适合于大分子扩散的催化剂载体,也可用于页岩气藏模型。表征纳米材料孔隙结构的方法有扫描电镜、氮吸附法及压汞法等,各有局限。本文利用核磁共振弛豫测量对纳米自组装γ-Al_2O_3孔隙结构进行研究和定量表征,并通过核磁共振实验和数值模拟对纳米自组装γ-Al_2O_3表面弛豫强度及孔径分布进行探索。结果表明,数值模拟核磁弛豫表征的纳米自组装γ-Al_2O_3的主体孔径为5-7 nm和30-42 nm,核磁弛豫实验通过误差函数法表征的主体孔径为5-9 nm和29-47 nm。相比于氮吸附仅表征微孔介孔及部分大孔,不能表征大于100 nm孔径,压汞法描述小于10 nm孔径相对不准确等问题,核磁弛豫能够全面表征2.8-315 nm纳米自组装γ-Al_2O_3的双峰孔隙系统。三个样品S-1、S-2、S-3的横向弛豫时间T_2谱小孔大孔波峰的信号幅度比0.603、1.15、1.84直接反映各自的化学小孔大孔氧化铝投料比0.85、1.38、1.7的变化。建立的表征方法可以应用于页岩气微观结构和机理研究中,前景广阔。     

Numerical approximation of a viscoelastic frictional contact problemApproximation numérique d'un problème viscoélastique de contact avec frottement

We consider a fully discrete scheme for a quasistatic frictional contact problem between a viscoelastic body and an obstacle. The contact is bilateral, the friction is modeled with Tresca's law and the behavior of the material is described with a viscoelastic constitutive law with long memory. We state an existence and uniqueness result for the discrete solution, followed by error estimate results. Then, we present numerical simulations in the study of a two-dimensional test example. To cite this article: Á. Rodríguez-Arós et al., C. R. Mecanique 334 (2006).     

Explicit iteration and unbounded solutions for fractional integral boundary value problem on an infinite interval

By employing the monotone iterative technique, we not only establish the existence of the unique solution for a fractional integral boundary value problem on semi-infinite intervals, but also develop an explicit iterative sequence for approximating the solution and give an error estimate for the approximation, which is an important improvement of existing results.     

Error estimates for the interpolating moving least-squares method in n-dimensional space

In this paper, the interpolating moving least-squares (IMLS) method is discussed in details. A simpler expression of the approximation function of the IMLS method is obtained. Compared with the moving least-squares (MLS) approximation, the shape function of the IMLS method satisfies the property of Kronecker δ function. Then the meshless method based on the IMLS method can overcome the difficulties of applying the essential boundary conditions. The error estimates of the approximation function and its first and second order derivatives of the IMLS method are presented in n-dimensional space. The theoretical results show that if the weight function is sufficiently smooth and the order of the polynomial basis functions is big enough, the approximation function and its partial derivatives are convergent to the exact values in terms of the maximum radius of the domains of influence of nodes. Then the interpolating element-free Galerkin (IEFG) method based on the IMLS method is presented for potential problems. The advantage of the IEFG method is that the essential boundary conditions can be applied directly and easily. For the purpose of demonstration, some selected numerical examples are given to prove the theories in this paper.     

Error bounds for linear complementarity problems of DB-matrices

Doubly B-matrices (DB-matrices), which properly contain B-matrices, are introduced by Peña (2003) [2]. In this paper we present error bounds for the linear complementarity problem when the matrix involved is a DB-matrix and a new bound for linear complementarity problem of a B-matrix. The numerical examples show that the bounds are sharp.