Banach空间中Mann迭代和Ishikawa迭代的等价性问题

用不同于已有的方法证明了任意实Banach空间中一致Lipschitz强连接伪压缩算子在具误差的修正的Mann迭代和具误差的修正的Ishikawa迭代下收敛和稳定的等价性,其中迭代参数{βn}仅需lim sup n→∞βn〈k/L（L＋1）,这推广和改进了目前需假设lim n→∞ βn=0和两迭代程序初始点的取值需相同条件下的已有结果.     

两水平无重复因析试验散度效应的估计

本文对两水平无重复因析试验给出了散度效应的一种新的估计,称为AMH估计,改进了文献中散度效应的较好的MH估计的一个缺陷,给出并证明了AMH估计的无偏条件,证明了AMH估计比MH估计有更小的方差下界.最后通过模拟试验比较了AMH和MH估计的偏度,方差和均方误差.     

Approximating the common fixed points of two sequences of uniformly quasi-Lipschitzian mappings in convex metric spaces

In this paper, a kind of Ishikawa type iterative scheme with errors for approximating a common fixed point of two sequences of uniformly quasi-Lipschitzian mappings is introduced and studied in convex metric spaces. Under some suitable conditions, the convergence theorems concerned with the Ishikawa type iterative scheme with errors to approximate a common fixed point of two sequences of uniformly quasi-Lipschitzian mappings were proved in convex metric spaces. The results presented in the paper generalize and improve some recent results of Wang and Liu (C. Wang, L.W. Liu, Convergence theorems for fixed points of uniformly quasi-Lipschitzian mappings in convex metric spaces, Nonlinear Anal., TMA 70 (2009), 2067-2071).     

A new high accuracy non-polynomial tension spline method for the solution of one dimensional wave equation in polar co-ordinates

In this paper, we propose a new three-level implicit nine point compact finite difference formulation of O(k² + h⁴) based on non-polynomial tension spline approximation in r-direction and finite difference approximation in t-direction for the numerical solution of one dimensional wave equation in polar co-ordinates. We describe the mathematical formulation procedure in details and also discuss the stability of the method. Numerical results are provided to justify the usefulness of the proposed method.     

Simulation of harmonic oscillators on the lattice

This work deals with the simulation of a two-dimensional ideal lattice having simple tetragonal geometry. The harmonic character of the oscillators give rise to a system of second-order linear differential equations, which can be recast into matrix form. The explicit solutions which govern the dynamics of this system can be expressed in terms of matrix trigonometric functions. For the derivation we employ the Lagrangian formalism to determine the correct solutions, which extremize the underlying action of the system. In the numerical evaluation we develop diverse state-of-the-art algorithms which efficiently tackle equations with matrix sine and cosine functions. For this purpose, we introduce two special series related to trigonometric functions. They provide approximate solutions of the system through a suitable combination. For the final computation an algorithm based on Taylor expansion with forward and backward error analysis for computing those series had to be devised. We also implement several MATLAB programs which simulate and visualize the two-dimensional lattice and check its energy conservation.     

Adaptive Penalized Weighted Least Absolute Deviations Estimation for the Accelerated Failure Time Model

The accelerated failure time model always offers a valuable complement to the traditional Cox proportional hazards model due to its direct and meaningful interpretation. We propose a variable selection method in the context of the accelerated failure time model for survival data, which can simultaneously complete variable selection and parameter estimation. Meanwhile, the proposed method can deal with the potential outliers in survival times as well as heteroscedastic model errors, which are frequently encountered in practice. Specifically, utilizing the general nonconvex penalty, we propose the adaptive penalized weighted least absolute deviation estimator for the accelerated failure time model. Under some regularity conditions, we show that the proposed method yields consistent estimator and possesses the oracle property. In addition, we propose a new algorithm to compute the estimate in the high dimensional settings, and evaluate the practical utility of the proposed method through extensive simulation studies and two real examples.     

Monitoring process for attributes with quality deterioration and diagnosis errors

The aim of this paper is to present an online economical quality-control procedure for attributes in a process subject to quality deterioration after random shift and misclassification errors during inspections. The process starts in control (State I) and, in a random time, it shifts to out of control (State II). Once at State II, the non-conforming fraction increases according to a non-decreasing function ψ(z), where z is the number of items produced after a shift. The monitoring procedure consists of inspecting a single item at every m produced items, which is examined r times independently to decide its condition. Once an inspected item is declared non-conforming, the process is stopped and adjusted. A direct search technique is used to find the optimum parameters which minimize the expected cost function. The proposed model is illustrated by a numerical example. Copyright © 2007 John Wiley & Sons, Ltd.     

Estimating Sampling Errors in REA Survey: A Model Approach for the Synthetic Presentation of Results for Main Variables Involved in Economic Analysis

A new sample business survey for agriculture, the REA survey, and a project of integration with the FADN network (RICA in Italy) have significantly changed the production of statistical information nowadays available with reference to the agricultural sector. On the basis of this relevant information, new economic analyses are being developed on farms’ performance, agricultural households’ income and the Common Agricultural Policy (CAP). In this paper the authors estimate the relationship between the levels of variables of interest and their sampling errors using models in order to improve the accessibility of the information on estimates accuracy to the final users (agricultural analysts, policy makers). The paper is the result of a joint research of the three authors. Sections 1–3 and 6 by Pizzoli, Sects. 4 and 5 by Rondinelli, Sect. 7 by Filiberti, conclusions joint to the three authors.     

Error estimation in measuring strain fields with DIC on planar sheet metal specimens with a non-perpendicular camera alignment

The determination of strain fields based on displacement components obtained via 2D-DIC is subject to several errors that originate from various sources. In this contribution, we study the impact of a non-perpendicular camera alignment to a planar sheet metal specimen's surface. The errors are estimated in a numerical experiment. To this purpose, deformed images - that were obtained by imposing finite element (FE) displacement fields on an undeformed image - are numerically rotated for various Euler angles. It is shown that a 3D-DIC stereo configuration induces a substantial compensation for the introduced image-plane displacement gradients. However, higher strain accuracy and precision are obtained - up to the level of a perfect perpendicular alignment - in a proposed “rectified” 2D-DIC setup. This compensating technique gains benefit from both 2D-DIC (single camera view, basic amount of correlation runs, no cross-camera matching nor triangulation) and 3D-DIC (oblique angle compensation). Our conclusions are validated in a real experiment on SS304.     

关于Banach空间中Lipschitz强伪压缩映象的带误差的Ishikawa型迭代序列

设Ｘ是任意实Ｂａｎａｃｈ空间Ｅ的闭子空间;Ｔ：Ｘ → Ｘ是 Ｌｉｐｓｃｈｉｔｚ强伪压缩映象,使得Ｔｘ＊＝ｘ＊,对某ｘ＊∈Ｘ．在没有条件 　之下,本文证明了带误差的Ｉｓｈｉｋａｗａ型迭代序列强收敛到ｘ＊．另外,相关结果又证明了,当Ｔ：Ｅ→Ｅ是Ｌｉｐｓｃｈｉｔｚ强增生算子时,带误差的Ｉｓｈｉｋａｗａ型迭代序列强收敛到方程Ｔｘ＝ｆ的唯一解．