Sufficient Conditions for Uniform Convergence on Layer-Adapted Grids

We study convergence properties of the simple upwind difference scheme and a Galerkin finite element method on generalized Shishkin grids. We derive conditions on the mesh-characterizing function that are sufficient for the convergence of the method, uniformly with respect to the perturbation parameter. These conditions are easy to check and enable one to immediately deduce the rate of convergence. Numerical experiments support these theoretical results and indicate that the estimates are sharp. The analysis is set in one dimension, but can be easily generalized to tensor product meshes in 2D. Received: December 21, 1998; revised March 17, 1999     

Theoretically supported scalable BETI method for variational inequalities

Summary The Boundary Element Tearing and Interconnecting (BETI) methods were recently introduced as boundary element counterparts of the well established Finite Element Tearing and Interconnecting (FETI) methods. Here we combine the BETI method preconditioned by the projector to the “natural coarse grid” with recently proposed optimal algorithms for the solution of bound and equality constrained quadratic programming problems in order to develop a theoretically supported scalable solver for elliptic multidomain boundary variational inequalities such as those describing the equilibrium of a system of bodies in mutual contact. The key observation is that the “natural coarse grid” defines a subspace that contains the solution, so that the preconditioning affects also the non-linear steps. The results are validated by numerical experiments.      

Global Convergence of a Class of Collinear Scaling Algorithms with Inexact Line Searches on Convex Functions

Ariyawansa [2] has presented a class of collinear scaling algorithms for unconstrained minimization. A certain family of algorithms contained in this class may be considered as an extension of quasi-Newton methods with the Broyden family [11] of approximants of the objective function Hessian. Byrd, Nocedal and Yuan [7] have shown that all members except the DFP [11] method of the Broyden convex family of quasi-Newton methods with Armijo [1] and Goldstein [12] line search termination criteria are globally and q-superlinearly convergent on uniformly convex functions. Extension of this result to the above class of collinear scaling algorithms of Ariyawansa [2] has been impossible because line search termination criteria for collinear scaling algorithms were not known until recently. Ariyawansa [4] has recently proposed such line search termination criteria. In this paper, we prove an analogue of the result of Byrd, Nocedal and Yuan [7] for the family of collinear scaling algorithms of Ariyawansa [2] with the line search termination criteria of Ariyawansa [4]. Received: May 8, 1996; revised January 27, 1999     

Modeling the yearly Value-at-Risk for operational risk in Chinese commercial banks

In this paper, we explore the loss data collection exercise for operational risk in Chinese commercial banks from 1999 to first half of 2006. Firstly, the above data are bootstrapped to analyze the capital allocation for a medium-scaled commercial bank in China. Secondly, for every selected cell, we calibrate two truncated distributions to fit the loss severity, one for ‘normal’ losses and the other for the ‘extreme’ losses. Moreover, a more realistic dependence structure - multivariate t copula function is used to measure the relation among the selected cells. In the final, the simulation results suggest that substantial savings can be achieved through measuring the dependence by means of multivariate t copula function than by means of perfect positive dependence.     

环境介质对ASTM A572 Gr65钢疲劳行为的影响

目的 探究不同环境对ASTM A572 Gr65低合金结构钢疲劳强度的影响。方法 在实验室、去离子水和NaCl(3.5%)水溶液环境下进行材料的旋转弯曲疲劳试验，利用疲劳试验设备和显微硬度仪探讨不同环境介质下ASTMA572Gr65低合金结构钢的疲劳强度和断口附近硬度的变化情况，并通过扫描电子显微镜（SEM）和能谱仪（EDS）等对断口腐蚀形貌及腐蚀产物进行分析。结果 ASTM A572 Gr65钢在实验室环境下的疲劳强度为380 MPa，在添加去离子水和NaCl水溶液时的疲劳强度分别为280、80 MPa，分别下降了约26.3%、78.9%；其微观组织为珠光体和铁素体，在疲劳破坏后靠近断口处试样的晶粒存在明显的细化现象，而远离断口的母材微观组织均匀，断口附近的显微硬度因位错运动约升高了10.4HV0.5，当距离增加，硬度逐渐趋于母材本身的硬度时，改变距离约为6mm；与实验室环境相比，在去离子水和NaCl水溶液中均存在多个裂纹源，这对于疲劳断裂破坏起到了加速作用，疲劳断口表面分区不明显，断口表面存在氧化腐蚀产物和二次裂纹。结论 在添加去离子水和NaCl水溶液后，会加速ASTMA572Gr...     

Extension of the Thomas Algorithm to a Class of Algebraic Linear Equation Systems Involving Quasi-Block-Tridiagonal Matrices with Isolated Block-Pentadiagonal Rows, Assuming Variable Block Dimensions

Received July 17, 2000; revised January 31, 2001     

Error estimation in the approximation of the solution of nonlinear fuzzy Fredholm integral equations

Using a fixed point technique, the sequence of successive approximations and a recent quadrature formula for fuzzy-number-valued functions, it is constructed a numerical method for the solution of nonlinear fuzzy Fredholm integral equations. Moreover, the error estimate of the method and a criterion to stop the corresponding algorithm are given.     

Numerical Verification of Solutions of Nekrasov’s Integral Equation

This paper describes numerical verification of solutions of Nekrasov’s integral equation which is a mathematical model of two-dimensional water waves. This nonlinear and periodic integral equation includes a logarithmic singular kernel which is typically found in some two-dimensional potential problems. We propose the verification method using some properties of the singular integral for trigonometric polynomials and Schauder’s fixed point theorem in the periodic Sobolev space. A numerical example shows effectiveness of the present method.     

盐城工学院图书馆节能技术集成应用研究

结合某新建图书馆工程实际,因地制宜,利用土壤源与闭式地表水复合式地源热泵技术,以地埋管换热器为主,提供建筑冬季所需热能,夏季利用地埋管换热系统、地表水(湖水)换热系统一起排出空调系统的热量,地表水(湖水)换热系统同时起到平衡地下排热与取热、保持地温稳定的作用,有效提高系统的安全性、减少系统造价。结合围护结构、遮阳技术、节能灯具设备等节能集成技术应用,使综合节能率达65%以上。     

SHA-65B型细纱胶辊应用浅析

围绕国产表面不处理胶辊长期存在抗绕性能差的问题，对比分析了几种国内外表面不处理胶辊对成纱质量的影响，指出SHA-65B型不处理胶辊能解决缠绕问题，同时提出胶辊选型是提高成纱质量的关键。