Regularization Techniques for Numerical Approximation of PDEs with Singularities

The rate of convergence for numerical methods approximating differential equations are often drastically reduced from lack of regularity in the solution. Typical examples are problems with singular source terms or discontinuous material coefficients. We shall discuss the technique of local regularization for handling these problems. New numerical methods are presented and analyzed and numerical examples are given. Some serious deficiencies in existing regularization methods are also pointed out.     

正项级数的审敛法

本文给出正项级数的一种审敛法，此审敛法可以概括常见的柯西审敛法。且由此方法还可以推出比柯西审剑法更为细致的结论。     

网页内容过滤技术中的特征提取

有害的网络内容日益猖獗,为封锁色情网页,论文通过统计和分析,主要从四个方面提取色情网页的特征:网页的布局,因特网内容选择平台(PICS)等级评定应用,暗示性条文和文档内容。从这四个方面的特征能几乎完全区分色情网页和非色情网页,该基本框架也适用于过滤网上除色情以外的其它不益内容。     

语言工具书法律术语释义辨析

汉语言文字既是语言学的研究对象,又是法律的规范领域(我国于2000年制定了《通用 语言文字法》)。语言工具书的质量应当引起语言学和法学的双重关注。以发行量极大、流行 范围极广的《现代汉语词典》为例,现行语言工具书对法律术语的释义存在着诸多常识性错误, 这些错误对读者构成法学知识和法律观念传递的障碍。本文以三组作为法律基本要素和法学 核心范畴的法律术语为例,对语言工具书的释义进行辨析,并提出修改建议。     

广义Cauchy判别法

文献[1]中曾讨论了广义D’Alemben判别法——Kummer法，我们以比较定理为基础，得出了广义Cauchy判别法Cg，并证明了K真包含Cg。     

商务术语误译的原因分析与对策探讨

从理解和表达两个方面，分析了商务术语汉译时出现错误的原因，并对纠正误译的相应对策进行了探讨。     

Wirtinger-based multiple integral inequality for stability of time-delay systems

Note that the conservatism of the delay-dependent stability criteria can be reduced by increasing the integral terms in Lyapunov–Krasovskii functional (LKF). This brief revisits the stability problem for a class of linear time-delay systems via multiple integral approach. The novelty of this brief lies in that a Wirtinger-based multiple integral inequality is employed to estimate the derivative of a class of LKF with multiple integral terms. Based on these innovations, a new delay-dependent stability criterion is derived in terms of linear matrix inequalities. Two numerical examples are exploited to demonstrate the effectiveness and superiority of the proposed method.     

A short guide to topological terms in the effective theories of condensed matter

Abstract

This article is meant as a gentle introduction to the topological terms that often play a decisive role in effective theories describing topological quantum effects in condensed matter systems. We first take up several prominent examples, mainly from the area of quantum magnetism and superfluids/superconductors. We then briefly discuss how these ideas are now finding incarnations in the studies of symmetry-protected topological phases, which are in a sense a generalization of the concept of topological insulators to a wider range of materials, including magnets and cold atoms.     

Novel delay-partitioning stabilization approach for networked control system via Wirtinger-based inequalities

This paper studies the problems of stability analysis and state feedback stabilization for networked control system. By developing a novel delay-partitioning approach, the information on both the range of network-induced delay and the maximum number of consecutive data packet dropouts can be taken into full consideration. Various augmented Lyapunov–Krasovskii functionals (LKFs) with triple-integral terms are constructed for the two delay subintervals. Moreover, the Wirtinger-based inequalities in combination with an improved reciprocal convexity are utilized to estimate the derivatives of LKFs more accurately. The proposed approaches have improved the stability conditions without increasing much computational complexity. Based on the obtained stability criterion, a stabilization controller design approach is also given. Finally, four numerical examples are presented to illustrate the effectiveness and outperformance of the proposed approaches.     

Development of surrogate models for the prediction of the flow around an aircraft propeller

In the present work, the derivation of two surrogate models (SMs) for modelling the flow around a propeller for small aircrafts is presented. Both methodologies use derived functions based on computations with the detailed propeller geometry. The computations were performed using k–ω shear stress transport for modelling turbulence. In the SMs, the modelling of the propeller was performed in a computational domain of disk-like geometry, where source terms were introduced in the momentum equations. In the first SM, the source terms were polynomial functions of swirl and thrust, mainly related to the propeller radius. In the second SM, regression analysis was used to correlate the source terms with the velocity distribution through the propeller. The proposed SMs achieved faster convergence, in relation to the detail model, by providing also results closer to the available operational data. The regression-based model was the most accurate and required less computational time for convergence.