A weighted H1 seminorm regularization method for Fredholm integral equations of the first kind

Many problems in mathematics and engineering lead to Fredholm integral equations of the first kind, e.g. signal and image processing. These kinds of equations are difficult to solve numerically since they are ill-posed. Therefore, regularization is required to obtain a reasonable approximate solution. This paper presents a new regularization method based on a weighted H¹ seminorm. Details of numerical implementation are given. Numerical examples, including one-dimensional and two-dimensional integral equations, are presented to illustrate the efficiency of the proposed approach. Numerical results show that the proposed regularization method can restore edges as well as details.     

High-accuracy quadrature methods for solving boundary integral equations of steady-state anisotropic heat conduction problems with Dirichlet conditions

This paper presents the mechanical quadrature methods (MQMs) for solving the boundary integral equations of steady-state anisotropic heat conduction equation on the smooth domains and polygons, respectively. The costless and high-accurate Sidi–Israeli quadrature formula are applied to deal with the integrals in which the kernels have a logarithmic singularity. Especially, the Sidi transformation is used for the polygon cases in order to obtain a rapid convergence by degrading the singularity at the corners on the boundary. The convergence and stability of the MQMs solution are proved based on Anselone's collective compact theory. In addition, asymptotic error expansion of the MQMs shows that the approximation order is of O(h³), where h is the partition size of the boundary. Finally, numerical examples are tested and results verify the theoretical analysis.     

A note on stabilization of locally damped wave equations with time delay

In this paper, we consider the wave equation with internal distributed time delay and local damping in a bounded and smooth domain Ω⊂Rⁿ. When the local damping acts on a neighborhood of a suitable part of the boundary of Ω, we show that an exponential stability result holds if the coefficient of the delay term is sufficiently small.     

Inhibition effect of a synthesized N, N＇-bis（2-hydroxybenzaldehyde）- 1, 3-propandiimine on corrosion of mild steel in HC1

The corrosion inhibition of mild steel in 1 mol/L HCl by N, N′-bis (2-hydroxybenzaldehyde)-1, 3-propandiimine (2-HBP) has been investigated by using potentiodynamic polarization, electrochemical impedance spectroscopy (EIS) and chronoamperometry measurements. The experimental results suggest that this compound is an excellent corrosion inhibitor for mild steel and the inhibition efficiency increases with the increase in inhibitor concentration. Polarization curves reveal that this organic compound is a mixed type inhibitor. The effect of temperature on the corrosion behavior of mild steel with the addition of the Schiff base was studied in the temperature range from 25℃ to 65℃. The experimentally obtained adsorption isotherms follow the Langmuir equation. Activation and thermodynamic adsorption parameters such as E a , ΔH, ΔS, K ads and ΔG ads were calculated by the corrosion currents at different temperatures and using the adsorption isotherm. The morphology of mild steel surface in the absence and presence of 2-HBP was examined by atomic force microscope (AFM) images.     

砂土的剪胀方程及其塑性势(Ⅰ):发展现状

以能量守恒原理为主线,在各向同性前提下,对Taylor剪胀方程、Cam-clay剪胀方程、修正Cam-clay剪胀方程、Rowe剪胀方程和扩展的Rowe剪胀方程等进行了较全面的综述.论证了剪胀方程和塑性势函数之间的相互转化关系.指出了Lade-Kim塑性势函数和Nova塑性势函数的缺陷之处,即这两个塑性势函数均没有合理耦合临界状态这一概念.     

电化学聚合研究进展

电化学聚合是近年来发展起来的一种新型的聚合方法，它除了可以合成一些常用方法所不能合成的聚合物外，还能改变某些聚合物的性能．现已广泛用于导电高分子的研究中．并具有潜在的工业化前景。本文从机理及应用方面综述了电化学聚合方法的研究进展。     

Modeling of the Electrostatic (Plasmon) Resonances in Metallic and Semiconductor Nanoparticles

Plasmon (electrostatic) resonances are treated as an eigenvalue problem for specific boundary integral equation. This leads to direct calculation of resonance values of permittivity and resonance frequency. The technique is illustrated by numerical examples of calculation of resonance frequencies for 3D nanoparticles.     

Reflected Appraisals, Academic Self-Perceptions, and Math/Science Performance During Early Adolescence.

The authors tested a model of the relations among adolescents' perceptions of parents', teachers', and classmates' support for, valuing of, and beliefs about their competence in math/science; adolescents' own academic self-perceptions concerning math/science; and their academic performance. The sample included 378 middle school students; 65% were Latino, and 21% were European American. Reflected appraisals of adults' beliefs concerning both the importance of and students' competence in math/science, as well as perceived support, predicted students' own self-perceived importance, competence, scholastic behavior, and performance in these courses. Latino students reported lower mean levels of perceived competence than did European American students (controlling for maternal education). Findings have important implications for understanding achievement socialization in ethnically diverse populations. (PsycINFO Database Record (c) 2010 APA, all rights reserved)