Enriched finite element subspaces for dual–dual mixed formulations in fluid mechanics and elasticity

In this paper we unify the derivation of finite element subspaces guaranteeing unique solvability and stability of the Galerkin schemes for a new class of dual-mixed variational formulations. The approach, which has been applied to several linear and nonlinear boundary value problems, is based on the introduction of additional unknowns given by the flux and the gradient of velocity, and by the stress and strain tensors and rotations, for fluid mechanics and elasticity problems, respectively. In this way, the procedure yields twofold saddle point operator equations as the resulting weak formulations (also named dual–dual ones), which are analyzed by means of a slight generalization of the well known Babuška–Brezzi theory. Then, in order to introduce well posed Galerkin schemes, we extend the arguments used in the continuous case to the discrete one, and show that some usual finite elements need to be suitably enriched, depending on the nature of the problem. This leads to piecewise constant functions, Raviart–Thomas of lowest order, PEERS elements, and the deviators of them, as the appropriate subspaces.     

Confinement of one-dimensional electrons in dimer row segments at Ge/Si(001) surfaces

During the initial growth, Si(001) surfaces were covered by thin Ge wetting layers. At the wetting layer surfaces, Ge atoms were reconstructed into dimers, which were aligned along the [110] direction to form one-dimensional (1D) ‘dimer rows’. In addition, the dimer rows were partitioned by dimer vacancy lines at the Ge/Si(001) surfaces. As a result, the surfaces were covered spontaneously by an array of 1D dimer row segments. Scanning tunneling microscope images demonstrated that the 1D free-electrons in the dimer rows are confined in each segment and form an ultra-high density array of 1D quantum wells at the surfaces.     

K‐12 Outreach: Identifying the Broader Impacts of Four Outreach Projects

Over the last four years, a series of outreach programs have been offered through the Colorado School of Mines to middle school teachers from eleven school districts in the State of Colorado in the United States. Each of these programs is designed to illustrate through hands‐on activities the application of mathematics to science and engineering. Each also has an academic year follow‐up such that a faculty member, an expert teacher, or a graduate student assists the teachers in the classroom. An expected outcome of this effort is the improvement of instruction in mathematics and science in the participating middle schools; an unexpected outcome has been the impact of these projects on the culture of the participating schools, both middle schools and university. Based on our assessment efforts, this article describes the qualitative and quantitative outcomes of this sequence of projects on middle school students, teachers, graduate students, professors, and college curriculum.     

基于RO模型的公钥加密方案安全性分析与证明

信息安全是信息社会存在的根基,而密码学是信息安全技术的核心部分,因此,对密码方案或协议的设计与应用的安全性成为人们最为关注的问题。本文首先介绍随机预言模型(RO)及相关的归约论断和敌手模型定义,并运用这种模型对公钥加密方案进行了安全性分析,同时给出了证明,结果达到预期的安全性目标。     

A finite element study of adhesion of soft thin elastic films cast on rough surfaces

Contact instability of thin elastic films rigidly bonded to patterned substrates, in comparison to those bonded to smooth substrates, were found to form highly miniaturized patterns at their free surfaces. Through finite element simulations, we have found that irrespective of the widely varying substrate patterns used (step, sinusoidal, sawtooth and noisy sinusoidal, with different substrate parameters), the salient miniaturized surface features engendered in these films are found to be same for identical RMS substrate-roughnesses. Columns formed at the film-contactor interfaces of these patterned-substrate films are found to be very slender with larger contact area and are comparatively able to bear very high stresses (responsible for higher peak debonding forces). These columns simultaneously display higher stress release during debonding that leads to almost identical snap-off distances and consequentially, higher work of adhesion is observed. Additionally, work of adhesion also increases for higher debonding velocities. The RMS substrate roughnesses promote these films to perform as potentially better adhesives and, their influence on pattern miniaturization can be harnessed to enhance other surface properties.     

广义Vandermonde矩阵的显式LU分解

利用对称函数给出了广义Vandermonde矩阵的显示LU分解和带宽为1的分解,从而可将广义Vandermonde矩阵表示为n个带宽为1的下三角矩阵和n个带宽为1的上三角矩阵的乘积。     

基于多最小支持度的关联规则挖掘

分析了单最小支持度关联规则挖掘的局限性,提出了基于多最小支持度的关联规则挖掘模型,重点研究了多最小支持度MS．Apriori算法的基本思想,指出了算法的优缺点并通过实例说明发现频繁项集的方法,最后指出该算法的不足及改进算法．     

基于用户意愿的智能手机安全监控方法研究

针对智能手机因中木马而产生话费给用户带来损失、杀毒软件无法查杀新木马、防火墙等手段不能很好解决木马问题的现状,对木马行为和正常业务行为进行了分析,提出一种基于业务行为特征的安全监控策略,通过对业务模块的认证达到安全监控的目的,有效阻止木马程序的破坏行为。