Stability analysis of discrete-time BAM neural networks based on standard neural network models

To facilitate stability analysis of discrete-time bidirectional associative memory (BAM) neural networks, they were converted into novel neural network models, termed standard neural network models (SNNMs), which interconnect linear dynamic systems and bounded static nonlinear operators. By combining a number of different Lyapunov functionals with S-procedure, some useful criteria of global asymptotic stability and global exponential stability of the equilibrium points of SNNMs were derived. These stability conditions were formulated as linear matrix inequalities (LMIs). So global stability of the discrete-time BAM neural networks could be analyzed by using the stability results of the SNNMs. Compared to the existing stability analysis methods, the proposed approach is easy to implement, less conservative, and is applicable to other recurrent neural networks.     

退化的广义逆函数值Padé逼近

A new generalized inverse function-valued Padé approximation (GIFPA) was defined. Existence condition of GIFPA was given and its uniqueness theorem was proved. All possible degeneracy cases of GIFPA were discussed and constructed. An example was given to illustrate its application.     

一类等式约束优化问题的改进牛顿算法

提出了牛顿方法与预优广义共轭梯度方法相结合的方法(简称为Newton-PGCG)求解库恩-塔克方程组。给出Newton-PGCG算法中预优广义共轭梯度法中预优阵的选取问题及其步数参数的确定原则，并在保证牛顿方法恰二阶收敛的条件下，证明了此算法也具有恰二阶收敛的优点。     

广义伴随Pell数列的平方类

设V是参数为t的广义伴随Pell数列．给出了V有平方类的充要条件．同时，本文证明了：V至多有1个平方类，而且该平方类仅含有2个元素．     

On modal energy in civil structural control

A new control strategy based on modal energy criterion is proposed to demonstrate the effectiveness of the control system in reducing structural earthquake responses. The modal control algorithm combining LQR （linear quadratic regulator） control algorithm is adopted in the discrete time-history analysis. The various modal energy forms are derived by definition of the generalized absolute displacement vector. A preliminary numerical study of the effectiveness of this control strategy is carried out on a 20-storey framed steel structural model. The controlled performance of the model is studied from the perspectives of both response and modal energy. Results show that the modal energy-based control strategy is very effective in reducing structural responses as well as in consuming a large amount of modal energy, while augmentation of additional generalized control force corresponding to the modes that contain little modal energy is unnecessary, as it does little help to improve the controlled structural performance.     

Representing the Twittersphere: Archiving a representative sample of Twitter data under resource constraints

The rising popularity of social media posts, most notably Twitter posts, as a data source for social science research poses significant problems with regard to access to representative, high-quality data for analysis. Cheap, publicly available data such as that obtained from Twitter's public application programming interfaces is often of low quality, while high-quality data is expensive both financially and computationally. Moreover, data is often available only in real-time, making post-hoc analysis difficult or impossible. We propose and test a methodology for inexpensively creating an archive of Twitter data through population sampling, yielding a database that is highly representative of the targeted user population (in this test case, the entire population of Japanese-language Twitter users). Comparing the tweet volume, keywords, and topics found in our sample data set with the ground truth of Twitter's full data feed confirmed a very high degree of representativeness in the sample. We conclude that this approach yields a data set that is suitable for a wide range of post-hoc analyses, while remaining cost effective and accessible to a wide range of researchers.     

Diversity as an opportunity or a challenge? A cross-national study of ethnic diversity and students’ generalized trust

In this study, we explore how ethnic diversity at the macro-level relates to students’ generalized trust by using cross-national data. Our analysis shows a positive relationship between ethnic diversity and generalized trust. This relationship is, however, inverted U-shaped curvilinear rather than linear, indicating that the positive relationship levels off and turns negative. While we also find that students’ educational experiences such as social relations at school are positively associated with generalized trust, ethnic diversity at the macro-level is still the most powerful factor in our analysis predicting students’ generalized trust. Theoretical and practical implications are discussed.     

一类随机Dirichlet级数的亏函数

通过对一类独立随机变量序列所决定的Dirichlet级数的研究，得出一个结果：右半平面上有限级的随机Dirichlet级数几乎必然没有亏函数．     

关于无界函数广义积分integralfromn=atob(f(x)dx(a为奇点))的两个性质

由无穷限广义积分和无界函数的广义积分的关系,得出了无界函数的广义积分integral from n=a to b (f(x)dx(a为奇点))收敛的两个性质。     

关于带第一特征值λ1具Sobolev临界指数2*的一类椭圆方程-Δu=λ1u+|u|2*-2u+τ(x,u)

给出了半线性椭圆方程-Δu=λ1u+|u|2*-2u+τ(x,u)的Dirichlet问题在对扰动项τ(x,u)增加适当条件后非平凡解的存在性定理,以及方程-Δu=λu-|u|2*-2u+h(x),λ∈[λ1,λk](这里λk是方程-Δu=λu的第k个互不相等的特征值)的非零解的存在性定理.