Exact separation theorem for closed sets in Asplund spaces

In this paper, in terms of the Fréchet normal cone, we establish exact separation results for finitely many disjoint closed sets in an Asplund space, which supplement the extremal principle and some fuzzy separation theorems. As an application, we provide a new optimality condition for a constraint optimization problem in terms of Fréchet subdifferential and Fréchet normal cone.     

Asymptotic behavior of solutions to the compressible nematic liquid crystal system in ℝ3

In this paper, we study a nematic liquid crystals system in three-dimensional whole space ?³ and obtain the time decay rates of the higher-order spatial derivatives of the solution by the method of spectral analysis and energy estimates if the initial data belongs to L¹?³ additionally.     

Certain properties related to well posedness of switching diffusions

This work is devoted to switching diffusions that have two components (a continuous component and a discrete component). Different from the so-called Markovian switching diffusions, in the setup, the discrete component (the switching) depends on the continuous component (the diffusion process). The objective of this paper is to provide a number of properties related to the well posedness. First, the differentiability with respect to initial data of the continuous component is established. Then, further properties including uniform continuity with respect to initial data, and smoothness of certain functionals are obtained. Moreover, Feller property is obtained under only local Lipschitz continuity. Finally, an example of Lotka–Volterra model under regime switching is provided as an illustration.     

控股股东对上市公司股利分配倾向的影响及实证分析——来自沪市A股上市公司的经验证据

当前对股利政策的研究主要集中在产权对股利政策的影响、自由现金流对股利政策的影响、公司过渡投资行为对股利政策的影响以及宏观经济波动对股利政策的影响等,而缺乏控股股东对股利政策的影响研究.现实中,控股股东对股利政策具有较大的影响,围绕控股股东对上市公司股利分配倾向的影响进行深入分析.具体而言,以2013-2014年度上证A股数据,建立Log斌ic模型和多元线性回归模型分析控股股东的几方面特征对股利分配倾向产生的多种影响.研究从理论上客观地评价了控股股东对股利分配倾向的影响,现实中对维护中小股东权益有重要意义.     

An alternating direction and projection algorithm for structure-enforced matrix factorization

Structure-enforced matrix factorization (SeMF) represents a large class of mathematical models appearing in various forms of principal component analysis, sparse coding, dictionary learning and other machine learning techniques useful in many applications including neuroscience and signal processing. In this paper, we present a unified algorithm framework, based on the classic alternating direction method of multipliers (ADMM), for solving a wide range of SeMF problems whose constraint sets permit low-complexity projections. We propose a strategy to adaptively adjust the penalty parameters which is the key to achieving good performance for ADMM. We conduct extensive numerical experiments to compare the proposed algorithm with a number of state-of-the-art special-purpose algorithms on test problems including dictionary learning for sparse representation and sparse nonnegative matrix factorization. Results show that our unified SeMF algorithm can solve different types of factorization problems as reliably and as efficiently as special-purpose algorithms. In particular, our SeMF algorithm provides the ability to explicitly enforce various combinatorial sparsity patterns that, to our knowledge, has not been considered in existing approaches.     

Sufficient Dimension Reduction and Variable Selection for Large-p-Small-n Data With Highly Correlated Predictors

Sufficient dimension reduction (SDR) is a paradigm for reducing the dimension of the predictors without losing regression information. Most SDR methods require inverting the covariance matrix of the predictors. This hinders their use in the analysis of contemporary datasets where the number of predictors exceeds the available sample size and the predictors are highly correlated. To this end, by incorporating the seeded SDR idea and the sequential dimension-reduction framework, we propose a SDR method for high-dimensional data with correlated predictors. The performance of the proposed method is studied via extensive simulations. To demonstrate its use, an application to microarray gene expression data where the response is the production rate of riboflavin (vitamin B₂) is presented.     

时滞离散网络模型的动力学分析与同步

复杂网络广泛存在于日常生活,首先,给出几类标准的网络模型;然后,利用稳定性控制方法设计并实现了具有时滞与非时滞耦合的复杂网络模型快速控制;最后,通过构造优化Lyapunov函数,讨论其模型的射影同步问题,得到了系统全局稳定的条件和有效的控制器,以实例数值验证其方法的可行性。     

指纹物质中毒品检测的研究进展

指纹作为案件现场中最常见的物证之一,不仅包含了可用于人身识别的形态特征,还蕴含了丰富的反映遗留人人身特点的化学信息。通过对指纹中毒品物质的检测及分析,可提供指纹遗留者毒品的吸食、接触情况,将其与特定案件相联系,反映个人生活方式信息,为涉毒人员的发现提供新思路。该文利用文献计量学方法总结了该领域的发展脉络以及研究现状与热点,主要总结了目前已建立的指纹物质中毒品分析检测的各种技术方法和特点,并对未来研究方向及难点进行评述,以期为实际案件指纹中的毒品检测提供参考。     

In Situ Polymerized 1,3-Dioxolane Electrolyte for Integrated Solid-State Lithium Batteries

Solid-state lithium batteries are promising and safe energy storage devices for mobile electronics and electric vehicles. In this work, we report a facile in situ polymerization of 1,3-dioxolane electrolytes to fabricate integrated solid-state lithium batteries. The in situ polymerization and formation of solid-state dioxolane electrolytes on interconnected carbon nanotubes (CNTs) and active materials is the key to realizing a high-performance battery with excellent interfacial contact among CNTs, active materials and electrolytes. Therefore, the electrodes could be tightly integrated into batteries through the CNTs and electrolyte. Electrons/ions enable full access to active materials in the whole electrode. Electrodes with a low resistance of 4.5 Ω □⁻¹ and high lithium-ion diffusion efficiency of 2.5×10⁻¹¹ cm² s⁻¹ can significantly improve the electrochemical kinetics. Subsequently, the batteries demonstrated high energy density, amazing charge/discharge rate and long cycle life.