SPECTRAL RADIUS,KRONECKER PRODUCTS AND STATIONARITY

Abstract. We provide a stochastic proof of the inequality ρ(A?A+B?B) ≥ρ(A?A), where ρ(M) denotes the spectral radius of any square matrix M, i.e. max{|eigenvalues| of M}, and M?N denotes the Kronecker product of any two matrices M and N. The inequality is then used to show that stationarity of the bilinear model will imply stationarity of the linear part, i.e. the linear ARMA model for r= 1 and q= 1. Furthermore, it is shown that stationarity of the subdiagonal model, i.e. the bilinear model with b_ij=0 for i< j, again implies stationarity of its linear part, provided that the stationarity condition given by Bhaskara Rao and his colleagues is met. Interestingly, the conclusion that stationarity of the subdiagonal models, implies that the linear component models cannot be extended to the general non-subdiagonal bilinear models. The last observation is demonstrated via a simple example with p=m= 1, r= 0 and q= 2.     

锅炉角焊结构的受力分析及改进建议

合理的焊缝形式对锅炉的安全性有着十分重要的作用。从提高安全性出发，对锅炉的角焊缝进行了受力分析，并提出了相应改善意见。     

大吨位小半径环向预应力设计和施工技术分析

通过军山大桥主跨斜拉桥索塔锚固区上塔柱足尺模型试验的研究与分析,阐述了大吨位小半径环向预应力应用的实际效果,对试验和施工应用中的相关问题作了客观的论述,并提出了合理的建议.     

多节等径直角弯头展开图的一种近似画法

本文介绍了一种用半径为R的圆弧绘制多节等径直角弯头展开曲线的方法——圆弧法。该方法能绘制任意弯头半径、管口直径、节数、剪开方位的斜口管展开图。并着重对圆弧法和精确作图的计算方法,进行了数学分析比较,其绝对误差和相对误差都较小,证明了用圆弧法绘展开图有一定的准确性,且随着节数增多、弯头半径增大,其准确度越高,因此,本方法绘图简便、灵活,有一定的实用价值。     

周期环境中尺度结构线性种群模型的适定性

该文考虑周期环境中具有尺度结构线性种群动力系统,应用Volterra积分方程及算子谱半径知识证明了该线性系统解的存在唯一性,并且给出解关于出生率和死亡率的单调性结果。     

A comparison of different geometrical elements to model fluid wicking in paper-based microfluidic devices

Recently, microfluidic paper-based analytical devices (μPADs) have outstripped polymeric microfluidic devices in the ease of fabrication and simplicity. Surface tension-based fluid motion in the paper's porous structure has made the paper a suitable substrate for multiple biological assays by directing fluid into multiple assay zones. The widespread assumption in most works for modeling wicking in a paper is that the paper is a combination of capillaries with the same diameter equal to the effective pore diameter. Although assuming paper as a bundle of capillaries gives a good insight into pressure force that drives the fluid inside the paper, there are some difficulties using the effective pore radius. The effective pore radius is totally different from the average geometrical pore radius which makes it impossible to predict wicking in μPADs based on geometrical parameters. In this article, we introduce different analytical and numerical models to investigate the possibility of determining the permeability of the paper, based on geometrical parameters rather than effective parameters. The lattice Boltzmann method is used for numerical simulations. The permeability of each of the proposed models was compared with the experimental permeability. Results indicated that assuming paper as a combination of capillaries and annuluses leads to accurate results that totally depend on average geometrical values rather than effective values. This paves the way for prediction of the fluid wicking only by considering average geometrical pore and fiber diameters.     

Effect of ionic radius on colossal permittivity properties of (A,Ta) co-doped TiO2 (A= alkaline-earth ions) ceramics

(A, B) co-doped TiO₂ ceramics attract great interests due to the excellent dielectric properties. In this work, the (A, Ta) co-doped TiO₂ ceramics were prepared by a solid state reaction process. The effect of the acceptors ionic radius on the structure and properties of TiO₂ ceramics was investigated. According to XRD analysis, the main phase is rutile TiO₂ for all samples. Due to the larger ionic radius, it is hard to replace Ti site in TiO₆ octahedron. As a result, the content of the secondary phase increased with increasing ionic radius. The dielectric properties were significantly enhanced by co-doping of alkaline-earth ions and tantalum ions, and the best dielectric constant obtained at 3% (Sr, Ta) co-doped compositions, where ε’ = 2.1 × 10⁵, tanδ = 0.21. Meanwhile, the XPS analysis suggested that the concentration of the defect dipoles exhibit a maximum in Sr-doped TiO₂ ceramics. The larger ionic radius of the acceptors leads to the more stability of the defect structure. However, for Ba ions, the replacement concentration decreased due to the excessive ionic radius, which in turn reduces the defect concentration. This work is meaningful for the further investigations on TiO₂-based colossal permittivity materials.     

Macromolecular motions and hydrodynamic radius variation in dilute solutions under shear action

Understanding the dynamics of single polymer chains and rheological mechanism in dilute polymer solutions under shear stress is essential for fields such as the petroleum and food industries, biomedical materials and drug delivery. Here we present an experimental method for measuring the viscosity of polymer solutions and studying the variation of single polymer chain conformation and the mechanism of molecular motions according to the relationship between the intrinsic viscosity, [η], and the shear rate. Of striking interest is that we find that [η] changing with the shear rate presents three stages which may explain the nature of the viscoelastic performance of polymer solutions and the isolated molecular motions. The significance of these results is the finding of the polymer chain deformation to match the pore throat which has enormous potential implications in drug delivery, genetics and biomedicine © 2014 Society of Chemical Industry.     

型腔模具的补加工研究

描述了如何利用留量模型来确定型腔部位的清根补加工和区域补加工的加工区域，并提出一种确定补加工刀具半径的计算方法，应用案例表明该方法是可行的。     

玄武岩纤维拉制过程的简化分析

分析了玄武岩纤维拉制的基本过程,应用特鲁顿拉伸定律和流体流动与传热原理,建立了玄武岩连续纤维拉制成形过程的简化数学模型,提出了数值模拟方法。在计算机上模拟研究了纤维拉力、漏嘴温度和半径等参数对纤维半径、纤维纵向温度和速度分布的影响,为纤维拉制过程的调控提供了基本数据。