Moving Averages of Random Vectors with Regularly Varying Tails

Regular variation is an analytic condition on the tails of a probability distribution which is necessary for an extended central limit theorem to hold, when the tails are too heavy to allow attraction to a normal limit. The limiting distributions which can occur are called operator stable. In this paper we show that moving averages of random vectors with regularly varying tails are in the generalized domain of attraction of an operator stable law. We also prove that the sample autocovariance matrix of these moving averages is in the generalized domain of attraction of an operator stable law on the vector space of symmetric matrices.
AMS 1990 subject classification. Primary 62M10, secondary 62E20, 62F12, 60F05.     

Influence of aorta extracellular matrix in electrospun polycaprolactone scaffolds

Cardiovascular disease is the leading cause of mortality worldwide. Therefore, new research strategies for the treatment of cardiovascular disease are required. Previously, extracellular matrices (ECMs) have been used alongside polymers to generate hybrid bioscaffolds. Herein, we propose combining aortic ECMs with a polycaprolactone electrospun scaffold and biomechanically evaluating the scaffolds. We electrospun three scaffolds with varying ECM concentrations and found that increasing the ECM concentration leads to decreased stiffness at low strains, increased elasticity at high strain, reduction in failure strain, and an increase in yield strength. We also noted a decrease in water droplet contact angle with the increasing ECM concentration. Furthermore, we found that all three scaffolds were capable of maintaining human umbilical vein endothelial cell attachment and survival. These findings show the wide spectrum of mechanical properties that can be achieved through the addition of different concentrations of ECM into the fibers. © 2019 The Authors. Journal of Applied Polymer Science published by Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2019 , 136, 48181.     

A WELL-CONDITIONED MATRIX FOR (kuX)X WITH DISCONTINUOUS k

The traditional tridiagonal matrix approximating the one-dimensional heat equation is ill-conditioned when heat conductivity changes radically. An algebraic reformulation of the tridiagonal produces a well-conditioned matrix. Additional variables are rates q=−ku_x at interfaces between radical changes in k. A reduced matrix amounts to a coarse approximation.     

Innovative light metals: metal matrix composites and foamed aluminium

Low weight is required especially for those means of transport, in which material properties have to be evaluated with respect to their specific mass. The possibility of increasing the specific properties of recyclable light metals are described: reinforcements by ceramic particulates, by continuous ceramic or carbon fibres, or by the reduction of weight by foaming the metal. Examples of castings, extrusions and forgings of particulate reinforced (<30 vol.%) aluminium alloys are given and their advantages including stiffness and wear resistance are presented. The technique of selective reinforcements by co-extrusion of particulate reinforced alloys together with conventional alloys is described. High volume fractions (>40 vol.%) of reinforcements can be produced by gas pressure infiltration of either particulate or fibre preforms. In the case of aluminium matrix, the specific strength can be increased by a factor of up to 15, and the specific stiffness by a factor of up to 7, whereas for carbon fibre reinforced magnesium the specific strength can be increased even more. The anisotropy of fibre reinforced metal matrix composites is discussed as well as the possibilities to use cross ply preforms. The technique of foaming aluminium alloys yields materials with a specific mass in the range of 0.3–1.0 g/cm³. Such structures with essentially closed pores exhibit higher specific stiffness for beams and membranes than massive metal. The measurement and definition of stiffness and strength values appropriate for aluminium foams are presented by referring to compression tests.     

Three‐dimensional finite element implementation of the nonuniform transformation field analysis

In this paper aspects of the nonuniform transformation field analysis (NTFA) introduced by Michel and Suquet (Int. J. Solids Struct. 2003; 40 :6937–6955) are investigated for materials with three‐dimensional microtopology. A novel implementation of the NTFA into the finite element method (FEM) is described in detail, whereas the NTFA was originally used in combination with the fast Fourier transformation (FFT). In particular, the discrete equivalents of the averaging operators required for the preprocessing steps and an algorithm for the implicit time integration and linearization of the constitutive equations of the homogenized material are provided. To the authors knowledge this is the first implementation of the method for three‐dimensional problems. Further, an alternative mode identification strategy is proposed with the aim of small computational cost in combination with good efficiency. The new identification strategy is applied to three‐dimensional metal matrix composites in order to investigate its effective non‐linear behaviour. The homogenized material model is implemented into ABAQUS/STANDARD. Numerical examples at integration point level and in terms of structural problems highlight the efficiency of the method for three‐dimensional problems. Copyright © 2010 John Wiley & Sons, Ltd.     

Fabrication of multi-walled carbon nanotube-reinforced carbon fiber/silicon carbide composites by polymer infiltration and pyrolysis process

Multi-walled carbon nanotube (MWNT)-reinforced carbon fiber/silicon carbide (C_f/SiC) composites were prepared using a polymer infiltration and pyrolysis (PIP) process. The MWNTs used in this study were modified using a chemical treatment. The MWNTs were found to be well dispersed in the matrix after ultrasonic dispersion, and the mechanical properties of the C_f/SiC composite were significantly improved by the addition of MWNTs. The addition of 1.5 wt.% of MWNTs to the C_f/SiC composite led to a 29.7% increase in the flexural strength, and a 27.9% increase in the fracture toughness.     

信息压缩阵在传感器智能化功能实现中的应用

传感器的智能化功能包括非线性校正、自校零与自校准、噪声抑制、自补偿、自诊断等，最小二乘法能较好地实现这些功能。而最小二乘法中模型的阶次和参数的确定是非常重要的，信息压缩阵能够方便地实现阶次和参数的同时确定,简化了运算，提高了工作效率。本文主要讨论了信息压缩阵在非线性校正中的应用。     

光纤型偏振OCT 系统中光偏振特性的研究

建立了偏振光在生物组织中传播的模型,并利用该模型模拟了偏振光在生物组织中传播的过程,重建了多种偏振态输入光的情况下光偏振态在生物组织中的分布及生物组织的偏振特性模型.分析了光偏振度与光被生物组织散射次数的关系,阐明了由于偏振光在组织中传播,其偏振态逐渐改变而造成的偏振OCT 干涉计两臂光束失去相干性及偏振OCT 图像质量下降现象.通过分析斯托克斯(Stokes)矢量和穆勒(Muller)矩阵在光纤型偏振OCT系统中的应用,说明Muller 矩阵不受输入光偏振态的影响,因此它比Stokes 矢量更适用于光纤型偏振OCT 系统研究.     

幅相误差对MUSIC算法空域谱及分辨性能影响的分析

基于正交投影矩阵扰动定理,推导了幅相误差条件下MUSIC算法空域谱的一阶统计表达式,并且给出了一种求解平均信噪比分辨门限的一元二次方程,从而能够计算出相应的信噪比分辨门限.相比目前已有的方法,空域谱的一阶统计表达式不需要计算理想协方差矩阵的特征值和特征向量,仅需要已知阵列流型向量和信源协方差矩阵,并且给出的平均信噪比分辨门限适用于信源功率不一致的情况.数值实验验证了理论分析的正确性.     

Influence of Al addition on microstructures of Cu−B alloys and Cu−ZrB2 composites

The influence of Al addition on the microstructure of Cu−B alloys and Cu−ZrB₂ composites was investigated using scanning electron microscopy, X-ray diffraction and first-principles calculation. The results show that the eutectic B in Cu−B alloys can be modified by Al from coarse needles to fine fibrous structure and primary B will form in hypoeutectic Cu−B alloys. As for Cu−ZrB₂ composites, Al can significantly refine and modify the morphology of ZrB₂ as well as improve its distribution, which should be due to its selective adsorption on ZrB₂ surfaces. The first-principles calculation results indicate that Al is preferentially adsobed on ZrB₂ (12(__)10), then on ZrB₂ (101(__)0), and finally on ZrB₂ (0001). As a result, smaller sized ZrB₂ with a polyhedron-like, even nearly sphere-like morphology, can form. Due to Al addition, the hardness of Cu−ZrB₂ composites is greatly enhanced, but the electrical conductivity of the composites is seriously reduced.