Grouped coordinate minimization using Newton's method for inexact minimization in one vector coordinate

Letf(x,y) be a function of the vector variablesx R ⁿ andy R ^m. The grouped (variable) coordinate minimization (GCM) method for minimizingf consists of alternating exact minimizations in either of the two vector variables, while holding the other fixed at the most recent value. This scheme is known to be locally,q-linearly convergent, and is most useful in certain types of statistical and pattern recognition problems where the necessary coordinate minimizers are available explicitly. In some important cases, the exact minimizer in one of the vector variables is not explicitly available, so that an iterative technique such as Newton's method must be employed. The main result proved here shows that a single iteration of Newton's method solves the coordinate minimization problem sufficiently well to preserve the overall rate of convergence of the GCM sequence.The authors are indebted to Professor R. A. Tapia for his help in improving this paper.     

A long-time tail for random walk in random scenery

Consider a simple random walk on ^d whose sites are colored black or white independently with probabilityq, resp. 1–q. Walk and coloring are independent. Letn _k be the number of steps by the walk between itskth and (k+1) th visits to a black site (i.e., the length of itskth white run), and let _k =E(n _k )–q ^–1. Our main result is a proof that (*) lim _k k ^d/2 _k = (1 –q)q ^{d/2 – 2}(d/2) ^d/2. Since it is known thatq ^{– 1} _k =E(n ₁ n _{k + 1} B) –E(n ₁ B)E(n _{k + 1} B), withB the event that the origin is black, (*) exhibits a long-time tail in the run length autocorrelation function. Numerical calculations of _k (1k100) ind=1, 2, and 3 show that there is an oscillatory behavior of _k for smallk. This damps exponentially fast, following which the power law sets in fairly rapidly. We prove that if the coloring is not independent, but is convex in the sense of FKG, then the decay of _k cannot be faster than (*).     

Dielectric relaxation of ball-like labels in polyisoprene

Ball-like molecules with strong dipoles (labels) were mixed with synthetic polyisoprene (IR305) in low concentrations (<1%) and measured dielectrically in the frequency range 10^–2–10⁷ Hz and the temperature range –70–0°C (glass relaxation region). Calorimetric measurements showed that this type of label has a plasticizing effect on the polymeric matrix. The dielectric measurements showed that these ball-like molecules relax through cooperative rotations with the polymeric segments and at the same relaxation frequency. In addition, the label molecules showed a high-frequency local relaxation process. The relaxation strength ratio of the local process (X _local) to the total relaxation strength of the label was found to be dependent on the volume as well as on the shape of the label. A comparison between the relaxation behaviors of the ball-and rod-like molecules, having the same volume, showed that the length of the label is also an important parameter for the determination of the local contribution as well as of the cooperative relaxation mechanism of the label. The label relaxation process is discussed in relation to the molecular packing of the host polymer.     

Random walk in an inhomogeneous medium with local impurities

In spite of Sinai's result that the decay of the velocity autocorrelation function for a random walk on ^d (d=2) can drastically change if local impurities are present, it is shown that local impurities can not abolish weak convergence to the Brownian motion if d2.     

含有大位移动边界的复杂流场的数值模拟

含有运动弹丸的膛口流场是典型的大位移动边界问题,同时弹丸在出膛过程中,流场的结构也会发生变化,增加了流场的复杂程度.在对该流场的数值模拟中,将它分为两个区:弹丸运动区和普通流场区,它们之间用一个特殊的分区边界联系,同时运用网格局部重构技术处理弹丸运动造成的网格变形问题,并将对称轴定义为网格变形边界,使得弹丸在对称轴上运动过程中不会导致对称轴上的网格体积为负.从计算结果可以看出整个膛口波系结构变化过程和弹丸先加速后减速的过程,从而表明该动网格处理方法是成功的.     

通过表面机械加工调控Zr52.5Cu17.9Ni14.6Al10Ti5非晶合金的结构和韧性

作为一种新型结构材料,非晶态合金的韧性需要进一步提高.提高非晶态合金韧性的方法有引入枝晶相、调整其成分改变其泊松比影响其剪切带衍生、裂纹扩展等.本文通过表面机械加工的方法来调控非晶态合金的微观结构及韧性.我们采用真空电弧熔炼、亚稳态薄板离心浇铸系统制备了Zr_52.5Cu_17.9Ni_14.6Al₁₀Ti₅(原子百分比)(Vit105)非晶合金板,并用表面机械研磨处理方法 (surface mechanical attrition treatment, SMAT),在Vit105板上形成纳米尺度局域类晶体序结构.基于差示扫描量热分析、纳米压痕实验,我们发现SMAT处理后的Vit105合金板表面附近弛豫焓更低,微观结构更加均匀、稳定.通过显微维氏硬度计测试,发现SMAT处理后样品的表面附近硬度增大,硬度值分布也更均匀.通过三点弯断裂实验,可得到SMAT处理后合金板缺口韧度值从70.7±4.7 MPa·m^1/2提高到112.8±3.7 MPa·m^1/2<...     

Local Intrinsic Dimensionality,Entropy and Statistical Divergences

Properties of data distributions can be assessed at both global and local scales. At a highly localized scale, a fundamental measure is the local intrinsic dimensionality (LID), which assesses growth rates of the cumulative distribution function within a restricted neighborhood and characterizes properties of the geometry of a local neighborhood. In this paper, we explore the connection of LID to other well known measures for complexity assessment and comparison, namely, entropy and statistical distances or divergences. In an asymptotic context, we develop analytical new expressions for these quantities in terms of LID. This reveals the fundamental nature of LID as a building block for characterizing and comparing data distributions, opening the door to new methods for distributional analysis at a local scale.     

X射线光谱数据处理平台的优化设计

在低计数率背景下X射线谱的高精度测量受X射线流的统计涨落影响,统计涨落决定了给定探测器能量分辨率的理论极限,而其他因素的影响则可以通过适当的噪声滤除和电子技术来降低.以往关于能量分辨率的研究大多利用谱反卷积对获取到的能谱进行后处理,从而降低特征峰的半高宽(FW H M).这些后处理方法是基于将获取到的能谱建模为输入能谱...     

预应力约束下混凝土梁端的边角受压极限承载力分析

根据摩尔库伦破坏准则,提出梁端混凝土在预应力钢筋约束下的边角受压极限承载力的计算方法,并得出极限承载力理论值.通过与有限元软件ABAQUS计算出梁端混凝土在预应力钢筋约束下的边角受压极限承载力结果进行比较,发现摩尔库伦破坏准则所得的理论公式与数值分析结果相近,验证了本文推导的理论公式的正确性.该理论公式表明,预应力能较好地改善梁端混凝土的受力状态,提升梁端的极限承载力.     

影响江西省高校网球选项课发展的因素分析及对策

通过对江西省38所普通高校网球选项课的现状进行走访调查,采用问卷调查法、文献资料法、访谈法和逻辑分析法,对影响江西高校网球选项课发展的诸因素进行了调查分析。结果表明,大学生一方面渴望开设网球选项课,但学校的场地、师资等严重制约了其发展,对如何促进江西省高校网球选