评价机械加工表面形貌的小波变换方法

提出了用小波变换计算粗糙表面分形维数的新方法，并基于Weierstrass-Mandelbrot函数(W-M函数Majumdar-Bhushan函数(M-B函数)对该方法进行了验证，结果表明该方法具有很高的 计算精度。应用小波变换方法对核态池沸腾试验板表面形貌的分形特征进行了评价，包括铜和不锈钢材料，轧制、砂纸打磨和表面机械抛光等3种加工方法生成5个粗糙度级别的试验板，研究结果表明该方法能有效评价表面形貌的分形特征。

Some Results on Fixed and Best Proximity Points of Multivalued

This paper is devoted to investigate the fixed points and best proximity points of multivalued cyclic self-mappings on a set of subsets of complete metric spaces endowed with a partial order under a generalized contractive condition involving a Hausdorff distance. The existence and uniqueness of fixed points of both the cyclic self-mapping and its associate composite self-mappings on each of the subsets are investigated, if the subsets in the cyclic disposal are nonempty, bounded and of nonempty convex intersection. The obtained results are extended to the existence of unique best proximity points in uniformly convex Banach spaces.

Long memory in return structures from developed markets

[En]The present study aimed at investigating the existence of long memory properties in ten developed stock markets across the globe. When return series exhibit long memory, the series realizations are not independent over time and past returns can help predict future returns, thus violating the market efficiency hypothesis. It poses a serious challenge to the supporters of random walk behavior of the stock returns indicating a potentially predictable component in the series dynamics. We computed Hurst-Mandelbrot’s Classical R/S statistic, Lo’s statistic and semi parametric GPH statistic using spectral regression. The findings suggest existence of long memory in volatility and random walk for logarithmic return series in general for all the selected stock market indices. Findings are in line with the stylized facts of financial time series.

Locally convex Riesz spaces and Archimedean quotient spaces

A Riesz space with a Hausdorff, locally convex topology determined by Riesz seminorms is called a locally convex Riesz space. A sequence {x_n} in a locally convex Riesz space L is said to converge locally to x ϵ L if for some topologically bounded set B and every real r ˃ 0 there exists N (r) and n ≥ N (r) implies x – x_n ϵ r^b. Local Cauchy sequences are defined analogously, and L is said to be locally complete if every local Cauchy sequence converges locally. Then L is locally complete if and only if every monotone local Cauchy sequence has a least upper bound. This is a somewhat more general form of the completeness criterion for Riesz – normed Riesz spaces given by Luxemburg and Zaanen. Locally complete, bound, locally convex Riesz spaces are barrelled. If the space is metrizable, local completeness and topological completeness are equivalent.

Two measures of the non-archimedean character of a non-archimedean Riesz space L are the smallest ideal A_o (L) such that quotient space is Archimedean and the ideal I (L) = { x ϵ L: for some 0 ≤ v ϵ L, n |x| ≤ v for n = 1, 2, …}. In general A_o (L) ᴝ I (L). If L is itself a quotient space, a necessary and sufficient condition that A_o (L) = I (L) is given. There is an example where A_o (L) ≠ I (L).

A necessary and sufficient condition that a Riesz space L have every quotient space Archimedean is that for every 0 ≤ u, v ϵ L there exist u₁ = sup (inf (n v, u): n = 1, 2, …), and real numbers m₁ and m₂ such that m₁ u₁ ≥ v₁ and m₂ v₁ ≥ u₁. If, in addition, L is Dedekind σ – complete, then L may be represented as the space of all functions which vanish off finite subsets of some non-empty set.

Coincidence and common fixed point theorems for Suzuki type hybrid contractions and applications

Coincidence and common fixed point theorems for a class of Suzuki hybrid contractions involving two pairs of single-valued and multivalued maps in a metric space are obtained. In addition, the existence of a common solution for a certain class of functional equations arising in a dynamic programming is also discussed.

北京地区植被景观的空间分布特征

本文利用地理信息系统(GIS)技术、景观生态学理论和方法、分形理论以及统计分析方法对北京地区植被景观的空间分布特征进行了分析，并对景观格局和景观多样性的分析方法进行了探讨，结果表明： (1)对几乎所有的斑块类型，其斑块大小的分布都不是对称的，而是右偏的。4种概率分布（Г—分布、对数正态分布、Weibull分布和（负）指数分布）都只能刻划部分斑块类型，并且服从对数正态分布的斑块类型最多，服从（负）指数分布的斑块类型最少。 (2)随着斑块面积的增加，边界效应越来越小，而斑块形状越来越不紧凑。 (3)分形分析识别出本地区植被景观中的两个尺度域：一个是斑块面积小于(大约)2.7km2，另一个是斑块面积大于(大约)2.7km2。两个域中的斑块复杂程度有很大差异，后一个域中的斑块明显比前一个域中的斑块复杂，并且随着斑块面积的增加，斑块形状越来越复杂。 (4)用斑块数作为多度指标时，该景观的斑块类型一多度分布服从（截断）对数正态分布和（截断）负二项分布，不服从对数级数分布和几何分布。用斑块面积作为多度指标时，该景观的斑块类型一多度分布服从对数正态分布、Weibull分布和Г—争布，不服从正态分布。从而该景观的斑块类型一多度分布不是对称的，也是右偏的。在4个优势度／多样性模型中，“生态位优先占领”模型和Zipf-Mandelbrot模型可以较好地刻划该景观的斑块类型一多度关系。 (5)样本大小对多样性测度有直接的影响。如果这种影响比较小，就说明测度指标比较稳定。三个丰富度指数中，Ri比R2和R3更稳定;五个多样性性指数中，D和Di最稳定，OD最不稳定，因此，OD是用于景观多样性监测的理想指标;五个均匀度指数中，Jgi最稳定。根据设计的3种计算临界样方数量（即多样性测度指标达到稳定时的样方数量）方法的计算结果，上述几个最稳定的测度指标在通常情况下只需要几个样方(即总抽样面积为数百km2)就达到稳定状态。 (6)斑块类型数目随面积的增加而增加。根据四个评价指标的评价结果，认为双曲线对该景观的斑块类型一面积关系的拟合效果最好。 (7)样本较大（对于一阶刀切估计，大于30个样方;对于二阶刀切估计，大于60个样方）时，刀切法能够给出斑块类型数目(NPT)较好的估计;样本较小（小于30个样方）时，Mingoti和Meeden提出的经验贝叶斯方法能够对NPT给出比刀切法和自助法更好的估计。斑块类型一面积曲线外推虽然也能给出NPT较好的估计，但这种方法需要慎重使用，不能外推得很远。 (8)列联表分析表明，该植被景观中的斑块类型与土壤类型、岩石类型、海拔高度和坡向各因子之间均存在显著的相关性。植被景观多样性与岩石类型多样性和地形多样性之间也均呈显著的正相关关系，即植被景观多样性随岩石类型多样性和地形多样性的增加而增加。但植被景观多样性与土壤类型多样性之间不存在显著的线性相关或秩相关关系，这可能是由于二者的分类体系不吻合。植被景观多样性与总的道路密度和第二类道路密度之间均呈显著的负相关关系，而与第一类和第三类道路密度之间的关系都不显著。这反映出景观样本单元(10kmxlOkm)的尺度对应于第二类道路的影响尺度。而道路密度在一定程度上反映了人类活动的强度，因此，在10kmxlOkm这个尺度上，人类活动愈剧烈，景观多样性就愈小。

Effect of surface roughness on rarefied-gas heat transfer in microbearings

In this Letter, the rarefaction and roughness effects on the heat transfer process in gas microbearings are investigated. A heat transfer model is developed by introducing two-variable Weierstrass-Mandelbrot (W-M) function with fractal geometry. The heat transfer problem in the multiscale self-affine rough microbearings at slip flow regime is analyzed and discussed. The results show that rarefaction has more significant effect on heat transfer in rough microbearings with lower fractal dimension. The negative influence of roughness on heat transfer found to be the Nusselt number reduction. The heat transfer performance can be optimized with increasing fractal dimension of the rough surface. © 2012 Elsevier B.V. All rights reserved.

Slip flow and heat transfer in microbearings with fractal surface topographies

The effects of random surface roughness on slip flow and heat transfer in microbearings are investigated. A three-dimensional random surface roughness model characterized by fractal geometry is used to describe the multiscale self-affine roughness, which is represented by the modified two-variable Weierstrass- Mandelbrot (W-M) functions, at micro-scale. Based on this fractal characterization, the roles of rarefaction and roughness on the thermal and flow properties in microbearings are predicted and evaluated using numerical analyses and simulations. The results show that the boundary conditions of velocity slip and temperature jump depend not only on the Knudsen number but also on the surface roughness. It is found that the effects of the gas rarefaction and surface roughness on flow behavior and heat transfer in the microbearing are strongly coupled. The negative influence of roughness on heat transfer found to be the Nusselt number reduction. In addition, the effects of temperature difference and relative roughness on the heat transfer in the bearing are also analyzed and discussed. © 2012 Elsevier Ltd. All rights reserved.

OpenMP循环调度算法及SpMV多核并行化研究

OpenMP是一种支持Fortran，C/C++的共享存储并行编程标准。它基于fork-join的并行执行模型，将程序划分为并行区和串行区。近几年来，OpenMP在SMP(Symmetric Multi-Processing)和多核体系结构的并行编程中得到了广泛的应用。随着多核处理器的发展，实际的应用程序如何充分利用多个处理器核来提高运算效率也成为研究的热点。 在科学计算中，循环结构是最核心的并行对象之一。考虑到负载平衡、调度开销、同步开销等多方面因素，OpenMP标准制定了Static调度、Dynamic调度、Guided调度和Runtime调度等不同策略。针对Guided调度策略不适合递减型循环结构的缺点，本文提出了一种改进的new_guided调度策略，并在OMPi编译器上加以实现。New_guided调度策略的主要思想是对前半部分的循环采用Static调度，后半部分的循环采用Guided调度。此外，本文针对不同的循环结构，在多核处理器上对不同的调度策略进行了评测。测试结果表明，在一般情况下，OpenMP默认的Static策略的调度性能最差；对于规则的循环结构和递增的循环结构，Dynamic调度策略、Guided调度策略和new_guided策略的性能差别不大；对于递减型的循环结构，Dynamic调度策略和new_guided策略的性能相当，要优于Guided调度策略；对于求解Mandelbrot集合这类计算量集中在中间的随机循环结构，Dynamic调度策略优于其它策略，new_guided策略的性能介于Dynamic调度和Guided调度之间。 随着多核处理器的问世和发展，多线程程序设计也已经成为一个不可回避的问题。稀疏矩阵向量乘(SpMV, Sparse Matrix-Vector Multiplication)是一个十分重要且经常被大量调用的科学计算内核。SpMV的存储访问一般都极不规则，导致现有的SpMV算法效率都比较低。目前，多核处理器芯片上的内核数量正在逐步增加。这使得在多核处理器上对SpMV进行并行化加速变得非常重要。本文介绍了稀疏矩阵的两种常用的存储格式CSR和BCSR，并采用OpenMP实现了SpMV的多核并行化。此外，本文还讨论了寄存器分块算法、压缩列索引等优化技术，以及不同调度策略对多线程并行后的SpMV的影响。在曙光天阔服务器S4800A1上的测试表明，大部分矩阵都取得了可扩展、甚至是超线性的加速比，但是对于部分规模较大的矩阵，加速效果并不明显。在我们的测试中，与基于CSR实现的多线程SpMV相比，采用寄存器分块算法优化后的SpMV运算速度平均提高了28.09%。在基于CSR实现的多线程SpMV中，采用列索引优化技术后的程序比优化前的速度平均提高了13.05%。此外，本文实现了一种基于非零元个数的调度策略。在该策略中，每个线程处理几乎相同数量的非零元。我们将它和OpenMP标准提供的三种调度策略进行了测试和分析。测试结果表明：与OpenMP提供的调度策略相比，基于非零元个数的调度策略能取得更好的负载平衡；Dynamic调度和Guided调度在多线程SpMV中的性能基本相当，均优于Static调度策略。

复杂背景下运动目标检测、分割与跟踪

本文研究的内容主要是序列图像中复杂背景下运动目标检测、分割与跟踪。分别提出了曲线演化策略及在运动目标检测与分割中的应用和基于特征点跟踪的运动目标检测与分割方法。关于目标跟踪，本文应用基于模型和基于特征的两种策略，提出了稳定、有效的四种跟踪方法。基于模型的算法包括基于粒子滤波和Hausdorff距离的运动目标跟踪及基于变形模板的目标跟踪。基于特征的方法分别是基于模糊测度的目标匹配与改进不变矩的目标匹配算法。 研究了曲线演化策略及在运动目标检测与分割中的应用，提出了基于最小半径准则和队列结构的聚类算法，消除孤立区域。提出基于试探策略并结合Fisher准则自适应地确定阈值的曲线演化算法分割运动目标。该算法具有良好的实时性和分割完整准确的优点。 在基于特征点跟踪的运动目标检测分割中，通过分析角点信息(灰度、梯度大小与方向)及其邻域信息，构造方向子邻域以提高匹配精度。提出了采用聚类方法消除运动目标上特征点对集合，同时也从剩余的特征点对集合中选取最优子集估计模型参数，检测运动目标。该算法可达到实时应用目的。 目标跟踪问题可看作状态空间中贝叶斯推理问题。在粒子滤波框架内，分别构造了跟踪过程的状态转移模型和测量模型，并提出了一种基于集合的模糊测度，实现了跟踪窗口随目标自适应变化、模板更新策略。对于刚体与非刚体的孤立目标，算法能够实现对目标的稳定跟踪。 在复杂场景下变形目标跟踪中，通过定义一种点到匹配点及其邻域的广义距离测度，增强了匹配的容错性。算法采用边缘相似点的距离均值和方差作为匹配的相似测度和置信准则。通过提出在8邻域内基于马尔可夫模型的启发式规则修正模板策略，阻止了模板窗口向背景的漂移。 在基于模糊测度的目标匹配中，提出了循环移位方法构造匹配特征向量，根据特征分布的模糊隶属度确定相似测度。该算法性能优于基于灰度相关匹配方法。 在基于不变矩的图像匹配中，引入误差带策略，计算图像边缘不变矩，取前N个匹配结果作为侯选目标，并根据契比雪夫不等式确定置信度。最后计算侯选目标的直方图的统计特性目标定位。该算法在性能上明显优于应用不变矩特征直接匹配方法和灰度相关的匹配方法。

A Note of Zipf's Law, Natural Languages, and Noncoding DNA Regions

In Phys. Rev. Letters (73:2), Mantegna et al. conclude on the basis of Zipf rank frequency data that noncoding DNA sequence regions are more like natural languages than coding regions. We argue on the contrary that an empirical fit to Zipf"s "law" cannot be used as a criterion for similarity to natural languages. Although DNA is a presumably "organized system of signs" in Mandelbrot"s (1961) sense, and observation of statistical featurs of the sort presented in the Mantegna et al. paper does not shed light on the similarity between DNA's "gramar" and natural language grammars, just as the observation of exact Zipf-like behavior cannot distinguish between the underlying processes of tossing an M-sided die or a finite-state branching process.

Optical determination of fractal dimensions using Fourier transforms

R. Zwiggelaar and C.R. Bull, 'Optical determination of fractal dimensions using Fourier transforms', Optical Engineering 34 (5), 1325-1332 (1995)

Tyrosine phosphorylation of G protein alpha subunits by pp60c-src.

A number of lines of evidence suggest that cross-talk exists between the cellular signal transduction pathways involving tyrosine phosphorylation catalyzed by members of the pp60c-src kinase family and those mediated by guanine nucleotide regulatory proteins (G proteins). In this study, we explore the possibility that direct interactions between pp60c-src and G proteins may occur with functional consequences. Preparations of pp60c-src isolated by immunoprecipitation phosphorylate on tyrosine residues the purified G-protein alpha subunits (G alpha) of several heterotrimeric G proteins. Phosphorylation is highly dependent on G-protein conformation, and G alpha(GDP) uncomplexed by beta gamma subunits appears to be the preferred substrate. In functional studies, phosphorylation of stimulatory G alpha (G alpha s) modestly increases the rate of binding of guanosine 5'-[gamma-[35S]thio]triphosphate to Gs as well as the receptor-stimulated steady-state rate of GTP hydrolysis by Gs. Heterotrimeric G proteins may represent a previously unappreciated class of potential substrates for pp60c-src.

Multiplicative spectra of Banach spaces

The multiplicative spectrum of a complex Banach space X is the class K(X) of all (automatically compact and Hausdorff) topological spaces appearing as spectra of Banach algebras (X,*) for all possible continuous multiplications on X turning X into a commutative associative complex algebra with the unity. The properties of the multiplicative spectrum are studied. In particular, we show that K(X^n) consists of countable compact spaces with at most n non-isolated points for any separable hereditarily indecomposable Banach space X. We prove that K(C[0,1]) coincides with the class of all metrizable compact spaces.

On weak and strong Peano theorems

We say that the Peano theorem holds for a topological vector space $E$ if, for any continuous mapping $f : {\Bbb R}\times E \to E$ and any $(t(0), x(0))$ is an element of ${\Bbb R}\times E$, the Cauchy problem $\dot x(t) = f(t,x(t))$, $x(t(0)) = x(0)$, has a solution in some neighborhood of $t(0)$. We say that the weak version of Peano theorem holds for $E$ if, for any continuous map $f : {\Bbb R}\times E \to E$, the equation $\dot x(t) = f (t, x(t))$ has a solution on some interval. We construct an example (answering a question posed by S. G. Lobanov) of a Hausdorff locally convex topological vector space E for which the weak version of Peano theorem holds and the Peano theorem fails to hold. We also construct a Hausdorff locally convex topological vector space E for which the Peano theorem holds and any barrel in E is neither compact nor sequentially compact.