基于多尺度信息融合的层次聚类算法

在体绘制领域和图像分割中,数据集通常具有流形结构,各部分边界连接紧密且伴随局部噪声,给传统聚类算法的应用带来了较大的困难．本文根据非参数密度估计方法提出了一种基于多尺度信息融合的层次聚类算法．新算法通过整合密度差异和边界信息构造了一种多尺度结构信息融合的相似性度量,通过水平集的图连接策略推导出一种层次化的类结构剖析过程以获取稳定的聚类结果．新算法不受数据集形状、密度类型的限制,无需对数据集进行假设,可自动识别数据集常见的聚类结构特征．同时聚类结果较为稳定,算法对噪声具有较强的鲁棒性．从人工数据集和真实数据集以及应用试验的测试结果可以看出新算法的优越性能．     

锥-逼近多值函数和集值优化的近似解

最优性条件和对偶理论是集值向量优化研究领域的重点问题之一．本文的目的是建立一类广义凸集值优化的最优性条件和对偶定理,在锥-逼近多值函数概念的基础上,定义集值映射的一类新的广义不变凸性,称之为次不变凸集值映射,在这类广义凸性假设下,研究最优性条件和对偶定理．利用分析的方法,本文得到了集值优化问题关于弱近似极小元的一个最优性充分条件,以及Mond-Weir和Wolfe两种模型下的弱对偶定理、强对偶定理和逆对偶定理．本文所得结果丰富和深化了集值优化理论及其应用的研究内容．     

Grain-to-grain variations in NbC particle size distributions in an austenitic stainless steel

Quantitative information has been obtained concerning the size distributions of NbC precipitate particles in different grains in a deformed and aged austenitic stainless steel specimen. The precipitate size distributions obtained differ from one grain to another. The average disparity measured between the mean precipitate sizes was a function of the distance betwen the grains compared. The results obtained are considered in terms of differences in precipitation behaviour due to variations in the levels of plastic strain in constituent grains of the deformed specimen.Formerly Department of Pure Mathematics and Mathematical Statistics, University of Cambridge     

Hilbert空间中由Rosenblatt过程驱动的带有限延迟的随机发展方程

Rosenblatt过程作为一个重要的自相似随机过程,常被用来刻画非高斯随机现象．为进一步研究Rosenblatt过程 对随机现象的刻画,本文考虑由Rosenblatt过程驱动的带有限延迟的一类时间相依随机发展方程适度解的问题．在实值 可分Hilbert空间中,运用Banach不动点定理得到了Rosenblatt过程驱动的带有限延迟的随机发展方程适应解 的存在性和唯一性,并通过例子说明所得结果是有效的．     

Hybrid GEE 方法和 QIF 方法的比较

在纵向数据分析中,广义估计方程（GEE）方法被广泛应用．无论相关矩阵是否正确识别,通过 GEE 方法得到的参数估计都是相合的．但是,当选取的工作相关矩阵与真实相关阵相差较大时,所得参数估计的效可能会较低．为了降低工作相关矩阵的选取对于参数估计的效的影响,研究者提出了二次推断函数（QIF）方法和 Hybrid GEE 方法．本文通过数值模拟对 QIF 方法和 Hybrid GEE 方法进行分析比较．     

一类具有阶段结构和饱和发生率的生态流行病模型的稳定性

本文研究一类食饵具有阶段结构且捕食者染病的具有饱和发生率的捕食者-食饵模型的稳定性及其Hopf分支,讨论了由疾病的潜伏期引起的时滞对种群动力学性态的影响．通过分析特征方程,运用Hurwitz判定定理,讨论了该模型边界平衡点和正平衡点的局部稳定性,并得到了Hopf分支存在的充分条件;通过构造适当的Lyapunov泛函,运用LaSall不变集原理,讨论了该模型边界平衡点和正平衡点的全局稳定性,从而得到了疾病流行而最终形成地方病及消灭的充分条件．     

无限弹性基底上热电薄膜的屈曲行为研究

本文研究了热电薄膜粘合到弹性基底结构的屈曲行为．将界面剪切应力和薄膜的轴向应力结合起来,建立了热电薄膜的计算模型,利用边界条件将所求问题转化为一个奇异积分方程．通过使用切比雪夫多项式展开求解奇异积分方程,得到归一化应力强度因子．确定了膜厚度和基材与膜刚度比对薄膜应力和界面应力强度因子的影响．讨论了薄膜长度和厚度比对薄膜应力和界面应力强度因子的影响．结果显示薄膜和基底之间的刚度比对薄膜的应力水平有着较明显的影响．     

变量选择集成方法

随着海量高维数据在众多研究和应用领域的不断涌现,如何利用数据的稀疏性特征,从中挖掘到有价值的信息显得至关重要．变量选择作为可解释性建模、提高统计推断和预测精度的有效工具,在高维数据的分析中发挥着愈来愈重要的作用．由于集成学习能显著提高选择精度、缓解变量选择过程的不稳定性、降低噪声变量被误选的机率,变量选择集成方法近年来得到了广泛研究．为了给相关方向的研究者提供一个系统的参考资料,论文对现有的变量选择集成方法进行了详细阐述,按照构建集成所用的不同策略将其分为两大类,分析了各类方法的特征,并采用数值试验研究了各类方法在变量选择、预测等方面的性能．最后,论文对变量选择集成方法在未来值得研究的方向进行了探讨．     

一类非标准离散霍乱动力学模型

本文旨在利用非标准有限差分方法离散并求解一个包含预防接种的霍乱传染病模型．该离散模型具有和对应的原连续模型一致的平衡点,正性和有界性等性质．其次本文证明当基本再生数小于 1 时,无病平衡点是局部渐近稳定和全局渐近稳定的;当基本再生数大于 1 时,通过构造适当的 Lyapunov 函数,地方病平衡点也是全局渐近稳定的．最后利用离散模型可以成功模拟 2008 年津巴布韦霍乱,并可数值证明离散模型的稳定性,且与步长和初始条件等无关,再与其他离散方法比较验证 NSFD 方法的优势所在．     

半线性时滞模糊微分方程解的存在性

模糊微分方程常用来模拟不确定条件下的变化过程．其理论被广泛的应用在很多不同的实际问题上．本文主要研究半线性时滞模糊微分方程解的存在性．在广义Hukuhara导数的框架下,运用了一个弱压缩映射的不动点定理,将半线性时滞模糊微分方程解的存在性问题转化为算子不动点的存在性问题,从而建立了方程解的存在性定理．文中例子说明了该理论结果的实用性．     

相依误差下异方差非参数回归模型的样条估计

一些经济金融等实际数据中含有非线性趋势、异方差和相依关系,固定设计和相依误差下的异方差非参数回归模型因其能够反映这些数据特征而有着重要的应用．样条方法是常用的非参数光滑方法之一．为了探究样条方法在这类模型中的可用性,本文在$\alpha$- 混合条件下,讨论了均值函数和方差函数的多项式样条估计的逐点相合性,得到了逐点收敛速度．此外,还对所讨论的方法进行了数值模拟,结果表明样条方法在这类模型的应用中是可行的．     

土壤溶质迁移方程的迎风稳定有限点法

针对土壤溶质迁移方程具有对流项的特性,构造了迎风稳定有限点方法．该方法采用自适应迎风格式使其支持域偏向于迎风侧,以获取到上游信息,在对流占优的情况下,避免数值震荡现象．通过对一维和二维土壤溶质迁移方程的数值计算,详细分析了在不同布点、不同时间步长、不同影响因子的作用下,新算法数值解的收敛性、收敛阶与稳定性．数值结果表明本文方法在边界及梯度变化大的区域内,可以有效地提高计算精度,达到消除数值震荡的目的．     

日本设计师泽田泰广

泽田泰广毕业于日本东京美术与音乐大学平面设计专业，1985年开始他的设计生涯，在日本著名的Suntory酒业公司创作部担任美术指导，1989年，泽田泰广创建了自己的公司——泽田泰广设计工作室，从事广告，出版、包装，纺织品及展览设计，1994年至今他担任日本著名设计学府多摩美术大学的平面设计系副教授。     

MHD flow past a sphere at low and moderate Reynolds numbers

The steady incompressible magnetohydrodynamic (MHD) flow past a sphere with an applied magnetic field parallel to the main flow is studied for the Reynolds number, Re, up to 100 and interaction parameter, N, up to 0.7. The magnetic Reynolds number is assumed to be small. It is observed that drag coefficient increases as N increases. The Finite difference method is used to solve the vorticity-stream function form of the non-linear Navier-Stokes equations. The multigrid method is used to solve the finite difference equations. The fifth decimal place convergent solutions are obtained upto the finest grid of 1024×512. Graphs of the streamlines, vorticity lines, surface vorticity and drag coefficient are presented.The authors are grateful to the Principal, Pondicherry Engineering College and Head, Department of Mathematics, Pondicherry Engineering College for providing the necessary facilities. The authors are thankful to Dr. Umamaheswara Rao, Department of Applied Mathematics, Andhra University, Visakhapatnam and Dr. R. Sivakumar, Department of Physics, Pondicherry Engineering College, for their encouragement.     

X-ray photoelectron spectroscopic studies of flux grown CsMnFeF6 single crystals

This letter is a dedication to Professor R. Srinivasan, Department of Crystallography and Biophysics, University of Madras, on his sixtieth birthday.     

Functions of singular random matrices with applications

This article describes how the Jacobian is found for certain functions of a singular random matrix, both in the general case and in that of a non-negative, definite random matrix. The Jacobian of the transformationV=S ² is found whenS is non-negative definite; in addition, the Jacobian of the transformationY=X ⁺ is determined whenX ⁺ is the generalized, or Moore-Penrose, inverse ofX. Expressions for the densities of the generalized inverse of the central beta and F singular random matrices are proposed. Finally, two applications in the field of Bayesian inference are presented. This work was supported in part by the research project 39017E of CONACYT-México This article was written during the first author's stay as a Visiting Professor in the Department of Statistics at the University of Granada, Spain     

Motion of decaying vortex rings with non-similar vorticity distributions

Summary The motion and decay of circular vortex rings with an inner viscous core is considered by systematic matching of inner and outer asymptotic expansions. The governing Navier-Stokes equations are reduced to a coupled integro-differential system. A method of construction of solutions for the integro-differential system is presented. The initial vorticity distribution may be non-similar. Also presented is a method for introducing a time shift which makes the first term in the series solution for the vorticity to be the best approximation. The analysis is then applied to the motion and decay of a pair of coaxial vortex rings.This work was supported by the United States Air Force, Office of Scientific Research, Contract AF-AFOSR 67-1062D. The author wishes to acknowledge the invaluable suggestions and discussions of Professor Lu Ting of the Department of Mathematics at New York University.     

Character sum constructions of constrained error-correcting codes

We estimate parameters of constrained error-correcting codes constructed by means of additive and multiplicative characters. To get the bounds we derive estimates for some incomplete character sums.This work was supported in part by the Academy of Finland. The first-named author would also like to express his gratitude to the Department of Mathematics of the University of Turku for the hospitality during his visit in August, 1992.     

Using Log Assignments to Foster Learning: Revisiting Writing across the Curriculum

During the past several years, the authors have conducted experiments in the use of writing to learn (WTL) techniques in sophomore‐level engineering mechanics courses at West Virginia University (WVU). The work was a collaborative effort between a doctoral candidate in the Curriculum and Instruction Department and an Associate Professor of Mechanical and Aerospace Engineering. This paper focuses on the effectiveness of several writing to learn strategies, assigned and completed in the Engineer's Log, which students identified as successful methods for learning. We present and discuss these strategies using sample log entries to illustrate their use and to suggest that expressive writing, or writing for the self, continues to prove itselfa successful technique for learning. Finally, we evaluate the data provided and discuss our results.     

Industrial design in a time of change

Professor Rams has been designing products for a quarter of a century. He describes himself as a pragmatist. His experience and problems are concrete. As Head of the Product Design Department he is responsible for the electrical and electronic consumer goods for which that company is known the world over. He has also designed some thirteen furniture systems for Wiese Vitsoe and teaches design to University students.In this thought provoking article Professor Rams describes the quest of the designer, the diffuculties he faces in modern society and the responsibilities he bears for the future. It is a rare insight into the principles and philosophy of one of the World's leading industrial designers.