高吸收ZnSe多晶无镜光学双稳的实验观测

本文对具高吸收的ZnSe多晶材料的增加吸收型光学双稳性进行了实验观测,发现在介质的吸收远高于过去提出的理论判据时,仍能获得双稳输出,并测定了阈值开关功率与光斑尺寸及样品厚度的关系.采用分层模型分析实验结果,定性地解释了实验现象.     

单调函数的列表判别法

本文讨论了单调函数和函数的最小列表，在此基础上提出单调函数、单调递增函数和单调递减函的列表判别方法，并举例说明了判别过程。     

记录值中的随机序与年龄性质

研究记录值中的随机序与年龄性质．证明了任何通过两个分布函数的行为所定义的随机序,均可以被它们相应的记录值所保持,而两个随机变量之间的剩余财富序,可以导致其相应记录值序列的平均连续增量的序关系．也讨论了K-记录值的连续增量的年龄性质．     

Assessing the reliability of a nanocomponent using nanocrack growth

In nanoscience and nanotechnology, much attention has been given to the dual problem of designing nanocomponents with novel physical properties and how such nanocomponents can be fabricated. Receiving less attention has been the question of the nanocomponent's reliability; how does a nanocomponent fail and how long does a nanocomponent survive under typical operating conditions? High reliability is necessary to guarantee the advancement and utilization of nanocomponents due to the fact that they account for a high proportion of costs of newly designed nanosystems as well as multiscale systems. A nanocomponent is a component that is made of atoms, and its reliability is determined by these atoms. There are situations where it is hard or impossible to extract information from a nanocomponent about its relationship to its atoms. In this article, we assess the nanocomponent's reliability by using its physical properties. Specifically, it is known that nanocrack growth involves considerable statistical variability and such variability should be accounted for assessing growth. In this paper, we first provide a stochastic nanocrack growth model and then evaluate the reliability of a nanocomponent based on this model. Various properties of this model are obtained. We also evaluate the reliability of a nanocomponent under different assumptions on our proposed growth model. This paper is a modification of the extensive literature on modeling fatigue cracks in materials on a larger scale, applied to nanoscale where growth is not a function of cumulative stress on the component but related to the time to first exceedance of a threshold. Copyright © 2013 John Wiley & Sons, Ltd.     

On allocating redundancies to k‐out‐of‐ n reliability systems

For two components in series and one redundancy with their lifetimes following the proportional hazard models, we build the likelihood ratio order and the hazard rate order for lifetimes of the redundant systems. Also, for k ‐out‐of‐ n system with components’ lifetimes having the arrangement increasing joint density and the redundancies having identically distributed lifetimes, allocating more redundancies to weaker components is shown to help improve the system's reliability. Copyright © 2014 John Wiley & Sons, Ltd.     

带反射边界的倒向随机微分方程解的收敛性

对有界区间和无穷区间上带反射边界的倒向随机微分方程, 本文证明了其解的收敛性结果.     

序Banach空间中一类算子方程的可解性

利用改进的Mnch紧性条件,研究了一类算子方程Lx=Nx的解的存在性．本文结果并没有要求算子L和N的连续性．作为应用,讨论了右端项不连续的隐式椭圆偏微分方程的边值问题的解的存在性．     

Least Squares Convex-Concave Data Smoothing

We consider n noisy measurements of a smooth (unknown) function, which suggest that the graph of the function consists of one convex and one concave section. Due to the noise the sequence of the second divided differences of the data exhibits more sign changes than those expected in the second derivative of the underlying function. We address the problem of smoothing the data so as to minimize the sum of squares of residuals subject to the condition that the sequence of successive second divided differences of the smoothed values changes sign at most once. It is a nonlinear problem, since the position of the sign change is also an unknown of the optimization process. We state a characterization theorem, which shows that the smoothed values can be derived by at most 2n – 2 quadratic programming calculations to subranges of data. Then, we develop an algorithm that solves the problem in about O(n ²) computer operations by employing several techniques, including B-splines, the use of active sets, quadratic programming and updating methods. A Fortran program has been written and some of its numerical results are presented. Applications of the smoothing technique may be found in scientific, economic and engineering calculations, when a potential shape for the underlying function is an S-curve. Generally, the smoothing calculation may arise from processes that show initially increasing and then decreasing rates of change.     

Perpendicular Dissections of Space

For each pair (Q _i ,Q _j ) of reference points and each real number r there is a unique hyperplane h \perp Q _i Q _j such that d(P,Q _i ) ² - d(P,Q _j ) ² = r for points P in h . Take n reference points in d -space and for each pair (Q _i ,Q _j ) a finite set of real numbers. The corresponding perpendiculars form an arrangement of hyperplanes. We explore the structure of the semilattice of intersections of the hyperplanes for generic reference points. The main theorem is that there is a real, additive gain graph (this is a graph with an additive real number associated invertibly to each edge) whose set of balanced flats has the same structure as the intersection semilattice. We examine the requirements for genericity, which are related to behavior at infinity but remain mysterious; also, variations in the construction rules for perpendiculars. We investigate several particular arrangements with a view to finding the exact numbers of faces of each dimension. The prototype, the arrangement of all perpendicular bisectors, was studied by Good and Tideman, motivated by a geometric voting theory. Most of our particular examples are suggested by extensions of that theory in which voters exercise finer discrimination. Throughout, we propose many research problems. Received July 20, 2000, and in revised form September 29, 2001, and October 12, 2001. Online publication March 4, 2002.