纤维复合材料中弹性波散射与动应力

基于弹性波动理论,对纤维增强复合材料结构中弹性波多重散射与动应力集中问题进行了分析研究,给出了介质各区域弹性波分析解的表达式.根据位移与应力在各区界面处的连续条件,确定了未知弹性波模式系数.采用Hankel函数的加法定理,将不同局部坐标系中散射波场的表达式变换到了同一个局部坐标系中,以给出弹性波模式系数和动应力集中因子的表达式.分析了多相纤维基体中两个散射体的间距、界层区材料性质以及界层区和纤维核区截面尺寸的变化,对各区界面动应力集中系数的影响.分析表明,两个散射体的间距、界层区材料性质和结构尺寸的变化对复合材料的力学特性具有显著影响.作为算例,给出了纤维增强复合材料结构中各区界面动应力集中系数的数值结果,并对其进行了分析讨论.     

基于裂纹尖端二阶弹性解的断裂过程区尺度

基于Westergaard应力函数裂纹尖端二阶弹性解,推导了裂纹尖端微裂区的轮廓线和特征尺寸的解析表达式;采用幂函数模型描述的拉应变软化模型,确定了在最大拉应力强度理论和最大拉应变强度理论下断裂过程区（FPZ）临界值的解析表达式;将基于Westergaard应力函数一阶弹性解及二阶弹性解、Muskhelishvili应力函数和Duan-Nakagawa模型确定的FPZ临界值进行了比较．结果表明裂纹尖端微裂区和FPZ临界值随着Poisson比的减小而增加并逐渐趋近于应用最大拉应力强度理论确定的结果;二阶弹性解确定的裂纹尖端微裂区和FPZ临界值大于一阶弹性解的值;FPZ临界值随着拉应变软化指数的增加而增加;二阶弹性解确定的FPZ临界值的精度远高于一阶弹性解确定的值.     

相依型不确定变量偏差和的性质

研究实值扩展负相依(END)不确定变量中部分偏差和的同题.在不确定变量期望定义和性质的基础上,利用变量之间实值负相依性和不确定性变量的性质,得到了不确定变量偏差和的上确界性质,并将其应用于风险理论,得到了较好的结果.     

弱有限元方法在线弹性问题中的应用

本文考虑弱有限元（简称WG）方法在线弹性问题中的应用.WG方法是传统有限元方法的推广,用于偏微分方程的数值求解.和传统有限元一样,它的基本思想源于变分原理.WG方法的特点是使用在剖分单元内部和剖分单元边界上分别有定义的分片多项式函数（即弱函数）作为近似函数来逼近真解,并针对弱函数定义相应的弱微分算子代入数值格式进行计算.除此之外,WG方法允许在数值格式中引进稳定子以实现近似函数的弱连续性.WG方法具有允许使用任意多边形或多面体剖分,数值格式与逼近函数构造简单,易于满足相应的稳定性条件等优点.本文考虑WG方法在求解线弹性问题中的应用.围绕线弹性问题数值求解中常见的三个问题,即：数值格式的强制性,闭锁性,应力张量的对称性介绍WG方法在线弹性问题求解中的应用.     

不确定广义系统的鲁棒稳定界

讨论了不确定广义系统的鲁棒稳定界问题 .利用奇异值分解方法和求解 Lyapunov方程 ,在一定条件下给出了使不确定广义系统正则、无脉冲且稳定的一个稳定界 .实例说明了上述方法的可行性 .     

一类奇异积分算子在加权空间的界的估计

设T是由Grubb和Moore引入的一类奇异积分算子,它的核满足一种新型利普希茨正则性.T*是由T确定的极大奇异积分算子.本文通过建立与T和T*相关的grand极大算子的弱型端点估计,得到了算子T和T*在加权空间的由Ap权常数表示的界的估计和弱型端点估计.     

沿LiNbO3 y方向的准纵波及其超声非线性系数

本文给出了沿LiNbO₃ y方向的准纵波的非线性运动方程及其解.由于LiNbO₃晶体的二阶弹性常数c₁₄比c₁₁和 c₄₄小很多,沿y方向的准纵波非常接近纯模式,为用超声二次谐波发生技术测量晶体的超声非线性系数和三阶弹性常数提供了一个新的传播模式.对于LiNbO₃(或其它具有3m对称的晶体)从这个传播模式的超声非线性系数,可以确定一个包括c₂₂₂,c₂₄₄,c₁₁₄,c₁₂₄和c₄₄₄5个三阶弹性常数的组合.在准静态近似下,求得了与这个传播模式有关的二阶和三阶弹性常数与压电耦合的关系.用超声二次谐波发生技术测量了该模式的超声非线性系数,并求得了相应的三阶弹性常数的组合.实验和利用其他作者发表的数据计算的结果相符合.     

基于后悔理论的多时点风险灰靶决策方法

针对属性值为区间灰数,时点权重未知的多时点风险决策问题,考虑决策者的心理行为,提出一种基于后悔理论的灰靶决策方法.给出区间灰数的大小比较方法和距离测度,定义正负理想方案,根据决策者相对于负理想方案的欣喜心理与相对于正理想方案的后悔心理定义欣喜后悔值函数,采用时间度和熵值相结合的方法确定时点权重,求出各方案多时点综合欣喜后悔值并最终确定出方案的排序.最后,通过具体算例分析结果验证了该方法的可行性和有效性.     

混合向量变分不等式标量化及间隙函数误差界

利用Konnov对变分不等式问题的标量化方法,对一般的强变分不等式（SVI）和弱变分不等式（WVI）进行了进一步的推广.主要介绍了基于集值映射的强广义混合向量变分不等式（SGMVVI）和弱广义混合向量变分不等式（WGMVVI）,考虑了与它们相关的间隙函数,在合适的条件下讨论了强广义混合集值变分不等式（SGMVI）的间隙函数和SGMVVI的间隙函数之间的关系,以及WGMVVI和SGMVI的间隙函数之间的关系,最后讨论了它们的间隙函数的全局误差界.     

大于70 岁老年慢性胃炎患者血清胃蛋白酶原测定和意义

目的 探讨＞70 岁老年患者慢性胃炎中胃蛋白酶原（PG）Ⅰ、Ⅱ变化及临床意义。方法 选择经胃镜和病理诊断的 慢性胃炎240 例，分为＞70岁老年研究组（慢性非萎缩性胃炎60 例+ 慢性萎缩性胃炎60例）和20~60岁的中青年对照组（慢性非萎缩性胃炎60例+慢性萎缩性胃炎60例）。分别测定患者血清中的PGⅠ、PGⅡ，计算PGⅠ/ PGⅡ（PGR）。结果 对照组中慢性非萎缩性胃炎和慢性萎缩性胃炎患者PGⅠ、PGR有统计学差异（P＞0.05）；研究组中慢性萎缩性胃炎较慢性非萎缩性胃炎患者PGⅠ、PGR明显下降（P＜0.05）；研究组较对照组PGⅠ、PGR降低（P＜0.05）。根据ROC 曲线＞70岁老年慢性萎缩性胃炎患者PGⅠ和PGR 的界值分别为97.25μg/L、6.75。结论 血清PG检测对老年患者慢性萎缩性胃炎的筛查有意义，针对老年患者需进一步研究确定其参考范围。     

Determining cutoff values of prognostic factors in survival data with competing risks

In clinical studies, patients are often classified into high or low risk groups based on prognostic factors related to survival outcomes. Using maximally selected linear rank statistics, several methods have been developed to determine a cutoff value of the prognostic factor. We propose an extension of these methods for the circumstances that competing risks are encountered in conjunction with an event outcome of interest. A simulation study is carried out to demonstrate the performance of the proposed method using some commonly used measures such as bias, precision, and power. We also apply our method to two real datasets involving lung cancer and hepatocellular carcinoma, illustrating optimal determinations of cutoff values for binary decisions on prognosis.     

基于可靠性弹性指标的系统弹性度量方法

为深入研究系统弹性问题,首先分析系统中不同节点和边的可靠性弹性指标。通过引入节点弹性与边弹性,并考虑节点弹性与边弹性二者的联系以及对系统弹性的影响,建立了能够反映系统拓扑结构变化的弹性度量方法模型。最后,在对弹性度量方法的验证环节中,引入了具有分层特性的交通系统,按照所述弹性度量方法对分层交通系统中的节点弹性以及边弹性进行了分析,发现该种分层交通系统的整体弹性程度一般,任何小的干扰或者故障都有可能造成该交通系统拥堵或瘫痪。     

A MATHEMATICAL REVIEW OF RESILIENCE IN ECOLOGY

Rising interest in the resilience of ecological systems has spawned diverse interpretations of the term's precise meaning, particularly in the context of resilience quantification. The purpose of this paper is twofold. The first aim is to use the language of dynamical systems to organize and scrutinize existing resilience definitions within a unified framework. The second aim is to provide an introduction for mathematicians to the ecological concept of resilience, a potential area for expanded quantitative research. To frame the discussion of resilience in dynamical systems terms, a model consisting of ordinary differential equations is assumed to represent the ecological system. The question “resilience of what to what?” posed by Carpenter et al. [2001] informs two broad categories of definitions, based on resilience to state variable perturbations and to parameter changes, respectively. Definitions of resilience to state variable perturbations include measures of basin size (relevant to one‐time perturbations) and basin steepness (relevant to repeated perturbations). Resilience to parameter changes has been quantified by viewing parameters as state variables but has also considered the reversibility of parameter shifts. Quantifying this reversibility and fully describing how recovery rates determine resilience to repeated state‐space perturbations emerge as two opportunities for mathematics research.     

Scoring decisions in the context of economic uncertainty

We consider methods for incorporating forecasts of future economic conditions into acquisition decisions for scored retail credit and loan portfolios. We suppose that a portfolio manager is faced with two possible future economic scenarios, each characterised by a known probability of occurrence and by known performance functions that give expected profit and volume. We suppose further that he must choose in advance the scoring strategy and score cutoffs to optimise performance. We show that, despite the uncertainty of performance induced by economic conditions, every efficient policy consists of a single cutoff, provided the expected profit and volume performance curves in each scenario are concave. If these curves are not concave, efficient operating points can be characterised as cutoffs on a redefined score. In cases in which two scorecards are available, we show that it may be advantageous to randomly choose the scorecard to be employed, and we provide methods for selecting efficient operating points. Discussion is limited to cases with two scorecards and two economic scenarios, but our approach and results generalise to more scorecards and more economic scenarios.     

Distribution management by means of cutoff order size: a case study

We present a case study on physical distribution management for a production company in Western Europe. The company delivers finished goods both from distribution centres and directly from plants to its customers. The lead time from distribution centres is shorter, but higher costs are involved. The choice for delivery of an individual order is based on the so-called stockmix and cutoff order size. The stockmix is the set of products stocked at the distribution centre, which for efficiency reasons is restricted. Orders smaller than the cutoff order size are delivered from the distribution centre closest to the customer, provided that the product ordered is present in its stockmix. Otherwise they are delivered from the production plant that makes the product. In this paper we develop methods to determine both the stockmix and the cutoff order size for each distribution centre. The objective considered is the minimisation of distribution and handling costs subject to service constraints.     

What is the optimal cutoff surface for ore bodies with more than one mineral?

In mine planning problems, cutoff grade optimization defines a threshold at every time period such that material above this value is processed, and the rest is considered waste. In orebodies with multiple minerals, which occur in practice, the natural extension is to consider a cutoff surface. We show that in two dimensions the optimal solution is a line, and in n dimensions it is a hyperplane.     

A study in the combination of two consumer credit scores

Credit scores measure the creditworthiness of individuals in a population of interest. In this paper, we employ the concepts of sufficiency and extraneousness to study the conditions under which scoring results can be improved through the combination of individual scores. The concept of sufficiency is used to identify scores that are dominant. Extraneousness is used to determine whether a particular score provides additional useful information relative to other scores. In addition, we employ a profit-based utility measure to evaluate the performance of different scores. We investigate the performance of a regression-based combination of a bureau credit score and an application credit score on a large historical data set. Our results show that the bureau score is dominated by the application score, but the bureau score is not extraneous to the combination. Thus, both scores contribute to the combined score, which indeed outperforms both of the scores upon which it is based.     

The effect of boundary geometry on Hankel operators belonging to the trace ideals of Bergman spaces

The characterization of thosef for which the Hankel operatorsH _f belongs to various trace ideals over Bergman spaces on pseudoconvex domains of finite type in complex dimension two is given. In particular, we determine how the cutoff values are affected by the boundary geometry.All three authors supported by grants from the National Science Foundation     

DROUGHT RESILIENCE IN AGRICULTURE: THE ROLE OF TECHNOLOGICAL OPTIONS,LAND USE DYNAMICS,AND RISK PERCEPTION

Abstract Sustained droughts coupled with increasing pressure from urbanization severely test the ability of farmers to continue in agriculture. Understanding farmers' resilience to such pressures is increasingly becoming a significant policy concern. In this paper, a new measure of resilience to severe and sustained droughts in agriculture is derived as the ability to continue farming by saving and carrying forward water through the adoption of water efficient technology. In addition, the role of behavioral factors—such as subjective risk perception over the probability of droughts, of the probability of land getting urbanized, and of resistance to revising beliefs over water scarcity situation—in determining farmers' resilience to droughts is explored. Findings highlight the key role played by behavioral factors in influencing the decision to adopt when the economic factors, such as the price of water, do not capture the true opportunity costs of water. The range of available technological options is found to be crucial too, as marginal improvements in technology do not encourage adoption. An empirical application to the case of lettuce farming in Western Australia reveals that in the presence of speculative benefits from land rezoning, technological adoption is done only for enhancing profits in agriculture and not for improving resilience to droughts. Land rezoning possibilities may further distort technology adoption decisions, thereby, reducing resilience to droughts.     

On the Boltzmann equation for Fermi-Dirac particles with very soft potentials: Global existence of weak solutions

For general initial data we prove the global existence and weak stability of weak solutions of the Boltzmann equation for Fermi-Dirac particles in a periodic box for very soft potentials (−5<γ?−3) with a weak angular cutoff. In particular the Coulomb interaction (γ=−3) with the weak angular cutoff is included. The conservation of energy and moment estimates are also proven under a further angular cutoff. The proof is based on the entropy inequality, velocity averaging compactness of weak solutions, and various continuity properties of general Boltzmann collision integral operators.