SENSITIVITY ANALYSIS OF THE STOCHASTIC GROWTH RATE: THREE EXTENSIONS†

The perturbation analysis of population growth rate plays an important role in population biology. The sensitivity and/or elasticity (proportional sensitivity) of population growth rate to changes in the vital rates are regularly used (i) to predict the effects of environmental perturbations, (ii) to characterize selection gradients on life‐history traits, (iii) to evaluate management tactics, (iv) to analyse life table response experiments, and (v) to calculate the sampling variance in population growth rate. In a stochastic environment, population growth is described by the stochastic growth rate, which gives, with probability 1, the asymptotic time‐averaged growth rate of any realization. Tuljapurkar derived the sensitivity and elasticity of the stochastic growth rate to changes in the entries of the stochastic matrices. This paper extends his result to cover three cases, each of which has arisen recently in applications. The first gives the response of the stochastic growth rate to environment‐specific perturbations, applied only in a specified subset of the possible environments. The second gives the sensitivity and elasticity of the stochastic growth rate to changes in lower‐level parameters. The third applies to stochastic seasonal models, in which the projection matrix for each year is a periodic product of matrices describing seasonal transitions. In this case interest focuses on the sensitivity of the stochastic growth rate to changes in the entries of the seasonal matrices, not entries in the annual matrices. The paper describes examples of problems where each of these extensions is needed, and the algorithms for each of the new calculations.     

手式元素周期表的构成及其应用

将元素周期性变化规律与手指结构特点相结合构造成手式元素周期表,为更好地掌握元素周期性变化规律,更直观地反映元素在周期表中的位置提供了一种快捷有效的方法。     

用一个平面磁控溅射靶合成金属多层膜

提出了一个很有价值的实验装置与方法,可以仅用一个平面磁控溅射靶来方便地合成各种金属多层膜。小角X光衍射(XRD)分析证实了采用此实验装置与方法制备的Fe/Al多层膜的良好周期性层状结构。     

一类具有反馈控制HollingⅡ类功能反应模型的研究

讨论了一类具有反馈控制Holling Ⅱ类功能反应的二维捕食系统持续生存的条件．给出了当系统为周期系统时，其周期解存在惟一和全局吸引的条件．     

古希腊筛法及其推广

由古希腊筛法推广出的XZG筛法引出相关数对,由素殆2相关数对推出完全相关数对.     

Jacobi椭圆函数展开法的应用

通过对Jacobi椭圆函数展开法适用条件——秩的分析，求解了Joseph—Egri方程的精确周期解，并且对椭圆函数展开法进行适当的扩充以求解变系数KdV方程的精确周期解．此方法同样适用于其它具有变系数的非线性演化方程（NLEEs）．     

具有状态脉冲的两种群竞争Lotka-Volterra系统的周期解

研究了一类具有状态脉冲的两种群竞争Lotka-Volterra系统.利用后继函数和类Poincaré准则,得到了该系统阶1周期解存在及其渐近稳定的充分条件,并用数值模拟验证了主要结论.     

我国经济增长周期模型的理论基础与建模思路

以经济增长周期理论为基础,从需求决定角度构建一个简单的经济增长周期模型,该模型共有GDP、投资、消费、出口、进口等16个内生变量,包括短期波动模型、中期波动模型、中长期波动模型、长期波动模型和动态均衡值模型等5个子模型。从模拟预测情况看,除短期波动模型模拟预测值与实际值偏差较大外,其他模型模拟预测值均与实际值高度一致,即经济增长周期模型能够较好地模拟样本区间内各内生变量的周期性波动及其动态均衡值发展状况。     

Efficiency of an almost unbiased two-parameter estimator in linear regression model

This paper deals with parameter estimation in the linear regression model and an almost unbiased two-parameter estimator is introduced. The performance of this new estimator over the ordinary least-squares estimator and the two-parameter estimator [M.R. Özkale and S. Kaçiranlar, The restricted and unrestricted two-parameter estimator, Comm. Statist. Theory Methods 36 (2007), pp. 2707–2725] in terms of scalar mean-squared error criterion is investigated and a simulation study is done.     

A general result in almost sure central limit theory for random fields

In this note, we investigate, under some mild conditions, the almost sure central limit theorem for random fields with general weight sequences.