中立型时滞模型的周期正解

本文通过使用某些新技巧，研究了中立型时滞模型Ｎ＇（ｔ）＝Ｎ（ｔ）［ａ（ｔ）－－β（ｔ）－ｂ（ｔ）Ｎ（ｔ－Ｔ（ｔ））－Ｃ（ｔ）Ｎ＇（ｔ－Ｔ（ｔ））］周期正解的存在性，解决了文［１］中的一个公开问题，并改正了文［２］中的错误。     

迭代微分方程x''(t)=ω(t)(ax(t)-bx(x(t)))(a>b>0)的周期解

本文讨论了一类非自治迭代微分方程ｘ’（ｔ）＝ω（ｔ）（ａｘ（ｔ）－ｂｘ（ｘ（ｔ）））（ａ＞ｂ＞０）的解的存在性、解的性态及周期．此结论推广了文［１］的定理．     

关于函数y=asec~tx-btg~tx的最值

关于函数ｙ＝ａｓｅｃｔｘ－ｂｔｇｔｘ的最值黄俊明（贵州省黔东南州民族林校５５６０００）关于函数ｙ＝ａｓｅｃｔｘ－ｂｔｇｔｘ（ａ，ｂ＞０，ｘ∈（０，π／２），ｔ为常数）的最值，文［１］用与［２］定理对偶的一个不等式，研讨了ｔ＝－ｎ（ｎ∈Ｎ），ｎ（ｎ≥３...     

中立型捕食者-被捕食者系统的周期正解

研究了中立型捕食者＿被捕食者模型Ｈ（ｔ）＝ｒＨ（ｔ）１－ａ１（ｔ）Ｈ（ｔ－τ）＋ａ２Ｈ（ｔ－τ）Ｋ－α（ｔ）Ｈ（ｔ）Ｐ（ｔ），Ｐ（ｔ）＝－ｂ（ｔ）Ｐ（ｔ）＋β（ｔ）Ｈ（ｔ）Ｐ（ｔ），｛的周期正解的存在性，具有ｒ，ａ２，ｋ，τ均为正常数，ａ１（ｔ），α（ｔ），ｂ（ｔ），β（ｔ）均为ω周期连续正函数     

一类中立型微分方程的比较定理及应用

考虑中立型微分方程［ｘ（ｔ）－ｘ（ｔ－τ）］（ｎ）＋Ｑ（ｔ）ｘ（ｔ－σ）＝０，ｔｔ０，其中ｎ１为奇数，τ∈（０，∞），σ∈Ｒ＋＝［０，∞），Ｑ∈Ｃ（［ｔ０，∞），Ｒ＋）．本文获得了此方程存在最终正解以及所有解振动的新的比较定理．并据此获得了所有解振动的“ｓｈａｒｐ″条件以及存在最终正解的一般性结果，改进了文［４］的主要结果．     

Notes on Oscillation of Solution for aCertain Second Order Neutral Equation

Ｉｎｔｈｉｓｐａｐｅｒ，ｗｅｃｏｎｓｉｄｅｒｏｓｃｉｌｌａｔｏｒｙｏｆｅｑｕａｔｉｏｎ（１）［ｘ（ｔ）＋ｃｘ（ｔ－τ）］″＋∫ｂａｐ（ｔ，ξ）ｘ［ｇ（ｔ，ξ）］ｄσ（ξ）＝０，（１）ｗｈｅｒｅτ０；ｐ（ｔ，ξ），ｇ（ｔ，ξ）∈Ｃ（［ｔ０，＋∞）×［ａ，ｂ］，Ｒ）；ｇ（ｔ，ξ）ｔ，ξ∈［ａ，ｂ］；ｇ（ｔ，ξ）ａｒｅｎｏｎ－ｄｅｃｒｅａｓｉｎｇｗｉｔｈｔｏｔ，ξ，ｒｅｓｐｅｃｔｉｖｅｌｙａｎｄｌｉｍｔ→＋∞ｍｉｎξ∈［ａ，ｂ］｛ｇ（ｔ，ξ）｝＝＋∞，σ（ξ）∈（［ａ，ｂ］，Ｒ）ｉｓｎｏｎｄｅｃｒ…     

非自治时滞微分方程的扰动全局吸引性

考虑具有扰动项的非自治时滞微分方程ｘ（ｔ）＝－ａ（ｔ）ｘ（ｔ－τ）＋Ｆ（ｔ，ｘｔ），ｔ≥０（）其中Ｆ：［０，∞）×Ｃ［－δ，０］→Ｒ且连续，Ｃ［－δ，０］表示将［－δ，０］映射到Ｒ的所有连续函数集合·Ｆ（ｔ，０）≡０，ａ（ｔ）∈Ｃ（（０，∞），（０，∞）），τ≥０·通常文献对ａ（ｔ）不依赖于ｔ即ａ（ｔ）为自治情形，研究了方程（）零解的局部或全局渐近性质［１～５，７］·本文对ａ（ｔ）为非自治即依赖于ｔ之情形，获得了方程（）零解全局吸引的充分条件，所得结论在某种意义上说是不可改进的·本文改进和推广了已有文献的相应结果，同时本文采用的方法可应用到非自治非线性扰动方程·     

一类时滞种群模型的周期正解

利用一些分析技巧和重合度理论,研究了一类时滞种群模型：Ｎ’（ｔ）＝Ｎ（ｔ）「ｂ（ｔ）－∞／∑／ｊ＝１ａｊｌｎＮ（ｔ＝ｒｊ）」周期正解的存在性,得到了一些新的判据,同时也改进了一些相关文献的结果。     

The Berry Esseen Bound and LIL of PP CM Statistics Testing Normal Distribution about Dimension and Sample Size

§１．ＩｎｔｒｏｄｕｃｔｉｏｎＳｕｐｐｏｓｅＸ１,Ｘ２,…,Ｘｎｉ．ｉ．ｄ～Ｎ（０,Ｉｐ）．ＳｅｔＱ（ｕ,ν）＝∫∞－∞［Ｉ［ｕｔ］－Φ（ｔ）］［Ｉ［νｔ］－Φ（ｔ）］（φ（ｔ））－１ｄｔ,ｗｈｅｒｅΦ（ｔ）ａｎｄφ（ｔ）ａｒｅ,ｒｅｓｐｅｃｔｉ...     

一类抛物型偏泛函微分方程解的强迫振动性

本文研究抛物型偏泛函微分方程γ／γｔ［ｕ－ｍΣｔ－１Ｃｔ（ｔ）ｕ（ｘ，ｔ－τｔ）］＝ａ（ｔ）Δｕ－Ｐ（ｘ，ｔ）ｕ－Ｑ（ｘ，ｔ）Ｇ［ｕ（ｘ，ｐ（ｔ）］＋Ｆ（ｘ，ｔ），（ｘ，ｔ）包含Ｄ×［０，＋∞］解的强近振动性，其中Ｄ为Ｒ＾ｎ中具有逐片光滑边办γＤ的有界区域，ｕ＝ｕ（ｘ，ｔ），Δ是Ｒ＾ｎ中的Ｌａｐｌａｃｅ算子。     

Fitting the three-parameter Weibull distribution with Cross Entropy

The Weibull distribution is widely used in applications such as reliability and lifetime studies. Although this distribution has three parameters, for simplicity, literature pertaining to Weibull parameter estimation relaxes one of its parameters in order to estimate the other two. When the three-parameter Weibull distribution is of interest, the estimation procedure is complicated. For example, the likelihood function for a three-parameter Weibull distribution is hard to maximize. In this paper, a Cross Entropy (CE) method is developed in the context of maximum likelihood estimation (MLE) of a three-parameter Weibull distribution. Performing a simulation study, a comparative analysis between the newly developed method and two existing methods is conducted. The results show the proposed method has better performance in terms of accuracy, precision and run time for different parameter settings and sample sizes.     

威布尔分布或极值分布可靠度置信下限的回归表示

对于定数截尾样本，给出了基于极值分布的位置和尺度参数的最好线性无偏估计（BLUE），获得了威布尔分布的可靠度的点估计和置信限之间的回归模型，从而可由威布 尔可靠度的点估计根据回归方程得到可靠度的置信下限，省去了大量的用表，为实际工作者带来了极大的方便，计算结果表明，回归方程有很高的精度。     

威布尔分布的Bayes可靠性分析

本文针对两参数的威布尔分布的元件，采用Ｂａｙｅｓ方法对其可靠性进行分析，文中分别对两种假设情况进行了讨论，第一种情况是形状参数为离散取值，尺度参数为连续取值的情况，第二种情况假设形状参数的先验分布为均匀分布，尺度参数的先验分布为逆伽玛分布，推出了对应的可靠性估计和置信下限估计，并给出了计算算法，最后用实例对算法进行了验证。     

A note on improving quadratic inference functions using a linear shrinkage approach

In some commonly used longitudinal clinical trials designs, the quadratic inference functions (QIF) method fails to work due to non-invertible estimation of the optimal weighting matrix. We propose a modified QIF method, in which the optimal weighting matrix is estimated by a linear shrinkage estimator, replacing the sample covariance matrix. We prove that the linear shrinkage estimator is consistent and asymptotically optimal under the expected quadratic loss, and will have more stable numerical performance than the sample covariance matrix. Simulations show that numerical improvements are acquired in light of a higher percentage of convergence, and smaller standard errors and mean square errors of parameter estimates.     

Weibull分布下基于遗传算法的设备寿命预测

本文研究了Weibull分布下设备可靠性寿命预测的问题.利用改进后的遗传算法,主要是对遗传算法编码、目标函数和遗传操作的改进,实现对Weibull参数的估计.获得了Weibull分布模型和设备的可靠性寿命模型.     

On a proper way to select population failure distribution and a stochastic optimization method in parameter estimation

It is widely accepted that the Weibull distribution plays an important role in reliability applications. The reliability of a product or a system is the probability that the product or the system will still function for a specified time period when operating under some confined conditions. Parameter estimation for the three parameter Weibull distribution has been studied by many researchers in the past. Maximum likelihood has traditionally been the main method of estimation for Weibull parameters along with other recently proposed hybrids of optimization methods. In this paper, we use a stochastic optimization method called the Markov Chain Monte Carlo (MCMC) to carry out the estimation. The method is extremely flexible and inference for any quantity of interest is easily obtained.     

Inference for a progressive stress model from Weibull distribution under progressive type-II censoring

Based on progressively type-II censored samples, this paper considers progressive stress accelerated life tests when the lifetime of an item under use condition follows the Weibull distribution with a scale parameter satisfying the inverse power law. It is assumed that the progressive stress is directly proportional to time and the cumulative exposure model for the effect of changing stress holds. Point estimation of the model parameters is obtained graphically by using Weibull probability paper plot that serves as a tool for model identification and also by using the maximum likelihood method. Interval estimation is performed by finding approximate confidence intervals (CIs) for the parameters as well as the studentized-t and percentile bootstrap CIs. Monte Carlo simulation study is carried out to investigate the precision of the estimates and compare the performance of CIs obtained. Finally, two examples are presented to illustrate our results.     

性能退化数据下的VDMOS可靠性分析

依据VDMOS可靠性实验获得的性能指标退化数据,选择导通阻抗作为表征VDMOS性能退化的关键指标,用二阶最小二乘估计的方法拟合了VDMOS关键性能指标退化数据的回归曲线.以该性能指标的相对增量(初始值的20%)为阈值,给出了VDMOS的伪寿命估计.然后基于获得的伪寿命数据,在VDMOS寿命服从Weibull分布的假设下,研究并估计了该分布的形状参数与尺度参数.最后结合W统计量对该假设进行了检验,进一步说明了Weibull分布假设的合理性.     

斑须蝽种群空间分布格局Weibull分布的拟合

Weibull分布的概率密度函数为f(x) =(c/b) [(x -a) /b]c -1exp [(x a) /b]c ,x≥a。本文首次用于拟合班须蝽三代卵块的空间分布 ,8批抽样数据拟合结果表明班须蝽三代卵块在烟田的空间分布遵循Weibull分布。从而丰富了班须蝽种群空间格局的分布理论。同时 ,利用斑须蝽种群空间格局的资料探讨了Weibull分布的参数b、c与种群密度及种群聚集度之间的关系 ,结果表明 ,尺度参数b与种群密度、种群聚集度间均分别存在极显著的线性相关关系 ,形状参数c与种群密度存在极显著的正幂函数相关关系 ,与种群聚集度之间存在极显著负幂函数关系。     

威布尔分布族刻度参数的经验Bayes检验函数的收敛速度

本文研究了在"加权线性损失"下,威布尔分布族刻度参数经验Bayes (EB)检验问题.利用概率密度函数的递归核估计,构造了刻度参数的经验Bayes检验函数,并获得了它的收敛速度,在适当的条件下,收敛速度的阶可任意接近O(n^-1),推广了文献的结果.最后给出一个有关本文主要结果的例子.