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We have derived the formulas for wavelet coefficients of the fractal signal and white noise separately on the basis of which the maximum likelihood method is used to estimate the fractal parameter.

分别推导了分形信号和白噪声的小波系数统计量的公式，在此基础上用最大似然法进行参数估计。

A model and an algorithm were provided for constructing phylogenetic tree based on the principle of maximum likelihood estimate.

利用最大似然估计原理，给出了构建系统发生树的模型和算法。

Then, the outturn table for poplar in Jiangsu has been constructed. By experiment on the poplar stand of different site- index, it shows that the equation fits the growth of poplar merchantable volume well, which can be used to estimate the yield of poplar stand in Jiangsu.

经对不同立地条件下的杨树林分出材量的估计实验，表明该方程适合江苏省杨树生长，为进一步编制全省杨树二元材种出材率表提供了理论与实验方法。

Markov proved the minimality of variance of LSE in 1900. this is the famous Gauss-Markov definition, which found the position for LSE in parameter estimate field.

后来， A。 A.Markov于1900 年证明了LSE 的方差最小性质，即著名的Gauss -Markov定理，奠定了LSE 在参数估计理论中的地位。

Economists estimate nonfarm payrolls shrank for the 20th consecutive month, shedding 233,000 jobs on top of the 247,000 lost in July.

经济学家估计非农就业人数将连续第20个月下降，在7月份减少24.7万人的基础上再减少23.3万人。

Considering the low effective of GARCH model for high frequency data,the nonparametric method is adopted to estimate the value at risk of high frequency data.

文章在GARCH模型对高频数据低效的情况下，从非参数的角度给出风险价值一个相合估计量，这个估计量不依赖于总体分布。

Later, we estimate our variational functional to get a nontrivial solution of the new equation and so the second solution for is obtained.

然后我们利用函数平移将原来的非齐次边界问题转化为奇次边界问题，验证了其对应的变分泛函满足不带条件的山路引理的两个条件，并给出了泛函临界点存在的一个充分条件，最后对具体的变分泛函进行估计，得到了新方程非平凡解的存在性结果，从而得到了原方程第二个正解的存在性结果。

The main results and novelties of the paper are as follows:Firstly, we study the existence of nontrivial solution for the following nonlinear equations with singular pontential By using variational methods and critical point theory, we construct linking type critical value of this kind of singular elliptic equations, with the properties of the eigenvalue, we estimate the critical value and prove the local condition holds to show the existence of the nontrivial solution.

论文的创新点及主要结果如下：首先研究有界区域上具有奇异位势的非线性方程的非平凡解的存在性，运用变分方法与临界点理论，构造这一类奇异椭圆方程的环绕型临界值，并由特征值的性质给出临界值的估计，同时证明局部条件成立，最终证明方程非平凡解的存在性。

In the meantime, a new relation between the coefficient of variation for a normal variate and its sample size is achieved, where the probability to make mistake Ⅱ is considered 5 The probability distribution of fatigue strength at given life under large sample size determined by a new method is found to follow the log-normal distribution and normal distribution, and a new method are developed to estimate the characteristic parameters of probability distribution of fatigue strength from the probability distribution of traditional tensile properties.

根据P-S-N曲线的要求，采用概率统计方法，导出了考虑犯Ⅱ类错误的概率时获取给定精度P-S-N曲线所需的最少子样容量，引入了不同方法获取的P-S-N曲线结果是否趋同的判别标准，得到了P-S-N曲线的寿命求解法和系数求解法获得趋同结果的条件。 5）研究了大子样条件下指定寿命时疲劳强度的概率分布，并提出了根据拉伸性能的分布估算材料疲劳强度概率分布参数的一种方法。

This paper presents the investigation of numerical stability and error estimate of SFBEM in elastic plane problems. Several conclusions regarding the above issues are obtained in this paper, which lays a solid foundation for its practical application.

本文主要针对弹性力学平面问题样条虚边界元法在数值稳定性与误差估计方面的问题展开讨论，获得了虚边界的布设规律及方法误差的直观度量，为该法的实际应用打下了更好的基础。

The split between the two groups can hardly be papered over.

这两个团体间的分歧难以掩饰。

This approach not only encourages a greater number of responses, but minimizes the likelihood of stale groupthink.

这种做法不仅鼓励了更多的反应，而且减少跟风的可能性。