证明

It is proved that, when the value of critical threshold less than 1, the disease free equilibrium point is globally asymptotically stable. Further more, Bursaphelenchtis Xylophilus is used to construct the Lyapunov function, and the stability theory of Lyapunov function is used to prove that the equilibrium point is Global asymptotic stable. It explains that the Bursaphelenchus Xylophilus wiil eventually disappear.

证明了当临界阈值小于1时，无病平衡点是局部渐近稳定的，进一步利用巴尔巴欣公式构造Lyapunov函数，运用Lyapunov稳定性理论证明了该平衡点的全局渐近稳定性，说明松材线虫病会最终消失；当临界阈值大于1时，病虫害平衡点是局部渐近稳定的。

Leter of Authorization We certificate that we authorise you****公司） to supply our product in your market.

就是说需要你们公司的证明文件，证明你们能允许货物在他们的市场和渠道销售。

The linear relationship between paternity index and avuncular index is exhibited.

当母亲的DNA未知时，可证明孩子的3种母系亲属的DNA在亲子鉴定中的作用是相同的，并得到计算相应父权指数的一般公式，以及检测或未检测母亲DNA时计算父权指数的一般公式，其中，对立假设既可以取"疑父是一随机男子"，也可以取"疑父是孩子的一位父系亲属"；同时还证明了叔伯系数与父权指数之间的线性关系。

The most important development in mathematical logic for the philosophy of mathematics was Godel's proof that any axiomatic system powerful enough to formalise arithmetic will be incomplete in the sense that there will be truths which are not provable within the system.

数理逻辑中最重要的数学哲学的发展是哥德尔的证明，任何公理系统足够强大以正式算术将在这个意义上不完全会有真理不属于系统内证明的。

By the instance of hydroxyl silicate mineral powder additives application on motor,the gas escape amount of bent axle box was measured,and based on the decrease feature of gas escape amount,it demonstrates that hydroxyl silicate mineral powder additive possesses self-repairing performance,and proves that the method of examination in-situ is valid.

以羟基硅酸盐矿物微粉添加剂在发动机上的应用为例，检测了发动机轴轴箱漏气量，根据漏气量减少这一特征证明矿物微粉添加剂具有良好的自修复性能，也证明此原位检测方法是有效的。

Secondly, we consider stochastic LQ optimal control problem driven by Lévy processes and Brownian motion. By applying the -Lévy formula, Gronwall's inequality, Young's inequality and Cauchy-Schwarz inequality, we obtain the closeness property of the solution of multi-dimensional backward stochastic Riccati differential equations.

第二部分首先研究由布朗运动和Lévy过程共同驱动的随机LQ最优控制问题，接着利用-Lévy公式、Gronwall不等式、Young不等式及Cauchy-Schwarz不等式证明多维倒向随机Riccati微分方程适应解的闭性质，并利用此性质证明一维BSRDE解的存在唯一性。

A verifier can be convinced that the committed number x is neither less than the integer a nor more than the integer baiter the protocol is operated only once, and hence the exact proof that x lies in the interval is achieved.

为了去掉这种方法上的重复性，通过联合运用两承诺值相等协议及CFT证明协议提出了一个证明承诺值位于特定区间的新协议，协议运行一次便可使验证者确信承诺值x位于区间中。

Finally, typological evidence from English, Baluchi and Greek proves that the grammaticalization cline proposed in Chinese from weak obligation modality to probability modality also applies in some other languages, and these two modalities are conceptually closely related.

最后，本文为从弱义务性情态语法化为或然性认识情态的语法化路径提供了类型学的证据，证明同样的语法化路径存在于英语、俾路支语和希腊语中，由此证明二者在概念上是密切关联的。

I need a bank statement to prove my annual earnings.

我需要一份银行证明来证明我的收入。

On the basis of linear intersection in space ,a surveying method of work base points in horizontal removal deformation measurement of Taihe dam is discussed.

基于空间距离三维交会的数学模型，提出针对太河水库大坝水平位移变形监测工作基点进行无角度观测方案，并对监测的精度进行了预计分析，证明此方案不仅经济快捷且合理可行，同时也证明空间距离交会定位取代传统量边、测角定位的可行性。

As she looked at Warrington's manly face, and dark, melancholy eyes, she had settled in her mind that he must have been the victim of an unhappy attachment.

每逢看到沃林顿那刚毅的脸，那乌黑、忧郁的眼睛，她便会相信，他一定作过不幸的爱情的受害者。

Maybe they'll disappear into a pothole.

也许他们将在壶穴里消失