证明性的

When the value of critical threshold larger than 1, the disease and insect pests equilibrium point is locally asymptotically stable An appropriate Dulac function should be choosed and Bendixson-Dulac creterion is used to prove that the limit cycle in this model does not exist. It explains that the disease and insect pests equilibrium point is globally asymptotically stable.

选取适当的Dulac函数，利用Bendixson-Dulac判别法证明了极限环的不存在性，说明局部渐近稳定的病虫害平衡点也全局渐近稳定。

In this paper, a semilinear elliptic equation with critical Sobolev-Hardy exponents is studied, the existence of nontrival solutions for which is proved by the linking theorem in variational calculus.

该文研究了一类带有Sobolev-Hardy临界指数的半线性椭圆方程，运用变分理论中的环绕定理证明了方程非平凡解的存在性。

After that the existence of a nontrival solution for the elliptic system is proved by means of Mountain-Pass Lemma. At last, we present two examples to illustrate that our condition is weaker than Boccardo and De.

Figueiredo(2002)的条件更弱的条件下满足条件，并利用山路引理证明了这类拟线性椭圆型方程组非平凡解的存在性，最后举出两个例子验证了文中所给条件的确比Boccardo和De。

We provided the first in vivo evidence that the calnexin and calreticulin function in the engulfment of apoptotic cells in C. elegans.

我们的实验以线虫为模式，进一步提供活体生物的证据，证明CNX和CRT在活体中亦同样地对於细胞计画性死亡的吞噬过程有所影响。

The unique existence theorem forutility function based on thenew axioms is obtained.

给出并证明了基于格序决策行为公理体系的效用函数的存在惟一性定理，为格序决策的研究奠定了理论基础。

In Chapter 4we make more study about the properties of the multifractal Hausdorff mea-sure.The existence of finite measure subsets and the Frostman theorem areproved in this chapter.

第四章我们进一步讨论重分形Hausdorff测度的性质，证明了关于重分形Hausdorff测度的有限测度子集的存在性及Frostman定理。

Using a new measure function to express the sparse prior information of SAR image, a regularized model is established. The model is solved by the fixed point iteration method and proved to be convergent.

本文采用一种新的度量函数表示SAR图像的稀疏先验，建立正则化模型，证明了不动点迭代求解的收敛性。

We establish some existence theorems for systems of vector equilibrium problems with_+-conditions by using the Kakutani-Fan-Glicksberg fixed point theorem.

运用经典的Kakutani-Fan-Glicksberg不动点定理证明了一类具_+-条件的向量均衡系统问题解的存在性。

It is proved that the fractional Fourier transform has the cascade feature, and the optical transfer function is the special case of fractional transfer function.

证明了其具有分数傅里叶变换的级联性，指出常规傅里叶变换下的光学传递函数为分数传递函数的特例。

In the condition weaker than the condition, the corresponding functional of the equation is first proved satisfying the condition.

在比条件更弱的条件下，先证明方程相应的泛函满足条件，再应用山路引理得到了该问题无穷多解的存在性。

By the time of its fall, most of the prisoners were writers who had written against the corruptions of the government.

到它被攻陷的时候，里面多数的犯人是写了反对政府贪污文章的作家。

The most obvious variation to ovum morphological character was that the color was changed from light green to sepiaceous in embryonic development, and all the ovums were almost hatched after 96h.

在胚胎发育过程中卵的形态特征最明显的变化是颜色从淡绿到深褐色，卵在发育96h后卵基本全部孵化。