利用锥上的不动点定理得到了一个正解和两个正解的存在性。
Using cone fixed point theorem we get the existence of one and two positive solutions.
所以那是通过散度定理得到的，其中使用了S是封闭曲面这一事实。
So, that's by the divergence theorem using the fact that s is a closed surface.
应用这些定理得到变质量高阶非完整系统的若干新型运动微分方程。
Using the theorems, the new equations of higher order non-holonomic mechanical systems with variable mass are obtained.
第二点信息是，我们从散度定理得到的，这就是我花费时间试图解释的。
And the second piece of information that we got was from the divergence theorem, and that was the one I spent time trying to explain.
本文首先在有限概率空间中，运用经典的最值定理得到了勒让得变换；
We first consider the classical case where the underlying probability space is finite.
主要运用比较定理得到了种群一致持续生存、弱持续生存以及绝灭的判据。
Sufficient criteria on uniform persistence, weak persistence and extinction of the consumer population are obtained by using mainly the comparison theorem.
定义了复合假设检验的可达速率对，利用多用户信息论信源编码定理得到了复合假设检验可达速率区域的一个内界。
We define achievable rate vector of composite hypothesis testing and obtain one inner bound of achievable rate region.
提出了一个新的支持向量机模型——基于边界调节的支持向量机，并利用拉格朗日定理得到了这种支持向量机的对偶目标函数。
In order for an SVM to be more robust to noise, a new SVM model i. e., the support vector machine based on adjustive boundary SVMAB is proposed.
浮力天平的测量是利用阿基米德定理，计算出配重物体受到的浮力，再通过杠杆平衡的原理得出配重物体浮力的变化即被测量物体的重量。
Based on Archimedes theorem and lever balance principle, we can calculate the buoyancy's variety of the balance objects. This variable just equals to the weight of the measured object.
浮力天平的测量是利用阿基米德定理，计算出配重物体受到的浮力，再通过杠杆平衡的原理得出配重物体浮力的变化即被测量物体的重量。
Based on Archimedes theorem and lever balance principle, we can calculate the buoyancy's variety of the balance objects. This variable just equals to the weight of the measured object.
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