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Firstly,we obtain the representa-tion for the characteristic functional of this particle system,furthermore,we obtain some properties for this system.

本文给出了此粒子系统的特征泛函的表达式（定理2.3），进而获得系统的一些性质。

Firstly, based on the algebra case of Wus method we give a modified algorithm of differential characteristic set for differential polynomial system - algorithm′.

算法′是在代数情形吴方法的算法的基础上推广而来。

Firstly, this paper describes the history and state of the research to the minimal polynomial and the characteristic polynomial and then gives the main methods and its computational complexities for computing the characteristic polynomial and of a constant matrix, the characteristic polynomial of a polynomial matrix and the minimal polynomial of a polynomial.

本文先叙述了对最小多项式和特征多项式的国内外的研究历史和现状，然后给出了已有的计算常数矩阵特征多项式、多项式矩阵的特征多项式和常数矩阵最小多项式的主要算法及其复杂性。

Firstly, the sensor image property which depends on the characteristic of the object surface is analyzed for the design of the detection method.

首先，分析旋转对称三角传感器图像的特性，这些特性取决于被测物体的表面特性，而这些图像特性将有助于传感器图像的处理方法的设计。

Firstly, the preparation and characterization of graphite oxide have been discussed.

首先，本文论述了氧化石墨的制备和表征。

In this paper, we used molecule dynamics simulation technique in researching dielectric property. By analyzing the information that is provided from molecule dynamics simulation, we can got some dielectric properties like dielectric constant and chargeability. Firstly, 3D model of silicon dioxide was been built and geometric optimization was been used to make the model more correctly. Then the model was been put in calculation of molecule dynamics simulation with a definitive temperature.

本文针对氮化硼晶体在极端高温下的介电性能开展研究，首先建立六方氮化硼晶体的微观结构模型，通过几何优化对其进行进一步的结构修正，然后选择合适的力场、系综、积分时间步长和压力温度控制方法，对微观结构模型进行某一温度下的分子动力学计算，动力学计算达到平衡后得到该温度下电介质材料的微观结构模型和动力学特性。

Firstly, based on the parameters of apparent resistivity, apparent chargeability, half decay time, decay rate and the relativity of water inflow, it uses multivariate regression method to establish the prediction model. Then, through the variance test, it shows that it is feasible to use the model to predict the water content quantitatively in the exploration region.

基于视电阻率、视极化率、半衰时、衰减度等参数和涌水量的相关性，利用多元回归方法建立地下水量预测模型，通过方差检验，说明用此模型对勘探区内进行含水量的定量预测是可行的。

Moreover, with its help people can also evaluate the fault-tolerant performance of ANN. In this paper, Chebyshev Inequality method, as a kind of evaluating thought, was firstly concerned in the faulttolerance analysis of ANN; 4. The variation of faulty behaviors of ANNs during the course of learning was studied by taking the discrete Hopfield neural network and Hebb learning algorithm as examples.

这种方法首次将切比雪夫不等式引入人工神经网络容错性分析当中，从而提出了对人工神经网络容错性分析采用估算的思想； 4 以离散型Hopfield神经网络和Hebb学习算法为例，着重研究了在学习过程中人工神经网络故障性能的变化。

In this paper, We firstly present a nonuniform sampling DCT method based on the relationship of Chebyshev polynomial interpolation and DCT, in which, the sampling points are chosen as zeros of Nth degree Chebyshev polynomials of the first kind.

文章首先利用Chebyshev多项式插值与DCT变换之间的相互关系，提出了基于第一类Chebyshev多项式的第N次多项式的零点作为非均匀取样点的DCT变换方法。

Firstly,I want to say,China,cheer up,because we are together.

首先，我想说，中国，加油，因为我们和你在一起。

According to the clear water experiment, aeration performance of the new equipment is good with high total oxygen transfer coefficient and oxygen utilization ratio.

曝气设备的动力效率在叶轮转速为120rpm～150rpm时取得最大值，此时氧利用率和充氧能力也具有较高值。

The environmental stability of that world - including its crushing pressures and icy darkness - means that some of its most famous inhabitants have survived for eons as evolutionary throwbacks, their bodies undergoing little change.

稳定的海底环境─包括能把人压扁的压力和冰冷的黑暗─意谓海底某些最知名的栖居生物已以演化返祖的样态活了万世，形体几无变化。