二项的

Prove that no four consecutive binomial coefficients can be in arithmetic progression.

证明不存在四个连续的二项系数成算术级数。

This dissertation is devoted to studying the ruin theory on the dual risk model with several dividend rates and on the bidimensional perturbed risk model with or without stochastic disturbance, which includes the discounted expected function about the dual risk model with three dividend rates and the ruin probability on the bidimensional perturbed risk model.

本文致力于研究分多段分红的对偶风险模型及二维风险模型的破产理论，主要研究了分三段分红的对偶风险模型的折现红利的期望函数，并对带有扰动项的二维风险模型的破产概率做了研究。

Events,Operation and Relation of Sets, Classical Probability, Geometrical Probability , Statistical Stability of a Frequency, Axioms of Probability, Conditional Probability, Total Probability Theorem, Bayes' Rule,Independent Events,Independent Repeated Trials, One Dimensional Random Variables, Discrete Random Variables, Distribution Function of a Random Variables , Continuous Random Variables, Normal Distribution, Distribution of a Function of a Random Variable, Multidimensional Random Variables, Joint Distribution Function, Marginal Distribution Function,Discrete Two—Dimensional Random Variables,Continuous Two—Dimensional Random Variables, Independent Random Variables, Distribution of Functions of Random Variables,Expectation,Variance, Covariance, Coefficient of Correlation, Bivariate Normal Distribution, Law of Large Numbers, The Central Limit Theorems, Sample and Population ,Chi—Squared, T and F Distributions , Sampling Distributions , Point Estimation , Interval Estimation , Testing Hypotheses , A Test of Significance for Parameters in a Single Sample From a Normally Distributed Population , A Test of Significance for Parameters in Two Sample From Normally Distributed Populations .

本课程的主要内容：概率的概念与运算、随机变量及其分布、随机变量的数字特征与极限定理、数理统计的基本概念、估计和检验的基本方法，随机事件与概率随机事件、事件的关系与运算、几何概率、统计概率等，条件概率、全概率公式、贝叶斯公式、事件的独立性、二项概率公式，随机变量的概念、离散型随机变量、随机变量的分布函数、连续型随机变量、随机变量函数的分布，多维随机变量及其分布函数、边缘分布函数、随机变量的独立性、二维随机变量函数的分布，数学期望、方差、协方差和相关系数、大数定律、中心极限定理，总体与样本， X 2-分布、 t-分布和 F-分布，统计量及抽样分布，假设检验的基本概念、单个正态总体参数的显著性检验、两个正态总体参数的显著性检验。

A new computational formula to nonlinear adjustment by parameters, in consideration of the second-order terms, is derived in this paper from the precise orthogonality condition equations to nonlinear least squares by analyzing the direct solving process and iterative computing method of the linearized model.

在分析线性化的非线性参数平差的近似直接解法与迭代解法基础上，利用非线性最小二乘的精确正交性条件方程，推导出顾及到二次项的非线性参数平差的一种新的计算公式。

We discuss the initial value value problems and boundary value problem for second-order integro-differential equation of mixed type in Banach space as follow:And give some results of maximal and minimal solutions of them.

我们讨论了如下带有一阶微分项的的二阶非线性积分-微分方程的最小最大解的存在性问题：{·犷"'，一刃，，，，T\x，"双，，、L工LU=工0，x LU=工L上t〔J 在够。3及笋。4中，'我们利用笋。1及笋。2的思路，讨论了相应的一阶、二阶脉冲积分一微分方程。

By Llibre's algebraic invariant theory, at first on the basis of classification for quadric and quadric homogeneous binary polynomial, the plane linear and cubic homogeneous polynomial differential systems are classified.

利用Llibre的代数不变式理论，首先由二元二次和二元四次多项式的分类结果，对一次和三次齐次多项式微分系统进行代数分类，同时补充了已有结果中出现的漏洞；其次，由称共变张量空间的性质，对缺二次项的三次微分系统在保证轨线走向不变的前提下进行代数分类，使分类后同类系统的示性多项式有相同零点；最后通过讨论一类简单系统的有界性说明了分类的方便方处。

Then,we improve CSFP Model in two aspects:when we ascertain the frequency of default,we use negative binomial distribution to substitute Poisson distribution so that the model can measure the data better;when we ascertain the loss distribution of default,we use Γ-distribution to substitute normal distribution.

其创新与特色一是对贷款组合的风险暴露数进行分段，在每一频段上分别确定风险暴露数分布，进而可以更准确的描述各笔贷款的风险暴露数。二是在确定风险暴露数分布时，用Γ分布替代了传统的正态分布，解决了贷款违约的风险暴露数分布的厚尾问题，进而解决了大宗贷款违约的风险度量问题。三是确定违约频率时，用负二项分布来代替传统的泊松分布，解决了违约频率的方差通常要大于其均值的分布拟合问题。

A multi-distance measurements method is employed in this paper. A single parameter fitting method and a double parameters (reduced scattering coefficient and amplitude factor) fitting method on the basis of the least square Newton fitting algorithm is used to derive the optical parameters respectively. For the finite-thickness homogenous tissue, it can be concluded that the rest terms in expressions of diffusion reflectance and transmittance for the corresponding tissue geometries that subtract the exponential term contained source-detector distance depend on the detected position weakly.

在多程测量的基础上，使用单参数最小二乘牛顿法拟合方法和双参数（约化散射系数、幅度因子）最小二乘牛顿法拟合方法，得到有限厚均匀组织的反射率分布和透射率分布公式中除去包含测量位置的指数项的其它部分对测量位置皆具有弱依赖性的结论，并对拟合结果进行了分析讨论；而对于有限厚平板状双层组织，可根据对反射测量结果及透射测量结果进行拟合所得的约化散射系数间的差异及常数因子的正负判断双层组织的可能结构分布。

Based on the forenamed theory, Estimated the Total Electron Content including the second-order ionospheric error. Established the 2°×2° geomagnetic vector grid-model over mostly area of China , then processed some dual-frequency data to indicate the algorithm is feasible and correct. Obtained some useful conclusion after analyzing the result of data processing.

本文计算了基于中心电离层单层模型的覆盖中国区域的2°×2°地磁场格网点的矢量值，对计算结果的X、Y、Z三个方向分量进行二次曲面拟合，对两种考虑地磁场影响计算包含电离层延迟误差二阶项的TEC估计结果进行了计算，验证了拟合模型的正确性和可行性，并对试算结果进行了分析，得到了一些有益的结论。

A survey of newspaper articles over the past two decades shows a sharp spike in mentions of the dreaded D-word, as commentators have started to think the worst. The prognostications may possibly turn out to be true, or perhaps the only thing we have to fear are the fears of journalists themselves.

从一项对于&危机&二字在过去20年的新闻报道中出现频率的调查中可以看到，令人胆颤的&危机&二字的出现频率明显凸显，以至于舆论导向不得不开始做最坏的打算，有关于危机的预警或许会被证实，亦或我们真正应该害怕的是新闻报道者们对于危机的自身恐惧。

Breath, muscle contraction of the buttocks; arch body, as far as possible to hold his head, right leg straight towards the ceiling (peg-leg knee in order to avoid muscle tension).

呼气，收缩臀部肌肉；拱起身体，尽量抬起头来，右腿伸直朝向天花板（膝微屈，以避免肌肉紧张）。

The cost of moving grain food products was unchanged from May, but year over year are up 8%.

粮食产品的运输费用与5月份相比没有变化，但却比去年同期高8％。