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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。

It has been showed that the quantum PCII can be still valid for the general case Jacobi J 1, which is different from quantum Noether theorem. The equivalence between quantum canonical equation and PCII is deflved at the quantum level. The comparisons of these results in quantum level with those in classical theories are discussed in detail. The relationship of canonical transformation with quantum PCII is obtained.

结果表明,当变换的Jacobi行列式不为1时,量子PC积分不变量仍然存在,从而把PC积分不变量推广到了最一般情形;在量子水平上,证明了量子正则方程与该积分不变量之间的等价性;比较了经典与量子PC积分不变量以及PC积分不变量与Noether定理;给出正则变换与量子PC积分不变量间的关系。

In presented method, the correlated variables are transformed into uncorrelated variables equivalently, and the performance functions in the correlated variables space are transformed into those in the equivalent uncorrelated variables space, in which the reliability sensitivity of the system failure probability with respect to the distribution parameters of the uncorrelated variables can be solved by the moment method for the uncorrelated variables. Finally the equivalent relationship between the correlated variables and the uncorrelated variables, the chain rule for derivative are employed to obtain the reliability sensitivity of the system failure probability with respect to the means of the correlated variables.

在所提的方法中,首先将相关变量空间等效转化为不相关变量空间,并将系统多个失效模式的功能函数转化为不相关变量空间的功能函数,进而利用矩方法得到多模式系统失效概率对不相关变量空间基本分布参数的灵敏度,最后利用相关变量空间与不相关变量空间的等价关系及复合函数求导法则,求得多模式系统失效概率对相关变量空间中变量均值的灵敏度。

In 2006 the concept of new chance space and hybrid variable was introduced by Baoding Liu.

混合变量则被定义为从机会空间到实数集的可测函数,随机变量,模糊变量,随机模糊变量,模糊随机变量则都属于混合变量的例子。

The main content of the study includes: the policy variables are classified into two types, which are continuous policy variable and discrete policy variable, and the two variable is analyzed respectively; as to the continuous policy variable, use reasonable weighting to synthesize comprehensive policy indicator to reflect the comprehensiveness of each main policy indicator; undertake regression analysis for the comprehensive policy indicator, economic and stock market variable and get the effect of all kinds of comprehensive policy indictor variables on the economy and stock market; undertake regression analysis for data on the economic indicator and the data on the stock market and get the relationship between the economy and the stock market; use event research method to analyze its effect on the stock market and get some corresponding conclusions; structure the differential or difference equation groups on the interactive relationship among the variable economy, stock market and policy and do the difference operation and constitute simultaneous equation with the original main variables one after another; use quantitative regression method and solve the coefficient of the simultaneous equation to predict the operating tendency.

本研究主要内容包括:将政策变量划分为连续性政策变量和离散政策变量两个类型,并分别进行分析;对于连续性政策变量,采取合理的权重来合成政策综合指标,反映各主要政策指标的综合力度大小;将各政策综合指标与经济、股市变量进行回归分析,获得各类政策综合指标变量对经济、股市影响程度的大小;将经济指标数据与股市数据进行回归分析,获得经济与股市之间关系的大小;采取事件研究方法来分析其对股市的影响程度;构建关于经济、股市与政策各主要变量之间互动关系的微分或差分方程组,进行差分运算,并以此与原来各主要变量组成联立方程;运用计量回归方法,求出联立方程系数用于预测。

This project also obtained several limit theorems for some important dependent random variables and stochastic processes, such as the Strassen law of the iterated logarithm for negatively dependent random variables, strong limit theorems for mixing random vectors in Banach spaces, sample path properties for two-parameter fractional Wiener processes, and so on.

随机环境中的随机变量与随机过程的研究在国内外相当活跃,本项目主要研究它们的极限性质,着重研究了随机风景中随机变量与随机过程的极限性质,主要取得了以下几个结果:首先对简单对称的Kesten-Spitzer随机游动在低阶矩的条件下给出了强逼近,大大减弱了前人要求任意阶矩的条件,然后对独立风景中的一般随机变量给出了强逼近的一般性结果,由此导出在风景和随机变量都只具有低阶矩的条件下的独立但不同分布、混合相依变量的强逼近,在只有弱高于二阶矩的条件下得到了重相对数律和弱收敛;给出了连续时间参数的Brown风景中Brown运动和稳定风景中稳定过程的滞后增量和连续模等精确样本轨道性质;同时给出了一些重要的相依随机变量和过程的若干极限定理,如负相关随机变量的Strassen重对数律、抽象空间上混合相依变量的一些强极限定理成立的充分必要条件、两参数分数Wiener过程的样本轨道性质等。

If the number of variables or arrays being added with ADDITIVE plus the number of existing variables exceeds the variable limit, Microsoft Visual FoxPro brings as many variables and arrays as possible into memory from the variable file or memo field.

如果使用 ADDITIVE 时,要添加的内存变量或内存变量数组的数目加上已有内存变量的数目超过了系统对内存变量数目的限制,Visual FoxPro 将从内存变量文件或备注字段中恢复尽可能多的内存变量和内存变量数组。

D. Declaration of nonprimitive types such as String, Vector ans so on allocates memory space for the object.

但是严格来讲此题的答案有待确定,因为只有原始类型的实例变量和类变量的声明在类对象被创建/类被加载时完成内存的自动分配,而原始类型的局部变量必须显式初始化,从这点来看原始类型的局部变量没有被自动分配内存,SL275中只提出了非原始数据类型的变量必须使用new Xxxx完成内存的分配而没有指出原始数据类型的变量是否在声明时即自动进行内存分配,而从局部变量不能在显式初始化前使用这点来看在声明时没有进行内存分配。

D. Declaration of nonprimitive types such as String, Vector ans so on allocates memory space for the object.

但是严格来讲此题的答案有待确定,因为只有原始类型的实例变量和类变量的声明在类对像被创建/类被加载时完成内存的自动分配,而原始类型的局部变量必须显式初始化,从这点来看原始类型的局部变量没有被自动分配内存,SL275中只提出了非原始数据类型的变量必须使用new Xxxx完成内存的分配而没有指出原始数据类型的变量是否在声明时即自动进行内存分配,而从局部变量不能在显式初始化前使用这点来看在声明时没有进行内存分配。

In the whole process, Behavioral Variables should act as the main variables, and Demographic Variables, Geographic Variables, Psychographic Variables as auxiliary variables.

认为技术创新市场细分变量选择时应该以行为变量作为主变量,以地理区域变量、人口和社会变量以及心理变量作为辅助变量

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