查询词典 probability curve

In this paper, a region approximation idea that means using a "fat curve" with a width to approximate the offset curve is proposed, and a complete set of algorithms to approximate offset curve using disk Bézier curve are given and implemented. In the algorithms, the optimal and uniform approximate curve of the offset curve as the central curve of the Disk Bézier curve is found by using Remez method, and then the upper optimal and uniform approximation principle is proposed to compute the error radius function of the Disk Bézier curve. Thus, the whole Disk Bézier curve can be obtained. In the end of this paper, the approximate effect of the Disk Bézier curve is not only analyzed and assessed, but also some specific examples are provided.

提出用一条带宽度的"胖曲线"来逼近上述等距曲线的区域逼近思想，并建立与实现了圆域Bézier曲线等距逼近的整套算法，包括应用Remez方法求出等距曲线的最佳一致逼近曲线作为圆域Bézier曲线的中心曲线，提出上控最佳一致逼近的原理求出圆域Bézier曲线的误差半径函数，以及确定整条圆域Bézier曲线，最后还对该圆域Bézier逼近的效果做了分析和考核，并给出了一些具体实例。

This paper establishes cubic spline function, analyzes subsection curve function and curve slope and curvature, at last decides to place the curve especial points which can be obtain easement curve length and other line parameters, such as the ZH point (end of line and beginning of transition curve), the HY point (end of transition curve and beginning of circular curve), the QZ point, the YH point (end of circular curve and beginning of transition curve), the HZ point (end of transition curve and beginning of line).

针对公路平面线形的8种组合类型，其线形元素特征则由最基本的直线、圆曲线、缓和曲线组成的特点，解析三次样条函数模型，得分段曲线函数、曲线斜率、曲率，从而确定曲线特征点（直缓ZH点、缓圆HY点、曲中QZ点、圆缓YH点、缓直HZ点）位置，进而得到曲线缓和曲线长度及其他线形参数。

Then we introduced transition probability kernel for the hidden state process and the confederated process. In the deep research, we found that some similar parameters of state transition probability, observation symbol probability and initial state probability were involved in the transition probability kernel of the confederated process. So we can complete the training of traditional HMM parameters by training the transition probability kernel of the confederated process. To our surprised, we got the consistency of transition probability kernel of the confederated process. Meanwhile, we proved the rationality and reliability of the parameters estimation equations under the classical B-W algorithm.

然后对联合过程的转移概率核展开研究，我们根据过程的取值空间的不同，引入了隐状态空间和联合过程空间上的转移概率核，研究中发现在联合空间上的转移概率核包含了在一般的隐马氏模型的参数估计中的所有类似的三组参数(转移概率，观测概率和初始概率)，因此对传统的隐马氏模型的参数训练我们可以通过联合过程的转移概率核的训练来完成，更令我们惊奇的是联合过程的转移概率核还具有一致性；同时对于Baum提出的经典的B-W算法给出的关于模型的参数重估计公式，证明了它的合理性和可靠性，即模型经过重估计后的参数能够满足给定的单观测序列在模型下发生的概率是单调递增的。

Chapter 1 we introduce the risk process with positive and negative risk sums,show the background of the risk process. Chapter 2 we show the integral and differential equation of birth probability,give the Lundberg inequation that the ruin probability satisfies with martingale approach,then discuss then ruin probability of the risk process with two dependent positive and negative risk sums,study how the dependence impacts on the ruin probability. Chapter 3 we compare the concrete examples by numbers,and makes further comparison between the two results coming out of independency and dependency,with the purpose of narrating their respective impacts on the probability of ruin probability.

本文第一章引入含正、负风险和的风险模型，介绍风险过程的实际背景；第二章给出生存概率Φ所满足的积分-微分方程，利用典型鞅方法给出破产概率Ψ满足的Lundberg不等式，并且讨论两个相关正、负风险和模型的破产概率，研究相关性对破产概率的影响；第三章对具体实例给出数值比较，进一步把相关性和独立性两种情形的结果进行比较，说明对破产概率的影响。

Based on probability theory, a method for describing and calculating the collision probability between rendezvous and docking vehicle and debris is presented, and the method involves quantitatively analyzing the collision probability using quasi maximum instantaneous collision probability and total collision probability. The method calculating the indexes is developed, and the input required to perform a calculation includes the respective state vectors, position error covariance matrices and physical sizes of objects involved.(3) Two methods to analyze relative trajectory safety between chaser and target are developed, which are 3-sigma ellipsoid based methodology and collision probability based methodology.

1分析了交会对接各阶段面临的主要轨迹安全威胁，阐述了被动和主动安全策略、目标器的交会对接控制区域等保证交会安全的措施；(2)基于概率思想发展了线性和非线性运动情况下飞行器与空间碎片的碰撞判断方法，提出采用总碰撞概率和拟最大瞬时碰撞概率来综合描述飞行器与空间碎片的碰撞危险程度，推导了通过飞行器和空间碎片各自的状态矢量、位置误差协方差矩阵以及形状尺寸来计算碰撞概率的公式；(3)提出了两种分析追踪器和目标器之间相对轨迹安全的新方法：基于3σ椭球的轨迹安全分析方法和基于碰撞概率的轨迹安全分析方法。

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。

Firstly,the classification of probability rule is analyzed on the base of classic rough set concepts and extended to the equal relation of set in the indefinite system,namely,the upper and lower approximation space of research set is expressed in the form of conditional probability;then,according to the measure of probability rule,the attributes reduction is carried out and the classification rule is extracted by using the related parameters of condition attributes' impend precision from the angle of conditional probability;Finally,the related simulation test result is given and the result shows the classification rules with probability measures is more rational.

首先在经典粗糙集概念的基础上分析概率规则的分类，并将其推广到不确定系统的集合等价关系中，即用条件概率的形式表示研究集合的上下近似空间；然后根据概率规则的测度从条件概率的角度利用条件属性的逼近精度的相关参数进行属性集的约简进而提取分类规则；最后给出了相关的仿真实验结果，结果表明带有概率测度的分类规则更合理。

Finally it analyzes the feasibility that using hydromechanics to analyze traffic flow by contrasting various characters between traffic flow and fluid flow. It analyzes influence of road alignment to basic expressway segment capacity by hydromechanics, and obtains viscous resistance and viscous movement differential equation when the vehicle drives on circular curve segment of expressway. And it infers that viscous resistance is correlated with sideway force coefficient, slope of crown and radius of circular curve. Radius of circular curve, sideway force coefficient and slope of crown are bigger, viscous resistance is smaller, the influence to capacity is smaller when the vehicle is running on nearside lane of circular curve; but radius of circular curve and sideway force coefficient are bigger, slope of crown is smaller, viscous resistance is smaller, the influence to capacity is smaller when the vehicle is running on fast lane of circular curve.

最后通过对比交通流与流体流的相似性，运用流体力学分析了道路线形对快速路基本路段通行能力的影响，求出了车辆在曲线路段的粘性阻力，建立了车辆在曲线路段的粘性运动微分方程，并由此推知，粘性阻力与横向力系数、路拱横坡度和圆曲线半径都有关系，当车辆在圆曲线外侧车道上行驶时，圆曲线半径、横向力系数和路拱横坡度越大，粘性阻力就越小，对道路的通行能力影响就越小；而当车辆在圆曲线内侧车道上行驶时，圆曲线半径和横向力系数越大，路拱横坡度越小，粘性阻力就越小，对道路的通行能力影响就越小。

Result: Scoliosis was identified in 58 cases with Marfan syndrome (38 males and 20 females), the prevalence rate was 42.03%, male-female sex ratio was 1.18:1, 6 cases were in younger than 10-year-old group. 12 cases were in 11~20-year-old group, 19 cases were in 21~30-year-old group, 11 cases were in 31~40-year-old group, 7 cases were in 41~50-year-old group, 3 cases were in 51~60-year-old group. Mean magnitude of Cobb angle in coronal plane was 26.8°±27.8°, the types of scoliosis curve included thoracic curve (36 cases), thoracolumbar curve (11 cases), lumbar curve (2 cases), double curve (6 cases) and triple curve (3 cases), apex vertebraes were convex to the right side among single curves in 38 cases while 11 cases were convex to the left side. Mean magnitude of kyphosis in sagittal plane was 14.3°±13.2°, 5 patients had thoracic lordosis and 40 patients had hypokyphosis and 12 patients had normal kyphosis.

结果：58例(42.03%)患者合并脊柱侧凸，男38例，女20例，男女患病率比例为1.18：1，其中≤10岁6例，11~20岁12例，21~30岁19例，31~40岁11例，41~50岁7例，51~60岁3例；平均冠状面Cobb角为26.8°±27.8°；胸弯36例，胸腰弯11例，腰弯2例，双弯6例，三弯3例；单弯中顶椎凸向右侧38例，凸向左侧11例；矢状面胸椎后凸平均为14.3°±13.2°，其中胸椎前凸5例，胸椎后凸不足40例，胸椎正常后凸12例，仅1例胸椎后凸45°；11例患者冠状面Cobb角＞40°，平均年龄15.9岁。

From a neutral gray balance curve, the curve Y, m, and the basic coincideut from neutral gray balance curve, the curve Y, m, and C coincideut basic curve the Y, m into a bow-shaped curve.

而从洋性灰不均弧线来看，Y、M弧线根基重分，而从洋性灰不均弧线来看，Y、M弧线根基重分，而C弧线则矮不入Y、M成为一条弓形弧线。

Diabetes is a social disease that affects several million people worldwide.

糖尿病是一个社会性疾病，全世界有数百万人罹患此病。

I'll call you on Friday to see if we can reschedule our luncheon meeting at your convenience.

我星期五会给您打电话在您方便的时候我们重新安排我们的午餐约会。