随机的

In the second aspect, a systematic study is made on random ambiguous point、random asymptotic ambiguous point、random intrinsic value and random intrinsic element of random operator.

在随机非线性算子与随机算子方程方面，深入研究了随机不动点的存在性与随机算子方程的随机解。

A virtual stochastic process is constructed so that the basic random variable becomes the value of the stochastic process at certain instants of time.

在此方法中，构造一个与基本随机变量相关的虚拟随机过程，使得基本随机变量成为该随机过程的截口随机变量。

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。

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。

Then basic mathematical models of unrepairable systems with fuzzy random lifetimes are established.

此外，我们建立了模糊随机不可修系统的基本模型，包括模糊随机串联系统、模糊随机并联系统、模糊随机串—并联系统、模糊随机并—串联系统以及模糊随机冷贮备系统。

To get from "protoplasmal primordial atomic globule"(as the Gilbert and Sullivan song put it) to sentient upright modern human has required you to mutate new traits over and over in a precisely timely manner for an exceedingly long while.

因为变化的过程是随机的。从细胞质的原始原子颗粒（像吉尔伯特和沙利文歌曲中唱到的那样）到一个有知觉能独立行走的现代人类的转变要求你在相当长的时间内以一种极为精确准时的方式反复的发生变异产生新品质。

Increased spin disorder and a decrease of with increasing Fe content are evident. It depopulates the hopping electrons and weakens the double exchange. From resistivity and magnetization data, it is expected that the addition of Fe can introduce grain boundaries and form antiferromagnetic clusters.

电阻率的峰值随着Fe的增加而增大，并且峰值对应的温度TIM向低温移动，随着外加磁场的增大电阻下降，产生MR效应，这是因为随着掺杂的增加，自旋无序增加，外场的增加抑制了自旋的扰动，在顺磁温区内，电子自旋形成了随机的磁结构，产生电子局域，破坏了极化子形成的环境，因此输运机制由绝热极化子输运转变为变程跳跃机制。

Ben Shore, MD, staff orthopaedic surgeon at the London Health Sciences Centre in Ontario, Canada, and colleagues randomized 64 patients to receive a cocktail of analgesics. The cocktail consisted of 30 mg of ketorolac, 5 mg of epimorphine, 0.6 mL of 0.1% epinephrine, and 400 mg of ropivacaine, in a 100 mL volume. This was injected at three local sites toward the end of the procedure. The investigators who evaluated the results were blinded regarding which patients received injections and which did not.

加拿大伦敦保健医学中心的Ben Shore医师负责研究的进行，他将64位患者以随机的方式投予止痛剂处方；该处方的成分为30mg 的ketorolac、5mg 的epimorphine、0.6mL的 0.1% epinephrine及400mg 的ropivacaine，一共100mL的容量；在手术接近终了时，将这些止痛剂分别于三个部位作局部注射；研究人员以盲性的方式，对接受注射者及未接受注射者进行评估。

Ben Shore, MD, staff orthopaedic surgeon at the London Health Sciences Centre in Ontario, Canada, and colleagues randomized 64 patients to receive a cocktail of analgesics. The cocktail consisted of 30 mg of ketorolac, 5 mg of epimorphine, 0.6 mL of 0.1% epinephrine, and 400 mg of ropivacaine, in a 100 mL volume. This was injected at three local sites toward the end of the procedure. The investigators who evaluated the results were blinded regarding which patients received injections and which did not.

加拿大伦敦保健医学中心的Ben Shore医师负责研究的进行，他将64位患者以随机的方式投予止痛剂处方；该处方的成分为30mg 的ketorolac、5mg 的epimorphine、0.6mL的 0.1% epinephrine及400mg 的ropivacaine，一共100mL的容量；在手术接近终了时，将这些止痛剂分别於三个部位作局部注射；研究人员以盲性的方式，对接受注射者及未接受注射者进行评估。

"Classic teaching in surgery has dictated that the use of analgesics should be withheld from children with acute abdominal pain until a surgeon establishes a definitive treatment plan," write Hannu Kokki, MD, from Kuopio University Hospital in Finland, and colleagues."It has been claimed that analgesia masks symptoms and physical findings, delays diagnosis, and leads to increased morbidity. Over the past few years, this traditional belief has been challenged."

孩童们被以随机的方式投予舌下oxycodone hydrochloride 0.1 mg/kg，或等量的生理食盐水；在第一次剂量投予前，1小时及3.5小时后，由同一位医师对参试者作身体检查、临时性诊断及临时性的病况判定；在第一次剂量的试验期中，每隔30分钟做一次疼痛指数的纪录，基线时也纪录一次，如此持续3.5小时；主要的效果指标，为疼痛程度的差异、有无腹部紧缩的状况及诊断的精确度等。

The split between the two groups can hardly be papered over.

这两个团体间的分歧难以掩饰。

This approach not only encourages a greater number of responses, but minimizes the likelihood of stale groupthink.

这种做法不仅鼓励了更多的反应，而且减少跟风的可能性。