ergodic

简明释义

英[ɜːˈɡɒdɪk]美[ɜːrˈɡɑdɪk]

adj. [数] 遍历性的；[数] 各态历经的

n. 遍历性

英英释义

单词用法

同义词

反义词

例句

1.A mathematical model of a hybrid-switched system has been built up by a two dimensional ergodic Markov process with the state-transition-rates diagram.

本文利用具有状态转移率的马尔柯夫过程建立了一种综合传输交换的数学模型。

2.This paper examines port queuing system with single berth. For its imbedded Markov chain, the author gives a necessary and sufficient condition under which the system is ergodic.

港口系统排队模型由两个排队子系统构成。本文对单个泊位(服务台)的情形讨论了它的嵌入马氏链，给出了系统遍历的充分必要条件。

3.Furthermore, we obtain a sufficient condition by which we can distinguish if an ordinary differntial system is a continuous ergodic system.

进一步我们也给出判别一个常微系统是连续遍历系统的充分条件。

4.In chapter 5, we obtain the invariant measure and the ergodic property of recurrent right processes.

在第五章里，我们得到了常返右过程的不变测度的存在性、唯一性及其遍历性。

5.In this paper we give the properties and structure of eigenfunctions and eigenvalues of the weakly ergodic homeomorphism on compact system.

本文给出紧致系统上弱遍历自同胚的特征值与特征函数的结构性态。

6.The most plausible operatorial generalization of result of preceding paragraph is known as the "mean ergodic theorem for unitary operators. ""

前段结果可以推广到算子去，其中最近情近理的推广是“单算子的平均遍历定理”。

7.Applying fixed points theorem, we give the sufficient conditions of the existence of positive ergodic solutions for a class of infinite nonlinear integral equations.

利用不动点理论，给出了一类非线性积分方程正的遍历解存在的充分条件。

8.Weakly ergodic is a new ergodic conception on compact system.

弱遍历是在紧致系统上的一种新的遍历概念。

9.In statistical mechanics, an ergodic system is one where the time average equals the ensemble average.

在统计力学中，ergodic 系统是指时间平均值等于集合平均值的系统。

10.The concept of ergodic theory is crucial in understanding complex dynamical systems.

理解复杂动态系统时，ergodic 理论的概念至关重要。

11.Many physical processes can be modeled as ergodic to simplify analysis.

许多物理过程可以建模为 ergodic 以简化分析。

12.In finance, an ergodic model assumes that past price movements predict future trends.

在金融中，ergodic 模型假设过去的价格走势能够预测未来趋势。

13.The ergodic hypothesis suggests that all accessible microstates are equally probable over a long period.

ergodic 假说表明，在长时间内，所有可接触的微观状态都是同样可能的。

作文

In the realm of mathematics and physics, the term ergodic (遍历的) has profound implications that extend beyond mere theoretical discussions. At its core, ergodic refers to a property of dynamical systems whereby their long-term average behavior can be deduced from a single, sufficiently long, random sample of the system's state. This concept is particularly significant in fields such as statistical mechanics, where it helps bridge the gap between microscopic laws governing individual particles and macroscopic properties observed in bulk materials. To better understand the relevance of ergodic theory, consider a simple analogy involving a deck of cards. If one were to shuffle the deck thoroughly and then draw cards at random, the sequence of cards drawn would represent a sample of the entire deck's arrangement. If the shuffling process is truly ergodic, then the statistical properties of the drawn cards—such as the frequency of each card appearing—would converge to the expected frequencies as more cards are drawn. This idea underscores the importance of random sampling in understanding complex systems, whether they are physical, biological, or social. In practical applications, the ergodic hypothesis serves as a powerful tool for researchers and scientists. For instance, in thermodynamics, the behavior of gases can be analyzed using ergodic principles, allowing scientists to predict how gas molecules will behave over time under various conditions. This predictive capability is crucial for developing new materials and understanding fundamental processes in nature. However, it is important to note that not all systems are ergodic. Some systems exhibit behavior that is highly dependent on initial conditions, leading to outcomes that can vary dramatically based on those starting points. Such non-ergodic systems can pose challenges in fields like finance, where market behaviors may not be predictable based solely on historical data. Understanding whether a system is ergodic or not is essential for applying the correct analytical techniques and for making informed predictions. In conclusion, the concept of ergodic (遍历的) plays a crucial role in various scientific disciplines, providing insights into how we can understand and predict the behavior of complex systems. Whether through the lens of mathematics, physics, or even economics, recognizing the ergodic properties of a system allows researchers to make more accurate assessments and foster advancements in technology and science. As we continue to explore the intricacies of our universe, the principles of ergodic theory will undoubtedly remain a cornerstone of our understanding, guiding us as we unravel the mysteries of both the micro and macro worlds around us.

在数学和物理的领域中，术语ergodic（遍历的）具有深远的意义，超越了单纯的理论讨论。它的核心含义是，ergodic指的是动态系统的一种特性，其长期平均行为可以通过对系统状态的单一、足够长的随机样本推导出来。这个概念在统计力学等领域尤为重要，它帮助弥合了支配个别粒子的微观法则与在大宗材料中观察到的宏观性质之间的差距。 为了更好地理解ergodic理论的相关性，可以考虑一个简单的比喻，涉及一副扑克牌。如果一个人彻底洗牌，然后随机抽取牌，所抽取的牌序列将代表整副牌的排列样本。如果洗牌过程是真正的ergodic，那么所抽取牌的统计特性——例如每张牌出现的频率——将在抽取更多牌时收敛到预期频率。这一思想强调了随机抽样在理解复杂系统中的重要性，无论这些系统是物理的、生物的还是社会的。 在实际应用中，ergodic假设为研究人员和科学家提供了强有力的工具。例如，在热力学中，气体的行为可以利用ergodic原理进行分析，使科学家能够预测气体分子在各种条件下的行为。这种预测能力对于开发新材料和理解自然中的基本过程至关重要。 然而，需要注意的是，并非所有系统都是ergodic。一些系统表现出高度依赖初始条件的行为，导致基于这些起始点的结果可能会显著不同。这种非ergodic系统在金融等领域可能会带来挑战，因为市场行为可能无法仅根据历史数据进行预测。了解一个系统是否为ergodic对于应用正确的分析技术和做出明智的预测至关重要。 总之，ergodic（遍历的）概念在各种科学学科中扮演着关键角色，为我们理解和预测复杂系统的行为提供了见解。无论是通过数学、物理甚至经济学的视角，认识到系统的ergodic特性使研究人员能够做出更准确的评估，并推动科技和科学的进步。在我们继续探索宇宙的复杂性时，ergodic理论的原则无疑将继续成为我们理解的基石，指导我们揭开微观和宏观世界的奥秘。