ergodicity

简明释义

英[ˌɜrɡəˈdɪsɪti]美[ˌɜrɡəˈdɪsɪti]

n. [数] 遍历性；各态遍历性

英英释义

单词用法

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例句

1.On the other hand, the dynamic properties of chaos signal such as ergodicity, aperiodic, uncorrelated, broadband and noise-like have been proved to be useful for communication.

同时，混沌信号具有遍历性、非周期、连续宽带频谱、似噪声的特性，特别适合于保密通信。

2.Applying the ideas for an extended class of continuous-time branching processes, one necessary condition is obtained for the strong ergodicity of the processes.

应用其方法研究了一类扩展的分支过程，得到该过程强遍历的一个必要条件。

3.The necessary and sufficient conditions for recurrence, positive recurrence, exponential ergodicity and strong ergodicity of the process are presented.

本文给出了具有突变率的广义生-灭过程的常返性、正常返性、指数遍历性及强遍历性的充分必要条件。

4.Secondly, we give an ergodicity algorithm to unknown environment as tree structure.

其次，本文提出了基于树结构的未知环境遍历算法。

5.Mutative scale chaos optimization algorithm (MSCOA) is a modified chaos optimization algorithm (COA), which possesses the properties of randomness, ergodicity and regularity of chaos movement.

变尺度混沌优化（MSCOA）是一种改进的混沌优化方法（COA），利用混沌运动的内在随机性、遍历性和规律性进行全局寻优；

6.Mutative scale chaos optimization algorithm (MSCOA) is a modified chaos optimization algorithm (COA), which possesses the properties of randomness, ergodicity and regularity of chaos movement.

变尺度混沌优化（MSCOA）是一种改进的混沌优化方法（COA），利用混沌运动的内在随机性、遍历性和规律性进行全局寻优；

7.The invariant measure and ergodicity of skew product Markov chain;

绕积马氏链的不变测度和遍历性；

8.Firstly, review a lot of relevant papers and conclude recent ergodicity algorithm and algorithm of detecting moving objects.

首先，通过大量的文献阅读，总结了现有遍历算法和移动物体检测算法。

9.In statistical mechanics, the concept of ergodicity 遍历性 implies that time averages are equivalent to ensemble averages.

在统计力学中，ergodicity 遍历性 的概念意味着时间平均值等同于集合平均值。

10.The study of ergodicity 遍历性 is crucial in understanding long-term behavior in dynamical systems.

研究ergodicity 遍历性 对于理解动态系统的长期行为至关重要。

11.Many stochastic processes exhibit ergodicity 遍历性, allowing predictions based on observed data.

许多随机过程表现出ergodicity 遍历性，使得基于观察数据的预测成为可能。

12.In finance, the assumption of ergodicity 遍历性 can simplify complex models of asset pricing.

在金融领域，ergodicity 遍历性 的假设可以简化复杂的资产定价模型。

13.Researchers often test for ergodicity 遍历性 in time series data to validate their models.

研究人员通常会在时间序列数据中检验ergodicity 遍历性以验证他们的模型。

作文

In the realm of mathematics and physics, the concept of ergodicity plays a crucial role in understanding the behavior of dynamic systems over time. At its core, ergodicity refers to the property of a system whereby its time averages and ensemble averages are equivalent. This means that, given enough time, the statistical properties of a single trajectory of the system will converge to those of the entire ensemble of possible trajectories. The implications of ergodicity are profound, especially in fields such as statistical mechanics, economics, and even information theory. To illustrate the concept, consider a simple example involving a gas in a container. If we observe the gas particles over a long period, we can measure various properties such as pressure, temperature, and volume. According to the principle of ergodicity, if we wait long enough, the average values we calculate from our observations will reflect the average values calculated from all possible configurations of the gas particles at a given moment. This equivalence is essential for making predictions about the system's behavior and for applying statistical methods. However, not all systems exhibit ergodicity. Some systems may be trapped in certain states or configurations, leading to behaviors that do not represent the overall dynamics of the system. For instance, in financial markets, certain assets may behave in an ergodic manner, while others may exhibit non-ergodic behavior due to market inefficiencies or external shocks. Understanding whether a system is ergodic or not can significantly impact decision-making and risk assessment. The concept of ergodicity also extends beyond physical systems into the realm of social sciences. In economics, the assumption of ergodicity underlies many models that predict consumer behavior and market trends. If economic agents are assumed to behave ergodically, it implies that their past experiences and future expectations are consistent over time. However, when agents exhibit non-ergodic behavior, it can lead to unpredictable outcomes and challenges in modeling economic phenomena. Moreover, the discussion around ergodicity has gained traction in recent years, particularly in the context of climate change and sustainability. As scientists study complex climate systems, they often grapple with questions of ergodicity in relation to long-term environmental changes. Understanding whether climate systems are ergodic can help us predict future states of the environment based on historical data, which is crucial for policy-making and mitigation strategies. In conclusion, ergodicity is a powerful concept that bridges various disciplines, providing insights into the behavior of complex systems. By recognizing the significance of ergodicity, researchers and practitioners can better understand and model the intricacies of dynamic systems, whether they pertain to physics, finance, or social sciences. Ultimately, the exploration of ergodicity not only enhances our theoretical knowledge but also equips us with practical tools to navigate the complexities of the world around us.

在数学和物理学领域，ergodicity的概念在理解动态系统随时间变化的行为中起着至关重要的作用。ergodicity的核心含义是指一个系统的时间平均值和集合平均值相等。这意味着，给定足够的时间，系统单一轨迹的统计性质将收敛于所有可能轨迹的整体集合的统计性质。ergodicity的含义深远，尤其是在统计力学、经济学甚至信息理论等领域。 为了说明这一概念，可以考虑一个简单的例子，涉及容器中的气体。如果我们长时间观察气体粒子，我们可以测量各种属性，如压力、温度和体积。根据ergodicity原理，如果我们等待足够长的时间，我们从观察中计算的平均值将反映在给定时刻气体粒子的所有可能配置中计算的平均值。这种等价性对于预测系统的行为和应用统计方法至关重要。 然而，并非所有系统都表现出ergodicity。某些系统可能被困在特定状态或配置中，导致的行为不代表系统的整体动态。例如，在金融市场中，某些资产可能以ergodic方式表现，而其他资产由于市场低效或外部冲击而表现出非ergodic行为。了解一个系统是否是ergodic可以显著影响决策和风险评估。 ergodicity的概念还扩展到社会科学领域。在经济学中，ergodicity的假设构成了许多预测消费者行为和市场趋势的模型的基础。如果假设经济主体的行为是ergodic，这意味着他们的过去经验和未来预期随着时间的一致性。然而，当主体表现出非ergodic行为时，可能会导致不可预测的结果以及在建模经济现象时的挑战。 此外，近年来关于ergodicity的讨论引起了广泛关注，特别是在气候变化和可持续性方面。当科学家研究复杂的气候系统时，他们常常面临关于长期环境变化的ergodicity问题。理解气候系统是否是ergodic可以帮助我们根据历史数据预测未来的环境状态，这对政策制定和减缓策略至关重要。 总之，ergodicity是一个强大的概念，连接了多个学科，为理解复杂系统的行为提供了见解。通过认识到ergodicity的重要性，研究人员和从业者可以更好地理解和建模动态系统的复杂性，无论它们涉及物理学、金融还是社会科学。最终，对ergodicity的探索不仅增强了我们的理论知识，还为我们提供了应对周围世界复杂性的实用工具。