monotonic

简明释义

英[ˌmɒnəˈtɒnɪk]美[ˌmɑnəˈtɑnɪk]

adj. 单调的；无变化的；产生单音调的

英英释义

单词用法

同义词

反义词

例句

1.A linear function is monotonic.

线性函数是单调的。

2.Differences in the height of the fence posts add interest to an otherwise monotonic rhythm.

栅栏桩柱高度的差异给原本单调的节奏增加了趣味。

3.Differences in the height of the fence posts add interest to an otherwise monotonic rhythm.

栅栏桩柱高度的差异给原本单调的节奏增加了趣味。

4.Its effect on corporate value is negative, but non-monotonic.

这就是说，国家持股对企业的绩效具有两面性的影响。

5.A monotonic relationship between two variables indicates that they move in the same direction.

两个变量之间的单调关系表明它们朝同一方向变化。

6.The stock price showed a monotonic increase over the last year.

过去一年中，股票价格表现出单调的上涨。

7.In a monotonic sequence, each term is greater than or equal to the previous term.

在一个单调序列中，每个项都大于或等于前一项。

8.To ensure convergence, the algorithm requires a monotonic step size.

为了确保收敛，该算法需要一个单调的步长。

9.The function is monotonic if it is either entirely non-increasing or non-decreasing.

如果一个函数完全不递减或不递增，那么它就是单调的。

作文

In mathematics and computer science, the term monotonic refers to a function that is either entirely non-increasing or non-decreasing. This concept is crucial in various fields, including calculus, statistics, and algorithm design. Understanding monotonic functions can help us analyze trends and make predictions based on data. For instance, if we have a monotonic increasing function, it means that as one variable increases, the other variable does not decrease. This property is particularly useful when dealing with datasets where we need to establish a clear relationship between two variables.A practical example of a monotonic function can be found in economics. Consider the relationship between supply and demand. If the price of a product increases, the quantity supplied typically increases as well, while the quantity demanded may decrease. This creates a monotonic relationship where one variable consistently affects the other in a predictable manner. By identifying monotonic trends within economic data, analysts can forecast future market behavior and make informed decisions.In computer science, monotonic functions are often used in algorithms, particularly in sorting and searching techniques. For example, a monotonic search algorithm can efficiently find an element in a sorted array. The monotonic nature of the function allows the algorithm to eliminate half of the search space with each iteration, significantly reducing the time complexity. This efficiency is vital for processing large datasets, making monotonic functions an essential concept in algorithm design.Moreover, the idea of monotonic sequences extends beyond functions. A sequence is considered monotonic if it is either entirely non-increasing or non-decreasing. For instance, in a monotonic increasing sequence, every term is less than or equal to the subsequent term. This property is particularly important in mathematical analysis and can be used to prove convergence or divergence of series. When studying sequences, recognizing whether they are monotonic can provide insights into their long-term behavior.In the context of data visualization, understanding monotonic relationships can enhance our ability to interpret graphs and charts. For example, a monotonic trend in a line graph indicates a consistent increase or decrease over time, which can signal important developments in various fields such as finance, health, and technology. By analyzing these trends, stakeholders can make strategic decisions based on reliable data.In conclusion, the concept of monotonic functions and sequences plays a vital role in mathematics, computer science, and data analysis. Whether we are examining economic trends, designing efficient algorithms, or interpreting data visualizations, recognizing monotonic relationships enables us to draw meaningful conclusions and make informed decisions. As we continue to explore the complexities of these fields, the importance of monotonic behavior remains a fundamental aspect of our understanding.

在数学和计算机科学中，术语monotonic指的是一个函数要么完全非递减，要么完全非递增。这个概念在微积分、统计学和算法设计等多个领域中至关重要。理解monotonic函数可以帮助我们分析趋势并根据数据做出预测。例如，如果我们有一个monotonic递增的函数，这意味着当一个变量增加时，另一个变量不会减少。这一特性在处理需要建立两个变量之间明确关系的数据集时特别有用。monotonic函数的一个实际例子可以在经济学中找到。考虑供需关系。如果一种产品的价格上涨，通常供应的数量也会增加，而需求的数量可能会减少。这就形成了一个monotonic关系，其中一个变量始终以可预测的方式影响另一个变量。通过识别经济数据中的monotonic趋势，分析师可以预测未来的市场行为并做出明智的决策。在计算机科学中，monotonic函数经常用于算法，特别是在排序和搜索技术中。例如，一个monotonic搜索算法可以有效地在排序数组中查找元素。函数的monotonic性质允许算法在每次迭代中消除一半的搜索空间，从而显著减少时间复杂度。这种效率对于处理大型数据集至关重要，使得monotonic函数成为算法设计中的一个重要概念。此外，monotonic序列的概念超出了函数的范围。如果一个序列要么完全非递减，要么完全非递增，则称其为monotonic序列。例如，在一个monotonic递增序列中，每个项都小于或等于后续项。这一特性在数学分析中尤为重要，可用于证明级数的收敛或发散。在研究序列时，识别它们是否为monotonic可以提供有关其长期行为的洞察。在数据可视化的背景下，理解monotonic关系可以增强我们解读图表和图形的能力。例如，线性图中的monotonic趋势表示随时间的一致增加或减少，这可能在金融、健康和技术等各个领域中发出重要的发展信号。通过分析这些趋势，利益相关者可以根据可靠的数据做出战略决策。总之，monotonic函数和序列的概念在数学、计算机科学和数据分析中扮演着至关重要的角色。无论我们是在检查经济趋势、设计高效算法，还是解读数据可视化，识别monotonic关系使我们能够得出有意义的结论并做出明智的决策。随着我们继续探索这些领域的复杂性，monotonic行为的重要性仍然是我们理解的基本方面。