monotonically

简明释义

英[mɒnə'tɒnɪklɪ]美[mɑːnəˈtɑːnɪkli]

adv. 单调地

英英释义

单词用法

同义词

反义词

例句

1.The average diameter decreases monotonically with increasing effective confining pressure, which is defined as the difference between confining pressure and pore water pressure.

试样的平均直径随着有效围压的增长而单调减小。在此，有效围压被定义为围压和孔隙水压之差。

2.I... nd that stock returns monotonically increase in idiosyncratic risk for relatively undervalued stocks and monotonically decrease in idiosyncratic risk for relatively overvalued stocks.

我发现，对于相对低估的股票，股票回报率在特质风险下单调递增；对于相对高估的股票，股票回报率在特质风险下单调递减。

3.A monotonically increasing amount of trace data is produced over a period of time, which is written continuously to a text file on the disk.

在一段时间的运行过程中，将不断地产生大量的跟踪数据，并持续地将其写入到磁盘上的文本文件中。

4.This value is monotonically increasing at the rate of the clock.

这个值是基于时钟的分辨率单调递增的。

5.We see that it varies monotonically from left to right as we move along a row.

当我们沿着表格横栏一一看过去时，它会从左到右单调变化。

6.Both spectral energy density and radiation pressure of the normal fluid are larger than those of the normal blackbody, furthermore, they are monotonically increasing functions of temperature.

正常流态的光谱能量密度和辐射压强都比普通黑体大并且随温度单调增加。

7.However, the simulation results of the superlattice with 4% lattice mismatch show that the thermal conductivity increases monotonically with the period length.

而对于具有4%晶格失配的超晶格模拟结果却表明，超晶格导热系数随周期长度的增大而单调上升。

8.These are based on the concept of UNIX run levels; the system starts at level one, and then monotonically increments until it hits the target start level.

这一概念是基于UNIX运行级别的概念：系统以级别1启动，然后单调递增，直到达到目标启动级别。

9.The function is increasing 单调地 as x approaches infinity.

当x趋近于无穷大时，函数是单调地增加的。

10.The stock price rose 单调地 over the past month.

在过去一个月中，股票价格单调地上涨。

11.In this algorithm, the values are updated 单调地 to ensure convergence.

在这个算法中，值被单调地更新以确保收敛。

12.The sequence of numbers is 单调地 decreasing.

这个数字序列是单调地递减的。

13.The temperature increased 单调地 throughout the day.

温度在一天内单调地上升。

作文

In mathematics and computer science, the concept of change is often described in terms of functions and sequences. One important characteristic of functions is whether they are increasing or decreasing. A function is said to be increasing if, for any two points in its domain, the value of the function at the second point is greater than or equal to the value at the first point. This leads us to a more specific term: monotonically (单调地). A function that is monotonically increasing will not decrease as its input increases; it either stays the same or increases. Consider the example of a temperature measurement over time. If we record the temperature every hour and find that it is always either rising or remaining constant, we can say that the temperature function is monotonically increasing. This kind of behavior is crucial in various real-world applications, such as predicting weather patterns or analyzing climate change data. On the other hand, a function may also be monotonically decreasing, meaning that as the input increases, the output does not increase but instead either decreases or stays the same. An example of this could be the amount of water in a tank being drained over time. As time progresses, the volume of water decreases, demonstrating a monotonically decreasing function. The importance of understanding monotonically behavior lies in its implications for stability and predictability in systems. For instance, in economics, when analyzing the demand curve, we often assume that as prices increase, the quantity demanded decreases. This relationship can be modeled as a monotonically decreasing function, which helps economists make predictions about market behaviors. Moreover, in the realm of algorithms, especially those related to searching and sorting, the concept of monotonically ordered sequences becomes vital. For example, binary search algorithms rely on the property that the array is sorted in a monotonically increasing order to efficiently locate an element. If the sequence were not monotonically ordered, the algorithm would fail to function correctly, leading to incorrect results. In summary, the term monotonically plays a significant role in various fields of study, from mathematics to economics and computer science. Its implications help us understand how different variables interact over time and under certain conditions. Recognizing when a function is monotonically increasing or decreasing allows researchers and practitioners to model behaviors accurately and make informed decisions based on those models. Thus, mastering the concept of monotonically is essential for anyone looking to delve deeper into analytical disciplines.

在数学和计算机科学中，变化的概念通常通过函数和序列来描述。函数的一个重要特征是它们是递增还是递减。如果对于其定义域中的任意两个点，第二个点的函数值大于或等于第一个点的函数值，则该函数被称为递增。这使我们得出一个更具体的术语：monotonically（单调地）。一个函数如果是monotonically递增的，那么随着输入的增加，其输出不会减少；它要么保持不变，要么增加。考虑一下温度随时间变化的例子。如果我们每小时记录一次温度，并发现它总是上升或保持不变，我们可以说温度函数是monotonically递增的。这种行为在各种现实世界的应用中至关重要，例如预测天气模式或分析气候变化数据。另一方面，函数也可能是monotonically递减的，这意味着随着输入的增加，输出不会增加，而是减少或保持不变。一个例子可以是一个水箱随时间排水的水量。随着时间的推移，水的体积减少，展示了一个monotonically递减的函数。理解monotonically行为的重要性在于它对系统稳定性和可预测性的影响。例如，在经济学中，当分析需求曲线时，我们通常假设价格上涨时，需求量会减少。这个关系可以建模为一个monotonically递减的函数，这帮助经济学家预测市场行为。此外，在算法领域，尤其是与搜索和排序相关的算法中，monotonically有序序列的概念变得至关重要。例如，二分搜索算法依赖于数组以monotonically递增的顺序进行排序，以有效定位元素。如果序列不是monotonically有序的，算法将无法正确运行，导致错误的结果。总之，术语monotonically在多个研究领域中发挥着重要作用，从数学到经济学和计算机科学。它的含义帮助我们理解不同变量在时间和特定条件下的相互作用。认识到一个函数是monotonically递增还是递减使研究人员和从业者能够准确建模行为，并根据这些模型做出明智的决策。因此，掌握monotonically的概念对任何希望深入分析学科的人来说都是至关重要的。