piecewise

简明释义

英[ˈpɪsˌwaɪs]美['pis,waɪz]

adj. [数] 分段的

adv. 分段地

英英释义

单词用法

同义词

反义词

例句

1.A hardware realizing method is proposed in this paper which is based on piecewise approximating.

本文提出了一种采用分段逼近的预失真硬件实现方法。

2.Use a method of time series piecewise linear representation based on feature points as a way for pattern representation.

使用一种基于特征点的时间序列线性分段方法作为时间序列的模式表示。

3.If is piecewise smooth, that is, consists of several smooth curves joined together.

如果是分段光滑的，即是由几段光滑曲线连接起来的。

4.Methods It is discussed by nonparametric piecewise polynomial estimation and least squares estimation.

方法利用非参数分段多项式估计和最小二乘法进行讨论。

5.The coefficient functions of the hyperbolic equations considered are assumed to be piecewise constant.

我们假设在所考虑的微分方程中，系数函数为片段常函数。

6.The relation between Piecewise Algebraic Curve and Four Color Conjecture is presented.

指出了分片线性代数曲线与四色猜想之间的内在联系。

7.The nonlinear response and bifurcation of piecewise dynamic system are investigated.

研究了存在分段线性情况下动力学系统响应的分叉。

8.The traditional method of autopilot design is piecewise linearization based gain scheduling approach.

自动驾驶仪设计的传统方法是基于分段线性化的增益规划法。

9.And this difference may be induced by the nonlinear function of piecewise-smooth map.

这个差异可能由分段光滑映象函数的非线性造成。

10.A piecewise 分段 linear function can be used to model the cost of production that changes with quantity.

可以使用<被包裹的>piecewise<被包裹的> <被包裹的>分段<被包裹的>线性函数来建模随数量变化的生产成本。

11.The software allows users to create piecewise 分段 defined curves for more complex designs.

该软件允许用户创建<被包裹的>piecewise<被包裹的> <被包裹的>分段<被包裹的>定义的曲线，以便进行更复杂的设计。

12.In calculus, we often deal with piecewise 分段 functions to analyze their behavior in different intervals.

在微积分中，我们经常处理<被包裹的>piecewise<被包裹的> <被包裹的>分段<被包裹的>函数，以分析它们在不同区间的行为。

13.The tax system is designed to be piecewise 分段, where different income levels are taxed at different rates.

税制设计为<被包裹的>piecewise<被包裹的> <被包裹的>分段<被包裹的>，不同收入水平按不同税率征税。

14.To solve this optimization problem, we need to define the objective function as piecewise 分段 based on the constraints.

为了求解这个优化问题，我们需要根据约束条件将目标函数定义为<被包裹的>piecewise<被包裹的> <被包裹的>分段<被包裹的>。

作文

In mathematics, the concept of a function is fundamental. However, not all functions can be described by a single formula. This is where the term piecewise comes into play. A piecewise function is defined by different expressions for different intervals of its domain. This means that for certain ranges of input values, the function behaves according to one rule, while for other ranges, it follows a different rule. Understanding piecewise functions is crucial not only in theoretical mathematics but also in practical applications such as engineering, economics, and computer science.To illustrate this concept, consider a simple example: a tax bracket system. In many countries, individuals are taxed at different rates depending on their income. For instance, if someone earns less than $10,000, they might be taxed at a rate of 10%. If their income falls between $10,000 and $20,000, the tax rate could increase to 15%. Finally, for those earning above $20,000, the tax rate might rise to 20%. Here, the tax calculation can be expressed as a piecewise function, where each segment of income corresponds to a different tax rate. Mathematically, we can express this tax function as follows:T(x) = { 0.1 * x, if x < 10000; 0.15 * (x - 10000) + 1000, if 10000 <= x < 20000; 0.2 * (x - 20000) + 2500, if x >= 20000 }This notation clearly shows how the function T(x) varies based on the income x. Each piece of the function is defined for a specific range, highlighting the piecewise nature of the tax system.The utility of piecewise functions extends beyond taxation. In engineering, for example, stress-strain relationships in materials can often be modeled using piecewise functions, reflecting different behaviors under various loads. Similarly, in computer graphics, piecewise functions are used to create smooth curves and surfaces, enabling the rendering of complex shapes and animations.Moreover, understanding piecewise functions helps in data analysis and statistics. For instance, when analyzing data trends, it may be necessary to apply different models to various segments of data. By using piecewise functions, analysts can better capture the nuances of the data, leading to more accurate predictions and insights.In conclusion, the term piecewise signifies a powerful concept in mathematics and its applications. Recognizing when and how to use piecewise functions allows us to tackle complex problems with greater precision. Whether in taxation, engineering, or data analysis, the ability to break down functions into manageable pieces enhances our understanding and capability in various fields. As we continue to explore the world of mathematics, the importance of piecewise functions will undoubtedly remain significant, providing clarity and structure to our analyses and solutions.

在数学中，函数的概念是基础。然而，并非所有的函数都可以用单一的公式来描述。这就是术语piecewise（分段）发挥作用的地方。Piecewise函数是通过不同的表达式为其定义域的不同区间而定义的。这意味着，对于某些输入值的范围，函数根据一个规则运行，而对于其他范围，它遵循另一个规则。理解piecewise函数不仅在理论数学中至关重要，而且在工程、经济学和计算机科学等实际应用中也非常重要。为了说明这个概念，考虑一个简单的例子：税率区间系统。在许多国家，个人的税收根据收入的不同而有所不同。例如，如果某人年收入低于10,000美元，他们可能会按10%的税率纳税。如果他们的收入在10,000到20,000美元之间，税率可能会提高到15%。最后，对于收入超过20,000美元的人，税率可能上升到20%。在这里，税收计算可以表示为一个piecewise函数，其中每个收入段对应着不同的税率。在数学上，我们可以将这个税收函数表示如下：T(x) = { 0.1 * x, 如果 x < 10000； 0.15 * (x - 10000) + 1000, 如果 10000 <= x < 20000； 0.2 * (x - 20000) + 2500, 如果 x >= 20000 }这个符号清楚地显示了函数T(x)如何根据收入x变化。函数的每个部分都是为特定范围定义的，突出了税收系统的piecewise特性。Piecewise函数的实用性超越了税收。在工程学中，例如，材料中的应力-应变关系通常可以使用piecewise函数建模，反映在不同负载下的不同行为。类似地，在计算机图形学中，piecewise函数用于创建平滑曲线和表面，使复杂形状和动画的渲染成为可能。此外，理解piecewise函数有助于数据分析和统计。例如，在分析数据趋势时，可能需要对不同的数据段应用不同的模型。通过使用piecewise函数，分析人员可以更好地捕捉数据的细微差别，从而得出更准确的预测和见解。总之，术语piecewise代表了数学及其应用中的一个强大概念。认识到何时以及如何使用piecewise函数使我们能够更精准地解决复杂问题。无论是在税收、工程还是数据分析中，将函数分解为可管理的部分的能力增强了我们在各个领域的理解和能力。随着我们继续探索数学世界，piecewise函数的重要性无疑会保持显著，为我们的分析和解决方案提供清晰和结构。