nonlinear

简明释义

英[nɒn'lɪnɪə]美[ˌnɑːnˈlɪniər]

adj. 非线性的

英英释义

单词用法

同义词

反义词

例句

1.The dimension accuracy of parts is very complicated nonlinear problem.

零件的尺寸精度是非常复杂的非线性问题。

2.For nonlinear filters, noise suppressing and detail preserving is a pair of contradictions.

对于非线性滤波器，噪声消除和细节保持为一对矛盾。

3.The method is suitable not only for nonlinear systems, but also for linear systems.

该方法不仅适用于线性系统，而且适用于非线性系统。

4.If one or more elemental equations are nonlinear, as is the case for a diode, then the overall system is nonlinear.

如果一个或多个基础方程是非线性的，例如在应用二极管的场合，那么整个系统也就成了非线性的。

5.This nonlinear one in the gas phase.

这是气相中的非线性曲线。

6.Ashby was an engineer interested in nonlinear control circuits and the virtues of positive feedback loops.

阿什比是一位工程师，他对非线性控制电路和主动反馈回路的优点感兴趣。

7.The investigation indicates the lager nonlinear-error and the disturbing errors of these methods.

研究表明，这些方法有较大的非线性误差和干扰误差。

8.The relationship between the variables is nonlinear, meaning it does not follow a straight line.

变量之间的关系是非线性的，这意味着它不遵循一条直线。

9.In nonlinear programming, the objective function or constraints can be represented by curves rather than straight lines.

在非线性编程中，目标函数或约束可以用曲线而不是直线表示。

10.Many real-world systems are nonlinear, such as weather patterns and population dynamics.

许多现实世界的系统是非线性的，例如天气模式和种群动态。

11.The equation describes a nonlinear system that exhibits chaotic behavior.

该方程描述了一个表现出混沌行为的非线性系统。

12.In finance, nonlinear models can better capture the complexities of market movements.

在金融领域，非线性模型可以更好地捕捉市场波动的复杂性。

作文

In the realm of mathematics and science, the term nonlinear refers to systems or equations that do not exhibit a direct proportionality between variables. Unlike linear relationships, where changes in one variable result in predictable changes in another, nonlinear systems can produce complex behaviors that are often difficult to predict. This concept is crucial in various fields, including physics, engineering, economics, and even biology. To illustrate the significance of nonlinear dynamics, consider the example of weather patterns. The atmosphere is a chaotic system governed by nonlinear interactions among numerous factors such as temperature, humidity, and wind speed. A small change in one of these factors can lead to vastly different outcomes, which is why weather forecasting remains a challenging task. The nonlinear nature of such systems means that they are sensitive to initial conditions, a phenomenon famously known as the 'butterfly effect.' In contrast to nonlinear systems, linear systems are characterized by their simplicity and predictability. For instance, in a linear equation like y = mx + b, the relationship between x and y is straightforward; any change in x results in a proportional change in y. This predictability makes linear models easier to analyze and solve, but they often fail to capture the complexities of real-world phenomena that are inherently nonlinear. Another area where nonlinear concepts play a critical role is in economics. Economic models that assume linear relationships between supply and demand may overlook important factors that cause market fluctuations. For example, consumer behavior is often nonlinear; a slight increase in price may lead to a drastic decrease in demand, or vice versa. Understanding these nonlinear dynamics can help economists develop better strategies for managing resources and anticipating market trends. Moreover, in the field of biology, nonlinear relationships are evident in population dynamics and ecosystems. The growth of a population is rarely linear; it can be influenced by factors such as food availability, predation, and disease, all of which interact in complex ways. Models that account for these nonlinear interactions can provide more accurate predictions about species survival and ecosystem health. In conclusion, the concept of nonlinear systems is fundamental to understanding the complexities of the world around us. While linear models offer simplicity and ease of analysis, they often fall short in capturing the intricate behaviors exhibited by nonlinear phenomena. Whether in meteorology, economics, or biology, recognizing and embracing the nonlinear nature of systems allows us to gain deeper insights and make more informed decisions. As we continue to explore the intricacies of our universe, the importance of nonlinear thinking will only grow, guiding us toward more effective solutions to the challenges we face.

在数学和科学领域，术语nonlinear（非线性）指的是不显示变量之间直接比例关系的系统或方程。与线性关系不同，在线性关系中，一个变量的变化会导致另一个变量的可预测变化，而nonlinear（非线性）系统则可能产生复杂的行为，这些行为往往难以预测。这个概念在物理学、工程学、经济学甚至生物学等多个领域至关重要。 为了说明nonlinear（非线性）动态的重要性，可以考虑天气模式的例子。大气是一个混沌系统，由多个因素（如温度、湿度和风速）之间的nonlinear（非线性）相互作用所支配。一个因素的小变化可能导致截然不同的结果，这就是为什么天气预报仍然是一项具有挑战性的任务。这样的系统的nonlinear（非线性）特性意味着它们对初始条件非常敏感，这一现象被称为“蝴蝶效应”。 与nonlinear（非线性）系统相比，线性系统的特点是简单和可预测。例如，在像y = mx + b这样的线性方程中，x和y之间的关系是直接的；x的任何变化都会导致y的成比例变化。这种可预测性使得线性模型更容易分析和解决，但它们往往无法捕捉到固有的nonlinear（非线性）现象的复杂性。 nonlinear（非线性）概念在经济学中也发挥着关键作用。假设供需之间存在线性关系的经济模型可能会忽视导致市场波动的重要因素。例如，消费者行为通常是nonlinear（非线性）的；价格的轻微上涨可能导致需求的急剧下降，反之亦然。理解这些nonlinear（非线性）动态可以帮助经济学家制定更好的资源管理策略和预测市场趋势。 此外，在生物学领域，nonlinear（非线性）关系在种群动态和生态系统中显而易见。种群的增长很少是线性的；它可能受到食物供应、捕食和疾病等因素的影响，所有这些因素以复杂的方式相互作用。考虑到这些nonlinear（非线性）相互作用的模型可以提供关于物种生存和生态系统健康的更准确预测。 总之，nonlinear（非线性）系统的概念对于理解我们周围世界的复杂性至关重要。虽然线性模型提供了简单性和分析的便利，但它们往往无法捕捉到nonlinear（非线性）现象所表现出的复杂行为。无论是在气象学、经济学还是生物学中，认识并接受系统的nonlinear（非线性）特性使我们能够获得更深入的见解，并做出更明智的决策。随着我们继续探索宇宙的复杂性，nonlinear（非线性）思维的重要性只会增加，引导我们找到更有效的解决方案来应对面临的挑战。