invariance

简明释义

英[ɪnˈveərɪəns]美[ɪnˈverɪəns]

n. 不变性；不变式

英英释义

单词用法

同义词

反义词

例句

1.This paper proved that this algebraic feature has some important properties of algebraic and geometric invariance.

该文证明了这样抽取的代数特征具有一些重要的代数和几何不变性。

2.This invariance requirement has been a strait jacket on the free invention of scientists.

这个不变性要求，已经成了套在科学家的自由创造上的一件紧身衣。

3.Such invariance reflects the principle of relativity.

序列不变性是相对论原理的一个反映。

4.Firstly, related knowledge of nonlinear cascade systems, invariance control, switching control and passivity, etc.

首先，介绍了级联系统、不变控制、切换控制、无源等相关的预备知识。

5.An application example is enumerated that the space plane parameters are confirmed based on invariance of cross radio.

列举一个应用实例，利用交比的不变性确定空间平面参数。

6.The rotating invariance of fingerprint images is solved by the rotating of feature models in feature matching.

在特征匹配阶段，通过对特征模板的旋转解决指纹图像的旋转不变性问题。

7.The climatic colding and warming change with time scale, but there is also invariance.

在气候资料中冷暖是随时间尺度而变化的，但也存在不变量。

8.Compared with the traditional de-nosing methods by threshold value and translation invariance, the algorithm increases the signal to noise ratio.

与传统的阈值去噪法和基于平移不变量的去噪算法相比，该算法提高了信噪比。

9.In physics, the principle of invariance refers to the idea that certain properties remain unchanged under specific transformations.

在物理学中，不变性原理指的是在特定变换下某些属性保持不变的思想。

10.The invariance of the laws of physics across different frames of reference is a fundamental concept.

物理定律在不同参考系中的不变性是一个基本概念。

11.Mathematical proofs often rely on the invariance of certain functions under various operations.

数学证明通常依赖于某些函数在各种运算下的不变性。

12.In computer vision, invariance to lighting changes is crucial for object recognition.

在计算机视觉中，对光照变化的不变性对于物体识别至关重要。

13.The concept of invariance is important in developing algorithms that can handle noise in data.

在开发能够处理数据噪声的算法时，不变性的概念是重要的。

作文

In the realm of science and mathematics, the concept of invariance plays a crucial role in understanding various phenomena. Invariance refers to the property of an object or a system that remains unchanged under certain transformations or conditions. This idea is not only fundamental in physics but also has significant implications in other fields such as computer science, economics, and even philosophy. To illustrate the importance of invariance, let’s consider the laws of physics. One of the most famous principles in physics is the principle of conservation of energy, which states that the total energy in a closed system remains constant over time. This principle embodies the idea of invariance because it signifies that regardless of the processes occurring within the system, the total amount of energy does not change. Such invariance allows scientists to predict the behavior of physical systems with remarkable accuracy. In mathematics, invariance is often observed in geometric transformations. For instance, when a shape is rotated or reflected, certain properties such as area and perimeter remain invariant. This invariance of geometric properties under transformation is essential for understanding symmetry and can be applied in various fields, including architecture and design. The study of invariance in mathematics also leads to deeper insights into algebraic structures and topological spaces, providing a framework for solving complex problems. Moreover, in computer science, the concept of invariance is vital in algorithm design and software development. Programmers often rely on invariants—conditions that must hold true during the execution of a program—to ensure correctness and reliability. By establishing invariance in their code, developers can create robust systems that behave predictably, even in the face of unexpected inputs or errors. This practice not only enhances the functionality of software but also simplifies debugging and maintenance processes. Economics also utilizes the notion of invariance in various theories and models. For example, the idea of utility invariance suggests that consumers' preferences remain consistent regardless of changes in their income or the prices of goods. Understanding this invariance helps economists predict consumer behavior and formulate strategies for market interventions. It highlights the stability of certain economic relationships, which is crucial for effective policy-making. In philosophy, invariance raises interesting questions about identity and change. Philosophers debate whether objects can maintain their identity over time despite undergoing transformations. The discussion often revolves around the concept of invariance as it pertains to the essence of entities. This exploration into invariance challenges our understanding of reality and encourages us to think critically about the nature of existence. In conclusion, the concept of invariance is a powerful tool across multiple disciplines. Whether in physics, mathematics, computer science, economics, or philosophy, invariance provides a framework for understanding stability amidst change. Its applications are vast and varied, demonstrating how this fundamental principle helps us make sense of the world around us. By embracing the idea of invariance, we can unlock new insights and foster innovation in our respective fields. As we continue to explore and apply the concept of invariance, we enhance our ability to navigate complexity and uncertainty in an ever-evolving landscape.

在科学和数学领域，不变性的概念在理解各种现象中发挥着至关重要的作用。不变性是指在某些变换或条件下，物体或系统保持不变的特性。这个思想不仅在物理学中是基础，在计算机科学、经济学甚至哲学等其他领域也有重要意义。 为了说明不变性的重要性，让我们考虑物理学的定律。物理学中最著名的原则之一是能量守恒原理，它指出在一个封闭系统中，总能量在时间上保持不变。这个原则体现了不变性的思想，因为它意味着无论系统内部发生什么过程，总能量的数量不会改变。这种不变性使科学家能够以惊人的准确性预测物理系统的行为。 在数学中，不变性常常在几何变换中观察到。例如，当一个形状被旋转或反射时，某些属性如面积和周长保持不变。这种几何属性在变换下的不变性对于理解对称性至关重要，并且可以应用于建筑和设计等各个领域。对数学中不变性的研究还深入洞察代数结构和拓扑空间，为解决复杂问题提供了框架。 此外，在计算机科学中，不变性在算法设计和软件开发中至关重要。程序员通常依赖于不变式——在程序执行过程中必须保持真实的条件——来确保正确性和可靠性。通过在代码中建立不变性，开发人员可以创建即使在面对意外输入或错误时也表现出可预测性的强大系统。这种做法不仅增强了软件的功能，还简化了调试和维护过程。 经济学也在各种理论和模型中利用了不变性的概念。例如，效用不变性的思想表明，消费者的偏好在收入或商品价格变化的情况下仍然保持一致。理解这种不变性帮助经济学家预测消费者行为并制定市场干预策略。它突显了某些经济关系的稳定性，这对于有效的政策制定至关重要。 在哲学中，不变性引发了关于身份和变化的有趣问题。哲学家们辩论物体是否可以在经历变换的同时保持其身份。讨论通常围绕着不变性与实体本质相关的概念展开。这种对不变性的探索挑战了我们对现实的理解，并鼓励我们批判性地思考存在的本质。 总之，不变性的概念是在多个学科中的强大工具。无论是在物理学、数学、计算机科学、经济学还是哲学中，不变性为理解变化中的稳定性提供了框架。它的应用广泛而多样，展示了这一基本原则如何帮助我们理解周围的世界。通过接受不变性的思想，我们可以解锁新的见解，并在各自的领域中促进创新。随着我们继续探索和应用不变性的概念，我们增强了在不断变化的环境中驾驭复杂性和不确定性的能力。