variational
简明释义
adj. 变化的；因变化而产生的；[生物] 变异的
英英释义
与变化或变动相关的 | |
In mathematics, pertaining to a method of finding functions or quantities that optimize a certain criterion, often involving the calculus of variations. | 在数学中，指寻找优化某一标准的函数或量的方法，通常涉及变分法 |
单词用法
[力]变分原理（等于variation principle） | |
变分法 |
同义词
| 波动的 | 波动分析 | ||
| 微分的 | 微分方程 | ||
| 参数的 | 参数建模 |
反义词
| 常数 | 光速被认为是物理学中的一个常数。 | ||
| 固定的 | The fixed parameters in the equation do not change regardless of the input. | 方程中的固定参数无论输入如何都不会改变。 |
例句
1.Introduction of variational analysis technology.
介绍了变量化分析技术。
2.The given charts of transfer coefficients do good on realizing their variational law.
所求取的传递系数曲线对认识其变化规律有所裨益。
3.In this paper, we first introduce a class of mixed variational-like inequalities problems.
本文中，我们首先给出了一类混合似变分不等式问题。
4.The complete Euler equation set contains all kinds of Euler equations of the variational problems.
该方程组涵盖了变分问题的各种欧拉方程。
5.Based on "modified variational method", a new dynamic analysis approach of aircraft panels has been derived in this paper.
本文以“修正的变分方法”为基础推导了一种新的飞机壁板结构动力分析方法。
6.The Boundary element approximation for the parabolic variational inequalities of the second kind is discussed.
讨论了第二类抛物型变分不等式的边界近似。
7.The mean field variational method is a basic variational approximate inference method.
均值场变分方法是图模型最基本的变分近似推理方法。
8.A common technique in image processing is to use variational 变分的 methods for denoising images.
图像处理中的一种常用技术是使用变分的方法进行图像去噪。
9.The variational 变分的 principle is a fundamental concept in physics that helps derive equations of motion.
变分的原理是物理学中的一个基本概念，有助于推导运动方程。
10.The variational 变分的 formulation of quantum mechanics offers a different perspective on wave functions.
量子力学的变分的表述提供了对波函数的不同视角。
11.In mathematics, a variational 变分的 approach is often used to find the extrema of functionals.
在数学中，变分的方法常用于寻找泛函的极值。
12.Researchers applied a variational 变分的 method to optimize the parameters of their model.
研究人员应用了一种变分的方法来优化他们模型的参数。
作文
In the field of mathematics and physics, the concept of variational (变分的) methods plays a crucial role in solving complex problems. These methods are particularly useful in optimization problems, where the goal is to find the best solution from a set of possible choices. The beauty of variational (变分的) principles lies in their ability to transform difficult problems into more manageable forms by focusing on the function that describes the system's behavior.One of the most well-known applications of variational (变分的) methods is in the calculus of variations, which deals with finding functions that minimize or maximize certain quantities. For instance, consider the problem of a hanging cable, known as the catenary problem. The shape of the cable can be determined by applying variational (变分的) principles, leading to a mathematical description that captures its physical properties.In physics, variational (变分的) approaches are often used in the formulation of classical mechanics. The principle of least action states that the path taken by a system between two points in space and time is the one for which the action is minimized. This idea can be expressed using variational (变分的) calculus, providing a powerful framework for understanding motion and dynamics.Moreover, variational (变分的) methods extend beyond classical mechanics into fields like quantum mechanics and general relativity. In quantum mechanics, the variational (变分的) principle can be used to approximate the ground state energy of a quantum system. By choosing a trial wave function and minimizing the energy expectation value, physicists can gain insights into the system's behavior without needing to solve the Schrödinger equation exactly.The versatility of variational (变分的) methods also finds application in engineering, particularly in structural optimization. Engineers often face challenges in designing structures that meet specific criteria while minimizing material use or cost. By applying variational (变分的) principles, they can model the structure's performance and adjust parameters to achieve optimal designs.In addition to practical applications, the theoretical foundation of variational (变分的) methods has led to significant advancements in mathematical analysis. Researchers have developed various variational (变分的) inequalities and equations that describe a wide range of phenomena, from fluid dynamics to image processing. These mathematical tools enable scientists and engineers to tackle real-world problems more effectively.In conclusion, the concept of variational (变分的) methods is integral to many scientific disciplines. Whether it is optimizing a physical system, understanding the principles of mechanics, or designing efficient structures, variational (变分的) approaches provide a powerful framework for analysis and problem-solving. As we continue to explore the complexities of the universe, the importance of variational (变分的) methods will only grow, underscoring their value in both theoretical and applied contexts.
