auxiliary condition

简明释义

附加条件;

英英释义

例句

1.Researchers often define auxiliary conditions 辅助条件 to narrow down their hypotheses.

研究人员通常定义辅助条件 auxiliary conditions以缩小他们的假设范围。

2.In economics, certain auxiliary conditions 辅助条件 can affect market equilibrium.

在经济学中，某些辅助条件 auxiliary conditions可以影响市场均衡。

3.The software requires specific auxiliary conditions 辅助条件 to function correctly.

该软件需要特定的辅助条件 auxiliary conditions才能正常运行。

4.In the context of machine learning, an auxiliary condition 辅助条件 may be used to improve model accuracy.

在机器学习的背景下，辅助条件 auxiliary condition 可以用来提高模型的准确性。

5.The engineer specified an auxiliary condition 辅助条件 for the structural integrity tests.

工程师为结构完整性测试指定了一个辅助条件 auxiliary condition。

作文

In the realm of mathematics and engineering, understanding various concepts is crucial for problem-solving. One such concept is the auxiliary condition, which refers to additional requirements or constraints that are imposed on a system to aid in finding a solution. These conditions are not part of the primary equations but serve as supplementary guidelines that help narrow down the possible solutions to a problem. For instance, when solving differential equations, engineers often introduce auxiliary conditions to specify the behavior of a system at certain points, such as initial values or boundary conditions.The importance of auxiliary conditions can be illustrated through a practical example in civil engineering. Consider the design of a bridge. The main equations governing the structural integrity of the bridge might include factors like load distribution and material strength. However, to ensure that the bridge performs safely under various conditions, engineers must apply auxiliary conditions such as wind load, temperature variations, and even the effects of seismic activity. By incorporating these additional constraints, engineers can create a more robust and reliable design.Moreover, auxiliary conditions play a significant role in optimization problems. When attempting to maximize or minimize a particular function, it is often necessary to impose certain restrictions. For example, in a manufacturing process, a company may want to minimize costs while adhering to specific quality standards. Here, the quality standards act as auxiliary conditions that guide the optimization process, ensuring that the final output meets the required specifications.In the field of physics, auxiliary conditions are equally vital. When studying the motion of objects, physicists often rely on Newton's laws of motion. However, to accurately predict the motion of a projectile, they must consider auxiliary conditions such as air resistance, gravitational forces, and initial velocity. These conditions provide a more comprehensive understanding of the system and enable scientists to make accurate predictions about the behavior of physical objects.Furthermore, in computer science, auxiliary conditions can be seen in algorithms and data structures. When developing an algorithm to sort a list of items, the programmer may need to define auxiliary conditions such as the order of sorting (ascending or descending) and any specific criteria that items must meet to be included in the final sorted list. These conditions help refine the algorithm's functionality and efficiency.In conclusion, the concept of auxiliary conditions is integral across various disciplines, including mathematics, engineering, physics, and computer science. They provide essential frameworks for problem-solving by adding necessary constraints that lead to more precise and applicable solutions. Understanding how to effectively utilize auxiliary conditions can greatly enhance one’s ability to tackle complex challenges and achieve desired outcomes in both theoretical and practical applications.

在数学和工程学领域，理解各种概念对于解决问题至关重要。其中一个概念是辅助条件，指的是对系统施加的额外要求或约束，以帮助找到解决方案。这些条件不是主要方程的一部分，而是作为补充指导，帮助缩小问题的可能解决方案。例如，在求解微分方程时，工程师通常会引入辅助条件以指定系统在某些点的行为，例如初始值或边界条件。辅助条件的重要性可以通过土木工程中的实际例子来说明。考虑桥梁的设计。支配桥梁结构完整性的主要方程可能包括荷载分布和材料强度等因素。然而，为了确保桥梁在各种条件下安全运行，工程师必须施加辅助条件，例如风载、温度变化，甚至地震活动的影响。通过结合这些额外的约束，工程师可以创建更稳健和可靠的设计。此外，辅助条件在优化问题中也发挥着重要作用。当试图最大化或最小化某个特定函数时，通常需要施加某些限制。例如，在生产过程中，一家公司可能希望在遵循特定质量标准的同时最小化成本。在这里，质量标准作为辅助条件，指导优化过程，确保最终输出符合所需规范。在物理学领域，辅助条件同样至关重要。当研究物体的运动时，物理学家通常依赖牛顿运动定律。然而，为了准确预测抛射物的运动，他们必须考虑辅助条件，如空气阻力、重力和初始速度。这些条件提供了对系统更全面的理解，使科学家能够准确预测物理物体的行为。此外，在计算机科学中，辅助条件可以在算法和数据结构中看到。当开发算法以对项目列表进行排序时，程序员可能需要定义辅助条件，例如排序的顺序（升序或降序）以及项目必须满足的任何特定标准，以便包含在最终排序列表中。这些条件有助于细化算法的功能和效率。总之，辅助条件的概念在数学、工程、物理和计算机科学等多个学科中都是不可或缺的。它们为解决问题提供了必要的框架，通过添加必要的约束，导致更精确和适用的解决方案。了解如何有效利用辅助条件可以大大增强个人应对复杂挑战和在理论及实践应用中实现预期结果的能力。