regular chain

简明释义

所有权联锁 ［连锁商店］

英英释义

例句

1.The company implemented a regular chain to ensure efficient communication among departments.

公司实施了一个常规链条以确保各部门之间的高效沟通。

2.A regular chain of events led to the successful launch of the project.

一系列的常规链条事件导致了项目的成功启动。

3.In logistics, a regular chain is vital for timely deliveries.

在物流中，常规链条对及时交货至关重要。

4.Using a regular chain of suppliers helps maintain consistent product quality.

使用常规链条供应商有助于保持产品质量的一致性。

5.The restaurant established a regular chain of suppliers to ensure fresh ingredients.

餐厅建立了一个常规链条供应商以确保新鲜食材。

作文

In the realm of mathematics, particularly in algebraic geometry, the concept of a regular chain is crucial for understanding the structure of algebraic varieties. A regular chain refers to a sequence of polynomials that are not only regular but also satisfy certain conditions that allow us to explore their geometric properties. These chains help mathematicians to analyze and decompose complex algebraic sets into simpler components, making it easier to study their properties and relationships.To delve deeper into the significance of a regular chain, we must first understand what is meant by 'regular' in this context. A polynomial is considered regular if it does not vanish at a given point in its domain. When we have a collection of such regular polynomials, they can be organized into a chain where each polynomial plays a role in defining the next one. This organization is essential because it allows us to create a structured approach to solving problems related to these polynomials.One of the primary applications of regular chains is in the field of computational algebra. For instance, when dealing with systems of polynomial equations, a regular chain can be utilized to simplify the problem. By identifying a regular chain within a set of polynomials, mathematicians can reduce the complexity of the equations, making it feasible to find solutions more efficiently. This method has proven invaluable in various areas of research, including robotics, computer vision, and control theory, where polynomial equations frequently arise.Moreover, regular chains also play a significant role in the study of ideal theory. In commutative algebra, an ideal is a special subset of a ring that allows for the definition of equivalence classes of polynomials. A regular chain can generate an ideal, and understanding the properties of this ideal can lead to insights about the original polynomials. For example, if a regular chain generates an ideal that is prime, it implies that the corresponding algebraic variety defined by the polynomials has certain desirable properties, such as being irreducible.The concept of regular chains is not limited to theoretical mathematics; it also has practical implications. In engineering fields, where optimization problems often involve polynomial constraints, recognizing a regular chain can facilitate the design of systems that meet specific performance criteria. Engineers can leverage this mathematical tool to ensure that their designs are both efficient and effective.In conclusion, the notion of a regular chain is a fundamental aspect of algebraic geometry and computational algebra. Its ability to organize polynomials into manageable sequences allows mathematicians and engineers alike to tackle complex problems with greater ease. As we continue to explore the depths of mathematics and its applications, the importance of regular chains will undoubtedly remain at the forefront of our endeavors, providing clarity and structure in a world often characterized by complexity and chaos.

在数学领域，特别是代数几何中，regular chain的概念对于理解代数簇的结构至关重要。regular chain指的是一系列不仅是正规而且满足某些条件的多项式，这些条件使我们能够探索它们的几何属性。这些链帮助数学家分析并将复杂的代数集合分解为更简单的组成部分，从而更容易研究它们的属性和关系。要深入了解regular chain的重要性，我们必须首先理解“正规”在这个上下文中的含义。如果一个多项式在其定义域的给定点上不消失，则该多项式被认为是正规的。当我们拥有这样一组正规的多项式时，它们可以组织成一条链，其中每个多项式在定义下一个多项式中发挥作用。这种组织至关重要，因为它使我们能够建立一个结构化的方法来解决与这些多项式相关的问题。Regular chains的主要应用之一是在计算代数领域。例如，在处理多项式方程组时，可以利用regular chain来简化问题。通过在多项式集合中识别出regular chain，数学家可以减少方程的复杂性，从而更有效地找到解决方案。这种方法在各个研究领域中被证明是无价的，包括机器人技术、计算机视觉和控制理论，其中多项式方程经常出现。此外，regular chains在理想理论的研究中也发挥着重要作用。在交换代数中，理想是环的一个特殊子集，允许定义多项式的等价类。Regular chain可以生成一个理想，理解这个理想的性质可以带来对原始多项式的见解。例如，如果regular chain生成的理想是素理想，则意味着由多项式定义的相应代数簇具有某些理想的性质，例如不可约性。Regular chains的概念不仅限于理论数学；它还具有实际意义。在工程领域，涉及多项式约束的优化问题经常出现，识别regular chain可以促进设计满足特定性能标准的系统。工程师可以利用这一数学工具确保他们的设计既高效又有效。总之，regular chain的概念是代数几何和计算代数的基本方面。它能将多项式组织成可管理的序列，使得数学家和工程师能够更轻松地应对复杂问题。随着我们继续探索数学及其应用的深度，regular chains的重要性无疑将在我们不断努力的前沿保持清晰和结构，在一个常常以复杂和混乱为特征的世界中提供清晰和结构。