convexity

简明释义

英[kɒnˈveksəti]美[kɑːnˈveksəti]

n. 凸面，凸状；中凸

复 数 c o n v e x i t i e s

英英释义

单词用法

同义词

反义词

例句

1.This paper presents a set of new CNN templates for recovering convexity of disturbed convex objects in digitized gray scale images.

本文提出了一组CNN新模板，用于恢复数字化灰度图像中扭曲凸物体像的凸性。

2.One is quasi-convexity and pseudo convexity of functions and quasimonotonicity and pseu-domonotonicity of their sub differentials .

一是函数的拟凸性、伪凸性及其次微分的拟单调性、伪单调性；

3.On the verge of the hour the heads of a group of children, of ages ranging from six to fourteen, rose above the stubbly convexity of the hill.

快到十一点的时候，一群年龄从六岁到十四岁的小孩子，从山坡上一块满是残茬的高地上露了出来。

4.Quasiconvex functions are studied by applying nearly convexity of sets. Under weaker assumptions, some equivalent conditions for quasiconvexity are derived.

用集合的近似凸性研究函数的拟凸性。在较弱假设下，获得了拟凸性的一些等价条件。

5.Interest rate immunization strategy in the asset-debt management is discussed using the duration convexity method.

运用久期—凸度方法，研究了资产负债管理的利率免疫策略。

6.Midpoint locally uniform convexity is generalized to the midpoint locally K-uniform convexity, and the relation between the two cases is discussed.

将中点局部一致凸性推广到中点局部k一致凸，并且讨论了它们之间的关系。

7.We introduce concepts of diagonal quasi-convexity and quasi-concavity in hyperconvex metric spaces.

我们介绍了超凸度量空间中对角拟凸和拟凹的概念。

8.The convexity of the shape allows for better aerodynamics in vehicle design.

形状的凸性使得车辆设计在空气动力学上更优越。

9.A convexity in the market can lead to increased investor confidence.

市场上的一个凸性可能会导致投资者信心的增加。

10.In finance, a bond's convexity can indicate its sensitivity to interest rate changes.

在金融中，债券的凸性可以指示其对利率变化的敏感性。

11.Mathematicians study the convexity of functions to understand their properties.

数学家研究函数的凸性以理解其属性。

12.The convexity of the lens determines how it focuses light.

镜头的凸性决定了它如何聚焦光线。

作文

In the realm of mathematics and economics, the concept of convexity (凸性) plays a crucial role in understanding various phenomena. To grasp the significance of convexity (凸性), we must first explore its definition and implications in different fields. Essentially, convexity (凸性) refers to the property of a shape or function where any line segment connecting two points on the boundary lies entirely within or on the boundary of the shape or function. This property is not only aesthetically pleasing but also carries profound implications for optimization and decision-making processes.In mathematics, particularly in the study of functions, convexity (凸性) indicates that the second derivative of a function is non-negative. This characteristic ensures that the function has a single global minimum, making it easier for mathematicians and economists to find optimal solutions. For example, when analyzing cost functions in economics, a convex cost function implies that as production increases, the additional cost of producing one more unit will not decrease. This allows businesses to predict their costs more accurately and make informed decisions about scaling production.Moreover, in finance, convexity (凸性) is a vital concept in bond pricing. It describes the relationship between bond prices and interest rates. A bond with high convexity (凸性) will experience less price volatility when interest rates change compared to a bond with low convexity (凸性). This means that investors often prefer bonds with higher convexity (凸性) as they provide greater protection against interest rate fluctuations. Understanding this relationship helps investors make strategic choices regarding their portfolios and manage risk effectively.In addition to its mathematical and financial applications, convexity (凸性) can also be observed in everyday life. For instance, consider the design of a bicycle frame. A well-designed frame exhibits convexity (凸性) in its structure, allowing for better aerodynamics and stability. Similarly, in architecture, buildings with convexity (凸性) in their design often enhance aesthetic appeal and structural integrity. These real-world examples illustrate how convexity (凸性) is not merely an abstract concept but rather a principle that influences various aspects of our lives.To further appreciate the importance of convexity (凸性), we can examine its implications in social sciences. In game theory, for instance, the concept of convexity (凸性) is essential in understanding cooperative games. When players form coalitions, the benefits derived from cooperation often exhibit convexity (凸性), indicating that the total payoff from collaboration is greater than the sum of individual payoffs. This insight encourages collaboration and strategic alliances among individuals and organizations, leading to mutually beneficial outcomes.In conclusion, convexity (凸性) is a multifaceted concept that permeates various disciplines, including mathematics, economics, finance, and even everyday life. Its significance lies in its ability to simplify complex problems, enhance decision-making processes, and foster collaboration. By understanding convexity (凸性) and its applications, we can better navigate the intricacies of both theoretical and practical challenges, ultimately leading to more informed and effective choices in our personal and professional lives.

在数学和经济学领域，convexity（凸性）的概念在理解各种现象中发挥着至关重要的作用。要掌握convexity（凸性）的意义，我们必须首先探讨其定义及其在不同领域的影响。本质上，convexity（凸性）指的是一种形状或函数的特性，其中连接边界上两个点的任何线段都完全位于该形状或函数的内部或边界上。这一特性不仅在美学上令人愉悦，而且对优化和决策过程具有深远的影响。在数学中，尤其是在函数研究中，convexity（凸性）表示一个函数的二阶导数是非负的。这一特性确保该函数具有唯一的全局最小值，使得数学家和经济学家更容易找到最佳解决方案。例如，在分析经济中的成本函数时，凸成本函数意味着随着生产的增加，生产一个额外单位的附加成本不会减少。这使企业能够更准确地预测其成本，并就扩大生产做出明智的决策。此外，在金融领域，convexity（凸性）是债券定价中的一个重要概念。它描述了债券价格与利率之间的关系。具有高convexity（凸性）的债券在利率变化时价格波动较小，而低convexity（凸性）的债券则相反。这意味着投资者通常更喜欢具有较高convexity（凸性）的债券，因为它们在利率波动时提供了更大的保护。理解这种关系帮助投资者在投资组合中做出战略选择，有效管理风险。除了在数学和金融中的应用，convexity（凸性）还可以在日常生活中观察到。例如，考虑自行车框架的设计。设计良好的框架在结构上表现出convexity（凸性），允许更好的空气动力学和稳定性。同样，在建筑中，具有convexity（凸性）设计的建筑往往增强了美学吸引力和结构完整性。这些现实世界的例子说明了convexity（凸性）不仅仅是一个抽象概念，而是影响我们生活各个方面的原则。为了进一步欣赏convexity（凸性）的重要性，我们可以考察其在社会科学中的影响。例如，在博弈论中，convexity（凸性）的概念在理解合作博弈中至关重要。当玩家形成联盟时，合作所带来的收益往往表现出convexity（凸性），这表明来自合作的总收益大于个人收益的总和。这一洞察力鼓励个人和组织之间的合作和战略联盟，从而导致互利的结果。总之，convexity（凸性）是一个多方面的概念，渗透到数学、经济学、金融乃至日常生活的各个学科中。它的重要性在于能够简化复杂问题，增强决策过程，并促进合作。通过理解convexity（凸性）及其应用，我们可以更好地驾驭理论和实践挑战的复杂性，最终在个人和职业生活中做出更明智和有效的选择。