concavity

简明释义

英[kɒnˈkævəti]美[kɑːnˈkævəti]

n. 凹面；凹度

复 数 c o n c a v i t i e s

英英释义

单词用法

同义词

反义词

例句

1.At the level of azygos vein, 100% of the lymph nodes of azygos vein and the superior aortic recess were located among the superior vena cava, arch of azygos vein, trachea and concavity of aortic arch.

在奇静脉弓平面，奇静脉弓淋巴结和主动脉上隐窝位于上腔静脉、奇静脉弓、气管和主动脉凹面所围成的气管前间隙内。

2.The formation of arch effects will bring the sand filling over the region of deep concavity hindered and the degree of compaction of molding sand at the deep concavity reduced.

它的形成会阻碍型砂向深凹区的填充，使得深凹处砂型紧实度降低。

3.With the concavity and integrability of sublinear terms near zero, the symmetry results for a class of sublinear elliptic equations are given by making use of the moving-plane method.

摘要本文利用次线性项在零点附近的凹性和可积性，用移动平面法给出了一类次线性椭圆方程正解的对称性。

4.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。

5.It is evident that curvature of doming whether on the crest (convexity) or on the flanks (concavity) have no major effect on fracture densities.

很明显，穹窿的曲率在波峰(突起)或两翼(凹陷)对断裂密度都没有很大影响。

6.Results Paranasal concavity deformities of 17 patients were corrected. The results were satisfactory and no complication such as infection or implant being extruded occurred.

结果：17例患者鼻旁区凹陷得以矫正，外形效果满意，无感染、假体外露等并发症。

7.Experimental investigations show that the semiempirical concavity calculation formulation given here are practical.

提出的计算凹度的半经验公式，经过实践考验证明具有一定的实用价值。

8.On the basis of analyzing shape features of tomatoes, leaves and branches, we extract features of roundness, slightness, concavity degree and denseness depending on Fourier description.

研究了西红柿、叶子、枝干的形状特征，通过傅立叶描绘子，提取基于傅立叶系数导出的如圆形度、细长度、凹度、密集度等形状特征。

9.Objective: To investigate the effects of variations in vertebral endplate concavity on the mechanical behaviors of the lumbar motion segment.

目的：研究终板凹陷程度变化对腰椎运动节段生物力学影响。

10.At the level of azygos vein, 100% of the lymph nodes of azygos vein and the superior aortic recess were located among the superior vena cava, arch of azygos vein, trachea and concavity of aortic arch.

在奇静脉弓平面，奇静脉弓淋巴结和主动脉上隐窝位于上腔静脉、奇静脉弓、气管和主动脉凹面所围成的气管前间隙内。

11.Architects consider the concavity of surfaces when designing buildings for aesthetic appeal.

建筑师在设计建筑时考虑表面的凹性以达到美学效果。

12.The concavity of the lens affects how light is focused.

镜头的凹性影响光线的聚焦方式。

13.In calculus, we often analyze the concavity of graphs to find inflection points.

在微积分中，我们经常分析图形的凹性以找到拐点。

14.The concavity of the bowl allows it to hold liquids without spilling.

碗的凹性使它能够盛放液体而不溢出。

15.The mathematician explained the concept of concavity to determine if the function was increasing or decreasing.

数学家解释了凹性的概念，以确定函数是增加还是减少。

作文

In mathematics, the term concavity refers to the curvature of a function. Specifically, it describes whether the curve of the function bends upwards or downwards. Understanding concavity is crucial when analyzing the behavior of functions, particularly when determining local maxima and minima. A function is said to be concave up on an interval if its second derivative is positive over that interval, indicating that the slope of the tangent line is increasing. Conversely, a function is concave down if its second derivative is negative, meaning the slope of the tangent line is decreasing. This concept not only applies to pure mathematics but also has practical implications in various fields such as economics, biology, and physics.For instance, in economics, the concavity of a utility function can indicate the preferences of consumers. A concave utility function suggests that a consumer experiences diminishing marginal utility; as they consume more of a good, the additional satisfaction gained from each extra unit decreases. This understanding helps economists model consumer behavior and predict how changes in prices or income levels affect consumption choices.In the realm of physics, the concavity of a trajectory can provide insights into motion. For example, when analyzing the path of a projectile, the concavity of its trajectory can reveal information about the forces acting upon it. If the trajectory curves downward (concave down), it indicates that gravitational force is dominating, while an upward curve (concave up) may suggest an opposing force at play, such as thrust.Moreover, the concept of concavity is essential in optimization problems. When trying to find the maximum or minimum values of a function, identifying the points where the concavity changes—known as inflection points—can lead to significant insights. At these points, the function transitions from being concave up to concave down or vice versa, which often indicates a local extremum. Therefore, understanding concavity aids in efficiently locating optimal solutions in various mathematical models.In conclusion, the notion of concavity extends beyond mere mathematical definitions; it serves as a vital tool for analysis across multiple disciplines. Whether it’s assessing consumer behavior in economics, understanding physical motion, or solving optimization problems, the principles surrounding concavity offer invaluable insights. As students and professionals delve deeper into their respective fields, a solid grasp of concavity will undoubtedly enhance their analytical capabilities and foster a greater appreciation for the interconnectedness of mathematical concepts and real-world applications.

在数学中，术语concavity指的是函数的曲率。具体来说，它描述了函数的曲线是向上弯曲还是向下弯曲。理解concavity在分析函数行为时至关重要，特别是在确定局部极大值和极小值时。如果一个函数在某个区间上是向上的（concave up），则其二阶导数在该区间上为正，这表明切线的斜率在增加。相反，如果一个函数是向下的（concave down），则其二阶导数为负，意味着切线的斜率在减少。这个概念不仅适用于纯数学，还在经济学、生物学和物理学等多个领域具有实际意义。例如，在经济学中，效用函数的concavity可以表明消费者的偏好。一个凹形效用函数表明消费者经历边际效用递减；随着他们消费更多商品，从每个额外单位中获得的额外满足感会减少。这种理解帮助经济学家建模消费者行为，并预测价格或收入水平变化如何影响消费选择。在物理学领域，轨迹的concavity可以提供运动的见解。例如，在分析抛射物的路径时，其轨迹的concavity可以揭示作用于其上的力的信息。如果轨迹向下弯曲（concave down），这表明重力正在主导，而向上弯曲（concave up）则可能表明存在对抗力，例如推力。此外，concavity的概念在优化问题中至关重要。当试图找到函数的最大值或最小值时，识别concavity变化的点——称为拐点——可以带来重要的见解。在这些点上，函数从凹形转变为凸形，反之亦然，这通常表示局部极值。因此，理解concavity有助于在各种数学模型中有效地定位最优解。总之，concavity的概念超越了单纯的数学定义；它作为分析多个学科的重要工具。无论是评估经济学中的消费者行为，理解物理运动，还是解决优化问题，围绕concavity的原则都提供了宝贵的见解。随着学生和专业人士深入各自领域，对concavity的扎实掌握无疑将增强他们的分析能力，并促进对数学概念与现实世界应用之间相互联系的更大欣赏。