extremal

简明释义

英[ɪkˈstriːməl]美[ɪksˈtriməl]

adj. 极值的

n. 极值曲线；致极函数

英英释义

单词用法

同义词

反义词

例句

1.The monotone iterative techniques is used to investigate the existence of extremal solution of periodic boundary value problems (PBVP) for neutral delay differential equation.

利用单调迭代方法给出了中立型滞后微分方程的周期边值问题极解的存在性定理。

2.Theorem 20 is the basis of a rather detailed study of the structure of extremal graphs.

定理20是极图构造更详细的研究的基础。

3.In this paper, inverse degree of unicyclic graphs and bicyclic graphs is discussed, and the extremal graphs that reach the upper and lower bounds are given.

研究了单圈图、双圈图的反比度，给出了它们的上下界并得到达到最大最小值的极图，还进一步给出多圈图的上下界的一个猜想。

4.This paper obtains a general result in the precise asymptotics for the point process of the jump times of an extremal process with wide range weighted functions and boudary functions.

为了解决学术期刊指标体系综合评价中不同评价方法结果不一致问题，文章利用中国科学技术信息研究所的医学院校学报数据，提出了一种新的基于极值法的组合评价方法。

5.The extremal formula of binary quadratic functions is studied by using method of undetermined coefficients, substitution method and method of completing the square.

用特定系数法、换元法、配方法探求二元二次函数的极值公式。

6.For the general hexagonal chains, the extremal problem of some important types of conjugated molecules have been solved previously.

对于一般的六角链，一些重要类型的共轭分子的极值问题已得到解决。

7.We obtain the existence of extremal solutions of the boundary value problem by using the method of lower and upper solutions coupled with monotone iterative technique.

研究一类四阶微分方程解的存在性，利用上下解及单调迭代的方法，得出这类四阶方程的最大解和最小解的存在。

8.The theory of quantile regression, Copula quantile regression, extremal quantiles and applications of quantile regression in many fields are discussed in this paper.

本文主要对分位数回归的理论、Copula分位数回归、极端分位数以及分位数回归在各个领域的应用进行了深入研究。

9.The detection algorithm that adopts tow-level finite difference and extremal theory is used to locate the R wave and the one-level and tow-level derivative methods is used when detect QRS wave.

对于R波，采用二级差分和极值方法定位，对QRS波群采用一阶导数与二阶导数并用算法进行检测。

10.In optimization problems, we often seek the extremal 极值的 values of a function.

在优化问题中，我们通常寻求一个函数的极值的 extremal 值。

11.The extremal 极端的 cases help us understand the limits of our model.

这些极端的 extremal 情况帮助我们理解模型的极限。

12.Researchers studied the extremal 极值的 behavior of the system under various conditions.

研究人员研究了系统在不同条件下的极值的 extremal 行为。

13.The extremal 极端的 points in the dataset were crucial for the analysis.

数据集中极端的 extremal 点对分析至关重要。

14.In mathematics, finding extremal 极值的 solutions is often the goal of calculus.

在数学中，寻找极值的 extremal 解通常是微积分的目标。

作文

In the field of mathematics, particularly in optimization and calculus, the term extremal is frequently used to refer to the maximum or minimum values of a function. Understanding the concept of extremal points is crucial for solving various mathematical problems, as these points often represent the best possible solutions under given constraints. For instance, when we talk about maximizing profit or minimizing cost in economics, we are essentially looking for the extremal values of a particular function that describes these relationships. To illustrate this concept, consider a simple example involving a quadratic function, which can be represented as f(x) = ax² + bx + c, where a, b, and c are constants. The graph of this function is a parabola, and depending on the sign of 'a', it can open upwards or downwards. If 'a' is positive, the extremal point will be the minimum value of the function, while if 'a' is negative, it will be the maximum value. By finding the vertex of the parabola, we can determine the extremal point, which gives us valuable information about the behavior of the function. In real-world applications, identifying extremal values can help in decision-making processes. For example, an engineer designing a bridge must calculate the extremal forces acting on the structure to ensure its stability and safety. Similarly, in finance, analysts look for extremal stock prices to make informed investment decisions. These extremal values can indicate potential risks and rewards, guiding investors toward more strategic choices. Moreover, the concept of extremal extends beyond just mathematics and economics. In physics, the laws of thermodynamics often involve extremal principles to describe equilibrium states. For instance, the second law of thermodynamics states that the entropy of an isolated system tends to reach a maximum, which corresponds to an extremal state of disorder. Understanding these extremal conditions allows scientists to predict how systems behave under various circumstances. Additionally, in computer science, algorithms that optimize certain functions often rely on finding extremal values. For example, machine learning models are trained to minimize error functions, which leads to the identification of extremal points that represent the best-fitting model for the data. This process is essential for creating effective predictive models that can be applied in numerous fields, from healthcare to marketing. In conclusion, the term extremal encapsulates a fundamental concept that permeates various disciplines, including mathematics, economics, physics, and computer science. Mastering the understanding of extremal values enables individuals to tackle complex problems, make informed decisions, and innovate within their respective fields. Whether one is calculating the extremal points of a function or analyzing extremal conditions in physical systems, the significance of this term cannot be overstated. As we continue to explore and apply the principles associated with extremal values, we unlock new possibilities for advancements in knowledge and technology.

在数学领域，尤其是优化和微积分中，术语extremal常用于指代函数的最大值或最小值。理解extremal点的概念对于解决各种数学问题至关重要，因为这些点通常代表在给定约束下最佳的解决方案。例如，当我们谈论最大化利润或最小化成本时，我们实际上是在寻找描述这些关系的特定函数的extremal值。 为了说明这一概念，考虑一个简单的二次函数，它可以表示为f(x) = ax² + bx + c，其中a、b和c是常数。该函数的图形是一个抛物线，取决于'a'的符号，它可以向上或向下打开。如果'a'为正，则extremal点将是函数的最小值，而如果'a'为负，则将是最大值。通过找到抛物线的顶点，我们可以确定extremal点，从而获得有关函数行为的宝贵信息。 在现实世界的应用中，识别extremal值可以帮助决策过程。例如，设计桥梁的工程师必须计算作用在结构上的extremal力，以确保其稳定性和安全性。同样，在金融领域，分析师寻找extremal股票价格以做出明智的投资决策。这些extremal值可以指示潜在的风险和回报，引导投资者朝着更具战略性的选择前进。 此外，extremal的概念不仅限于数学和经济学。在物理学中，热力学定律通常涉及extremal原理来描述平衡状态。例如，热力学第二定律指出，孤立系统的熵趋向于达到最大，这对应于一种extremal无序状态。理解这些extremal条件使科学家能够预测系统在各种情况下的行为。 此外，在计算机科学中，优化某些函数的算法通常依赖于找到extremal值。例如，机器学习模型被训练以最小化误差函数，从而导致识别出代表数据最佳拟合模型的extremal点。这个过程对于创建有效的预测模型至关重要，这些模型可以应用于多个领域，从医疗保健到市场营销。 总之，术语extremal包含了一个基本概念，该概念渗透到多个学科，包括数学、经济学、物理学和计算机科学。掌握extremal值的理解使个人能够应对复杂问题、做出明智决策并在各自领域进行创新。无论是计算函数的extremal点，还是分析物理系统中的extremal条件，这个术语的重要性都不容小觑。随着我们继续探索和应用与extremal值相关的原则，我们为知识和技术的进步打开了新的可能性。