epsilon

简明释义

英[ˈepsɪlɒn;epˈsaɪlən]美[ˈepsɪlɑːn]

n. 希腊语字母表的第五个字母；小的正数；（一系列项目、分类中的）第五

n. （Epsilon） ε星（星座中的第五颗星）

n. （Epsilon）（美、俄、希腊）埃鄱西龙（人名）

英英释义

单词用法

同义词

反义词

例句

1.Perhaps, Rusted says, without this second capability, epsilon 4's benefits fallby the wayside.

拉什特说，也许，失掉后面这个能力后E4的好处就形同虚设了。

2.Rustedsuggests that epsilon 4 helps people focus on important information.

拉什特认为E4帮助个体将注意力放在重要的信息上。

3.So here's epsilon zero, 0 two epsilon zero, 0 three epsilon zero, It says, you know, if kT is about ten times bigger than epsilon zero.

这是ε,这是2ε,还有3ε,它表示，如果kT大约是ε0的十倍。

4.Epsilon Eridani is located about 10 light-years away in the constellation Eridanus and is visible in the night skies with the naked eye.

EpsilonEridani位于波江星座以外10光年的地方，地球的夜空中目力可及。

5.Epsilon assured its clients that the leak was confined to E-mail addresses and did not compromise their customers' financial information. See article.

Epsilon向其客户保证导致电邮地址泄漏的漏洞已经修复，并没有危及客户的财务信息。

6.The Epsilon Series is the most compact digital servo drive in the Numatics lineup.

在小量系列是最精巧的纽曼帝克系列数字伺服驱动器。

7.But the system variance is going to be on the order of the square root of N times epsilon.

但是系统能量的变化量大约,会是N的平方根乘以ε

8.Epsilon lies at the western edge of the constellation.

星位于这个星座的西边缘。

9.In calculus, the limit of a function is often defined using an arbitrary small value, typically denoted as epsilon, which represents a positive number that can be made as small as desired.

在微积分中，函数的极限通常使用一个任意的小值来定义，通常用epsilon表示，代表可以尽量小的正数。

10.When discussing numerical methods, we may say that the error must be less than epsilon to ensure the accuracy of the solution.

在讨论数值方法时，我们可能会说误差必须小于epsilon以确保解的准确性。

11.In machine learning, a small value like epsilon is often added to avoid division by zero in algorithms.

在机器学习中，像epsilon这样的一个小值常常被加到算法中，以避免除以零的情况。

12.In statistical hypothesis testing, epsilon can represent the significance level, indicating how unlikely a result is under the null hypothesis.

在统计假设检验中，epsilon可以表示显著性水平，指示在原假设下结果有多不可能。

13.In optimization problems, we might set a convergence criterion such that the change in the objective function is less than epsilon.

在优化问题中，我们可能会设置一个收敛标准，使得目标函数的变化小于epsilon。

作文

In the field of mathematics and science, the term epsilon is often used to represent a very small positive quantity. This concept is crucial in various branches such as calculus, physics, and engineering. The Greek letter ε (epsilon) symbolizes this tiny value, which can be thought of as approaching zero but never actually reaching it. Understanding epsilon is essential for grasping limits, continuity, and differentiability in calculus. For instance, when we say that a function approaches a limit as x approaches a certain value, we often express this using the notion of epsilon. Specifically, we might state that for every epsilon greater than zero, there exists a corresponding delta that defines how close x must be to that value to ensure the function's output is within epsilon of the limit. This relationship helps us understand the behavior of functions in a rigorous manner. Moreover, epsilon plays a vital role in numerical analysis, where precision is key. In computational methods, errors are often measured in terms of epsilon, indicating the smallest difference that can be recognized by a computer. This usage emphasizes the importance of epsilon in ensuring the reliability and accuracy of numerical simulations and calculations. When algorithms are designed, they often incorporate epsilon to determine convergence criteria or to establish thresholds for acceptable error margins. In physics, epsilon can also represent small quantities in equations that describe physical phenomena. For example, in electromagnetism, the permittivity of free space is denoted by ε, which is a fundamental constant in the equations governing electric fields. Understanding how epsilon functions in these contexts allows scientists and engineers to make accurate predictions about the behavior of systems under various conditions. Furthermore, the concept of epsilon extends beyond mathematics and physics into other disciplines such as economics and statistics. In economics, epsilon may refer to a small change in variables that can significantly affect outcomes, such as elasticity in demand and supply. In statistics, epsilon is often used in hypothesis testing, representing the margin of error or the significance level in experiments. In conclusion, epsilon is not just a simple Greek letter; it embodies a fundamental idea of infinitesimal quantities that permeate various scientific disciplines. Its applications are vast, ranging from defining limits in calculus to measuring precision in computational methods, and even influencing theories in economics. By understanding epsilon, one gains insight into the underlying principles that govern many aspects of the natural and social sciences. Thus, mastering the concept of epsilon is crucial for anyone looking to deepen their knowledge in mathematics, physics, engineering, or any field that relies on precise measurements and theoretical foundations. The versatility and significance of epsilon make it a cornerstone of analytical thinking and problem-solving in our increasingly complex world.

在数学和科学领域，术语epsilon通常用于表示一个非常小的正数量。这个概念在微积分、物理学和工程等各个分支中至关重要。希腊字母ε（epsilon）象征着这个微小的值，可以被视为接近零但从未真正达到。理解epsilon对于掌握微积分中的极限、连续性和可微性是必不可少的。例如，当我们说一个函数在x接近某个值时趋近于一个极限时，我们通常会使用epsilon的概念来表达。具体来说，我们可能会声明，对于每一个大于零的epsilon，存在一个对应的delta，定义了x必须接近该值的程度，以确保函数的输出在epsilon范围内接近极限。这种关系帮助我们以严谨的方式理解函数的行为。 此外，epsilon在数值分析中也发挥着至关重要的作用，其中精度是关键。在计算方法中，误差通常以epsilon来衡量，表示计算机能够识别的最小差异。这种用法强调了epsilon在确保数值模拟和计算的可靠性与准确性方面的重要性。当算法被设计时，通常会结合epsilon来确定收敛标准或建立可接受误差边界的阈值。 在物理学中，epsilon也可以表示在描述物理现象的方程中出现的小量。例如，在电磁学中，自由空间的介电常数用ε表示，这是描述电场的基本常数之一。理解epsilon在这些上下文中的功能使得科学家和工程师能够对系统在各种条件下的行为做出准确的预测。 此外，epsilon的概念不仅限于数学和物理，还扩展到经济学和统计学等其他学科。在经济学中，epsilon可能指变量的小变化，这些变化会显著影响结果，例如需求和供给的弹性。在统计学中，epsilon常用于假设检验，表示实验中的误差范围或显著性水平。 总之，epsilon不仅仅是一个简单的希腊字母；它体现了无穷小量的基本思想，这一思想渗透到许多科学学科中。其应用范围广泛，从定义微积分中的极限到测量计算方法中的精度，甚至影响经济学中的理论。通过理解epsilon，人们可以深入了解支配自然和社会科学许多方面的基本原则。因此，掌握epsilon的概念对于任何希望加深数学、物理、工程或任何依赖精确测量和理论基础的领域知识的人来说都是至关重要的。epsilon的多样性和重要性使其成为我们日益复杂的世界中分析思维和解决问题的基石。