singularities

简明释义

英[ˌsɪŋɡjʊˈlærɪtiz]美[ˌsɪŋɡjəˈlɛrɪtiz]

n. 奇异性；[数]奇异点（singularity 的复数）

英英释义

单词用法

同义词

反义词

例句

1.The Fourier transform is a classical method for analyzing signal singularities.

傅立叶变换是分析信号奇异性的传统方法。

2.There are abundant and complicated singularities in parallel mechanisms, which have great effects on the accuracy, stiffness and motion ability of parallel mechanisms.

丰富而复杂的奇异位形是并联机构的一个重要特点，位形空间中的奇异位形对并联机构的精度、刚度以及运动性能有着重要的影响。

3.In this paper, we study the direct method of solution for a class of singular integral equations with solutions having singularities of order one.

本文研究了一类具有一阶奇异性解的完全奇异积分方程的直接解法。

4.Stronger singularities can only be dealt with for special matrix potentials.

更强的奇异性仅能被用于处理特殊的矩阵势。

5.We pointed out the main distinctions between strong singularity problems in topology optimization and those which only have weak singularities.

详细论述了此类拓扑优化问题与仅具有弱奇异性的拓扑优化问题之间的本质区别。

6.Such singularities must be treated with special computations.

奇异点必须用特殊的计算处理。

7.The singularities of signals and noises are investigated. A conclusion is drawn that the wavelet modulus maxima of signals have contrary behaviors from that of noises.

通过对信号与噪声奇异性的分析，得出信号与噪声的小波变换模极大值在各个尺度上的表现截然相反的结论。

8.In reality, nearly all scientists encounter setbacks, singularities that disturb the local time-career continuum.

在现实中，几乎所有的科学家们都会遇到挫折和奇特的事情，扰乱时间和职业生涯的继续。

9.In mathematics, we often encounter singularities 奇点 when analyzing functions that behave abnormally at certain points.

在数学中，我们经常在分析在某些点行为异常的函数时遇到奇点.

10.Astrophysicists are particularly interested in the singularities 奇点 that exist at the centers of galaxies.

天体物理学家特别关注存在于星系中心的奇点.

11.The study of singularities 奇点 in dynamical systems helps us understand stability and chaos.

对动态系统中奇点的研究帮助我们理解稳定性和混沌.

12.In computer science, singularities 奇点 can refer to points where algorithms fail or produce unexpected results.

在计算机科学中，奇点可以指算法失败或产生意外结果的点.

13.The physicist explained how black holes represent singularities 奇点 in the fabric of spacetime.

物理学家解释了黑洞如何代表时空结构中的奇点.

作文

In the realm of science and mathematics, the term singularities refers to points at which a given mathematical object is not defined or behaves in an anomalous manner. For instance, in physics, particularly in the study of black holes, singularities represent regions where the gravitational forces are so intense that spacetime curves infinitely, leading to breakdowns in our understanding of the fundamental laws of physics. The concept of singularities challenges scientists and mathematicians alike, as it pushes the boundaries of what we know and compels us to seek deeper explanations. The occurrence of singularities can be observed in various fields beyond physics. In mathematics, a function may exhibit a singularity when it approaches a point where it cannot be evaluated, such as dividing by zero. These mathematical singularities often require special treatment, such as limits or alternative formulations, to make sense of the behavior of functions near these problematic points. Thus, understanding singularities is essential for mathematicians to navigate complex equations and models.Moreover, singularities also appear in the context of technology and artificial intelligence. The idea of a technological singularity suggests a future moment when artificial intelligence surpasses human intelligence, leading to rapid advancements that could fundamentally change society. This notion raises philosophical and ethical questions about the role of humanity in a world dominated by superintelligent machines. As we approach this potential singularity, it is crucial to consider the implications for governance, ethics, and the nature of consciousness itself.In literature and art, singularities can symbolize moments of profound change or transformation. Authors often use the concept to depict turning points in characters' lives, where they confront challenges that lead to personal growth or revelation. These narrative singularities serve as catalysts for character development, emphasizing the importance of conflict and resolution in storytelling.Ultimately, the exploration of singularities across various disciplines reveals a common thread: the quest for understanding amidst complexity. Whether in the physical universe, abstract mathematics, technological advancements, or the human experience, singularities challenge us to think critically and creatively. They remind us that knowledge is not static but rather an evolving landscape filled with mysteries waiting to be unraveled. As we continue to investigate and learn from these singularities, we must remain open to new ideas and perspectives, embracing the unknown as a vital part of our intellectual journey. In conclusion, singularities are not merely obstacles to be overcome; they are opportunities for growth and discovery. By studying singularities, we gain insights into the nature of reality, the limits of human understanding, and the potential for future innovations. As we navigate through our lives and the universe, let us embrace the singularities that challenge us, for they may very well lead us to the most profound truths about existence itself.

在科学和数学的领域中，术语singularities指的是一个给定的数学对象未定义或表现出异常行为的点。例如，在物理学中，尤其是在黑洞研究中，singularities代表着引力如此强大以至于时空无限弯曲的区域，这导致我们对基本物理法则的理解崩溃。singularities的概念挑战着科学家和数学家，因为它推动了我们知识的边界，并迫使我们寻求更深层次的解释。singularities的出现不仅可以在物理学中观察到。在数学中，当一个函数接近一个无法评估的点，例如除以零时，它可能会表现出singularity。这些数学singularities通常需要特殊处理，例如极限或替代公式，以便理解函数在这些问题点附近的行为。因此，理解singularities对于数学家来说是导航复杂方程和模型的关键。此外，singularities还出现在技术和人工智能的背景下。技术singularity的概念暗示着一个未来的时刻，当人工智能超越人类智能时，将导致快速的进步，从而可能根本改变社会。这一概念引发了关于人类在被超级智能机器主导的世界中的角色的哲学和伦理问题。随着我们接近这个潜在的singularity，考虑治理、伦理以及意识本质的影响变得至关重要。在文学和艺术中，singularities可以象征深刻变化或转变的时刻。作家们常常用这一概念来描绘角色生活中的转折点，他们面临挑战，从而导致个人成长或启示。这些叙事singularities作为角色发展的催化剂，强调冲突与解决在叙事中的重要性。最终，不同学科对singularities的探索揭示了一条共同的线索：在复杂性中追求理解。无论是在物理宇宙、抽象数学、技术进步还是人类经历中，singularities都挑战我们进行批判性和创造性思考。它们提醒我们，知识并非静态，而是一个充满等待被解开的神秘的不断演变的景观。随着我们继续调查和学习这些singularities，我们必须保持开放的心态，接受未知作为我们智识旅程的重要组成部分。总之，singularities不仅仅是需要克服的障碍；它们是成长和发现的机会。通过研究singularities，我们获得了对现实本质、人类理解的局限性以及未来创新潜力的洞察。当我们在生活和宇宙中航行时，让我们拥抱那些挑战我们的singularities，因为它们很可能会引领我们发现存在的最深刻真理。