asymptotically

简明释义

英[ˌæ.symˈtɒ.tɪ.kəl.i]美[ˌæs.ɪmˈtɑ.tɪ.kli]

adv. 渐近地

英英释义

单词用法

同义词

反义词

例句

1.In this paper we discuss the existence of solution of an asymptotically linear wave equation.

本文讨论渐近线性强迫波方程周期解的存在性。

2.Moreover, for some Special cases, it is proved that there exists unique equilibrium solution and it is global asymptotically stable.

在适当条件下，证明了平衡解方程有唯一解且是全局渐近稳定的。

3.An observer can asymptotically reconstruct the state of a system and enable the realization of feedback controls.

观测器能重构系统的状态，从而使反馈控制得以实现。

4.Using the controller and the parameter adaptive laws proposed, the output of the general system asymptotically synchronizes with any scalar chaotic signal.

通用系统的输出在控制器与自适应律的控制下，渐近同步于任意标量混沌信号。

5.An elastic_viscoplastic model is adopted to investigate asymptotically the stress and strain fields at a propagating crack_tip.

采用弹粘塑性力学模型，对扩展裂纹尖端的应力和应变场进行了渐近分析。

6.Multiple Lyapunov functions method is introduced to design the switching law between controllers, the system is asymptotically stable under the switching law.

采用多李亚普诺夫函数方法设计控制器的切换律，系统在此切换律下可以达到渐近稳定。

7.Under some additional assumptions, the whole system is semi-global asymptotically stable (Semi-GAS).

在适当的假设下，得到了系统的半全局渐近稳定。

8.By the corollary to Theorem 4.3, the origin is asymptotically stable.

根据定理4.3的推论，原点是渐近稳定的。

9.The function approaches its limit asymptotically 渐近地 as x tends to infinity.

当x趋向于无穷大时，该函数渐近地接近其极限。

10.In computer science, algorithms can be compared based on their asymptotic 渐近的 behavior.

在计算机科学中，算法可以根据它们的渐近的行为进行比较。

11.The population growth is expected to stabilize asymptotically 渐近地 at a certain carrying capacity.

预计人口增长将在某个承载能力上渐近地稳定。

12.The cost function behaves asymptotically 渐近地 like a linear function for large inputs.

对于大输入，成本函数的行为渐近地像一个线性函数。

13.The series converges asymptotically 渐近地 to a finite value.

该级数渐近地收敛到一个有限值。

作文

In mathematics and computer science, the term asymptotically (渐近地) is often used to describe the behavior of functions as they approach a certain limit. This concept is crucial for analyzing algorithms and understanding their efficiency, especially when dealing with large inputs. When we say that an algorithm runs in asymptotically (渐近地) linear time, we mean that as the size of the input grows, the time it takes to complete the algorithm increases linearly. This provides valuable insights into how the algorithm will perform under different conditions. For example, consider a simple sorting algorithm like bubble sort. The performance of bubble sort can be evaluated by examining its asymptotic (渐近的) behavior. In the worst-case scenario, bubble sort has a time complexity of O(n^2), which indicates that the time taken grows quadratically as the number of elements increases. In contrast, a more efficient algorithm like quicksort has an asymptotic (渐近的) time complexity of O(n log n). This means that for large datasets, quicksort will outperform bubble sort significantly. Understanding asymptotic (渐近的) analysis is not only important for theoretical studies but also for practical applications. For instance, software developers must choose algorithms that are efficient enough to handle large datasets without excessive computation time. By analyzing the asymptotic (渐近的) performance of different algorithms, developers can make informed decisions that impact the overall performance of their applications. Moreover, the concept of asymptotic (渐近的) behavior extends beyond just time complexity; it also applies to space complexity. For instance, an algorithm might use a constant amount of additional space, which can be described as having asymptotically (渐近地) constant space complexity, denoted as O(1). This means that regardless of the input size, the space required by the algorithm does not change significantly. Such characteristics are particularly valuable in memory-constrained environments. In addition to algorithms, asymptotic (渐近的) analysis is also utilized in various fields such as physics and economics. In physics, scientists often study the asymptotic (渐近的) behavior of physical systems as they approach equilibrium. Similarly, in economics, analysts may look at the asymptotic (渐近的) trends in market behavior to predict future movements. The ability to understand and apply the concept of asymptotically (渐近地) allows researchers and professionals to model complex systems and derive meaningful conclusions from their analyses. In conclusion, the term asymptotically (渐近地) plays a vital role in various disciplines, particularly in mathematics and computer science. It helps us understand how functions behave as they approach limits, enabling us to analyze and compare the efficiency of algorithms. By mastering the concept of asymptotic (渐近的) analysis, we can make better decisions in algorithm selection and gain deeper insights into the behavior of complex systems across different fields. Whether in programming or scientific research, the implications of asymptotically (渐近地) understanding are profound and far-reaching.

在数学和计算机科学中，术语asymptotically（渐近地）通常用于描述函数在接近某个极限时的行为。这个概念对于分析算法和理解它们的效率至关重要，尤其是在处理大型输入时。当我们说一个算法的运行时间是asymptotically（渐近地）线性时，我们的意思是随着输入大小的增长，完成算法所需的时间也线性增加。这为我们提供了关于算法在不同条件下表现的宝贵见解。 例如，考虑一个简单的排序算法，如冒泡排序。可以通过检查冒泡排序的asymptotic（渐近的）行为来评估其性能。在最坏的情况下，冒泡排序的时间复杂度为O(n^2)，这表明随着元素数量的增加，所需的时间呈二次增长。相比之下，更高效的算法如快速排序的asymptotic（渐近的）时间复杂度为O(n log n)。这意味着对于大型数据集，快速排序将显著优于冒泡排序。 理解asymptotic（渐近的）分析不仅对理论研究重要，而且对实际应用也至关重要。例如，软件开发人员必须选择足够高效的算法，以处理大型数据集而不会过度消耗计算时间。通过分析不同算法的asymptotic（渐近的）性能，开发人员可以做出影响其应用程序整体性能的明智决策。 此外，asymptotic（渐近的）行为的概念不仅适用于时间复杂度；它还适用于空间复杂度。例如，一个算法可能使用恒定量的额外空间，这可以描述为具有asymptotically（渐近地）常量空间复杂度，表示为O(1)。这意味着无论输入大小如何，算法所需的空间不会发生显著变化。这种特性在内存受限的环境中特别有价值。 除了算法，asymptotic（渐近的）分析还被广泛应用于物理学和经济学等多个领域。在物理学中，科学家通常研究物理系统在接近平衡时的asymptotic（渐近的）行为。类似地，在经济学中，分析师可能会观察市场行为的asymptotic（渐近的）趋势，以预测未来的走势。理解和应用asymptotically（渐近地）的概念使研究人员和专业人士能够建模复杂系统，并从分析中得出有意义的结论。 总之，术语asymptotically（渐近地）在各个学科中扮演着重要角色，特别是在数学和计算机科学中。它帮助我们理解函数在接近极限时的行为，使我们能够分析和比较算法的效率。通过掌握asymptotic（渐近的）分析的概念，我们可以在算法选择上做出更好的决策，并深入了解不同领域复杂系统的行为。无论是在编程还是科学研究中，理解asymptotically（渐近地）的含义都是深远且广泛的。