The asymptotic variance is a measure of the variability of an estimator as the sample size approaches infinity. It represents the limit of the variance of the estimator as the sample size becomes very large. In statistical theory, it is used to assess the precision and reliability of an estimator in the long run. A smaller asymptotic variance indicates that the estimator is more efficient and provides more precise estimates as the sample size increases. **

The asymptotic terminal velocity is the maximum constant velocity that an object can reach when falling through a fluid, such as air or water, due to the balance between the gravitational force pulling the object downward and the drag force pushing against it. As the object falls, the drag force increases until it equals the gravitational force, at which point the object stops accelerating and reaches its terminal velocity. This velocity is asymptotic because the object will never actually reach it due to factors like air resistance and other external forces. **

We have an asymptotic equality here because as the input size grows larger, the difference between the two functions becomes negligible. In other words, the growth rate of the two functions becomes very similar as the input size approaches infinity. This allows us to simplify the comparison of the two functions and focus on their overall growth behavior rather than their specific values. As a result, we can use asymptotic analysis to make general statements about the performance of algorithms or the behavior of mathematical functions without getting bogged down in the details of specific input sizes. **

In this task, you are required to analyze the asymptotic growth of the given functions. This involves determining the rate at which the functions grow as their input values become very large. You need to compare the growth rates of the functions using big-O notation to understand their relative efficiencies. By identifying the dominant terms in the functions and simplifying them to their most significant parts, you can determine which function grows faster or slower in the long run. **

The caricature of the summit conference in Helsinki shows the leaders of the United States and Russia, Donald Trump and Vladimir Putin, sitting at a table with Trump holding a puppet string attached to Putin. This caricature is a satirical representation of the perception that Trump is under the control or influence of Putin, suggesting that Putin is pulling the strings and manipulating Trump. The image reflects the controversy and speculation surrounding the relationship between the two leaders and the potential influence of Russia on the United States. **

A symposium is a formal gathering or meeting where experts in a particular field come together to discuss and exchange ideas on a specific topic. It is often organized as a series of presentations, panel discussions, and Q&A sessions, allowing participants to share their knowledge and insights with each other. Symposia are commonly held in academic and professional settings, providing a platform for networking, collaboration, and learning within a specific discipline or industry. **

"Der Kongress tanzt" is a German phrase that translates to "The Congress Dances" in English. The phrase originated from the Congress of Vienna in 1814-1815, where European diplomats and leaders gathered to reorganize Europe after the Napoleonic Wars. The phrase is a metaphor for the diplomatic and political maneuvering that took place during the Congress, likening it to a dance where participants carefully navigated their relationships and alliances. It reflects the complex and intricate nature of international diplomacy and negotiations during this historic event. **

A convention is a formal agreement or a set of accepted norms and practices that govern behavior in a particular context or industry. It is a customary way of doing things that is widely recognized and followed by a group of people. Conventions help to establish consistency, order, and predictability in social interactions or professional settings. They can vary across different cultures, societies, or fields of study. **