Playing Catch-up with Iterated Exponentials
نویسندگان
چکیده
Suppose that we have two animals that make the same number of strides per minute, but one of them makes larger strides than the other. If the strides of the smaller animal (the prey) have length a, and those of the larger animal (the predator) have length b, it is easy to see that a persistent predator will always be able to catch up with its prey. Let us assume that the prey starts one step ahead of the predator. After n steps the distance between the two is
منابع مشابه
Extensions by Antiderivatives, Exponentials of Integrals and by Iterated Logarithms
Let F be a characteristic zero differential field with an algebraically closed field of constants C, E ⊃ F be a no new constant extension by antiderivatives of F and let y1, · · · yn be antiderivatives of E. The antiderivatives y1, · · · , yn of E are called J-I-E antiderivatives if y′i ∈ E satisfies certain conditions. We will discuss a new proof for the KolchinOstrowski theorem and generalize...
متن کاملIterated Local Reeection Vs Iterated Consistency
For \natural enough" systems of ordinal notation we show that times iterated local reeection schema over a suuciently strong arithmetic T proves the same 0 1-sentences as ! times iterated consistency. A corollary is that the two hierarchies catch up modulo relative interpretability exactly at-numbers. We also derive the following more general \mixed" formulas estimating the consistency strength...
متن کاملLaguerre-type exponentials and generalized Appell polynomials
General classes of two variables Appell polynomials are introduced by exploiting properties of an iterated isomorphism, related to the so called Laguerre-type exponentials. Further extensions to the multi-index and multivariable cases are mentioned. 2000 Mathematics Subject Classification. 33C45, 33C99, 30D05, 33B10.
متن کاملThe method of iterated commutators for ordinary di erential equations on Lie groups
We construct numerical methods to integrate ordinary di erential equations that evolve on Lie groups. These schemes are based on exponentials and iterated commutators, they are explicit and their order analysis is relatively simple. Thus we can construct group-invariant integrators of arbitrarily high order. Among other applications we show that this approach can be used to obtain new symplecti...
متن کاملWheeled Robots playing Chain Catch: Strategies and Evaluation (Extended Abstract)
Robots playing games that humans are adept in is a challenge. We studied robotic agents playing Chain Catch game as a Multi-Agent System (MAS). Our game starts with a traditional Catch game similar to Pursuit evasion, and further extends it to form a growing chain of predator agents to chase remaining preys. Hence Chain Catch is a combination of two challenges pursuit domain and robotic chain f...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- The American Mathematical Monthly
دوره 111 شماره
صفحات -
تاریخ انتشار 2004