ترجمه مقاله نقش ضروری ارتباطات 6G با چشم انداز صنعت 4.0
- مبلغ: ۸۶,۰۰۰ تومان
ترجمه مقاله پایداری توسعه شهری، تعدیل ساختار صنعتی و کارایی کاربری زمین
- مبلغ: ۹۱,۰۰۰ تومان
Abstract.
Rooted plane trees are reduced by four different operations on the fringe. The number of surviving nodes after reducing the tree repeatedly for a fixed number of times is asymptotically analyzed. The four different operations include cutting all or only the leftmost leaves or maximal paths. This generalizes the concept of pruning a tree. The results include exact expressions and asymptotic expansions for the expected value and the variance as well as central limit theorems.
6. Future work
It seems likely that similar results also hold for reductions where one can cut a different structure as long as it is allowed to cut a single leaf. An example is cutting either single leaves or cherries (a root with two children). At least a formulation as an operator as in (9) seems possible in general. How much information about the moments and the central limit theorem can be extracted from that may vary (as it varies in this article already). Also the case of cutting old structures might be more difficult to handle in general.