—This paper presents the advances of a research using a combination of recurrent and feed-forward neural networks for long term prediction of chaotic time series. It is known tha...
We consider the transition graphs of regular ground tree (or term) rewriting systems. The vertex set of such a graph is a (possibly infinite) set of trees. Thus, with a finite tree...
In [Kit1] Kitaev discussed simultaneous avoidance of two 3-patterns with no internal dashes, that is, where the patterns correspond to contiguous subwords in a permutation. In thre...
Let Fk(x) = n=0 Fk n xn . Using the interpretation of Fibonacci numbers in the terms of Morse codes, we give a bijective proof of Riordan's formula (1 - Lkx + (-1)k x2 )Fk(x...
Lucas chains are a special type of addition chains satisfying an extra condition: for the representation ak = aj + ai of each element ak in the chain, the difference aj - ai must a...