The boundedness, the oscillatory behavior and the global stability of the nonnegative solutions of the difference equation ${x_{n + 1}} = \frac{{\alpha + \beta {x_{n ...

We study the large exceedance probabilities and large exceedance paths of the recursive sequence Vn = Mn Vn−1 + Qn, where {(Mn, Qn)} is an i.i.d. sequence, and M1 is a d × d random matrix and Q1 is a ...

Recursion -- the computational capacity to embed elements within elements of the same kind -- has been lauded as the intellectual cornerstone of language, tool use and mathematics. A ...

The DNA sequences containing multifarious novel symmetrical structure frequently play crucial role in how genomes work. Here we present a new scheme for understanding the structural features and ...