Abstract Random numbers are very important in many fields of computer science. Generating high-quality random using only basic arithmetic operations is challenging, especially for devices with limited hardware capabilities, such as Internet Things (IoT) devices. In this paper, we present a novel pseudorandom number generator, the simple chain automaton generator (SCARNG), based on compositions ...

We obtain and investigate mean values of the exponential centroid operator for periodic Heisenberg XX0 chain on a ring. The generating function directed lattice paths is obtained in terms circulant matrices which leads to generalizations Ramus identity. two-time correlation expressed Cauchy determinant thus explicitly calculated.

The main topological characteristics of altan-benzenoids were established. In particular, it was shown that the perimeter of Kekuléan altan-benzenoids is of size 4k , having a destablizing (anti-aromatic) energy effect, similar to (4k)-annulenes.