An explicit finite BkB_k-sequence

For any $n$ and $k$, we provide an explicit (that is, computable in polynomial time) example of integer $B_k$-sequence of size $n$ consisting of elements bounded by $n^{k+o(k)}$.Comment: 4 page

Fast encryption of various types of messages

The problem of misleading illegal message interceptors while transferring messages is being solved in the article. Different variants of intensified defense of the most important fragments of messages with usage of both Boolean and matrix transformations in the GF (2) Galois field of transferred text are considered

On application of dynamical system methods in biomedical engineering

The spectrum of various methods and tools used for solving bioengineering problems is sufficiently wide. Dynamical systems (including the symbolic ones) in many cases become a base for design and implementation of methods of investigation and computer modeling complex processes. Whereas for solving direct problems we have many well-developed methods, results for inverse problems are much more modest. We discuss two methods for such tasks: Takens’ method for reconstruction attractor by a time series, and the based on ideas of symbolic dynamics method for digital image analysis using stationary flow on graph and weighted entropy. The results of numerical experiments are given