2019
Том 71
№ 10

# Tyrygin I. Ya.

Articles: 4
Brief Communications (Russian)

### Estimates for information quantity in probability model in image encoding

Ukr. Mat. Zh. - 1995. - 47, № 4. - pp. 573-576

Upper bounds are obtained for the amount of information in functional classes with initial uncertainty. These classes are similar to the classes of images with bounded variance. We use the probability model of the theory of information complexity. Unlike the case of classes $KH_{0}^{ α}$ , it turns out that, in this case, the method of differential pulse-code modulation does not give any advantage as compared to the deterministic case.

Article (Ukrainian)

### Refined estimates for the ε-entropy of the classes $KH_0^α$

Ukr. Mat. Zh. - 1994. - 46, № 6. - pp. 760–764

By the methods of differential pulse-code modulation and “generalized” polygonal lines, we obtain almost exact estimates for the ɛ-entropy of classes simulating signals of various types. The complexity of coding and reconstruction of functions from the classes under consideration is investigated. We present a numerical solution of the problem of minimization of constants in the order-of-magnitude inequality for the ɛ-entropy of the classes $KH_0^α$.

Article (Russian)

### A Kolmogorov type criterion for the best approximating operator

Ukr. Mat. Zh. - 1993. - 45, № 1. - pp. 114–119

For the best approximating operator, a criterion is established, equivalent to the well known Kolmogorov theorem, which characterizes the best approximation element. The practical use of this criterion is illustrated by examples.

Article (Ukrainian)

### Turan-type inequalities in certain integral metrics

Ukr. Mat. Zh. - 1988. - 40, № 2. - pp. 256-260