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There are numerous domestic and foreign studies of periodontal disease in pregnant women, but there are still a number of unresolved issues. The data about the development of periodontal tissue diseases in pregnant women in terms of age is not enough. The purpose of this work was to study the development of periodontal disease in pregnant women in different age groups. Material and methods. A survey of 83 women in the ІІ and ІІІ trimesters of pregnancy, aged 19-45 years, was divided into three groups according to age. Group I (34 people) included pregnant women aged 19-25 years, group II (29 people) had pregnant women aged 26-35 years, group III (20 people) comprised pregnant women aged 36-45 years. Periodontal and hygienic indices were determined to assess the clinical signs of periodontal disease (to assess the clinical signs of periodontal disease, periodontal and hygienic indices were determined (papillary-marginal-alveolar index, degree of bleeding gums, Schiller-Pisarev test, numerical value of Schiller-Pisarev test – Svrakov's number and simplified index of cavity hygiene). Results and discussion. The obtained results indicated a high level of periodontal disease in pregnant women. Periodontal disease was found in 74.7% of subjects. The study found a significant progression of periodontal tissue pathology in pregnant women over 26 years of age, indicating that women in this age group were at significant risk of periodontal disease. The obtained data indicated that the value of the bleeding index was the lowest in pregnant women with periodontal disease of group I, and the highest in women of group III. The value of the PMA index differed 1.3 times (p˂0.05) in pregnant women of groups I and II, 1.2 times (p˂0.05) in women of groups II and III, and 1.5 times (p˂0.05) in pregnant women of groups I and III. In addition, the likelihood of developing periodontal disease increased with age of women. Conclusion. The values of the Svrakov's number had a similar tendency to increase in age groups, as well as the results of the previously described indices. Hygiene in pregnant women of all ages who had periodontal disease was not very good. Thus, special attention should be paid to the timely diagnosis, treatment and prevention of periodontal disease in pregnant women, taking into account their age

Peculiarities of the large numbers law in conditions of disturbances of statistical stability are studied. It is shown that for random sequences the sample mean may converge to a finite number, converge to positive or negative infinity or fluctuate in a fixed interval. A series of theorems are proven, which describe the large numbers law for hyper-random sequence. It is demonstrated that the sample mean in case of a hyper-random quantity may converge to a finite number, converge to a set of finite numbers, fluctuate in non-intersecting intervals of conditional boundaries, fluctuate in unconditional boundaries interval or converge to positive or negative infinity. Differences in convergence types of random and hyper-random sequences should be accounted for when studying radio-engineering devices and systems.

The known ways of representing hyper-random quantities and processes are analyzed with respect to the appropriateness of their application to describe various types of transformations. A series of relations between characteristics and parameters of transformed and initial hyper-random quantities and processes is obtained. Recommendations on the use of various ways of representing scalar and vector hyper-random quantities in the cases of linear and non-linear transformations as well as processes subject to non-inertial and inertial transformations are given.

A mathematical model for measuring values has been proposed taking into account the uncertainty of statistical conditions of forming the measured value and its estimate. This model is based on presenting measured value and its estimate as hyper-random values. The point and interval methods of estimating hyper-random values have been developed. The notions of biased, consistent and efficient estimates were extended to the case of hyper-random estimates. The potential accuracy of measurements was investigated. It was shown that under the conditions of statistically uncertain conditions the potential accuracy of value measurement was limited and determined by the parameters of estimate bias.

For underwater acoustic systems that work in complicated conditions a new space–time signal processing (STSP) optimisation approach has been developed. It considers, in complex, antenna's motion, structure of the noise, and particularities of the medium. For coherent and stochastic signals STSP algorithms, matched with complicated antenna's motion, multicomponent noises and non-uniform medium together were produced and researched. It was found that in some cases complicated antenna's motion led to rising of noise immunity of the STSP systems. This effect may be used, in particular, in the systems with line arrays for alienating ambiguity in the estimation of signal direction.

Analytical expressions that link statistical instability parameters with process’s spectrum are obtained. It is shown that statistical stability is determined solely by the character of spectral power density dependence on frequency. It is revealed that statistically stable noises are those with rising intensity when frequency is increased, white noise, and equilibrium flicker noise described by the dependence 1/f β where the spectrum shape parameter is 0 < β < 1 as well as fractal Gaussian noise. Statistically instable noises are nonequilibrium flicker noises with spectral power density 1/f β when β >= 1. It is determined that not only random nonstationary and deterministic processes are statistically instable as it was considered earlier, but stationary processes as well.

New parameters describing destructions of statistical stability in finite observation interval have been proposed. For known and new statistical instability parameters, metric units that open possibility to characterize destructions of statistical stability in terms of quantity have been introduced. It is shown that essential rule in disturbances of statistical stability plays fluctuations of expectation of the process that lead to change expectation of average, and also fluctuations of variance of the process under definite parameter’s relationship. Change ranges of sampling value of parameters of statistical instability weakly depend from distribution type.