In this paper, the dynamic behavior of the damping system is analyzed with a two-mass pendulum absorber, the equations of motion of non-linear mechanical systems are built accordingly. AFC equation systems have been identified in the non-linear formulation. To obtain the frequency response, the Ritz averaging method is used. A new numerical method of determining the parameters of optimal tuning two-mass pendulum absorber in the non-linear formulation has been Proposed and implemented.

As elliptic curve cryptography is one of the popular ways of constructing an encoding and decoding processes, public-key algorithms as its basis provide people a comfortable way of exchanging pieces of encoded information. As the time goes by, a lot of algorithms have emerged, some of them are still in use today; some others are still being developed into new forms. The main point of algorithm innovation is to reduce the number of processed operations during every possible step to find maximum efficiency and highest speed while performing the calculations. This article describes an improved method of the López-Dahab-Montgomery (LD-Montgomery) scalar point multiplication in terms of working with binary elliptic curves. It is shown in the article that the possible improvement lies in reordering the set of operations which is used in LD-Montgomery scalar point multiplication algorithm. The algorithm is used to compute point multiplication results of the curves over binary Galois Fields featuring the following m values: . The article also presents the experimental results based on different scalars.

Dynamic behavior of a heavy homogeneous sphere in a spherical cavity of a supporting body that performs specified translational movements in space has been studied. Using the Appel formalism, the equations of ball motion in a moving spherical cavity without slip are constructed and a numerical analysis of the evolution of the ball motion is carried out.

The paper presents the method of medical images similarity estimation based on feature extraction and analysis. The proposed method has been developed for and tested on rat brain histological images, however, it can be applied for other types of medical images, since the general approach is based on consideration of the shape of core components present in a given template image. The proposed method can be used in image analysis tools in a wide range of image-based medical investigations, in particular, in the brain researches.
The theoretical background of the proposed method is presented in the paper. The expert evaluation approach used for assessment of the proposed method effectiveness is explained and illustrated by examples. The method of medical images similarity estimation based on feature analysis consists of several stages: colour model conversion, image normalization, anti-noise filtering, contours search, conversion, and feature analysis. The results of the proposed method algorithmic realization are demonstrated and discussed.

The forced oscillations of the damping mechanical system of solids "Ball Vibration Absorber (BVA) with linearly viscous resistance – a movable carrier body" under the influence of external harmonic excitation are considered. Based on Appell's formalism, the dynamic equations for the joint motion of a heavy ball without sliding into a spherical cavity of a carrier body are formulated and numerically studied. The amplitude-frequency characteristic of the damping mechanical system and the curves of the dependences of the maximum amplitude of the oscillations of the carrier body on the values of the radius of the spherical cavity and the coefficient of viscous resistance of the BVA are obtained. The conditions and restrictions on the rolling of a heavy ball in the spherical recess of the absorber without sliding are determined.

The proposed method of graphical data protection is a combined crypto-steganographic method. It is based on a bit values transformation according to both a certain Boolean function and a specific scheme of correspondence between MSB and LSB. The scheme of correspondence is considered as a secret key. The proposed method should be used for protection of large amounts of secret graphical data.