This paper proposes an approach to the geospatial assessment of a territorial road network based on the fractals theory. This approach allows us to obtain quantitative values of spatial complexity for any transport network and, in contrast to the classical indicators of the transport provisions of a territory (Botcher, Henkel, Engel, Goltz, Uspensky, etc.), consider only the complexity level of the network itself, regardless of the area of the territory. The degree of complexity is measured by a fractal dimension. A method for calculating the fractal dimension based on a combination of box counting and GIS analysis is proposed. We created a geoprocessing script tool for the GIS software system ESRI ArcGIS 10.7, and a study of the spatial pattern of the transport network of the Ukraine territory, and other countries of the world, was made. The results of the study will help to better understand the different aspects of the development of transport networks, their changes over time and the impact on the socioeconomic indicators of urban development.

Development of the method for dynamic regularization of selected estimates in the correlation matrices of observations

The S-box is a key component of modern ciphers, determining the quality and performance of the cryptographic algorithms in which it is applied. Many constructions for synthesizing high-quality S-boxes have been established, and those based on Galois fields theory—for example, the Nyberg construction applied in the AES cryptographic algorithm—are particularly important. An integral component of the Nyberg construction is the affine transformation, which is used to improve the avalanche and correlation properties of the S-box. In this paper, a new approach is adopted for synthesizing affine transformations for S-boxes based on the quaternary matrices over the Galois field GF(4). We describe four basic structures that serve as the foundation for synthesizing a complete class of 648 affine transformation matrices of order n = 3 and a class of 7776 matrices of order n = 4 and introduce a recurrent structure to facilitate the synthesis of matrices for higher orders. Using these matrices in combination with the Nyberg construction, it is possible to construct bijective S-boxes that outperform the original Nyberg construction and many other known S-boxes in terms of strict avalanche criterion (SAC) and bit independence criterion strict avalanche criterion (BIC SAC) values, while maintaining a maximal level of nonlinearity and good cryptographic properties. We also propose modified GF(4) affine transformations that can be applied to specialized S-boxes which already satisfy the SAC for both component Boolean and 4-functions, as well as the criterion of minimal correlation between input and output, allowing us to enhance their nonlinearity to the value of N_f = 96. We integrate the synthesized S-boxes into the AES algorithm and evaluate their practical performance. The encryption outputs successfully pass the NIST statistical test suite in 96 out of 100 cases, outperforming both the original AES S-box and other reference constructions, confirming the practical strength of the proposed method.

This paper addresses the problem of improving the robustness of image steganographic methods under lossy compression while preserving high perceptual quality and low computational complexity. The paper proposes an adaptive code-controlled steganographic method that enables spectrally selective embedding in the spatial domain through structured codewords. The proposed approach introduces block-level adaptivity in which the energy of the embedding codeword is dynamically selected according to the robustness characteristics of each image block. Instead of applying uniform embedding strength, the method determines the minimal codeword energy required to guarantee reliable message extraction under a predefined worst-case JPEG compression level. Experimental evaluation demonstrates that the proposed adaptive strategy significantly improves robustness to compression attacks while preserving high perceptual reliability and strong resistance to statistical steganalysis techniques. In particular, for JPEG quality factor (QF) = 50, the bit error rate is reduced to 1.25% while a high perceptual quality of 52.07 dB peak signal-to-noise ratio (PSNR) is achieved. For stronger attack conditions, QF = 20, the method achieves 6.6% bit errors with a PSNR of 47.7 dB. Overall, the proposed adaptive energy selection provides up to 22.68% fewer errors or up to 6.05 dB higher PSNR compared to the classical code-controlled steganographic method, confirming its effectiveness for practical steganographic applications.

The article considers a new method of joint analog-to-digital broadcasting in the range of very high frequencies. The method includes a broadcast on the transmitting side of monaural total signal of left and right channels in the frequency band 0,03-15 kHz, and of pilot tone of stereophonic transmission with a frequency 19 kHz, of Radio Data System signal at the frequency of 57 kHz. To transmit the difference signal generated from the frequencies limited to 7 kHz of the left and right channels, we used the balance-modulated signal with the lower and upper sidebands in the frequency range 31-45 kHz. To transmit the digital signal of additional program we used the bands of frequencies 23-30 kHz, and on the transmitting side in the frequency band 46-53 kHz we transmitted the inverted to 180 ° digital signal of the additional programs transmitted in the frequency band 23-30 kHz. Such a construction of the signal spectrum provides the capability to conduct the stereophonic digital broadcasting in the channel of transmission of the main analog transmission maintaining all the basic services and reducing the interference of components of the spectrum.