The paper is devoted to the algorithm for the placement of orthogonal polyhedrons represented as a set of orthogonal objects with a fixed position relative to each other. The proposed algorithm is implemented invariantly with respect to the dimension of the objects to be placed, which makes it applicable for solving the cutting and packing problems of arbitrary dimension. Examples of the placement of two-dimensional and three-dimensional orthogonal polyhedrons are presented.

The rectangular cutting and orthogonal packing problems which have many practical applications in industry and engineering are considered. Increasing the density of placement schemes leads to reducing the material usage at solving the rectangular cutting problems and reducing the unused resources at solving the orthogonal packing problems. The article contains the description of the developed packing compaction algorithm and its investigation. This algorithm uses six object selection rules, which select objects from a container for deleting and subsequent reallocation of them into freed spaces of the container. The packing compaction algorithm iteratively applies a one-pass heuristic algorithm which finds the best placement of the deleted objects in order to increase the density of the result packing. The effectiveness of application of the proposed algorithm is investigated on the standard two-dimensional strip packing problems which are the rectangular cutting problems with only one container of a fixed width and an infinite length. Based on the test results the effectively sequence of application of the proposed rules used as the part of the packing algorithm was determined. The packing compaction algorithm is implemented in a general form which makes it possible for application in the rectangular cutting and orthogonal packing problems of arbitrary dimension.

The paper is devoted to the selection of leader nodes in evolving directed random networks for information spreading. We consider non-homogeneous networks consisting of several connected subgraphs with different distributions of nodes characteristics. This is a plausible situation for real complex networks. The evolution of the network in time starting from a seed set of nodes is provided by the preferential attachment tool. The seed set is used to send messages to the entire developing graph. Our objectives are to compare the spreading information by the graph evolution with a well-known algorithm.

The contribution examines the problem of the expediency of using modern digital technologies in gerontomarketing. The authors systematize studies reflecting the trend of increasing involvement of older people in the active use of modern technologies, which opens up prospects for the effective use of digital marketing tools in interaction with gerontoconsumers. The work shows that the widespread stereotypes about the conservatism of older people and their unwillingness to master new technologies are largely unfounded, which is confirmed by both official statistics and the results of independent studies. According to the authors, the study of the portrait and behavior of gerontoconsumers contributes to overcoming negative stereotypes about the elderly. According to the results of the study, the authors confirmed the hypothesis about the prospects of using digital technologies in gerontomarketing in the Russian consumer market.

The paper focuses on pedestrian navigation with foot-mounted strapdown inertial navigation systems (SINS). Zero velocity updates (ZUPT) during the stance phase are commonly applied in such systems to improve the accuracy. Zero velocity data are processed by the extended Kalman filter (EKF). Zero velocity condition is written in two forms: in reference and body frames. The first form traditional for pedestrian navigation is shown to provide an inconsistent EKF. The second form provides a correct ZUPT algorithm, which is naturally written in so-called dynamic errors. The analyzed algorithm for data fusion from two SINS is based on the bound on foot-to-foot distance. It is shown how EKF inconsistency can be manifested, and how it can be avoided by proceeding back to dynamic errors. The results are obtained analytically using observability theory and covariance analysis.