Nº 4 (2024)

A linearly implicit conservative difference scheme is applied to discretize the attractive coupled nonlinear Schroedinger equations with fractional Laplacian. In this case complex symmetric linear systems appear, with indefinite and Toeplitz-plus-diagonal system matrices. Standard fast methods of direct solution or iteration using a preconditioner are not applicable for such systems. A novel iterative method is proposed, based on the normal splitting of the equivalent real block form of linear systems. Unconditional convergence is proved and the quasi-optimal iteration parameter is deducted. The preconditioner for this method is obtained naturally; it is constructed and efficiently implemented using the fast Fourier transform. Theoretical analysis shows that the eigenvalues of the preconditioned system matrix are closely clustered. Numerical experiments demonstrate new preconditioner significantly speeds up the convergence rate of iterative Krylov subspace methods. In particular, the convergence behavior of the corresponding preconditioned generalized minimum residual method is independent of the mesh size and almost insensitive to the fractional order. Moreover, the linearly implicit conservative difference scheme in this case preserves mass and energy with a given accuracy.

Тематическая сегментация – это задача разделения неструктурированного текста на тематически связные сегменты (такие, в которых речь идет об одном и том же). Граф знаний – графовая структура, вершинами которой являются различные объекты, а ребрами – отношения между ними. Как задача тематической сегментации, так и задача автоматического построения графа знаний не будут новыми, поэтому существует множество алгоритмов для их решения. Однако методы решения задачи тематической сегментации с помощью графов знаний до сих пор исследованы мало. Более того, пока еще нельзя сказать, что задача тематической сегментации решена в общем виде, т.е.существуют алгоритмы, способные при должной настройке решить задачу с требуемым качеством на конкретном наборе данных. Предлагается новый метод решения задачи тематической сегментации на основе графов знаний. Применение графов знаний при сегментации позволяет использовать больше информации о словах в тексте: помимо того чтобы основываться на co-occurrance и семантических расстояниях (как классические алгоритмы), методы на базе графов знаний могут применять расстояние между словами на графе, инкорпорируя тем самым фактологическую информацию из графа знаний в процесс принятия решений о биении текста на сегменты.

The problem of bi-decomposition of a Boolean function is to represent a given Boolean function as a logic algebra operation over two Boolean functions. A meth-od based on bi-decomposition of Boolean functions is suggested to implement sys-tems of incompletely specified (partial) Boolean functions in the basis of two-input gates. This basis can be the basis of NOR gates, NAND gates or the basis of AND and OR gates with accessible input complements. The used method for bi-decomposition is reduced to the search for two-block weighted cover of a complete bipartite weighted graph with complete bipartite subgraphs (bi-cliques). The graph represents differences between the rows of Boolean matrices that specify the given system of partial Boolean functions. The system is given by two Boolean matrices, one of which represents the domain of Boolean space where the values of the given functions are specified, and the other the values of the functions on the elements of the domain. Every bi-clique in the obtained cover is assigned in a certain way with а set of variables that are the arguments of the function. This set is the weight of the bi-clique. Every of those bi-cliques defines a Boolean function whose arguments are the variables assigned to it. The functions obtained in such a way constitute the re-quired decomposition. The process of synthesis of a combinational circuit consists in successive application of bi-decomposition to the obtained functions. The meth-od for two-block covering the orthogonality graph of rows of ternary matrices is de-scribed.

Modern machine translation systems are trained on large volumes of parallel data obtained using heuristic methods of the Internet bypassing. The poor quality of the data leads to systematic translation errors, which can be quite noticeable from the human point of view. To fix such errors a human based models hypotheses re-ranking is introduced in this work. In this paper the use of human markup is shown not only to increase the overall quality of translation, but also to significantly reduce the number of systematic translation errors. In addition, the relative simplicity of human markup and its integration in the model training process opens up new opportunities in the field of domain adaptation of translation models for new domains like online retail.

A method for motion detecting in a frame and large-sized object identification is described in the article. The use-case of the method is illustrated by the example from the maritime transport industry. The example shows the solution of the task of monitoring the position of an autonomous marine large-tonnage ship relative to the berth when performing loading and unloading operations and mooring operations. The paper incudes description of the structure of a measuring complex which includes optical meters. An operating principle of the complex is based on the method of motion detecting in a frame and large-sized object identification. A diagram of the algorithm for motion detecting in the frame and large-sized object identification is presented in the paper. The performance of the software implementation of the algorithm for motion detecting in the frame and large-sized object identification has been assessed in the article.

The branch and bound method used to select the optimal production program is considered, based on the calculation of the upper, lower and current upper estimates when analyzing various options for production programs. An upper bound for the number of feasible solutions to the problem under consideration is given. Models for choosing an optimal production program in conditions of production expansion are considered, as well as issues of analyzing the stability of these programs when changing the initial data of the model and when changing the criterion for the optimality of the model. The use of models for selecting the optimal production program within the framework of project management at enterprises will ensure increased efficiency of activities, including at the stages of planning and implementation of projects, classification and selection of a method for implementing projects.

In global navigation satellite systems, positioning quality indicators depend on both environmental conditions and user behaviour. The environment affects the reception quality of the radio signals that are available for positioning. An adaptive navigation solution is required to operate in different environmental conditions, which will detect the type of environment and apply different methods for navigation solution. The features formed from the received navigation signal data that can be used to determine the type of environment are discussed. This paper is devoted to finding an optimal feature vector for determining the type of environment from information from global navigation satellite systems. Experimental navigation data for different types of environment are collected. Criteria and methods for determining the optimal feature vector using algorithms from mathematical statistics are considered. The optimal feature vector that contributes the most to the determination of different types of environment is proposed.