Applied Mathematics and Control Sciences

The question of the longitudinal bending of a rod consisting of rigid links connected by hinges is being studied. It is shown that, as in the classical version of a solid rod, the problem can be posed as a variational minimum energy problem, but given by a functional defined on a class of functions with a discrete domain of definition. The main provisions of the classical calculus of variations are transferred to functionals of this type: the formula of variation is found, a generalization of the main lemma of the calculus of variations is proved, an analogue of the Euler equation, which is a difference equation, is obtained. Applying the results obtained and the known properties of classical difference equations, we succeeded in solving an analogue of the Euler problem for two types of a hinge rod: for a rod consisting of links of the same length, and for an arbitrary choice of lengths of links. In both cases we find the critical Euler force, as well as the equation and the form of the deflection curve.

Nowadays, the process of integrating autonomous robotic systems (ARS) and military personnel formation is actively underway. Such a new object in the armed forces (AF) should have the property of self-sufficient behavior that guarantees mission fulfillment. The problem is in the construction of information processes in control systems that ensure a predictable behavior of an autonomous artificial system within the Armed Force subdivisions similar to a human one. Currently, the solution for this problem is the development of artificial entities that use symbolic or neural network methods and models for acquiring and formalizing “knowledge”. Ontologies made it possible to make these methods and knowledge models interpretable in natural language semantics and to bring the problem of human-machine interaction to a new level, which was noted by a number of researchers. Nevertheless, it should be noted that as long as there is no cognition process model, the theoretical results obtained are not in demand in practice and are only of theoretical interest. There is a gap between primitive behavior models of artificial entities, their interaction models and expectations from practice. The purpose of this work is to propose an approach to the intellectualization of the artificial entities’ behavior by revising the logical and mathematical abstractions underlying the construction of their onboard control systems based on the pattern theory development. Such approach ensures the transfer of effective human experience to the control systems of artificial entities, as well as the compatibility of the theological and causal approach. It is shown that the choice under severe time constraints is based on behavioral patterns that reflect effective experience. Patterns form both the information structure of representations and a set of possible variants of representations. Subject’s assessments of satisfaction with the current choice situation lead to a change in a subject's interest structure, and he can choose it. There is a developed formal model of the behavioral pattern and a method of logical inference on patterns. The paper considers the problems of identification and construction of pattern models. It proposes to use four positions of information processing for these purposes. The paper proposes an approach to developing software for intelligent control systems for autonomous systems based on the pattern theory. There are the results of behavioral pattern identification solutions that use new generation training systems with voice control. The paper considers the issues of constructing the architecture of unmanned undersea vehicles with an onboard control system that uses pattern models and a pattern inference system. It also solves the problem of the behavior tactics of the node - autonomous unmanned vehicle based on the onboard sensor system data.

The transition mainly to a distance learning format for teaching staff over 65 years of age in the higher education system, due to the complex epidemiological situation in the world associated with the emergence and spread of new strains of coronavirus infection, has updated the problem of completing the library fund of the university library with popular printed publications in a new way. The authors of the article considered it expedient to include the format of study at the university or the correlating factor of the teacher's age in the mathematical model of acquisition of the library fund with demanded printed publications among the educational and organizational factors affecting the demand for educational literature, and to assess its impact on the target function of the demand for printed publications. The conducted research has shown that the introduced factor is significant and significantly affects the demand for educational literature and, as a result, should be included in the developed mathematical model formulated in the form of an optimization problem. Taking into account the results obtained in the course of the scientific research, it is proposed to strengthen the teaching and methodological activities of the teaching staff in order to improve the quality of the acquisition of the library fund of the university library with popular educational literature in the conditions of the Covid-19 pandemic. The article focuses on the possibility of finding only rational solutions in the initial and refined optimization problem of choosing printed publications from a variety of alternatives offered by book publishers, since it describes the functioning of the university library as an organizational and technical system with such qualities as, for example, multidimensionality, self-organization and complexity.

The study identifies the growing problem of mismatch between the competencies of IT graduates of educational institutions and the requirements of employers. The goal is to develop a set of models and algorithms, as well as software that implements them to improve the efficiency of IT training. The analysis of existing approaches to its solution is made. Prospective directions of specialist modeling are revealed. The methods of labor market analysis in the field of IT-sphere based on vacancies from aggregator sites, approaches to individualization of educational programs and involvement of employers in the training process, as well as means of automation of specialist modeling were considered. Ontological approaches to specialist modeling based on expert knowledge are also studied. The concept of organizing IT training based on open weakly structured data has been developed. An approach based on natural language processing and denotative analytics is described. The proposed concept includes monitoring and collecting data on vacancies from aggregator sites with a given frequency; their subsequent processing to build a dynamic model of an IT specialist, describing the key concepts necessary for professional activity and satisfying employers' requirements; enriching the resulting model with open data on the subject area and information contained in regulatory documents; building a graduate specialist model, taking into account the links between the key concepts by constructing a denotative graph to reconstruct the hierarchy of the enriched set of concepts; forming on its basis a set of recommendations for drawing up and adjusting educational programs. The model of specialist from employer's point of view based on fuzzy sets, model of specialist-graduate including data enrichment algorithm, as well as the algorithm of recommendations formation for making and correction of educational programs were developed. The software for decision support system that implements the mentioned models and algorithms has been developed. Experimental testing with the involvement of experts from the IT industry was conducted. Positive results were obtained as a result of the experiment. The developed system can be used for drawing up and adjusting work programs of disciplines, professional retraining programs, programs of additional education in the field of directions related to information technology.