MODELS OF THEORY AND METHODOLOGY OF INTEGRATING BALANCING RESOURCE MANAGEMENT OF THE INTELLECTUAL LABOR AND CAPITAL IN THE CONDITIONS OF SINGULARITY OF TECHNOLOGIES: MATHEMATICAL AND METHODOLOGICAL FOUNDATIONS OF RESEARCH

Abstract

The relevance of the mathematical substantiation of the models of the theory and methodology, the development of methods for the implementation of integration-balancing management of labor and capital resources in the context of the singularity of technologies is determined by the practical needs of a post-industrial economy.The unresolved problems of the practical use of the analytical mapping of the jump-like processes of transition to the characteristics of such an economy are due to the insufficient development and organizational adaptation of the mathematical and methodological foundations of management.They do not take into account the specific conditions of the space-time complementary integration of resources and the inclusion of objects into the complex being formed.This defined the purpose of the study as the development of mathematical and methodological foundations for the implementation of models of the theory and methodology of integration-balancing resource management.The use of the author's theoretical-methodological approach has determined the direction of the development of the methodological apparatus of this stage of the study, including: methods of dynamic assessment and management quality control; author's interpretation of the organizational meaning of higher-order derivatives of approximations of a singular function for displaying jump processes; methods for evaluating management quality indicators (directivity and amplitude of the indicator-property when used, effects of integration-balancing mechanism parameters (accelerators regulating the speed of impacts, resource integrators and regulators of entropy synergy); methods for determining the critical points of stability loss.The following are scientific and practical value results: identification and study of new properties of spasmodic development; regulation of statics and dynamics of processes as a conditional effect expanding the space and time of managerial decision-making under the conditions of singularity of technologies, the ability to analyze short-term processes, identify new patterns of dynamics of discontinuous processes in the zone of maximum effect, recommendations on adjusting the timing and intensity of measures for changing priorities and impact targeting by the criterion of compromise on the goals of efficiency and innovation development complex; recommendations on the choice of methods for managing the resources of high-tech development type 4.0 industry in the organizational-cognitive model of improving professional competencies of intellectual capital.

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