STRATEGIC PLANNING OF ORGANIZATIONS ' TRANSITION TO THE SIXTH TECHNOLOGICAL ORDER IN THE NATIONAL ECONOMY

The paper discusses the strategic planning of the transition to the sixth technological structure of the economy; the object of the article is the sixth technological order in the national economy; the aim is to increase the effectiveness of strategic planning of development of the sixth technological order in the national economy; to achieve this goal the following tasks: a concept of "technological system"; describes the methodological principles of a scientific theory of technological structures; developed data grid technological structures; synthesized tables of the properties of technological structures; the table is formed of animation technologies of new and previous orders; it formed a methodology for strategic planning of the sixth technological structure; scientifically speaking, strategic planning, algebra, logic, analysis and synthesis, systematic approach, search and normative forecasting, heuristic forecasting, expert methods, logical and comparative analysis; the scientific novelty of the work is determined by the formation of the methodology of strategic planning of the transition of organizations to the sixth technological order in the national economy; the results of the work will be useful for various economic entities (the state, corporations, technology platforms, clusters, innovative firms).

Nonstandard Analysis, Deformation Quantization and Some Logical Aspects of (Non)Commutative Algebraic Geometry

This paper surveys results related to well-known works of B. Plotkin and V. Remeslennikov on the edge of algebra, logic and geometry. We start from a brief review of the paper and motivations. The first sections deal with model theory. In the first part of the second section we describe the geometric equivalence, the elementary equivalence, and the isotypicity of algebras. We look at these notions from the positions of universal algebraic geometry and make emphasis on the cases of the first order rigidity. In this setting Plotkin’s problem on the structure of automorphisms of (auto)endomorphisms of free objects, and auto-equivalence of categories is pretty natural and important. The second part of the second section is dedicated to particular cases of Plotkin’s problem. The last part of the second section is devoted to Plotkin’s problem for automorphisms of the group of polynomial symplectomorphisms. This setting has applications to mathematical physics through the use of model theory (non-standard analysis) in the studying of homomorphisms between groups of symplectomorphisms and automorphisms of the Weyl algebra. The last sections deal with algorithmic problems for noncommutative and commutative algebraic geometry.The first part of it is devoted to the Gröbner basis in non-commutative situation. Despite the existence of an algorithm for checking equalities, the zero divisors and nilpotency problems are algorithmically unsolvable. The second part of the last section is connected with the problem of embedding of algebraic varieties; a sketch of the proof of its algorithmic undecidability over a field of characteristic zero is given.