Elements of Vector Analysis and Field Theory

RESEARCH OF STATIONARY PLANE FIELDS BY MEANS OF COMPLEX POTENTIAL

METHODS AND DEVICES OF QUALITY CONTROL ◽

10.31471/1993-9981-2019-1(42)-39-46 ◽

2019 ◽

pp. 39-46

Author(s):

V. P. Nisonskii ◽

Yu. V Kornuta ◽

I. M-B. Katamai

Keyword(s):

Field Theory ◽

Complex Variable ◽

Complex Potential ◽

Vector Fields ◽

Oil And Gas ◽

Water Reservoir ◽

Singular Points ◽

Vector Analysis ◽

Variable Theory ◽

Complex Variable Theory

Some of the most frequently encountered and generic types of plane vector fields with singular points at the origin of the coordinate system have been studied using complex variable theory methods combined with complex potential methods and field theory methods. The basic concepts of field theory and vector analysis, which are used to study vector fields and the main numerical characteristics of these fields, have been considered. The study of the most frequently encountered vector fields with singular points of four types, namely the generator, the vortical point, the eddy source, the dipole, have been conducted. The application of the complex potential for finding the main characteristics of the vector fields of the considered types, namely their divergence and rotor, has been shown. Equipotential lines and streamlines of the considered vector fields have been obtained and graphically constructed using the method of complex potential. Studied using the vector analysis methods and the methods of the theory of complex variable functions (complex potential) characteristics of vector fields can be used for mathematical modeling of various problems, arising during the study of layers, namely soil and water reservoir filtration problems, as well as in studying the flow of fluid or gas in layers problems. The developed and considered mathematical models of flat vector fields and the found numerical characteristics of these fields can be used to solve other problems of the oil and gas complex, which require studies of the flow of liquids or gases in gas- or oil-bearing beds.

Forecasting the behavior of the innovative potential of an entity subject to macroeconomic regulation in terms of trends in the long Kondratieff cycle

Economic Analysis Theory and Practice ◽

10.24891/ea.19.4.722 ◽

2020 ◽

Vol 19 (4) ◽

pp. 722-744

Author(s):

S.V. Istomina ◽

T.A. Lychagina ◽

A.V. Pakhomov ◽

E.A. Pakhomova

Keyword(s):

Field Theory ◽

Triple Helix ◽

New Technologies ◽

Economic Situation ◽

Vector Analysis ◽

Technological Revolution ◽

Innovative Potential ◽

Potential Factors ◽

Economic Developments ◽

The Given

Subject. We evaluate the innovative potential of an macroeconomically managed entity using our mathematical tools, field theory and vector analysis based on the Triple Helix concept. Objectives. The research analyzes whether the economic situation is predicable if we use the mathematical tools to determine the innovative potential of the macroentity and the theory of long Kondratieff waves proved by C. Perez. Methods. We review the total results, which were inferred with the mathematical tools intended to determine the innovative potential of the macroentity and the theory of Carlota Perez. Results. We forecast how the innovative potential of the macroentity will develop, referring to the Russian case, exploring the economic situation within 2000–2015, and adhering to the theory of Carlota Perez in order to detect the phase of the long Kondratieff wave. The mathematical tools helped us observe the innovative potential trends for the given period. Combining the two approaches, we managed to figure out the further trend in the economic situation for the macroentity. The tools allow to forecast further economic developments by analyzing three components of the innovative potential – factors of knowledge intensiveness, profitability, productive capabilities. Conclusions. Combining our tool and the theory of long Kondratieff waves, we conclude that Russia is about to face another technological revolution, approaching the forth phase of the Long Kondratieff Cycle. According to Carlota Perez's theory, the forth phase end is the time of great ambivalence. So, for smoother transition, we need measures to create absolutely new technologies, preserve and/or revive the existing expertise.

The technique for determining the innovative potential of socio-economic actors at different hierarchical levels through elements of the vector analysis and field theory

National Interests Priorities and Security ◽

10.24891/ni.14.1.97 ◽

2018 ◽

Vol 14 (1) ◽

pp. 97-120 ◽

Cited By ~ 1

Author(s):

S.V. Istomina ◽

◽

T.A. Lychagina ◽

E.A. Pakhomova ◽

A.V. Pakhomov ◽

...

Keyword(s):

Field Theory ◽

Vector Analysis ◽

Hierarchical Levels ◽

Innovative Potential

VECTOR ANALYSIS AND FIELD THEORY

A Course of Higher Mathematics ◽

10.1016/b978-0-08-010207-8.50009-5 ◽

1964 ◽

pp. 298-348

Author(s):

V.I. SMIRNOV

Keyword(s):

Field Theory ◽

Vector Analysis