# Gorbunov Vladimir Konstantinovich

**Gorbunov** **Vladimir Konstantinovich**, doctor of Physical and Mathematical Sciences, professor, Honoured Worker of Higher Professional Education of Russia.

**Scientific biography:**

1969 – Graduation from Moscow Institute of Physics and Technology, (engineer-physicist in «Systems of automated control»);

1970 – 1976, Lenin Tashkent State University: a junior researcher, a senior researcher, a senior lecturer;

1974 – Dissertation for candidate of sciences in Mathematical Cybernetics, advisor F.L. Chernous'ko, defended at MIPT;

1976 – 1990, Institute of Mathematics of Academy of Sciences, Kyrgyz SSR (Frunze): a senior researcher, chief of the laboratory;

1991 – doctoral thesis of sciences «Extremum problems for the experiment data processing» (phys.-math. in"Numerical mathematics"), defended at the Computer Center of Siberian Branch of the USSR Academy of Sciences (Novosibirsk);

1990 – till present, Ulyanovsk State University: associate professor, professor, and head of department (2002-2012).

**Scientific achievements: **

Gorbunov's works in the period from graduation till the beginning of 2000 were devoted to optimal control problems and ill-posed ones of data processing for physical and geophysical experiment. They, starting with diploma thesis (1970), were published in editions of the USSR Academy of Sciences. The main results of this period that are reflected in world scientific literature were the parametrization method for solving optimal control problems (1979-80) and the normal splines method (1989) for solving linear differential and integral equations particular singular in different senses. The following developments of these works were published in 1990th and 2000 in editions of the Russian Academy of Sciences (2003, 2004) as well as Springer (2003) and Elsevier (2009).

In 1983 he participated in the International congress of mathematicians (ICM-82, Warsaw).

In 1980th Gorbunov also investigated demographic processes in view of their ethnic heterogeneity which was one of the main factors of economic and political crisis in the USSR, and which more and more escalate problems in contemporary world. He prepared his first disciple in this area for the candidate degree (PhD, it was defended in Moscow State University at 1987).

Since the end of 1990th the main Gorbunov's researches deal with mathematical economics and economic theorywhich state, as it is known for specialists, doesn't conform to scientific requirements that are accepted in natural sciences: objectiveness, proofness, and verifiability. He established that the root of the problem lies in the principle of methodological individualism which is the cornerstone of the modern (neoclassical) economic theory (Economics). Correspondingly, the overcoming of crisis of economic theory demands reconsideration of demand theory and equilibrium theory on the holistic principle.

Such reconsiderationis fulfilled in the series of Gorbunov's works based on the notion of the "statistical ensemble of consumers" of the market under investigation.The latter is the origin object of new theories of demand and equilibrium. The recent book «Consumers' Demand: Analytical Theory and Applications»(project of the Russian Foundation for Basic Research, 2015) represents the author's reconsideration of the neoclassical demand theory relating in Economics to an individual. Here the origin object is not artificial Homo Economicus but real observable object. Axioms of the neoclassical theory of individual demand are being transferred on the market demand theory as hypotheses which should be verified on trade statistics, so the theory of market (collective) demand becomes the scientific theory. The constructedmarket demand theory creates the basis for economic index numbers which were defined within demand theory (of an individual in Economics) in order to taking consumers' preferences into account. Also on the basis of the new demand theory the reconsideration of equilibrium theory is begun.

Besides, the generalized theory of consumers' demand is constructed. Here consumers' preferences are represented via vector field which can be non-potential in common case. The potentiality case corresponds to the classical theory with utility function which is potential of the preferences' field. In production theory the notion of effective capital is formalized, and the model of its formation is constructed.

Research programs of Gorbunov are being supported permanently by RFBR, Russian Humanitarian Research Foundation, and the Ministry of Education and Science of the RF.

During his working for USU, he prepared five candidates of science. Four of them work at the department of economic-mathematical methods and information technologies.

Gorbunov V.K. is a
reviewer for the international journals «Zentralblatt für Mathematik»
(Springer) and «Mathematical Review**»
(**AMS**). **