On the 100th Anniversary of Academician Volodymyr Lohvynovych Rvachov
Today, October 21, 2026, marks the 100th anniversary of the birth of the prominent Ukrainian scientist in mathematics, mechanics, and cybernetics, Full Member (Academician) of the National Academy of Sciences of Ukraine, Laureate of the State Prize of Ukraine in Science and Technology, Honored Scientist and Engineer of Ukraine, Doctor of Physical and Mathematical Sciences, Professor, and founder of a world-renowned scientific school on the R-function method
Volodymyr Lohvynovych Rvachov
One of the main outcomes of the theory of R-functions is the solution to the inverse problem of analytic geometry. The essence of this problem is to construct an equation for a given geometric object (locus) – that is, a function whose set of zeros coincides with this object. Historically, this problem dates back to René Descartes, the father of analytic geometry, and by the mid-20th century, it had been solved only for isolated, individual cases. Academician V.L. Rvachov succeeded in solving this problem in such a way that it became possible to construct equations for arbitrarily complex geometric objects in the form of a single analytical expression representing an elementary function.
Another primary application of the theory of R-functions is the mathematical modeling of physical and mechanical fields. For analyzing the corresponding problems of mathematical physics, the R-function method allows for the construction of so-called solution structures for boundary value problems – bundles of functions that exactly satisfy all boundary conditions of a problem while depending on certain arbitrary components.
Thus, the results obtained by V.L. Rvachov opened broad perspectives not only for various geometric applications but also gave impetus to the development of numerical methods for solving boundary value problems of mathematical physics. In particular, it became possible to construct coordinate sequences when implementing variational and projection methods for various types of boundary conditions and their combinations.
Furthermore, V.L. Rvachov is one of the founders of the theory of atomic functions, which has found practical application in approximation theory problems, radiophysics, digital signal processing, and other fields.
In 1989, V.L. Rvachov proposed a new non-Archimedean calculus, algebraically isomorphic to classical calculus. In his works during the 1990s and early 2000s, the application of this calculus was developed further, particularly towards a new understanding of deep space physics.
Volodymyr Lohvynovych Rvachov was born on October 21, 1926, in the town of Chyhyryn, Cherkasy region, into a family of teachers.
In 1943, V.L. Rvachov entered the Kharkiv Institute of Railway Engineers, which was evacuated at the time to Tashkent. In 1944, following the re-evacuation of the institute, he moved to Kharkiv, from where he was drafted into active service in the Navy in October 1944.
In 1947, after demobilization, V.L. Rvachov entered the Faculty of Physics and Mathematics at Ivan Franko Lviv State University, graduating with honors in 1952 with a major in Mechanics. In 1955, he defended his Candidate’s thesis (Ph.D.) at the same university.
From September 1, 1955, V.L. Rvachov worked at the Berdyansk (until 1958 – Osypenko) State Pedagogical Institute as a Senior Lecturer, Associate Professor, and from August 23, 1959, as Professor and Head of the Department of Mathematics. While working at the institute, V.L. Rvachov actively developed an interest in computing machinery and numerical methods for boundary value problems in mathematical physics. On his initiative and with his direct participation, a computer center was established at the Berdyansk Pedagogical Institute.
In 1960, V.L. Rvachov defended his Doctoral dissertation (D.Sc.) at the Institute of Mechanics Problems of the USSR Academy of Sciences.
In 1961, V.L. Rvachov was awarded the academic title of Professor in the Department of Theoretical Mechanics.
In 1963, V.L. Rvachov moved to Kharkiv, where at the Kharkiv Institute of Mining Machinery, Automation, and Computing Technology (now Kharkiv National University of Radio Electronics), he initially headed the Department of Computer Engineering, and later the Department of Mathematical Programming and Modeling, as well as the Department of Computational Mathematics (now the Department of Applied Mathematics). In 1964, V.L. Rvachov became Vice-Rector for Research. On September 20, 1965, he was appointed Acting Rector, and on April 25, 1965, Rector of the Institute. On June 13, 1966, the Kharkiv Institute of Mining Machinery, Automation, and Computing Technology was reorganized into the Kharkiv Institute of Radio Electronics (KhIRE), making V.L. Rvachov its first Rector. On July 23, 1966, he resigned from the position of Rector at his own request, remaining Head of the Department of Computational Mathematics.
From November 1967, V.L. Rvachov worked at the Kharkiv Branch of the Institute of Mechanics of the Academy of Sciences of the UkrSSR, heading the Department of Applied Mathematics (later the Department of Applied Mathematics and Computational Methods). In 1970, the Kharkiv Branch of the Institute of Mechanics was reorganized into the Kharkiv Branch of the Institute of Engineering Thermophysics, and in 1972 – into the Institute for Problems in Machinery of the Academy of Sciences of the UkrSSR (now A.M. Pidhorny Institute of Power Machines and Systems of the National Academy of Sciences of Ukraine).
In 1992, Volodymyr Lohvynovych returned to the Department of Applied Mathematics at Kharkiv State Technical University of Radio Electronics as a Professor (part-time). He served as Head of the Department of Applied Mathematics and Computational Methods at the Institute for Problems in Machinery and as Professor (part-time) at the Department of Applied Mathematics at Kharkiv State Technical (since 2001 – National) University of Radio Electronics until the end of his life.
In 1972, V.L. Rvachov was elected Corresponding Member, and in 1978 – Full Member (Academician) of the Academy of Sciences of the UkrSSR (since March 1994 – National Academy of Sciences of Ukraine). He built an extensive scientific school comprising over 70 Candidates of Sciences (Ph.D.) and more than 20 Doctors of Sciences (D.Sc.).
Among Volodymyr Lohvynovych’s students are Corresponding Members of the NAS of Ukraine (Yu.H. Stoyan and O.Ye. Bozhko), Laureates of the State Prize of Ukraine in Science and Technology (Yu.H. Stoyan, V.S. Protsenko, H.P. Man’ko, T.I. Sheyko, M.S. Syniekop, A.P. Slesarenko), and Laureate of the V.M. Glushkov and M.V. Ostrohradskyi Prizes (O.M. Lytvyn).
Many of Volodymyr Lohvynovych’s pupils led or currently lead departments at higher education institutions in Kharkiv and across Ukraine (M.V. Sidorov, B.M. Borysenko, V.P. Buz’ko, V.M. Verzhykovskyi, I.V. Honchariuk, V.D. Kozhukhov, L.V. Kurpa, L.N. Kutsenko, O.M. Lytvyn, V.S. Protsenko, M.S. Syniekop, I.B. Sirodzha, V.P. Fed’ko, Yu.P. Shabanov-Kushnarenko, T.I. Sheyko, L.I. Shkliarov, A.V. Shmatko, and others).
Volodymyr Lohvynovych’s multifaceted and fruitful scientific and pedagogical activities were recognized with state awards, including the Orders of the Red Banner of Labour (1961), Friendship of Peoples (1976), Badge of Honour (1976), Order of Prince Yaroslav the Wise, V Class (2001), and medals. The Academy of Sciences of the UkrSSR recognized V.L. Rvachov’s contribution to mathematical physics by awarding him the prestigious O.M. Dynnyk Prize and Medal in 1976. In 1980, for the creation, development, and implementation of the theory of R-functions in the national economy, V.L. Rvachov (team leader) and his students (V.S. Protsenko, M.S. Syniekop, T.I. Sheyko, A.P. Slesarenko, H.P. Man’ko, Yu.H. Stoyan) were awarded the State Prize of the UkrSSR in Science and Technology. In 1997, V.L. Rvachov was granted the title of Honored Scientist and Engineer of Ukraine.
V.L. Rvachov passed away on April 26, 2005, in Kharkiv. (Note: The date 2004 in the source line below reflects a minor typo in the original text; historical records confirm April 26, 2005).
Volodymyr Lohvynovych Rvachov dedicated his entire life to the advancement of fundamental science in Ukraine. The legacy he initiated lives on through a constellation of talented disciples and numerous adherents of his ideas.
Among Volodymyr Lohvynovych’s students are current faculty members of the Department of Applied Mathematics at Kharkiv National University of Radio Electronics. Today, the department is headed by his pupil – Doctor of Physical and Mathematical Sciences, Professor Maksym Sidorov. Over the years, other pupils of V.L. Rvachov also served in the department:
– Corresponding Member of the NAS of Ukraine, Doctor of Engineering Sciences, Professor Yurii Hryhorovych Stoyan;
– Doctor of Physical and Mathematical Sciences, Professor Oleh Mykolaiovych Lytvyn;
– Candidate of Physical and Mathematical Sciences, Associate Professor Svitlana Vasylivna Kolosova;
– Candidate of Physical and Mathematical Sciences, Associate Professor Oleksandra Hryhorivna Lytvyn (Hlushko);
– Candidate of Physical and Mathematical Sciences, Associate Professor Leonid Yosyfovych Shkliarov.
Volodymyr Lohvynovych Rvachov
(October 21, 1926 – April 26, 2005)
Doctor of Physical and Mathematical Sciences, Professor,
Academician of the National Academy of Sciences of Ukraine