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

The opening of the project was attended by O.A. Kobylin, Head of the Department of Informatics at Kharkiv National University of Radio Electronics; I.M. Zhovtonizhko, Associate Professor at the Department of Applied Mathematics; O.Ie. Putiatina, Senior Lecturer at the Department of Informatics; as well as representatives of the Novobavarskyi District Education Department.

During the introductory meeting, the students learned about the degree programs, majors, and educational opportunities offered at NURE. They were introduced to the main goals and features of the project, career development prospects in the IT industry, and the opportunities provided by education in IT. Special attention was devoted to preparing for the first stage of the All-Ukrainian School Olympiad in Computer Science.

The first lesson brought together around 25 students who demonstrated a keen interest in programming, modern technologies, and intellectual competitions.

The “Q-Bit Programming” project involves mastering the fundamentals of programming, completing practical assignments, and step-by-step preparation for solving Olympiad-level problems. Participants will have the opportunity to deepen their knowledge of computer science, develop algorithmic and logical thinking, learn to find effective solutions to complex problems, and apply their knowledge in practice.

This educational initiative makes a direct contribution to the implementation of the UN Sustainable Development Goals, in particular:

• Goal 4: Quality Education — by providing school students with access to advanced mathematical and IT training, fostering digital skills, and cultivating critical and algorithmic thinking;
• Goal 8: Decent Work and Economic Growth — through early career guidance for youth, preparing highly qualified future specialists for the high-tech sector of the economy, and increasing their competitiveness.

The project aims not only to help school students prepare for intellectual competitions, but also to unlock their potential, support their interest in computer science, and encourage an informed choice of a future career in IT.

Запись Launch of the “Q-Bit Programming” Educational Career Guidance Project for School Students Preparing for Computer Science Olympiads впервые опубликована на сайте Department of Applied Mathematics.]]> https://am.nure.ua/en/school-of-the-future-vector-of-profile-education Thu, 24 Sep 2026 15:54:58 +0000 https://am.nure.ua/?p=10065 On September 24, 2026, Kharkiv National University of Radio Electronics hosted a round table discussion titled “School of the Future: Vector of Profile Education.” The event brought together university faculty and computer science teachers from the Shevchenkivskyi district of Kharkiv to discuss the transformation of the educational environment, the implementation of specialized profile education, and the enhancement of career guidance efforts. Senior Lecturer Mykyta Hvozdev represented the Department of Applied Mathematics at NURE. During the discussion, he proposed several collaborative educational initiatives to the educators of the Shevchenkivskyi district, including offline and online NMT preparation courses in mathematics, as well […]

On September 24, 2026, Kharkiv National University of Radio Electronics hosted a round table discussion titled “School of the Future: Vector of Profile Education.” The event brought together university faculty and computer science teachers from the Shevchenkivskyi district of Kharkiv to discuss the transformation of the educational environment, the implementation of specialized profile education, and the enhancement of career guidance efforts.

Senior Lecturer Mykyta Hvozdev represented the Department of Applied Mathematics at NURE. During the discussion, he proposed several collaborative educational initiatives to the educators of the Shevchenkivskyi district, including offline and online NMT preparation courses in mathematics, as well as systematic coaching for school math Olympiads.

Regular participation in such events enables the Department of Applied Mathematics at NURE to actively develop its career orientation outreach, elevate the preparation quality of prospective applicants, and implement modern approaches to popularizing exact sciences.

The event makes a direct contribution to UN Sustainable Development Goal 4: Quality Education by expanding school students’ access to high standards of mathematical education, fostering systems thinking among youth, and building a strong bridge between secondary and higher education.

Запись School of the Future: Vector of Profile Education впервые опубликована на сайте Department of Applied Mathematics.]]>

The opening ceremony was attended by Professor Maksym Sidorov, Head of the Department of Applied Mathematics at Kharkiv National University of Radio Electronics; Associate Professor Iryna Zhovtonizhko; Senior Lecturers Ravil Yanbekov and Mykyta Hvozdev; as well as representatives of the Novobavarskyi District Education Department.

During the introduction, Prof. Maksym Sidorov presented the university’s degree programs, focusing on the majors “F1 Applied Mathematics” and “F4 System Analysis and Data Science.” Following this, Ravil Yanbekov shared his experience working in an IT company and demonstrated how mathematics is applied in the development of artificial intelligence.

More than 60 participants attended the first lesson. This project is envisioned to be much more for the students than just exam preparation. The in-person meetings at Lyceum No. 162 will serve as a space where students can not only acquire knowledge, but also connect, support one another, share dreams, and stay motivated.

The “NMT to 200 with NURE” project contributes directly to UN Sustainable Development Goal 4: Quality Education (SDG 4) by offering free access to high-quality mathematical training for school students from diverse social and educational backgrounds, creating an inclusive environment for learning, self-realization, and personal growth. This initiative will not only help improve the participants’ test results, but will also boost their motivation to pursue higher education in the future.

Research Supervisor: Yuliia Ihorivna Pershina, Doctor of Physical and Mathematical Sciences, Professor, Professor at the Department of Applied Mathematics, NURE (part-time).

Based on the defense, the specialized academic council DF 64.052.072, chaired by Maksym Viktorovych Sidorov, Doctor of Physical and Mathematical Sciences, Professor, and Head of the Department of Applied Mathematics, awarded Artem Dmytrovych Kovtun the degree of Doctor of Philosophy in field of study 11 Mathematics and Statistics, specialty 113 Applied Mathematics.

The research topic makes a direct contribution to the UN Sustainable Development Goals (SDGs), including:

• Goal 13: Climate Action — by improving the accuracy of mathematical modeling of environmental pollution transport processes;
• Goal 15: Life on Land — by developing effective tools for monitoring, assessing, and forecasting the ecological state of natural resources.

The staff of the Department of Applied Mathematics sincerely congratulates Artem Dmytrovych Kovtun and his research supervisor Yuliia Ihorivna Pershina, wishing them continued scientific achievements!

The Navier–Stokes equations form the foundation of fluid dynamics, describing the motion of viscous fluids and gases. The core of the problem lies in determining whether these equations always have smooth (continuous) solutions. As highlighted by media outlets, including Hromadske’s coverage of OpenAI’s achievement, the company’s algorithms constructed an example of a finite-time blowup, thereby confirming the scenario of breakdown in smoothness.

To achieve this result, the swarm system exchanged 2.7 million messages and generated 130 billion tokens. OpenAI emphasized that it is waiving the $1 million prize from the Clay Mathematics Institute in favor of scientific progress. At the same time, as analytical publication Implicator AI highlights regarding the Clay Institute’s position, the international scientific community is in no rush to officially record a victory, as peer review and proof verification by experts will take months. Furthermore, observers at ResultSense point to a priority dispute concerning source usage and algorithmic autonomy.

On the eve of Knowledge Day, on August 31, 2026, NURE hosted traditional ceremonial events dedicated to First-Year Student Day. The celebration took place in a warm atmosphere at the Regional Organizational and Methodological Theatrical and Concert Center.

First-year students, faculty members, and representatives of the university administration and the Department of Applied Mathematics attended the festivities. This event marked the very first step for a new wave of students entering the large NURE university family. Ahead of our freshmen lie engaging lectures, practical research, introduction to faculty members, and unlocking their potential in IT, mathematical modeling, and analytics.

The Department of Applied Mathematics extends its heartfelt congratulations to all students, faculty, and researchers on Knowledge Day!

We offer special greetings to our first-year students—thank you for your choice and trust. We wish you endless inspiration, smooth studies, peaceful skies, and confidence in your abilities. May your journey at NURE be bright, and may the knowledge gained serve as a solid foundation for a successful career!

Happy new 2026/2027 academic year! 🎓🚀

The students of this graduating class faced an extraordinary journey, as their entire studies since September 2022 took place under martial law. Despite all the challenges, they received a high-quality education and successfully defended their bachelor’s theses.

This event carries special significance within the framework of the Sustainable Development Goals (SDGs). Notwithstanding global and national challenges, the University managed to maintain high educational standards, ensure the continuity of the learning process, and train specialists ready to meet modern challenges (SDG 4: Quality Education).

Graduates of the Department of Applied Mathematics gained not only fundamental knowledge but also essential skills needed to build successful careers in IT, science, and analytics. This makes them active contributors to societal development and economic growth (SDG 8: Decent Work and Economic Growth).

Every Bachelor’s diploma represents another step toward a future where the knowledge, intellect, and resilience of youth serve as the foundation for Ukraine’s sustainable development.

The Department of Applied Mathematics at Kharkiv National University of Radio Electronics is immensely proud of its graduates and wishes them inspiration, peaceful skies, and new professional achievements!

Anastasiia is already building her professional career path while working at the “Gas Transit Research Institute” branch of JSC Ukrtransgaz.

In the Metrology Department, she applies the fundamental knowledge gained at the Department of Applied Mathematics to solve real operational tasks. In her daily practice, she relies on tools from mathematics, statistics, and Machine Learning.

Thanks to a flexible schedule provided by both the university and the company, Anastasiia successfully manages her work responsibilities alongside classes, exams, and professional self-development. Experienced mentor Viktor Lutsenko and her team of colleagues at Ukrtransgaz help her master the nuances of the profession.

“Even before receiving a diploma, students get acquainted with their profession in practice, learn from experienced specialists, and understand which direction they want to develop” Ukrtransgaz noted.

The Department of Applied Mathematics is proud of its students’ achievements! We wish Anastasiia new professional accomplishments, scientific inspiration, and continued success in her studies!

Image: Укртрансгаз – Оператор газосховищ України

The defenses were held for two of the department’s specialties:

• July 15 — 113 Applied Mathematics
• July 16 — 124 Systems Analysis

The examination board noted that all works were executed at a high scientific and technical level, and the graduates demonstrated profound knowledge and the ability to apply complex mathematical apparatus to solve real-world problems.

This year, the students’ research covered the following leading scientific fields:

• Artificial Intelligence and Machine Learning
• Mathematical modeling of complex processes
• Data analysis and time series forecasting
• Systems analysis and IT management
• Optimization methods and navigation
• Applied geometry

All graduates successfully defended their works, confirming their high qualifications and readiness for the challenges of the modern IT industry and analytics.

The Department of Applied Mathematics sincerely congratulates the young specialists on achieving this important milestone! We wish you a peaceful sky, inspiration, and steady career growth, and we look forward to welcoming you to the master’s program to continue your scientific journey!

Main photo: https://www.vecteezy.com/members/yganko