**History of foundation and development of the Institute**

The Pidstryhach Institute for Applied Problems of Mechanics and Mathematics (Pidstryhach IAPMM), National Academy of Sciences of Ukraine (NASU), is a leading research institution in Western Ukraine. It develops actively important investigations in mathematics, mathematical problems of mechanics and mathematical modeling. The skilled researchers employed at the Institute are known both in Ukraine and in the world.

1978 is the official date of foundation of the Institute, but already since 1973 it started functioning as a separate research institution – the L’viv Branch for Mathematical Physics of Institute of Mathematics, NASU. However formation of this scientific body started much earlier, when Ya. S. Pidstryhach (1928-1990) together with his colleagues and followers Ya.Yo. Burak, H.S.Kit, P.S.Kazimirs'ky (1925-1990), Yu.M.Kolyano (1936-1990), B.L.Pelekh (1940-1995) and V.Ya.Skorobohat’ko (1927-1996) began their researches in the Institute of Mechanical Engineering and Automatics and later on in the Physical-Mechanical Institute, NASU. Here Ya. S. Pidstryhach, Academician of NASU, formed the preface of future Institute. He managed to form a skilled researched body that started its studies in various physical nature processes using the means of applied mathematics and mathematical modeling.

Ya. S. Pidstryhach, Academician of NASU, was the Director of the Institute up to his death. In 1990-2002 the Institute’s Director was H.S.Kit, Associate Member of NASU. He did much for further development of the scientific potential of the Institute (now H.S.Kit is the adviser at the board of directors of the Institute). Since January 2003 the Institute’s Director is Prof. Roman Mykhailovych Kushnir.

In 1973 99 researchers of the Sector of Mathematics and Mechanics of the Physical-Mechanical Institute, NASU, were transferred to the L’viv Branch for Mathematical Physics of Institute of Mathematics, NASU. They were distributed into 5 research departments:

- mechanics of real bodies (Ya.S.Pidstryhach);
- theory of differential equations (V.Ya.Skorobohat’ko);
- mathematical physics (Ya.Yo. Burak):
- algebra and modeling (P.S.Kazimirs’ky);
- mathematical theory of deformation and fracture of thin-walled elements of design (B.L.Pelekh).

In addition, 4 geophysical subsections were joined to the Institute.

The Branch begins to carry out actively investigations in mechanics of deformable bodies, thermomechanics, non-equilibrium thermodynamics, mathematical modeling of interconnected processes of different nature, fundamental and applied problems of mathematics that were generally recognized and supported by the academic community. The applied aspects of these investigations are aimed at calculation of elements of design, operating in corrosive media at high temperature under varying heat and force loadings, in powerful electromagnetic fields with regard for interconnection of physical-mechanical processes, surface phenomena, material structure and other factors of different nature. They are used in industry on developing the know-how and modern engineering equipment.

During 5 years the research body of the Branch was formed, its scientific potential increased; a series of important results both in the field of fundamental studies and in realization essential applied elaborations was obtained. All this was a cause for approval the resolution by the Council of Ministers of Ukr.SSR No 428, September 22, 1978 “About organization of the Institute for Applied Problems of Mechanics and Mathematics, Academy of Sciences of Ukrainian SSR in L’viv”. And according to this resolution of the Institute was founded on the basis of the L’viv Branch for Mathematical Physics of Institute of Mathematics, ASU. It was Ya. S. Pidstryhach, Academician of ASU, who was at the head of the Institute.

The newly formed Institute had to realize the following researches in such directions:

- study of fundamental and applied problems of deformable bodies;
- investigation of the processes of origin, interaction and propagation of various nature fields concerning the problems of mechanics, physical materials science, geophysics and modern technology;
- construction of theoretical models of deformable bodies with extended physical-mechanical properties;
- development of theoretical and applied problems of mathematics concerning non-classical problems of mechanics.

8 research departments were carrying out their investigations in the following directions:

- mechanics of deformable bodies (Ya.S.Pidstryhach) with non-structural laboratory of geodynamics (M.I.Mel’nychuk);
- theory of differential equations (V.Ya.Skorobohat’ko);
- theory of physical-mechanical fields (Ya.Yo.Burak) with 2 non-structural laboratories of electromagnetic field of Earth (A.I.Bilins’ky) and electrometry (Ya.S.Sapuzhak);
- algebra and modeling (P.S.Kazimirs’ky);
- mechanics of thin-walled elements of design (B.L.Pelekh);
- theory and methods for physical-mechanical modeling (H.V.Pliatsko);
- integral equations (Yu.Yo. Chers’ky);
- thermechanics (Yu.M.Kolyano).

322 researchers worked at the Institute in 1978 (7 Doctors and 48 Cand. Sci. including).

In 1975 the Computation Centre (334 researchers) began to function.

The structure of the Institute changed, its scientific potential increased. So 75 Doctor’s degree and 300 Candidate’s degree theses were defended in the Institute.

The research potential of the Institute has increased what made it possible to form new departments:

- 1980 - mathematical methods of fracture mechanics (H.S.Kit);
- 1982 –mechanics of inhomogeneous bodies (V.A.Osadchuk);
- 1983 - numerical methods of mathematical physics (M.M.Voitovych);
- 1985 – special design office (SDO) of the Institute and department of physical-mechanical methods of geofields modeling and study (Ya.S.Sapuzhak);
- 1987 - nonlinear mathematical analysis (A.K.Prykarpats’ky);
- 1988 – mathematical theory of programming and decision support systems (V.O.Valkovsky) and boundary-value problems with partial derivatives (in Chernivtsi; S.D.Ivasyshen);
- 1989 - mathematical physics (B. Yo. Ptashnyk);
- 1991 - mathematical modeling of self-organization phenomena (V.V.Hafijchuk);
- 1992 – optimization of controlled systems (V.E.Berbiuk).

In 1991 on the basis of two departments the Carpathian branch of Subbotin Institute for Geophysics, NASU, was founded.

In 1990 the Institute was named after Ya. S. Pidstryhach, Academician of NASU.

In 1992 the Computation Center of the Institute was reorganized into the Research–Educational Centre of Mathematical Modeling (CMM), and the Centre for Information Problems of Territory (CIPT) was organized, and the Special Design Office was reorganized into the Centre of Aeronautic Information and Ecological Monitoring at the Institute of Cybernetics, AS Ukraine.

**Contemporary**** State**** **

For the time being the Institute comprises 15 research departments. 235 employees work at the Institute, including 190 researchers (43 of them are Doctors, four - Associate Members of NASU and 103 Cand. Sci.). The Institute is concluded in the department of Mathematics, NASU.

In the Centre of Mathematical Modeling there are 49 employees, 25 researchers (one Associate Member of NASU, 7 Doctors and 12 Cand. Sci. including). 12 employees work in the Centre for Information Problems of Territory, 4 Cand. Sci. including.

The researches of priority in the Institute at present are:

- operator methods of functional analysis and linear algebra and their applications;
- theory of differential equations and dynamic systems;
- thermodynamic fundamentals for constructing the mathematical models of mechanics of deformable bodies, considering the structure and interconnection between different nature processes;
- mathematical methods for calculation, optimization and prediction of the deformability, strength, durability and behavior of mechanical systems.

The following departments are carrying out their studies in the above-mentioned areas.

The researches of priority in the CMM are in the field of mathematical modeling, mathematical physics, calculation experiment and optimization.

IAPMM NASU, maintains and increases its high research potential. The research schools for mathematical modeling and analysis of physical-mechanical processes and contact phenomena in homogeneous bodies and inhomogeneous composite structures with constant and temperature-dependent properties; for the problems of continual-thermodynamic modeling and optimization of nonlinear locally non-equilibrium systems; for non-classical problems of the theory of differential equations with partial derivatives and analytical methods of approximation theory were firmly established. Lately the research schools were formed for: mathematical problems of electro-mechanic-thermo-diffusion, functionally operator and algebraic methods, and the theory of integrable and dissipative dynamic systems on infinite dimensional manifolds with utilization of self-organization phenomena.

The investigations of Center of Mathematical Modeling, IAPMM NASU, are carried out within the framework of research school for continual-thermodynamic modeling and optimization of nonlinear locally non-equilibrium systems .

The Institute has a specialized research council on Doctor’s and Candidate’s degree qualification (speciality – “Mechanics of deformable bodies” and “Mathematical modeling and calculation methods”). The post-graduate course attached to the Institute works in 8 specialities:

- mathematical analysis;
- differential equations;
- mathematical physics;
- algebra and number theory;
- geometry and topology;
- calculation mathematics;
- mechanics of deformable bodies;
- mathematical modeling and calculation methods

and a course for a Doctor’s degree in 5 specialities:

- mathematical analysis;
- differential equations;
- algebra and number theory;
- mechanics of deformable bodies;
- mathematical modeling and calculation methods.

The Institute prepares young specialists at the chair of mathematical modeling of physical-mechanical processes of the L’viv Iv. Franko National University and Branch of the chair for laser technology and optoelectric systems of National University “L’viv Polytechnic”. In 2006 the research-educational complex for applied mathematics of IAPMM, NASU and Institute for Applied Mathematics and Fundamental Sciences of National University “L’viv Polytechnic” was organized.

The researchers of Institute train abroad, and in particular, in the leading research centers of Austria, England, Italy, Canada, Netherlands, Germany, Poland, USA, Czech Republic, France, Switzerland, Sweden etc.

Since 1975 the Institute is publishing the journal “Mathematical methods and physical-mechanical fields” (translated by Springer under title Journal of Mathematical Sciences). In 2003 the annual scientific collection of works “Applied Problems of Mechanics and Mathematics” started its publication. In 2004 the Center of Mathematical Modeling of the Institute began to publish “Physical-mechanical modeling and information technologies”. The Institute collaborates with many foreign research institutions within the collaboration programs and plans, concluded agreements about common researches. The researchers of the Institute participate in many International Conferences.

The scientists of the Institute are members of many international scientific societies, in particular: American Mathematical Society (AMS), European Society of Mechanics (Euromech), International Federation of Nonlinear Analysts (IFNA), European Society of Integrity of Structures (ESIS), International Institute of Engineers-Electronicists (IEEE), German Society of Applied Mathematics and Mechanics (GAMM) etc. The Institute collaborates within the concluded agreements about common investigations with the Institute of mathematics of Belorus’ AS, Institute of Problems of Mechanics, Russian AS, Institute of Radioelectronics of Warsaw Polytechnic (Poland), Barselona Mathematical Scientific Centre (Spain), Opole Polytechnic (Poland), Chalmer Technical University (Sweden), Institute for Fundamental Technological Studies of Polish AS (Warsaw), Chair of Applied Mathematics of Mining-Metallurgical Academy (Krakow, Poland), Institute of Metallurgy and Engineering of Materials (Polish AS) etc.

In the Institute the West Ukraine Chapter of international scientific technical society of IEEE functions, the activity of which is aimed at organization of seminars and conferences, spreading the information about international research conferences, supporting students’ scientific activity etc.

The Institute organizes regularly scientific conferences, symposia and seminars. Every year in May the traditional scientific readings dedicated to memory of Academician Ya.S.Pidstryhach are held in the Institute. Since 1983 once in four years the Institute organizes the international research conference “Mathematical Problems of Non-homogeneous Structures”, the idea of which belongs to Ya. S. Pidstryhach, Academician of NASU and prof. Yu.M.Kolyano. Once in three years the International scientific mathematical conference in memory of V.Ya.Skorobohat’ko is held.

The researchers of the Institute work actively in order to win individual and collective grants from international funds needed for their scientific studies. Nearly one fourth of the employees of the Institute are young researchers. The Institute has the Council of young researchers and specialists. The young researchers were granted by stipends of the President of Ukraine, NASU, the Chair of Regional State Administration, grants of Ukrainian and international scientific funds.

The Institute plans to further develop the fundamental and applied investigations in mechanics, mathematics, mathematical modeling, and physical materials science. Having concentrated the scientists scientific potential on realization of themes of priority, on the basis of deep fundamental studies we plan to obtain the results of applied character and to work out recommendations as to their applied usage when estimating and predicting strength and durability of designs. The Institute will further extend its scientific connections, carry out the work on strengthening scientific potential and training high qualification specialists, it will increase the team of scientists by young researchers.