Czesław Olech
Encyclopedia
Czesław Olech is a Polish mathematician. He is a representative of the Kraków school of mathematics
Kraków School of Mathematics
Kraków School of Mathematics was a sub-group of Polish School of Mathematics represented by mathematicians from the Kraków universities—Jagiellonian University and the AGH University of Science and Technology, active during the interwar period...

, especially the differential equation
Differential equation
A differential equation is a mathematical equation for an unknown function of one or several variables that relates the values of the function itself and its derivatives of various orders...

s school of Tadeusz Ważewski
Tadeusz Wazewski
Tadeusz Ważewski was a Polish mathematician.Ważewski made important contributions to the theory of ordinary differential equations, partial differential equations, control theory and the theory of analytic spaces...

.

Education and career

In 1954 he completed his mathematical studies at the Jagiellonian University
Jagiellonian University
The Jagiellonian University was established in 1364 by Casimir III the Great in Kazimierz . It is the oldest university in Poland, the second oldest university in Central Europe and one of the oldest universities in the world....

 in Kraków
Kraków
Kraków also Krakow, or Cracow , is the second largest and one of the oldest cities in Poland. Situated on the Vistula River in the Lesser Poland region, the city dates back to the 7th century. Kraków has traditionally been one of the leading centres of Polish academic, cultural, and artistic life...

, obtained his doctorate at the Institute of Mathematical Sciences in 1958, habilitation in 1962, the title of associate professor in 1966, and the title of professor in 1973.
  • 1970-1986: director of The Institute of Mathematics, Polish Academy of Sciences
    Polish Academy of Sciences
    The Polish Academy of Sciences, headquartered in Warsaw, is one of two Polish institutions having the nature of an academy of sciences.-History:...

    .
  • 1972-1991: director of Stefan Banach International Mathematical Center in Warsaw
    Warsaw
    Warsaw is the capital and largest city of Poland. It is located on the Vistula River, roughly from the Baltic Sea and from the Carpathian Mountains. Its population in 2010 was estimated at 1,716,855 residents with a greater metropolitan area of 2,631,902 residents, making Warsaw the 10th most...

    .
  • 1979-1986: member of the Executive Committee, International Mathematical Union
    International Mathematical Union
    The International Mathematical Union is an international non-governmental organisation devoted to international cooperation in the field of mathematics across the world. It is a member of the International Council for Science and supports the International Congress of Mathematicians...

    .
  • 1982-1983: president of the Organizing Committee, International Congress of Mathematicians
    International Congress of Mathematicians
    The International Congress of Mathematicians is the largest conference for the topic of mathematics. It meets once every four years, hosted by the International Mathematical Union ....

     in Warsaw
    Warsaw
    Warsaw is the capital and largest city of Poland. It is located on the Vistula River, roughly from the Baltic Sea and from the Carpathian Mountains. Its population in 2010 was estimated at 1,716,855 residents with a greater metropolitan area of 2,631,902 residents, making Warsaw the 10th most...

    ,
  • 1987-1989: president of the Board of Mathematics, Polish Academy of Sciences
    Polish Academy of Sciences
    The Polish Academy of Sciences, headquartered in Warsaw, is one of two Polish institutions having the nature of an academy of sciences.-History:...

    .
  • 1990-2002: president of the Scientific Council, Institute of Mathematics of the Polish Academy of Sciences
    Polish Academy of Sciences
    The Polish Academy of Sciences, headquartered in Warsaw, is one of two Polish institutions having the nature of an academy of sciences.-History:...

    .

Czeslaw Olech, often as a visiting professor, was invited by the world's leading mathematical centers in the United States, USSR (later Russia), Canada and many European countries. He cooperated with Solomon Lefschetz
Solomon Lefschetz
Solomon Lefschetz was an American mathematician who did fundamental work on algebraic topology, its applications to algebraic geometry, and the theory of non-linear ordinary differential equations.-Life:...

, Sergey Nikolsky, Philip Hartman and Roberto Conti, the most distinguished mathematicians involved in the theory of differential equations. Professor S. Lefschetz highly valued prof. Ważewski's school, and especially the retract method, which prof. Olech applied by developing, among other things, control theory
Control theory
Control theory is an interdisciplinary branch of engineering and mathematics that deals with the behavior of dynamical systems. The desired output of a system is called the reference...

. He supervised nine doctoral dissertations, and reviewed a number of doctoral theses and dissertations.

Main fields of research interest

  • Contributions to ordinary differential equations:
    • various applications of Tadeusz Ważewski
      Tadeusz Wazewski
      Tadeusz Ważewski was a Polish mathematician.Ważewski made important contributions to the theory of ordinary differential equations, partial differential equations, control theory and the theory of analytic spaces...

       topological method in studying asymptotic behaviour
      Asymptotic analysis
      In mathematical analysis, asymptotic analysis is a method of describing limiting behavior. The methodology has applications across science. Examples are...

       of solutions;
    • exact estimates of exponential growth of solution of second-order linear differential equation
      Linear differential equation
      Linear differential equations are of the formwhere the differential operator L is a linear operator, y is the unknown function , and the right hand side ƒ is a given function of the same nature as y...

      s with bounded coefficients;
    • theorem
      Theorem
      In mathematics, a theorem is a statement that has been proven on the basis of previously established statements, such as other theorems, and previously accepted statements, such as axioms...

      s concerning global asymptotic stability
      Lyapunov stability
      Various types of stability may be discussed for the solutions of differential equations describing dynamical systems. The most important type is that concerning the stability of solutions near to a point of equilibrium. This may be discussed by the theory of Lyapunov...

       of the autonomous system on the plane with stable Jacobian matrix at each point of the plane, results establishing relation between question of global asymptotic stability of an autonomous system and that of global one-to-oneness of a differentiable map;
    • contribution to the question whether unicity condition implies convergence of successive approximation to solutions of ordinary differential equations.
  • Contribution to optimal control theory
    Control theory
    Control theory is an interdisciplinary branch of engineering and mathematics that deals with the behavior of dynamical systems. The desired output of a system is called the reference...

    :
    • establishing a most general version of the so-called bang-bang
      Bang-bang control
      In control theory, a bang–bang controller , also known as a hysteresis controller, is a feedback controller that switches abruptly between two states. These controllers may be realized in terms of any element that provides hysteresis...

       principle for linear control problem by detailed study of the integral of set valued map;
    • existence theorem
      Theorem
      In mathematics, a theorem is a statement that has been proven on the basis of previously established statements, such as other theorems, and previously accepted statements, such as axioms...

      s for optimal control
      Optimal control
      Optimal control theory, an extension of the calculus of variations, is a mathematical optimization method for deriving control policies. The method is largely due to the work of Lev Pontryagin and his collaborators in the Soviet Union and Richard Bellman in the United States.-General method:Optimal...

       problem with unbounded controls and multidimensional cost functions;
    • existence of solution of differential inclusions with nonconvex right-hand side;
    • characterization of controllability of convex processes.

Recognition

Honorary doctorates:
  • Vilnius University
    Vilnius University
    Vilnius University is the oldest university in the Baltic states and one of the oldest in Eastern Europe. It is also the largest university in Lithuania....

     1989
  • Jagiellonian University
    Jagiellonian University
    The Jagiellonian University was established in 1364 by Casimir III the Great in Kazimierz . It is the oldest university in Poland, the second oldest university in Central Europe and one of the oldest universities in the world....

     in Kraków
    Kraków
    Kraków also Krakow, or Cracow , is the second largest and one of the oldest cities in Poland. Situated on the Vistula River in the Lesser Poland region, the city dates back to the 7th century. Kraków has traditionally been one of the leading centres of Polish academic, cultural, and artistic life...

     2006
  • AGH University of Science and Technology
    AGH University of Science and Technology
    AGH University of Science and Technology is the second largest technical university in Poland, located in Kraków. The university was established in 1919, and was formerly known as the University of Mining and Metallurgy...

     in Kraków
    Kraków
    Kraków also Krakow, or Cracow , is the second largest and one of the oldest cities in Poland. Situated on the Vistula River in the Lesser Poland region, the city dates back to the 7th century. Kraków has traditionally been one of the leading centres of Polish academic, cultural, and artistic life...

     2009.

Membership of:
  • PAN Polish Academy of Sciences
    Polish Academy of Sciences
    The Polish Academy of Sciences, headquartered in Warsaw, is one of two Polish institutions having the nature of an academy of sciences.-History:...

     (member of the Presidium),
  • PAU Polish Academy of Arts and Sciences
    Polish Academy of Learning
    The Polish Academy of Arts and Sciences or Polish Academy of Learning , headquartered in Kraków, is one of two institutions in contemporary Poland having the nature of an academy of sciences....

  • Pontifical Academy of Sciences
    Pontifical Academy of Sciences
    The Pontifical Academy of Sciences is a scientific academy of the Vatican, founded in 1936 by Pope Pius XI. It is placed under the protection of the reigning Supreme Pontiff. Its aim is to promote the progress of the mathematical, physical and natural sciences and the study of related...

  • Russian Academy of Sciences
    Russian Academy of Sciences
    The Russian Academy of Sciences consists of the national academy of Russia and a network of scientific research institutes from across the Russian Federation as well as auxiliary scientific and social units like libraries, publishers and hospitals....

  • Polish Mathematical Society
    Polish Mathematical Society
    The Polish Mathematical Society began in Kraków, Poland in 1917. It was originally simply called the Mathematical Society. It was officially constituted on April 2, 1919.Hugo Steinhaus, Stefan Banach and Otto Nikodym were among the founders....

  • European Mathematical Society
    European Mathematical Society
    The European Mathematical Society is a European organization dedicated to the development of mathematics in Europe. Its members are different mathematical societies in Europe, academic institutions and individual mathematicians...

  • American Mathematical Society
    American Mathematical Society
    The American Mathematical Society is an association of professional mathematicians dedicated to the interests of mathematical research and scholarship, which it does with various publications and conferences as well as annual monetary awards and prizes to mathematicians.The society is one of the...



Awards and honours:
  • State Prize of Poland 1st Class
  • The Commander's Cross of the Order of Polonia Restituta
  • Marin Drinov
    Marin Drinov
    Professor Marin Stoyanov Drinov was a Bulgarian historian and philologist from the National Revival period who lived and worked in Russia through most of his life...

     Golden Medal, Bulgarian Academy of Sciences
    Bulgarian Academy of Sciences
    The Bulgarian Academy of Sciences is the National Academy of Bulgaria, established in 1869. The Academy is autonomous and has a Society of Academicians, Correspondent Members and Foreign Members...

  • Bernard Bolzano
    Bernard Bolzano
    Bernhard Placidus Johann Nepomuk Bolzano , Bernard Bolzano in English, was a Bohemian mathematician, logician, philosopher, theologian, Catholic priest and antimilitarist of German mother tongue.-Family:Bolzano was the son of two pious Catholics...

     Golden Medal, Czechoslovak Academy of Sciences
    Czechoslovak Academy of Sciences
    The Czechoslovak Academy of Sciences was established in 1953 to be the scientific center for Czechoslovakia. It was succeeded by the Academy of Sciences of the Czech Republic in 1992.-History:...

  • Stefan Banach Medal, Polish Academy of Sciences
    Polish Academy of Sciences
    The Polish Academy of Sciences, headquartered in Warsaw, is one of two Polish institutions having the nature of an academy of sciences.-History:...

  • Mikołaj Kopernik
    Nicolaus Copernicus
    Nicolaus Copernicus was a Renaissance astronomer and the first person to formulate a comprehensive heliocentric cosmology which displaced the Earth from the center of the universe....

     Medal, Polish Academy of Sciences
    Polish Academy of Sciences
    The Polish Academy of Sciences, headquartered in Warsaw, is one of two Polish institutions having the nature of an academy of sciences.-History:...


Publications

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