Czesław Olech

Czesław Olech
Born	May 22, 1931 (1931-05-22) (age 80) Pińczów, Poland
Nationality	Polish
Alma mater	Jagiellonian University, Cracow
Occupation	Mathematician
Spouse	Jadwiga Jastrzębska, mathematician and teacher
Children	Teresa *1955, Anna *1956, Wanda *1959, Barbara *1963, Janusz *1963, thirteen grandchildren

Czesław Olech (born May 22, 1931) is a Polish mathematician. He is a representative of the Kraków school of mathematics, especially the differential equations school of Tadeusz Ważewski.

Contents 1 Education and career 2 Main fields of research interest 3 Recognition 4 Publications 5 Notes and references

Education and career

In 1954 he completed his mathematical studies at the Jagiellonian University in Kraków, 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.
• 1972-1991: director of Stefan Banach International Mathematical Center in Warsaw.
• 1979-1986: member of the Executive Committee, International Mathematical Union.
• 1982-1983: president of the Organizing Committee, International Congress of Mathematicians in Warsaw,
• 1987-1989: president of the Board of Mathematics, Polish Academy of Sciences.
• 1990-2002: president of the Scientific Council, Institute of Mathematics of the Polish Academy of Sciences.

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, 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. He supervised nine doctoral dissertations, and reviewed a number of doctoral theses and dissertations.^[1]

Main fields of research interest

• Contributions to ordinary differential equations:
  • various applications of Tadeusz Ważewski topological method in studying asymptotic behaviour of solutions;
  • exact estimates of exponential growth of solution of second-order linear differential equations with bounded coefficients;
  • theorems concerning global asymptotic stability 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:
  • establishing a most general version of the so-called bang-bang principle for linear control problem by detailed study of the integral of set valued map;
  • existence theorems for optimal control 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.^[2]

Recognition

Honorary doctorates:

• Vilnius University 1989
• Jagiellonian University in Kraków 2006
• AGH University of Science and Technology in Kraków 2009.

Membership of:

• PAN Polish Academy of Sciences (member of the Presidium),
• PAU Polish Academy of Arts and Sciences
• Pontifical Academy of Sciences
• Russian Academy of Sciences
• Polish Mathematical Society
• European Mathematical Society
• American Mathematical Society^[3]

Awards and honours:

• State Prize of Poland 1st Class
• The Commander's Cross of the Order of Polonia Restituta
• Marin Drinov Golden Medal, Bulgarian Academy of Sciences
• Bernard Bolzano Golden Medal, Czechoslovak Academy of Sciences
• Stefan Banach Medal, Polish Academy of Sciences
• Mikołaj Kopernik Medal, Polish Academy of Sciences^[4]

Publications

• A talk on the occasion of receiving an honorary degree. (Polish) Wiadom. Mat. 42 (2006), 55—58.
• On the Ważewski equation. Proceedings of the Conference Topological Methods in Differential Equations and Dynamical Systems (Kraków-Przegorzaƚy, 1996). Univ. Iagel. Acta Math. No. 36 (1998), 55—64.
• My contacts with Professor Kuratowski, 1970--1980. (Polish) X School of the history of mathematics (Międzyzdroje, 1996). Zesz. Nauk. Uniw. Opol. Mat. 30 (1997), 109—114.
• with Janas, J. ; Szafraniec, F. H. Wƚodzimierz Mlak (1931--1994). Volume dedicated to the memory of Wƚodzimierz Mlak. Ann. Polon. Math. 66 (1997), 1--9.
• with Meisters, Gary H. Global stability, injectivity, and the Jacobian conjecture. World Congress of Nonlinear Analysts '92, Vol. I--IV (Tampa, FL, 1992), 1059—1072, de Gruyter, Berlin, 1996.
• with Meisters, Gary H. Power-exact, nilpotent, homogeneous matrices. Linear and Multilinear Algebra 35 (1993), no. 3-4, 225—236.
• Introduction. New directions in differential equations and dynamical systems, viii—x, Royal Soc. Edinburgh, Edinburgh, 1991.
• with Meisters, Gary H. Strong nilpotence holds in dimensions up to five only. Linear and Multilinear Algebra 30 (1991), no. 4, 231—255.
• with Parthasarathy, T. ; Ravindran, G. Almost N-matrices and linear complementarity. Linear Algebra Appl. 145 (1991), 107—125.
• with Parthasarathy, T. ; Ravindran, G. A class of globally univalent differentiable mappings. Arch. Math. (Brno) 26 (1990), no. 2-3, 165—172.
• with Meisters, Gary H. A Jacobian condition for injectivity of differentiable plane maps. Ann. Polon. Math. 51 (1990), 249—254.
• with Lasota, A. Zdzisƚaw Opial---a mathematician (1930--1974). Ann. Polon. Math. 51 (1990), 7--13.
• The Lyapunov theorem: its extensions and applications. Methods of nonconvex analysis (Varenna, 1989), 84—103, Lecture Notes in Math., 1446, Springer, Berlin, 1990.
• Global diffeomorphism question and differential equations. Qualitative theory of differential equations (Szeged, 1988), 465—471, Colloq. Math. Soc. János Bolyai, 53, North-Holland, Amsterdam, 1990.
• with Meisters, Gary H. Solution of the global asymptotic stability Jacobian conjecture for the polynomial case. Analyse mathématique et applications, 373—381, Gauthier-Villars, Montrouge, 1988.
• with Meisters, Gary H. A poly-flow formulation of the Jacobian conjecture. Bull. Polish Acad. Sci. Math. 35 (1987), no. 11-12, 725—731.
• Global asymptotic stability and global univalence on the plane. Proceedings of the Eleventh International Conference on Nonlinear Oscillations (Budapest, 1987), 189—194, János Bolyai Math. Soc., Budapest, 1987.
• Some remarks concerning controllability. Contributions to modern calculus of variations (Bologna, 1985), 184—188, Pitman Res. Notes Math. Ser., 148, Longman Sci. Tech., Harlow, 1987.
• On n-dimensional extensions of Fatou's lemma. Z. Angew. Math. Phys. 38 (1987), no. 2, 266—272.
• with Aubin, Jean-Pierre ; Frankowska, Halina. Controllability of convex processes. SIAM J. Control Optim. 24 (1986), no. 6, 1192—1211.
• with Meisters, Gary H. Global asymptotic stability for plane polynomial flows. Časopis Pěst. Mat. 111 (1986), no. 2, 123—126.
• with Aubin, Jean-Pierre ; Frankowska, Halina. Contrôlabilité des processus convexes[Controllability of convex processes]. C. R. Acad. Sci. Paris Sér. I Math. 301 (1985), no. 5, 153—156.
• Decomposability as a substitute for convexity. Multifunctions and integrands (Catania, 1983), 193—205, Lecture Notes in Math., 1091, Springer, Berlin, 1984.
• with Frankowska, Halina. Boundary solutions of differential inclusion. Special issue dedicated to J. P. LaSalle. J. Differential Equations 44 (1982), no. 2, 156—165.
• with Frankowska, Halina. R-convexity of the integral of set-valued functions. Contributions to analysis and geometry (Baltimore, Md., 1980), pp. 117–129, Johns Hopkins Univ. Press, Baltimore, Md., 1981.
• Lower semiconductivity of integral functionals. Analysis and control of systems (IRIA Sem., Rocquencourt, 1978), pp. 109–117, IRIA, Rocquencourt, 1978.
• Differential games of evasion. Differential equations (Proc. Internat. Conf., Uppsala, 1977), pp. 155–161. Sympos. Univ. Upsaliensis Ann. Quingentesimum Celebrantis, No. 7, Almqvist & Wiksell, Stockholm, 1977.
• A characterization of L\sb{1}-weak lower semicontinuity of integral functionals. Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys. 25 (1977), no. 2, 135—142.
• Existence theory in optimal control. Control theory and topics in functional analysis (Internat. Sem., Internat. Centre Theoret. Phys., Trieste, 1974), Vol. I, pp. 291–328. Internat. Atomic Energy Agency, Vienna, 1976.
• The achievements of Tadeusz Ważewski in the mathematical theory of optimal control. (Polish) Wiadom. Mat. (2) 20 (1976), no. 1, 66—69. 49-03
• with Szarski, J. ; Szmydt, Z. Tadeusz Ważewski (1896--1972). (Polish) Wiadom. Mat. (2) 20 (1976), no. 1, 55—62.
• Weak lower semicontinuity of integral functionals. Existence theorem issue. J. Optimization Theory Appl. 19 (1976), no. 1, 3--16.
• Existence theory in optimal control problems in the underlying ideas. International Conference on Differential Equations (Proc., Univ. Southern California, Los Angeles, Calif., 1974), pp. 612–635. Academic Press, New York, 1975.
• Existence of solutions of non-convex orientor fields. Collection of articles dedicated to Giovanni Sansone on the occasion of his eighty-fifth birthday. Boll. Un. Mat. Ital. (4) 11 (1975), no. 3, suppl., 189—197.
• The characterization of the weak closure of certain sets of integrable functions. Collection of articles dedicated to the memory of Lucien W. Neustadt. SIAM J. Control 12 (1974), 311—318.
• with Kaczyński, H. Existence of solutions of orientor fields with non-convex right-hand side. Collection of articles dedicated to the memory of Tadeusz Ważewski. Ann. Polon. Math. 29 (1974), 61—66.
• with Szarski, J. ; Szmydt, Z. Tadeusz Ważewski (1896--1972). Collection of articles dedicated to the memory of Tadeusz Ważewski. Ann. Polon. Math. 29 (1974), 1--13.
• with Węgrzyn, S. ; Skowronek, M. Optimization of a sequence of operations at limitations imposed on particular operations. Bull. Acad. Polon. Sci. Sér. Sci. Tech. 20 (1972), 65—68.
• Convexity in existence theory of optimal solution. Actes du Congrès International des Mathématiciens (Nice, 1970), Tome 3, pp. 187–192. Gauthier-Villars, Paris, 1971.
• with Węgrzyn, Stefan ; Skowronek, Marcin. Optimization of sequences of operations under constraints on the individual operations. (Polish) Podstawy Sterowania 1 (1971), 147—151.
• Existence theorems for optimal control problems involving multiple integrals. J. Differential Equations 6 1969 512—526.
• Existence theorems for optimal problems with vector-valued cost function. Trans. Amer. Math. Soc. 136 1969 159—180.
• with Lasota, A. On Cesari's semicontinuity condition for set valued mappings. Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys. 16 1968 711—716.
• On the range of an unbounded vector-valued measure. Math. Systems Theory 2 1968 251—256.
• On Approximation of set-valued functions by continuous functions. Colloq. Math. 19 1968 285—293.
• with Szegë, G. P. ; Cellina, A. On the stability properties of a third order system. Ann. Mat. Pura Appl. (4) 78 1968 91—103.
• Lexicographical order, range of integrals and "bang-bang" principle. 1967 Mathematical Theory of Control (Proc. Conf., Los Angeles, Calif., 1967) pp. 35–45 Academic Press, New York
• with Klee, Victor. Characterizations of a class of convex sets. Math. Scand 20 1967 290—296.
• with Pliś, A. Monotonicity assumption in uniqueness criteria for differential equations. Colloq. Math. 18 1967 43—58.
• On a system of integral inequalities. Colloq. Math. 16 1967 137—139.
• with Lasota, A. On the closedness of the set of trajectories of a control system. Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys. 14 1966 615—621.
• with Lasota, A. An optimal solution of Nicoletti's boundary value problem. Ann. Polon. Math. 18 1966 131—139.
• Extremal solutions of a control system. J. Differential Equations 2 1966 74—101.
• Contribution to the time optimal control problem. Abh. Deutsch. Akad. Wiss. Berlin Kl. Math. Phys. Tech. 1965 1965 no. 2, 438—446 (1966).
• A note concerning set-valued measurable functions. Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys. 13 1965 317—321.
• A note concerning extremal points of a convex set. Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys. 13 1965 347—351.
• Global phase-portrait of a plane autonomous system. Ann. Inst. Fourier (Grenoble) 14 1964 fasc. 1, 87—97.
• with Mlak, W. Integration of infinite systems of differential inequalities. Ann. Polon. Math. 13 1963 105—112.
• On the global stability of an autonomous system on the plane. Contributions to Differential Equations 1 1963 389—400.
• with Meisters, Gary H. Locally one-to-one mappings and a classical theorem on schlicht functions. Duke Math. J. 30 1963 63—80.
• with Hartman, Philip. On global asymptotic stability of solutions of differential equations. Trans. Amer. Math. Soc. 104 1962 154—178.
• A connection between two certain methods of successive approximations in differential equations. Ann. Polon. Math. 11 1962 237—245.
• On the asymptotic coincidence of sets filled up by integrals of two systems of ordinary differential equations. Ann. Polon. Math. 11 1961 49—74.
• On the existence and uniqueness of solutions of an ordinary differential equation in the case of Banach space. Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys. 8 1960 667—673.
• Remarks concerning criteria for uniqueness of solutions of ordinary differential equations. Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys. 8 1960 661—666.
• A simple proof of a certain result of Z. Opial. Ann. Polon. Math. 8 1960 61—63.
• with Opial, Z. Sur une inégalité différentielle. (Italian) Ann. Polon. Math. 7 1960 247—254.
• Estimates of the exponential growth of solutions of a second order ordinary differential equation. Bull. Acad. Polon. Sci. Sér. Sci. Math. Astr. Phys. 7 1959 487—494 (unbound insert).
• Periodic solutions of a system of two ordinary differential equations. Bull. Acad. Polon. Sci. Sér. Sci. Math. Astr. Phys. 7 1959 137—140.
• Asymptotic behaviour of the solutions of second order differential equations. Bull. Acad. Polon. Sci. Sér. Sci. Math. Astr. Phys. 7 1959 319—326 (unbound insert).
• On the characteristic exponents of the second order linear ordinary differential equation. Bull. Acad. Polon. Sci. Sér. Sci. Math. Astr. Phys. 6 1958 573—579.
• Sur un problème de M. G. Sansone lié à la théorie du synchrotrone. (French) Ann. Mat. Pura Appl. (4) 44 1957 317—329.
• On surfaces filled up by asymptotic integrals of a system of ordinary differential equations. Bull. Acad. Polon. Sci. Cl. III. 5 (1957), 935—941, LXXIX.
• with Opial, Z. ; Ważewski, T. Sur le problème d'oscillation des intégrales de l'équation y"+g(t)y=0. (French) Bull. Acad. Polon. Sci. Cl. III. 5 (1957), 621—626, LIII.
• Sur certaines propriétés des intégrales de l'équation y'=f(x,y), dont le second membre est doublement périodique. (French) Ann. Polon. Math. 3 (1957), 189—199.
• On the asymptotic behaviour of the solutions of a system of ordinary non-linear differential equations. Bull. Acad. Polon. Sci. Cl. III. 4 (1956), 555—561.
• with Gołąb, S. Contribution à la théorie de la formule simpsonienne des quadratures approchées. (French) Ann. Polon. Math. 1, (1954). 176—183.^[5]

Notes and references

Persondata
Name	Olech, Czeslaw
Alternative names
Short description
Date of birth	May 22, 1931
Place of birth	Pińczów, Poland
Date of death
Place of death