I. Personal Details

Name:	Zalman I. BALANOV
Position:	Associate Professor
Working address:	Department of Computer Sciences and Mathematics, Netanya Academic  College   1 University str., Netanya 42365Israel
Office:	5208
Phone Number:	(972-9)-8607-831 balanov@mail.netanya.ac.il

                                   

II. Academic Degree

Ph.D. in Mathematics    (1989) Bellorussian State University, Minsk, USSR Supervisor: Prof. P. Zabrejko

III. Research interests

Topological Methods in Nonlinear Analysis, Brouwer Degree of Equivariant Maps, Equivariant Degree, Nonlinear Equations with Symmetries, Elliptic Variational Problems with Symmetries, Bifurcation Theory, Morse Theory, Minimax Theory, Hamiltonian Systems, Elasticity Theory, Non-associative Algebras, Asymptotically homogeneous ODE’s, Numerical Methods of Analysis 

IV. Teaching Experience

Lectured courses: Mathematical analysis, functional analysis, ordinary differential equations, linear

algebra, general topology, differential topology, algebraic topology, calculus of variations, Morse Theory, degree theory, topological methods in nonlinear analysis, numerical methods, applied mathematics, Fourier series and integral transformations.

V. Conferences

1. Joint meeting between AMS and RSME, Sevilla, Spain, June 2003.
2. International Conference on Topological and Variational Methods in Nonlinear Analysis, Bedlewo, Poland, June 2003.
3. International Conference on Functional Differential Equations, Beer Sheva, Israel, June 2002.
4. International Conference “Equadiff 10”, Prague, Czech Republik, August 2001.
5. World Congress of Nonlinear Analysts, Catania, Italy, July 2000.
6. International Conference on Topological and Variational Methods in Nonlinear   Analysis, Bedlewo, Poland, June 2000.
7. Edmonton Workshop on Methods of Nonlinear Analysis and Applications Edmonton, Canada, August 1999.
8. International Congress of Mathematicians 98, Berlin, Germany, August 1998.
9. Nonlinear Phenomena in Dynamical Systems, Whitehorse, Canada, July 1997.
10. World Congress of Nonlinear Analysts, Athens, Greece, July 1996.
11. International Conference on Topological Methods in Nonlinear Analysis, Banach enter, Warsaw, Poland, June 1996.
12. International Conference on Topology, Heidelberg, Germany, April 1996.
13. International Conference on Topological Methods in Nonlinear Analysis, Gdansk, Poland, December 1995.
14. International Conference on Topological Methods in Nonlinear Analysis, Gdansk, Poland, September 1994.
15. International Conference "Topology and Analysis", Jerusalem, Israel, March 1993.
16. Annual International Workshop on PDE, Jerusalem, Israel, March 1992.
17. Annual International Workshop on PDE, Haifa, Israel, November 1991.
18. Conference on Qualitative Theory of Differential Equations, Russe, Bulgaria, July     1989.
19. Annual Conference on Operator Theory in Functional Spaces, Novgorod, Russia, 1989.

VII. Invited Presentations

1. sity of Munich, Munich, Germany, June-August, 2004
2. University of Munich, Munich, Germany, July-August, 2003.
3. University of Alberta, Edmonton, Canada, August 2002.
4. University of Alberta, Edmonton, Canada, June-July 2001.
5. University of Padova, Padova, Italy, July 2000.
6. University of Munich, Munich, Germany, July-August 2000.
7. University of Alberta, Edmonton, Canada, July 1999.
8. University of Munich, Munich, Germany, July-August, 1998.
9. York University, North York, Canada, February 1998.
10. University of Texas at Dallas, Dallas, USA, November 1997.
11. University of Alberta, Edmonton, Canada, July 1997.
12. University of Munich, Munich, Germany, January-July, 1996.
13. University of Gdansk, Gdansk, Poland, December 1995.
14. University of Torun, Torun, Poland, December 1995.
15. University of Poznan, Poznan, Poland, December 1995.
16. Polish Academy of Sciences, Warsaw, Poland, December 1995.
17. University of Heidelberg, Heidelberg, Germany, April-November 1995.
18. University of Heidelberg, Heidelberg, Germany, June 1993.
19. Brandeis University, Waltham, USA, June-September,1991.

 VIII. Alexander von Humboldt Fellowship

 IX. LIST OF PUBLICATIONS

A. MONOGRAPH

1.   Kushkuley, A. and Balanov, Z., Geometric methods in degree theory

      for  equivariant maps, Lect. Notes in Math. No 1632, Springer-Verlag,

      Berlin-Heidelberg, 1996.

B. TEXTBOOK FOR STUDENTS

2.   Balanov, Z., Geometric methods in a theory of equivariant vector fields,

      Riga Technical University, Riga, 1988 (Russian).

C. PAPERS

3.       Balanov Z, Krawcewicz W. and Zur, S., On the orbital topological equivalence of cubic ODE’s in two-dimensional algebras (to appear in “Topological Methods       of Nonlinear Analysis).

4.       Balanov, Z., Farzamirad, M. and Krawcewicz, W., Symmetric systems of van der Pol Equations (submitted to "Topological Methods in Nonlinear Analysis").

5.       Balanov, Z. and Krasnov, Y., Complex structures in real algebras. Part I:  Two dimensional commutative case, Communications in Algebra, 31 (2003), 4571-4609.  

6.       Balanov, Z., Krawcewicz, W. and Rai, B., Taylor-Couette problem and  related topics, Nonlinear Analysis. RWA, 4 (2003), 541-559.

7.       Balanov, Z., Krawcewicz, W. and Steinlein, H., SO(3) x S –equivariant degree with applications to symmetric bifurcation problems: the case of one free parameter , Topo- logical Methods in Nonlinear Analysis, 20 (2002), 335-374.

8.       Balanov, Z., Krasnov, Y. and Krawcewicz, W., Complex structures in real algebras and bounded solutions to quadratic ODE’s, Functional Differential Equations, 10 (2003),65-81.

9.       Balanov, Z., Krawcewicz, W. and Steinlein, H., Reduced SO(3) x S –equivariant degree with applications to symmetric bifurcations problems, Nonlinear Analysis TMA,47 (2001), 1617-1628.

10.   Balanov, Z., Krawcewicz, W., Kushkuley, A.. and Zabreiko., P., On a local Lipschitz constant of the maps related to LU-decomposition, Zeitschrift fur Analysis und ihre Anwendungen, 19 (2000), 1047-1055.

11.   Balanov, Z. and Krawcewicz, W., Remarks on the equivariant degree theory, Topological Methods in Nonlinear Analysis, 13 (1999), 91-103.

12.   Balanov, Z. and Schwartzman, Y., Morse complex, even functionals and asymptotically linear differential equations with resonance at infinity, Topological Methods in Nonlinear Analysis, 12 (1998), 323-366.

13.   Balanov, Z., Krawcewicz, W. and Kushkuley, A., Brouwer degrees, equivariant maps and tensor powers, Abstract and Applied Analysis, 3 (1998), 401-409.

14.   Balanov, Z., Equivariant Hopf Theorem, Nonlinear Analysis. TMA, 30 (1997), 3463-3474.

15.   Balanov, Z. and Schwartzman, Y., Asymptotically linear  elliptic equations with resonance at infinity, Appl. Mat. Letters,  10 (1997), 35-39

16.   Balanov, Z. and Schwartzman, Y., Morse complex, even functionals and buckling of a thin elastic plate, Comptes Rendus Academie des Sciences Paris, Ser. I, 320  (1995),  273-278.

17.   Balanov, Z. and Kushkuley, A., On the problem of equivariant homotopic classification, Archiv der Mathematik , 65 (1995), 546-552.

18.   Balanov, Z. and Schwartzman, Y., Buckling of a thin elastic plate, Applied Mathematics Letters, 8 (1995), 69-74.

19.   Balanov, Z. and Brodsky, S., On the genus of some subsets of G-spheres,Topological Methods in Nonlinear Analysis, 5 (1995), 101-110.

20.   Balanov, Z. and Kushkuley, A., A comparison principle and extension of equivariant maps, Manuscripta Mathematica, 83 (1994),  239-264.

21.   Balanov, Z. and Ayevski, V., On the solutions of nonlinear systems of elliptic equations with group symmetries, Acta Comment. Univ. Tartuensis, 960 (1993), 3-12.

22.   Balanov, Z., Fundamental domains and some problems of equivariant topology, Applications of topology in Algebra and Differential Geometry, Tartu "Ulik. Toimetised, Tartu University, Tartu, 836 (1989), 36-60 (Russian).

23.   Balanov, Z., On a comparison principle of Krasnoselskii in infinite dimensional  spaces for compact groups, Latvian Mathematical Annual, Riga University, Riga, 31 (1988), 207-215 (Russian).

24.   Balanov, Z., On the finite coverings of n-dimensional spheres and Ljusternik Theorem, Topological Structures and Their Mappings, Riga University, Riga (1987), 27-33 (Russian).

25.   Balanov Z. and Vinnichenko, S., Towards the comparison principle of Krasnoselskii for compact groups, Topological Spaces and Their Mappings, Riga University, Riga (1985), 8-9 (Russian).

26.   Balanov, Z. and Vinnichenko, S., On a problem of the calculation of the equivariant field winding number, Qualitative and Approximative Methods of Operator Equation Investigations, Yaroslavl University, Yaroslavl (1985), 89-98 (Russian).

27.   Balanov, Z. and Brodsky, S., Comparison principle of Krasnoselskii and extension of equivariant mappings, Functional Analysis. Operator Theory, Ul`yanovsk Pedagogical Institute, Ul`yanovsk, 23 (1984), 18-31 (Russian).

4. ABSTRACTS AND PROCEEDINGS OF CONFERENCES

28.   Balanov, Z. and Krasnov, Y., Complex structures in non-associative algebras,  First Joint RSME/AMS Meeting, Sevilla, Spain, June 18-21 (2003), Session 27:  Non-asso-ciative algebras and their applications, Abstracts, 2.

29.   Balanov, Z. and Krasnov, Y., Complex structures in real non-associative algebras and bounded solutions to quadratic ODE’s , Intern. Conf. “Funct. Dif. Eq. Appl.”, Beer-Sheva,  June (2002), 7-8.

30.   Balanov, Z. and Krasnov, Y.,  Phase portraits of quadratic ODE’s and polynomial equations in non-associative commutative algebras, Equadiff 10,Math. Inst. Acad. Sci. Czech Rep.,  Prague (2001), 111-112.  

31.   Balanov, Z. and Brodsky, S., On a homotopic topology application to the problem of equation solvability in groups, Conf. in Theoret. and Appl. Problems in Math., Tartu Univ., Tartu  (1990), 9-11.

32.   Balanov, Z. and Ayevsky, V., On the solutions of nonlinear systems of elliptic equations with symmetries, 4th Conf. in Diff. Equat. Operator Theory in Funct. Spaces, Part 1, Novgorod Ped. Inst., Novogorod  (1989), 7 (Russian).

33.   Balanov, Z., On the existence of solution for equations with potential operators, 8th All-Union Conf. in Qualitative Theory of Differential Equations, Riga  University, Riga (1989), 20 (Russian).

34.   Balanov, Z., On the Dold Theorem about the equivariant mapping existence, 8^th All-Union Conf. in Qualitative Theory of Diff. Equat., Riga Univ., Riga (1989),19 (Russian).

35.   Balanov, Z., Bardachenko, V. and Kushkuley, A., On a local Lipschitz constant of the maps connected with LU-decomposition, Abstracts presented to the AMS, 9 (1988),  93.

36.   Balanov, Z. and Kushkuley, A., On the comparison principle for equivariant maps, Abstracts of papers presented to the AMS, 9 (1988),  224.

37.   Balanov, Z. and Kushkuley, A., A comparison principle for equivariant maps from manifold into sphere, Conf. in Problems of Pure and Appl. Math., Tula Polytechnic Inst., Tula (1988), 28-33 (Russian).

38.   Balanov, Z., On the winding number of equivariant vector fields, Conf. in Theoretical and Numerical Methods for Boundary Problems of Ordinary Differential Equations, Riga University, Riga (1988), 11 (Russian).

39.   Balanov Z., Towards the comparison principle for equivariant mappings, Seminar in Probable Methods of Cybernetics, Latvian Mathematical Year-book, Riga University, Riga, 32 (1988), 230 (Russian).

40.   Balanov, Z., On the winding number of equivariant vector field in infinite dimensional spaces, All-Union Conf. in Algebra and Analysis, Tartu University,Tartu (1988), 143-145 (Russian).

41.   Balanov Z. and Brodsky, S., On a comparison principle of Krasnoselskii, 8th All Union Conf. in the Operator Theory in Functional Spaces, Part 1, Riga University, Riga (1983), 15-16 (Russian).

E. PREPRINTS

42.   Balanov, Z., Kushkuley, A. and Zabrejko, P., Geometric methods in a degree theory for equivariant maps, Preprint No.137/1990, Ruhr University, Bochum  (1990), 15 p.

43.   Balanov, Z., Kushkuley, A. and Zabrejko, P., A degree theory for equivariant mappings: geometric approach, Preprint No 47, Heidelberg University, Juli  (1992), 22 p.

44.   Balanov, Z. and Schwartzman, Y., Morse complex, even functionals and       bucklingof a thin elastic plate, Preprint No 994, Haifa Technion, July (1994),  70p.

45.   Balanov, Z. and Kushkuley, A., Brouwer degrees of equivariant maps, Preprint No 129, Heidelberg University, November (1995), 47 p

46.   Balanov, Z. and Kushkuley, A., Brouwer degrees of equivariant maps and  equivariant homotopy classification, Preprint No gk-mp-9605/37, University of Munchen, May (1996), 54 p.

F. PAPERS IN PREPARATION

47.   Balanov, Z., Krawcewicz , W. and  Ruan, H., Applied equivariant degree. Part I: axiomatic approach to the primary part.

48.   Balanov, Z. and Krasnov, Y., Polynomial equations in  non-associative algebras and  geometric equivalence of two-dimensional quadratic dynamical systems.

49.   Balanov, Z., Farzamirad, M. and Krawcewicz, W., Symmetric Hopf bifurcation for  functional differential equiations.

G. MONOGRAPH IN PREPARATION

50.   Balanov, Z., Krawcewicz, W. and Steinlein, H. Applied Equivariant Degree.

H. THESIS

51.   Balanov, Z., A comparison principle for equivariant mappings in nonlinear analytical problems, Bellorussian University, 1989 (Russian)