Course Outlines for 1996-2005 (On Leave, 2006-2008)

MATHEMATICAL PAPERS IN REFEREED JOURNALS (updated, June 2007)

55. Forced oscillation of higher order nonlinear differential equations (with YG. Sun)
In Press  Applied Math. Comput. (2007)

54. A complete asymptotic analysis of an oscillation free nonlinear equation of Bessel type with a pole in the dependent variable (with J.M. Pacheco-Castelao and S. Melkonian),
Nonlinear Oscillations To appear (2007)

53. A study of fuzzy and many-valued logics in cellular automata,
J.  Cellular Automata, 1 (3) (2006), 233-252

52. On the existence of solutions an abstract integral equation of Chandrasekhar type in the theory of radiative transfer (with K. Sadarangani and J. Caballero )
Electron. J. Diff. Eqns., 2006 (2006), (57) 1-11

51. The infinite product representation of solutions of Sturm-Liouville problems with two turning points (with Ali Jodayree Akbarfam)
Arabian J. of Science and Technology   31 (1A), (2006), 69-85

50. The global evolution of general fuzzy cellular automata
J. Cellular Automata, 1 (2) (2006), 141-164

49.  A glimpse into the life and times of F.V. Atkinson
Math. Nachr , 278 (12-13) (2005), 1-29.

48. Conjugate points in the gravitational n-body problem (with C. M. F. Mingarelli)
Celestial Mechanics and Dynamical Astronomy , 91 (2005), 391-401

47. Duality for an inverse Sturm-Liouville problem (with A. Jodayree Akbarfam)
J. Math. Analysis Appl. 312 (2), (2005), 435-463

46. Favard's Theorem for Almost Periodic Processes on Banach Space (with Z. Hu)
Dynamic Systems Appl., 14 (2005), 615-632.

45. Nonlinear functionals in differential matrix systems oscillation and a theorem of Sun (with S. Dubé)
J. Math. Analysis Appl. 308 (1) (2005), 208–220

44. The uniqueness of the solution of dual equations of an inverse indefinite Sturm-Liouville problem (with A. Jodayree Akbarfam and H. Kheiri)
J. Math. Analysis Appl. 306 (1) (2005), 269-281

43. A non-oscillation theorem for differential matrix systems  (with S. Dubé)
J. Math. Analysis Appl. 306 (1) (2005), 349-363

42. Almost periodicity of solutions for evolution equations  (with Z. Hu)
Differential and Integral Equations, 18 (4) (2005), 469-480

41. Higher order asymptotics of the eigenvalues of Sturm-Liouville problems with a turning point of arbitrary order (with Ali Jodayree Akbarfam)
 Canad. Applied Math. Quarterly 12 (3) (2004), 275-301

40. Characterizing degenerate Sturm-Liouville problems
Electronic J. Diff. Eqns., 2004 (130) (2004), 1-8.

39. The dynamics of fuzzy cellular automata: Rule 30 (with E. Beres)
WSEAS Trans. Circuits and Systems,  10 (3) (2004), 2211-2216.

38. Note on a non-oscillation theorem of Atkinson (with S. Dubé)
Electron. J. Diff. Eqns., Vol. 2004 (22) (2004), pp. 1-6.

37. On a Theorem of Favard (with Z. Hu)
Proc. Amer. Math. Soc.,132 (2004), 417-428.

36. Nonlinear functionals in oscillation theory of matrix differential systems
Comm. Pure Applied Analysis, 3 (1) (2004), 75-84.

35. Fuzzy rule 110 dynamics and the golden number,  WSEAS Trans. Computers, 2 (4) (2003), 1102-1107.

34. Oscillation of Linear Hamiltonian Systems (with F. Meng)
Proc. Amer. Math. Soc, 131 (2003), 897-904

33. Higher order asymptotic distribution of the eigenvalues of non-definite Sturm-Liouville problems with one turning point (with A. J. Akbarfam)J. Comp. Applied Math.  149 (2002), 423-437

32. The canonical product of the solution of a Sturm-Liouville equation with one turning point (with A.J. Akbarfam)
Canad. Applied Math. Quarterly, 8 (4) (2000), 305-320

31. A Generalized Inverse Eigenvalue Problem for Symmetric Matrices (with K. Ghanbari)
International J. Applied Math,. 4, (2) (2000), 199-209

30. Convergence and aperiodicity in Fuzzy Cellular Automata: Revisiting Rule 90
(with P. Flocchini, N. Santoro and F. Geurts).
Physica D,  142 (2000), 20-28

29. On a question in almost periodic differential equations (with Zuosheng Hu)
Proc. Amer. Math. Soc. 127 (1999), pp. 2665-2670.

28. The Global Flow of the Manev Problem (with J. Delgado, F. Diacu, E. Lacomba, V. Mioc, E. Perez, C. Stoica)
J. Math. Phys., 37, (1996), 2748-2761

27. A counter-example in the theory of almost-periodic differential equations (with F.Q. Pu and L. Zheng)
Rocky Mtn. J. Math., 25, (1), (1995), 437-440

26. A class of maps in an algebra with indefinite metric
Proc. Amer. Math. Soc., 121, (1994), 1177-1183

25. On the zeros of certain cosine polynomials (with S.Y. Wang)
Proc. Amer. Math. Soc., 118  (1993), 1103-1106

24. A maximum principle and related problems for a Laplacian in Hilbert Space (with S. Wang)
Differential Equations and Dynamical Systems, 1 (1993), 23-34

23. Sturm-Liouville problems and Hammerstein operators
J. Integral Equations Appl., 4 (1992), 83-88

22. Sturm-Liouville equations with Besicovitch almost-periodicity (with A. Dzurnak)
Proc. Amer. Math. Soc., 106 (1989), 647-653

21. Boundary value problems of the second order with an indefinite weight-function (with W. Allegretto)
J. für die Reine und Ang. Math., 398 (1989), 1-24

20. Asymptotics of the number of zeros and of the eigenvalues of general weighted Sturm-Liouville problems (with F.V. Atkinson)
J. für die Reine und Ang. Math., 375/376 (1987), 380-393

19. Riccati techniques and variational principles in oscillation theory for linear systems (with G. Butler and L. Erbe)
Trans. Amer. Math. Soc., 303 (1987), 263-282

18. On the oscillation of almost-periodic Sturm-Liouville operators with an arbitrary coupling constant  (with S. G. Halvorsen)
Proc. Amer. Math. Soc., 97 (1986), 279-283

17. On the discrete spectra of Dirac systems (with D. Hinton, T. Read and J. Shaw)
Proc. Edinburgh Math. Soc., 29 (1986), 367-378

16. On the non-existence of positive solutions for a Schrodinger equation with an indefinite weight-function (with W. Allegretto)
C.R. Math. Rep. Acad. Sci. Canada, 8 (1986), 69-73

15. A note on some differential inequalities
Bull. Inst. Math. Acad. Sinica, 14 (1986), 287-288

14. On the existence of conjugate points for a second order ordinary differential equation
S.I.A.M. Journal Math. Analysis, 17 (1986), 1-6

13. Propriétés oscillatoires de l'équation de Sturm-Liouville à coéfficients presque-périodiques (with S.G. Halvorsen)
C. R. Acad. Sci. Paris, 299 (1984), 907-909

12. Oscillation of linear second order differential systems (with M.K. Kwong, H.G. Kaper, K. Akiyama)
Proc. Amer. Math. Soc., 91 (1984), 85-91

11. Some remarks on the order of an entire function associated with a second order differential equation, II
C.R. Math. Rep. Acad. Sci. Canada, 6 (1984), 79-83

10. The non-real point spectrum of generalized eigenvalue problems
C.R. Math. Rep. Acad. Sci. Canada, 6 (1984), 117-121

9. On the existence of non-simple real eigenvalues for general Sturm-Liouville problems
Proc. Amer. Math. Soc., 89 (1983), 457-460

8. Legendre type polynomials under an indefinite inner product (with A.M. Krall)
S.I.A.M. Journal Math. Analysis, 14 (1983), 399-402

7. Laguerre type polynomials under an indefinite inner product (with A.M. Krall)
Acta Math. Acad. Sci. Hungaricae, 40 (1982), 237-239

6. On a Stieltjes version of Gronwall's inequality
Proc. Amer. Math. Soc., 82 (1981), 249-252

5. On a conjecture for oscillation of second order ordinary differential systems
Proc. Amer. Math. Soc., 82 (1981), 593-598

4. Jacobi type polynomials under an indefinite inner product (with A.M. Krall)
Proc. Royal Soc. Edinburgh, 90A (1981), 147-153

3. A limit-point criterion for a three-term recurrence relation
C.R. Math. Rep. Acad. Sci. Canada, 3 (1981), 171-175

2. An oscillation criterion for second order self-adjoint differential systems
C.R. Math. Rep. Acad. Sci. Canada, 2 (1980), 287-290

1. Some extensions of the Sturm-Picone theorem
C.R. Math. Rep. Acad. Sci. Canada, 1 (1979), 2

PAPERS IN REFEREED CONFERENCE PROCEEDINGS

20. Control of fuzzy cellular automata: the case of rule 90 (with Samira El Yacoubi)
In Press, in Parallel Computing Technologies, V. Malyshkin Ed., Proceedings of the 9^th International Conference on, PaCT 2007, Pereslav-Zalessky, Sept. 2007. Lecture Notes in Computer Sciences, Springer, New York, (2007)

19.Sturm and Differential Equations (with J. Lutzen),
In Press, in Sturm Bicentennial Volume, Collected Works of J.C.F. Sturm (1803-1855)
Geneva, 2006.

18. On the dynamics of some exceptional fuzzy cellular automata (with D. Dunne)
in El Yacoubi et al (Eds), ACRI 2006, Lecture Notes in Computer Science 4173, Springer-Verlag, Berlin, Heidelberg, 2006, 71-87.

17. On the decidability of the evolution of the fuzzy cellular automaton, FCA 184  (with S. El Yacoubi),
in V.N.Alexandrov et al. (Eds), ICCS 2006, Part III, Lecture Notes in Computer Science 3993, Springer-Verlag, Berlin, Heidelberg, 2006: 360-366.

16. Oscillation and non-oscillation theorems for non-conjoined second order matrix differential systems (with N. Parhi), in Proceedings of The 2005 International Conference on Scientific Computing, CSC 2005, Las Vegas, Nevada, USA, June 20-23,2005, H.R.Arabnia and G.A. Gravvanis,eds. CSREA Press.  258-265.

15. The dynamics of general fuzzy cellular automata
In Proceedings of the International Conference on Computational Science, Emory University, Atlanta, May 22-25, 2005. Lecture Notes in Computer Science  3515 Springer-Verlag, New York, 2005, 351-359.

14. The dynamics of fuzzy cellular automata: Rule 30. (with E. Beres)
in Proceedings of the WSEAS Conferences on Systems Theory and Scientific Computation, Nikos Mastorakis Ed., Puerto de la Cruz, Spain, Dec. 17-19, 2004.
World Scientific Engineering Academy and Society, (2004)  ISBN: 960-8457-06-08 on CD-ROM., pp. 1-6.

13. Fuzzy rule 110 dynamics and the golden number,
in Proceedings of the WSEAS Conferences on Systems, Nikos Mastorakis Ed., Rhodos, Greece, World Scientific Engineering Academy and Society, Rhodes, Greece, (2003)  ISBN: 960-8052-90-4 on CD-ROM., pp. 1-6.

12. An inverse matrix eigenvalue problem (with A. Alaca)
in Spectral Theory and computational methods of Sturm-Liouville Problems,
D.B. Hinton and P.W. Schaefer eds., Marcel Dekker, New York, (1997), 135-148

11. The Manev two-body problem: Quantitative and qualitative theory  (with F.Diacu, V. Mioc and C. Stoica)
in Dynamical Systems and Applications,  World Scientific Series in Applicable Analysis, Vol. 4, World Scientific  Publishing, Singapore, 1995.

10. A Laplace operator in infinite dimensional space (with S. Wang)
in Recent trends in Differential Equations,
World Scientific Series in Applicable Analysis, Vol. 1, World Scientific, Singapore and Philadelphia, 1992, 431- 44

9. Non-real eigenvalue estimates for boundary problems asssociated with weighted Sturm-Liouville equations in Differential Equations and Applications, Vol II, Ohio University Press, Athens, Ohio, 1989: 222

8. A survey of the regular weighted Sturm-Liouville problem: the non-definite case
in Applied Differential Equations, World Scientific, Singapore and Philadelphia, 1986: 109-137

7. Some remarks on a generalized eigenvalue problem
in Qualitative Theory of Differential Equations, Department of Mathematics, University of Alberta, 1985: 301-306

6. A non-oscillation theorem for second order linear equations (with M. Kwong and S. G. Halvorsen)
in Argonne National Laboratory Reprint No. ANL-84-73
Argonne, Illinois, 1984: 119-122

5. Some remarks on the order of an entire function associated with a second order differential equation
in Ordinary Differential Equations and Operators
Lecture Notes in Mathematics 1032,
Springer-Verlag, New York, 1983: 384-389

4. Asymptotic distribution of the eigenvalues of indefinite Sturm-Liouville problems
in Ordinary Differential Equations and Operators
Lecture Notes in Mathematics 1032,
Springer-Verlag, New York, 1983: 375-383

3. On the eigenvalues of non-definite elliptic operators (with J. Fleckinger)
in Spectral Theory of Differential Operators,  North-Holland, Amsterdam, 1983: 219-227

2. Indefinite Sturm-Liouville problems
in Ordinary and Partial Differential Equations
Lecture Notes in Mathematics 964,
Springer-Verlag, New York, 1982: 519-528

1. Sturm theory in n-space
in Spectral Theory of Differential Operators, North Holland, New York, 1981: 337-341