Publications List of Harry Gingold





1. A Summability method due to linear differential equations, Proceedings of the Edinburgh Mathematical Society, Vol. 20, (1974), pp.41-51.

2. A necessary condition for a power series to be a formal solution of a singular linear differential equation of order k, Journal of Mathematical Analysis and Applications, Vol.. 52, (1975), pp. 546-552.

3. On matrix methods preserving summability. Periodica Mathematical Hungaria Vol. 7(1), (1976), pp. 49-57.

4. Simplification of linear homogeneous differential equations with moving singularities, Fukcialaj Ekvacioj, Vol. 19, No. 3, (1976), pp. 203-225.

5. Dichotomies and moving singularities simplification of linear systems, Rendiconti Circolo Matermatico-di-Palermo, TOMO XXIX, (1980), pp.61-78.

6. Introduction to differential equations with moving singularities, Rocky Mountain Journal of Mathematics Vol. 6, No.4, (1976), pp. 571-574.

7. (With S. R. Rosenblat) Differential equations with moving singularities, SIAM, J. of Math. Anal., Vol. 7, No.6, (1976), pp. 942-957.

8. (With R. Redheffer) The Existence of limits for solutions of singular differential inequalities, Math. Monthly, Vol.84, No. 4, (1977), pp. 270-273.

9. On the global existence of a simplifying transforming matrix, Siam J. Math., Vol.9, (1978), pp.1076-1082.

10. Uniqueness of solutions to boundary value problems of systems of ordinary differential equations, Pacific J. Math., Vol. 75, (1978), pp. 107-136.

11. On continuous triangularization of matrix valued functions, SIAM J. Math. Anal., Vol. 10, No.4, (1979), pp. 709- 719.

12. Uniqueness of boundary value problems of second order differential systems and equations, J. Math. Anal. Appl., Vol. 73, No.2, (1980), pp.392-410.

13. A new basis for singularly perturbed problems, a representation theorem, Adv. Appl. Math., (1980), Vol. 1, pp. 67 - 107.

12. Problems of Mathematical physics which depend on a parameter and Jacobi Series, Adv. Appl. Math.,Vol. 5, (1984), pp. 1 - 67.

14. On the location of zeros of oscillatory solutions, Trans. Amer. Math. Soc., Vol. 279, (1983), pp. 471-496.

15. (With P. Hsieh) On global simplification of a singularly perturbed system of linear ordinary differential equations, Funkc. Ekavac., Vol. 25, (1982), pp. 269 - 281.

16. An asymptotic decomposition method applied to multi-turning point problems, SIAM J. Math., Anal., Vol. 15, (1985), pp. 7 - 27.

17. On the location of zeros of oscillatory solutions of y (x) = c(x)y, Pacific J. Math., Vol.119, (1985), pp. 317-336.

18. (With P. Hsieh), Global simplification of a singularly perturbed almost diagonal system, SIAM J. Math. Anal., 17, (1986), pp. 1-22.

19. Almost diagonal systems in asymptotic integration, Proceedings of the Edinburgh Mathematical Society, Vol. 28, (1985), pp. 143 - 158.

20. (With P. Hsieh) Note on global simplification of a singularly perturbed linear ordinary differential system, Tamsui Oxford Journal of Management Science, Vol. 1(1985), pp. 39 - 45.

21. (With G. B. Gustafson) Uniqueness for n-th order De-La-Vallee Poussin boundary value problems, Applicable Anal., Vol. 20 (1985), pp. 201 -220.

22. Boundedly asymptotic decompositions on an entire interval for second order linear differential equations with multi- coalescing transition points, Ann. Diff. Eqs. 3(4), (1987), pp. 381 - 402.

23. On the relation between globality and linearity of solutions of analytic ODE's, J. Math. Res. & Exposition, 4, (1987), pp. 611 - 614.

24. Conformal maps in methods of asymptotic continuation, Proceedings of the Royal Society of Edinburgh, 105A, (1987), pp. 319 - 335.

25. (With P. Hsieh) Global approximation of perturbed Hamiltonian differential equations with several turning points, SIAM J. Math, Anal. Appl., Vol. 18, (1987), pp. 1275 - 1293.

26. In general, the less degeneracy the less transition. A principle for time dependent Hamiltonian systems in quantum mechanics, J. Math. Physics. Vol. 28(1987), pp. 2400 - 2406.

27. (With P. Hsieh) A global study of singularly perturbed almost diagonal systems, Ann. Diff. Eq. 2, (1986), pp. 383 - 398.

28. (With P. Hsieh) A global study of Hamiltonian system with multi-turning points. Lecture Notes in Mathematics, Springer-Verlag, Berlin, Vol. 1151 (1985), pp. 164-171.

29. On a family of nonoscillatory equations y '' = f(x,e)y. J. Math. Anal. Appl. Vol. 135(1988), pp. 309 -325.

30. An invariant asymptotic formula for solutions of second order linear ODE's. J. Asymp. Anal. Vol. 1, (1988), pp. 309 - 325.

31. (With P. Hsieh) Asymptotic solution of a Hamiltonian system with several turning points, SIAM J. Math. Anal. Vol.19, (1988), pp. 1142 - 1150.

32. (With H. Gould and M. Mays) Power product expansions, Utilitas Mathematica, Vol. 34, (1988), pp. 143 - 161.

33. On asymptotic and oscillation of second order linear ordinary differential equations, Differential Equations & Applications, Proceedings of the International Conference on Theory and Applications of Differential Equations. Edited by A. R. Aftabizadeh, (1988), Vol. 1, pp. 310-314.

34. (With P. Hsieh) On asymptotic solutions of a Hamiltonian system with several turning points, Differential Equations & Applications, Proceeding of the International Conference on Theory and Applications of Differential Equations. Edited by A. R. Aftabizadeh, (1988), Vol. 1, pp. 315 - 319.

35. (With V. Trutzer) On resonance in linear conservation laws without source terms, Utilitas Mathematica, 37(1990), pp. 65 - 78.

36. A note on reduction of operations via power product approximations, Utilitas Mathematica, 37(1990), pp. 79 - 90.

37. A virtual perturbation method for singular systems, IEEE, Ch2917 (1990), pp. 3607 - 3610. (Proceedings of the 29thConference on Decision and Control, Honolulu, Hawaii, December 1990).

38. A counterexample and a modification to the adiabatic approximation theorem in quantum mechanics. International J. of Quantum Chemistry, Vol. XL, (1991), pp. 3 - 9.

39. A resolution to the inconclusive portion of Kneser's test of oscillation via asymptotic, Proc. Asian Math. Conf., (1990), pp. 144 - 148. World Scientific, Singapore. Editors, Li Zhong, K. P. Shum, C. c. Yang, Yang Le.

40. (With P. Hsieh) Globally analytic triangularization of a matrix function - an algorithm, Proc. Asian Math. Conference, 91990), pp. 149 - 154. World Scientific, Singapore. Editors, Li Zhong, P. K. Shum, C.C. Yang, Yang Le.

41. (With P. Hsieh) Note on an algorithm for globally analytic triangularization of a matrix function. Graph Theory, Combinatorics, Algorithms, & Applications, edited by Y. Alavi, F.R.K. Chung, R. L. Graham, S.O.F. Hsu, SIAM Proceedings, (1991), pp. 239 - 253.

42. On totally invertible matrices and Carlian Sets. Graph Theory, Combinatorics, Algorithms, & applications, edited by Y. Alavi, F.R.K. Chung, R. L. Graham, S.O.F. Hsu, SIAM Proceedings Series, (1991), pp. 190 - 197.

43. Eventual summability at a singular point. Approximation, Interpolation, and summability. S. Baron and D. Leviatan editors. Israel Mathematical conference Proceedings, Vol. 4, (1991), pp. 135 - 145.

44. (With Hu) Transcendentally small reflections of waves for problems with/without turning points near infinity: A new uniform approach", J. Math. Phys. 32, (1991), pp. 3278 - 3284.

45. (with She and Zorumski) "Reflection of sound waves by sound-speed inhomogeneities", J. Acoust. Soc. Am. 91, (1992), pp. 1262-1269.

46. Carlian Multisets and totally invertible matrices, Utilitas Mathematical Vol. 42, (1992), pp. 205 - 212.

47. (With Hsieh, P.F.) Globally Analytic Triangularization of a Matrix Function, Linear Algebra and its Applications, Vol. 169, (1992), pp.75-101.

48. (With V. Trutzer) The large time pointwise behaviour of linear degenerate hyperbolic systems. In Partial Differential Equations. Editors J. Wiener and J. Hale. Pitman Research Notes in Mathematics Series. Longman Scientific and Technical, Essex, 1992.

49. (With a Knopfmacher and D.S. Lubinsky) The zero distribution of the partial products of power product expansions. Analysis, Vol. 13, (1993), pp. 133 - 157.

50. (With J. She and W.E. Zorumski) Local principles of wave propagation in inhomogeneous media, J. Acoust. Soc. Am. 93(2), (1993), pp. 599 - 604.

51. Approximation of solutions of y" = p(x, e)y with several transition points and moving singularities, Asymptotic Analysis, 6(1993), pp. 335 - 364.

52. (With Yu Lihong) The local asymptotic behaviour of solutions of second order linear differential equations in a nutshell, J. of Math. Research & Exposition, Vol. 13(1993), pp. 337 - 350.

53. (With P. Hsieh & Y. Sibuya) Globally analytic simplification and the Levinson theorem, J. Math. Anal. & Appl. Vol. 182(1994), pp. 269 - 286.

54. A mechanism for connection. Trends and developments in ODE's. Editors Y. Alavi and Po-Fang Hsieh, World Scientific, Singapore, (1994), pp. 77 - 85. Proceedings of the International Symposium held at Kalamazoo, Michigan, May 1993.

55. (With T. Hempleman) Distribution of real eigenvalues in Sturm-Liouville problems with infinitely many turning points. Trends and Developments in ODE's. Editors Y. Alavi and Po-Fang Hsieh, World Scientific, Singapore, (1994), pp. 113 - 121. Proceeding of the international symposium held at Kalamazoo, Michigan, May 1993.

56. (With P. Hsieh) Globally analytic decomposition of a matrix function. Trends and Developments in ODE's. Editors Y. Alavi and Po-Fang Hsieh, World Scientific, Singapore, (1994), pp. 113 - 121. Proceedings of the International Symposium held at Kalamazoo, Michigan, May 1993.

57. (With D. Gera) A modified heat conduction model, preliminary analysis. Proceedings of the 71st JSME Spring Annual Meeting [No. 940-10], (1994), pp. 511 - 513.

58. (With U. Elias) Oscillation of two term differential equations through asymptotics. Equa. Diff. Vol. 1, editors C. Perello, C. Simo, J. Sola-Morales, (1993), pp. 403 - 407. International Conference on Differential Equations held at Barcelona, Spain, August 1991.

59. (With D. Gera) A modified heat conduction model, Chinese J. Mechanical Engineering, Vol.8, (1995), pp.175-186.

60. (With D. Gera) A modified heat conduction model, Proc. of 30th National Heat Transfer Conference, 1995, Vol. 9. ASME 1995, HTD Vol. 311.

61. (With U. Elias) Oscillation of two-term differential equations through asymptotics, J. Math. Anal. & Appl., Vol. 186 (1994), pp. 283 -305.

62. (With A. Knopfmacher) Analytic properties of power product expansions, Canadian J. of math., Vol. 47(6), (1995), pp. 1219 - 1239.

63. (With U. Elias) Oscillation and block diagonalization, J. Math. Anal. Appl., Vol. 199, (1996), pp. 202 - 212.

64. (With D. Gera) A new approach to model viscosity in the momentum equations, Proc. 74th JSME Fall Annual Meeting, (1996), pp. 229 - 232.

65. (With D. Gera) Modified heat conduction model - part 2, Proc. 3rd KSME-JSME Thermal Engineering Conference, (1996), pp. 423 - 428, Kyongju Korea.

66. (With U. Elias) Asymptotic approximation for matrix differential equations and applications, Differential and Integral Equations, vol. 10, (1997), pp. 137-152.

67. (With V. Trutzer) Removing small divisors in the method of characteristics, Applicable Analysis, Vol. 66, (1997), pp. 333-356.

68. (With Tovbis) Solutions of finitely smooth nonlinear singular differential equations and problems of diagonalization and triangularization. SIAM J.Math. Anal., Vol. 29 (1998), pp. 757-778.

69. Flattening of ellipses by growing nonlinearities, J. Nonlinear Analysis, Vol. 35, (1999 ), pp.781-795.

70. Global and Uniform approximations for solutions of the Bessel equation, Dynamics of Continuous, Discrete and Impulsive Systems, Vol.5, (1999), pp. 405-414.

71. (With U.Elias) More on Asymptotic Approximation for Matrix Differential Equations, J. Math. Anal. Appl. Vol. 230, (1999), pp. 97-111.

72. (With W.Fang) Solutions of a Nonlinear Boundary Value Problem with a Large Parameter, J.Math. Anal. Appl., Vol. 236, 1999, pp. 520-533.A Summability method due to linear differential equations, Proceedings of the Edinburgh Mathematical Society, Vol. 20, (1974), pp.41-51.



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