DATE AND PLACE OF BIRTH: August 11, 1937, Savannah, Tennessee
EDUCATION:
B.S., University of Tennessee, 1960 (Electrical Engineering)
Ph.D., University of Tennessee, 1963 (Mathematics)
EMPLOYMENT:
September, 1974 to present, Professor, University of Tennessee
September, 1970, to August, 1974, Associate Professor, University of
Tennessee.
September, 1968, to August, 1970, Associate Professor,University of
Georgia.
September, 1964, to August, 1968, Assistant Professor, University of
Georgia.
September, 1963, to June, 1964, Assistant Professor, University of
Tennessee.
Consulting work: September 1963 to July 1964, O.R.N.L.
Visiting positions: Spring quarter, 1983, Virginia Tech
Winter quarter, 1988, University of Alabama Birmingham
Spring semester, 1990, Virginia Tech
Summer, 1993, University of Dortmund
PUBLICATIONS:
1. Don B. Hinton, "Disconjugate properties of a system of differential equations," J. Differential Equations, 2: 420-437. 1966.
2. _____, "A Stieltjes-Volterra integral equation theory," Canadian J. Math., 18: 314-331. 1966.
3. _____, "Clamped end boundary conditions for fourth-order self-adjoint
differential equations," Duke Math. J., 34: 131-138.
1967.
4. _____, "Some stability conditions for y" + qy = 0 ," J. Math. Anal. and Applications, 21: 126-131. 1968.
5. _____, "A criterion for n - n oscillations in differential equations of order 2n ," Proc. Amer. Math. Soc., 19: 511-518. 1968.
6. _____, "Asymptotic behavior of solutions of (ry(m))(k)) + qy =0 ," J. Differential Equations, 4: 590-596. 1968.
7. _____, "Some stability conditions for a nonlinear differential equation," Trans. Amer. Math. Soc., 139: 349-358. 1969.
8. _____, "An oscillation criterion for solutions of (ry')' + qy = 0 ," Michigan Math. J., 16: 349-353. 1969.
9. _____, "Continuous spectra of second-order differential operators," Pacific J. Math., 33: 641-644. 1970.
10. _____, and Jack Heidel, "The existence of oscillatory solutions
for a nonlinear differential equation," SIAM J. Math. Anal., Vol. 3,
No. 2, May, 1972, 344-351.
11. _____, "Limit point criteria for differential equations," Can. J. Math., Vol. XXIV, No. 2, 293-305. 1972.
12. _____, "Solutions of (ry(n)) (n) + qy = 0 of class Lp [0, ], "Proc. Amer. Math. Soc., 32: 134-138. 1972.
13. _____, "Asymptotic formulae for linear equations," Glasgow Math. Journal, 13: 147-152. 1972.
14. _____, "Limit point criteria for positive definite fourth order differential operators," Quart. J. Math., 24: 367-376. 1973.
15. _____, "Limit point criteria for differential equations, II," Can. J. Math., 26: 340-351. 1974.
16. _____, "Continuous spectra of an even order differential operator," Illinois J. Math., 18: 444-450. 1974.
17. _____, W.N. Everitt and J.S.W. Wong, "On the strong limit-n classification
of linear ordinary differential expressions of order
2n ," J. London Math. Soc., (3)29: 351-367. 1974.
18. _____, "Limit point-limit circle criteria for (pu')' + qy = ky",
Proc. Dundee Conference on differential equations, 1974.
Lectures Notes in Mathematics, Vol. 415, (Springer-Verlag, Berlin).
19. _____, and Roger Lewis, "Discrete spectra criteria for singular
operators with middle terms," Proc. Cambridge Phil. Soc., 77: pp.
337-347, 1975.
20. _____, "Principal solutions of positive linear Hamiltonian systems," Journal Australian Math. Society, 1976, pp. 411-420.
21. _____, "On the eigenfunction expansions of singular ordinary differential
equations," Journal of Differential Equations, Vol. 24,
1977, pp. 282-308.
22. _____, and Roger Lewis, "Spectral analysis of second order difference
equations," Journal of Mathematical Analysis and Appl.
Vol. 63, 1978, pp. 421-438.
23. _____, "Strong limit-point and dirichlet criteria for ordinary differential
expressions of order 2n," Proc. Royal Society of
Edinburgh, 76A, 1977, pp. 301-310.
24. _____, Eigenfunction expansions and spectral matrices of singular
differential operators," Proc. Royal Society of Edinburgh, 80A,
(1978), pp. 289-308.
25. _____, "Deficiency indices of odd-order differential operators,"Rocky Mt. J. Math. 8(1978), 627-640.
26. _____, and Roger Lewis, "Oscillation theory at a finite singularity," J. of Diff. Eqs. 30(1978), 235-247.
27. _____, and Roger Lewis, "Singular differential operators with spectra
discrete and bounded below," Proc. Royal Soc. Edinburgh,
84A(1979), 117-134.
28. _____, "Molchanov's discrete spectra criterion for a weighted operator," Canad. Math. Bull., 22, 4(1979), 425-431.
29. ____, "An expansion theorem for an eigenvalue problem with eigenvalue
problem with eigenvalue parameter in the boundary
condition," Quart. J. Math. Oxford (2), (30)(1979), 33-42.
30. _____, and Roger Lewis, "Oscillation theory for generalized second-order equations," Rocky Mt. J. Math., 10(1980), 751-766.
31. _____, Roger Lewis and Calvin Ahlbrandt, "Necessary and sufficient
conditions for the discreteness of the spectrum of certain
singular differential operators," Can. J. Math., 33(1981), 229-246.
32. _____, John Bradley and Robert Kauffman, "On the minimization of
singular quadratic functionals," Proc. Royal soc. Edinburgh,
87A(1981), 193-208.
33. _____, Calvin Ahlbrandt and Robert Lewis, "Some unitarily equivalent
differential operators with finite and infinite
singularities," Proc. 1980 Dundee Conference on differential equations,
Lecture Notes in Mathematics, Vol. 846, (Springer-Verlag,
Berlin).
34. _____, Calvin Ahlbrandt and Roger Lewis, "The effect of variable
change on oscillation and disconjugacy criteria with applications to
spectral theory and asymptotic theory," J. Math. Anal. Appl., 81(1981),
234-277.
35. _____, "Eigenfunction expansions for a singular eigenvalue problem
with eigenparameter in the boundary condition," SIAM J.
Math., Anal. 12(1981), 572-584.
36. _____, "On the deficiency index problem," Contributions to Analysis
and Geometry, D.N. Clark, G. Pecelli and R. Sacksteder, eds.
John Hopkins University Press, Baltimore, 1982, 151-161.
37. _____, and Ken Shaw, "On Titchmarsh-Weyl M( )-functions for linear Hamiltonian systems," J. Diff. Eqs., 40(1981), 316-342.
38. _____, and Ken Shaw, "On the spectrum of a singular Hamiltonian system," Quaestiones Mathematicae, 5(1982), 29-81.
39. _____, and Ken Shaw, "Titchmarsh-Weyl theory for Hamiltonian system,"
Spectral theory of differential operators, I.W. Knowles and
R.T. Lewis, eds., North Holland, Amsterdam, 1981, 219-231.
40. _____, Calvin Ahlbrandt and Roger Lewis, "Transformations of ordinary
differential operators," Spectral theory of differential
operators, I.W. Knowles and R.T. Lewis, eds., North Holland, Amsterdam,
1981, 1-7.
41. _____, Calvin Ahlbrandt and Roger Lewis, "Transformations of second
order ordinary and partial differential operators," Proc.
Royal Soc. Edinburgh 92A(1982), 31-49.
42. _____, and Ken Shaw, "Titchmarsh's -dependent boundary conditions
for Hamiltonian systems", Proc. of Dundee Conference on
differential equations, Lecture Notes in Mathematics, Vol. 964 (Springer-Verlag).
43. _____, and Ken Shaw, "Well-posed boundary problems for Hamiltonian
systems of limit point or limit circle type", Proc. of
Dundee Conference on differential equations, Lecture Notes in Mathematics,
Vol. 964 (Springer-Verlag).
44. _____, and Ken Shaw, "Parameterization of the M( ) functions for a Hamiltonian system of limit circle type," Proc. Royal Soc. Edinburgh, 93A(1983), 349-360.
45. _____, and Ken Shaw, "Hamiltonian systems of limit point or limit
circle type with both endpoints singular," J. Diff. Eqs. 50(1983),
444-464.
46. _____, and Ken Shaw, "On boundary value problems for Hamiltonian
systems with two singular points," SIAM J. Math. Anal. 15(1984),
272-286.
47. _____, W.N. Everitt and Ken Shaw, "The asymptotic form of the Titchmarsh-Weyl
coefficient for Dirac systems," J. London Math. Soc.
27(1983), 465-476.
48. _____, Calvin Ahlbrandt and Roger Lewis, "Inversion in the unit
sphere for powers of the Laplacian," 1982 Dundee Symposium, Lecture
Notes in Math., Vol. 1032 (Springer-Verlag).
49. _____, and Ken Shaw, "On the spectrum of a singular Hamiltonian system, II," Quaestiones Mathematicae, 10(1987), 1-48.
50. _____, "Asymptotic behavior of solutions of disconjugate differential
equations," Differential Equations, I.W. Knowles and
R.T. Lewis, eds., North Holland, Amsterdam, 1984, 293-300.
51. _____, and Ken Shaw, "On the spectrum of a Hamiltonian system with
two singular endpoints," and "Boundary conditions for
differential systems in intermediate limit situations," (Allen Krall
and Ken Shaw), Differential Equations, I.W. Knowles and R.T. Lewis,
eds., North Holland, Amsterdam, 1984, 307-312; 301-306.
52. _____, and Ken Shaw, "The asymptotic form of the Titchmarsh-Weyl
coefficient for a fourth order differential equation," Proc. Royal
Soc. Edinburgh, 97A(1984), 109-123.
53. _____, and Ken Shaw, "Absolutely continuous spectra of 2nd order
differential operators with short and long range potentials," SIAM J.
Math. Anal., 17(1986), 182-196.
54. _____, and Ken Shaw, "On the absolutely continuous spectrum of the
perturbed Hill's equation," Proc. London Math. Soc., (3),
50(1985), 175-192.
55. _____, and R.C. Brown, "Sufficient conditions for weighted inequalities of sum form," J. Math. Anal. Appl., 112(1985), 563-578.
56. _____, and Ken Shaw, "Absolutely continuous spectra of Dirac systems
with long range, short range, and oscillating potentials,"
Quart. J. Math. 36(1985), 183-213.
57. _____, and Ken Shaw, "Some extensions of a result of Titchmarsh
on Dirac systems," Proceedings of the 1984 Workshop: Spectral Theory
of Sturm-Liouville Differential Operators, Argonne National Laboratory
ANL-84-73, pp. 135-144.
58. _____, and Ken Shaw, "Dirac systems with oscillating potentials
and absolutely continuous spectra," Proceedings of the 1984 Workshop:
Spectral theory of Sturm-Liouville Differential Operators, Argonne
National Laboratory ANL-84-73, pp. 195-202.
59. _____, and Ken Shaw, "Dirac systems with discrete spectra," Can. Math. J., 39(1987), 100-122.
60. _____, and Ken Shaw, "Spectral concentration for Hamiltonian systems," Helvetica Physica Acta, 58(1985), 982-994.
61. _____, T.T. Read, A.B. Mangarelli and J.K. Shaw, "On the Number
of Eigenvalues in the Spectral Gap of A Dirac System", Proc. Edinburgh
Math. Soc., 29(1986), 367-378.
62. _____, and R.C. Brown, "Sufficient conditions for weighted Gabushin inequalities," Casopis Pro Pest. Mat. 111(1986), 113-122.
63. _____, and Ken Shaw, "Absolutely continuous spectra of perturbed periodic Hamiltonian systems," Rocky Mt. J. Math., 17(1987), 727-748.
64. _____, Allan Krall, and Ken Shaw, "Boundary Conditions for Differential
Operators with Intermediate Deficiency Index,"
Applicable Analysis 25(1987), 43-53.
65. _____ and J.K. Shaw, "Asymptotics of solutions and spectra of perturbed
periodic Hamiltonian systems," Proc. of 1986 International
Conference on Differential Equations and Mathematical Physics, Lecture
Notes in Mathematics, vol. 1285, 169-174.
66. _____ and R.C. Brown, "On the Dirichlet Index conjecture," Proc.of
1986 International Conference on Differential Equations and
Mathematical Physics, Lecture Notes in Mathematics, vol. 1285, 39-45.
67. _____ and R.C. Brown, "Necessary and sufficient conditions for one
variable weighted interpolation inequalities," J. London Math.
Soc. (2)35(1987), 439-453.
68. _____ and J.K. Shaw, "Spectrum of a Hamiltonian system with spectral
parameter in a boundary condition," Oscillation,
Bifurcation, and Chaos: Proc. of 1986 CMS Seminar, American Math. Soc.,
Providence, 1987, pp. 171-186.
69. _____ and R.C. Brown, "Weighted interpolation inequalities of sum
and product form in Rn," Proc. London Math. Soc., (3)56(1988),
261-280.
70. _____, M. Klaus, and J.K. Shaw, "Levinson's theorem and Titchmarsh-Weyl
m( ) theory for Dirac systems," Proc. Royal Soc.
Edinburgh, 109A (1988), 173-186.
71. ______, M. Klaus and J.K. Shaw, "Asymptotic phase, asymptotic modulus
and Titchmarsh-Weyl Coefficient for a Dirac system," J. Math.
Anal. Appl. 142 (1989), 108-129.
72. _____, M. Klaus and J.K. Shaw, "Titchmarsh-Weyl-Levinson theory
for a four-dimensional Hamiltonian system," Proc. London Math. Soc.,
(3) 59 (1989), 339-372.
73. _____ and R. C. Brown, "Sufficient conditions for weighted sum inequalities
in Rn," In: Proc. 1986-87 Focused Research Program on
"Spectral Theory and Boundary Value Problems," Hans G. Kaper, Man Kam
Kwong, and Anton Zettl (eds), Argonne National Laboratory ANL-87-26.
74. _____ and J.K. Shaw, "Differential operators with spectral parameter
incompletely in the boundary conditions," Funkcialaj
Ekvacioj, 33 (1990), 363-385.
75. _____, M. Klaus, and J.K. Shaw, "Series representation and asymptotics
for Titchmarsh-Weyl m-functions," J. of Differential and
Integral equations," 2 (1989), 419-429.
76. _____, M. Klaus, and J.K. Shaw, "On the Titchmarsh-Weyl function
for the half-line perturbed periodic Hill's equation," Quart. J.
Math. Oxford, (2) 41 (1990), 189-224.
77. _____, M. Klaus, and J.K. Shaw, "High-energy asymptotics for the
scattering matrix on the line," Inverse Problems, 5 (1989),
1049-1056.
78. _____, and R. C. Brown, "Weighted interpolation inequalities and embeddings in Rn," Can. J. Math., 42 (1990), 959-980.
79. _____, M. Klaus and J. K. Shaw, "Halfbound states and Levinson's
theorem for discrete systems," SIAM J. of Math. Anal., 22 (1991),
754-768.
80. _____, M. Klaus and J. K. Shaw, "Embedded halfbound states for potentials
of Wigner-von Newmann type," Proc. London Math. Soc., (3)
62 (1991), 607-646.
81. _____, M. Klaus, and J.K. Shaw, "Inverse scattering on the line for a Dirac system," J. Math. Physics 32 (1991), 3015-3030.
82. _____, M. Ashbaugh, and R.C. Brown, "Interpolation inequalities
and nonoscillatory differential equations," General Inequalities VI,
243-255, International Series of Numerical Math., vol. 103,Birkhäuser,
1992.
83. _____, and R.C. Brown, "Interpolation inequalities with power weights
for functions of one variable," J. Math. Anal. Appl., 172
(1993), 233-242.
84. _____, and R.C. Brown, "A weighted Hardy's inequality and nonoscillatory
differential equations," Quaestiones Mathematicae, 15
(1992), 197-212.
85. _____, and Robert Kauffman, "Discreteness of some continuous spectrum
eigenfunction expansions," Proc. Amer. Math. Soc., 119
(1993), 235-243.
86. _____, and Steve Clark, "Strong nonsubordinacy and absolutely continuous
spectra for Sturm - Liouville operators," J. Differential
and Integral Equations, 6 (1993), 573-586.
87. _____, and Albert Schneider, "On the Titchmarsh - Weyl coefficients
for singular S-Hermitian systems I," Math. Nachrichten,
163 (1993), 323-342.
88. _____, and R. C. Brown, "Finding good upper bounds for the best
constant in a generalized Hardy Littlewood inequality," Partial
Differential Equations, Longman Scientific and Technical, 1992, PP
11-15.
89. _____, R.C. Brown, and M. K. Kwong, "A remark on a weighted Landau
inequality of Kwong and Zettl," Canad. Math. Bull 38(1995),
34-41.
90. _____, and R. C. Brown, "An interpolation inequality and applications,"
In: Inequalities and applications, World Scientific,
Singapore, 87-101, 1994.
91. _____, and R.C. Brown, "Weighted interpolation and Hardy-type inequalities
with some spectral theoretic applications," In: Proc.
of the Fourth International Colloquium on Differential Equations, VSP
International Science Publisher, 55-70, 1994.
92. _____, R.C. Brown, D. Edmunds, and J. Rakosnik, "Some weighted Poincare-type
inequalities in one and higher dimensions," In: Proc.
of the Fifth International Colloquium on Differential Equations, VSP
International Science Publisher, 49-60, 1995.
93. _____, R.C. Brown, and S. Schwabik, "Applications of a one dimensional
Sobolev inequality to eigenvalue problems," J. of
Differential and Integral Equations, 9 (1996), 481-498.
94. _____, and R.C. Brown, "Norm eigenvalue bounds for some weighted Sturm-Liouville problems," General Inequalities VII, (1997), 129-144.
95. _____, R. Brown, and A. Kufner, "Sufficient conditions for three
weight sum inequalities in Lebesque spaces," Real Analysis Exchange
22 (1996-97), 292- 317.
96. _____, and R. Brown, "Opial's inequality and oscillation of second
order equations", Proc. Amer. Math Soc, 125 (1997),
1123-1129.
97. _____, and A. Schneider, "On the Titchmarsh - Weyl coefficients
for singular S-Hermitian systems II," Math. Nachr. 185 (1997),
67-84.
98. _____, and Terry Anderson, "Relative boundedness and compactness theory for second-order differential operators," J. of Inequalities and Applications 1 (1997), 375-400.
99. _____, and Philip Schaefer, editors, "Spectral Theory and Computational Methods of Sturm-Liouville Problems," Lecture Notes in Pure and Applied Mathematics, vol. 191, Marcel Dekker, New York, 1997.
100. _____, and Albert Schneider, " On the spectral representation for singular self-adjoint boundary eigenvalue problems, " Operator Theory volume 106, Birkhauser, 1998, 217-251.
101. ______, R. Brown, and T. Anderson, " Perturbation theory for a one-term weighted differential operator, " in Spectral Theory and Computational Methods of Sturm-Liouville Problems, pp. 149-170, Lecture Notes in Pure and Applied Mathematics, vol. 191, Marcel Dekker, New York, 1997.
102. _____, and Steve Clark, "A Liapunov inequality for linear Hamiltonian systems," Mathematical Inequalities and Applications 1 (1998), 201-209.
103. _____, and Steve Clark, " Discrete Liapunov Inequalities," Dynamic Systems and Applications 8 (1999), 369-380.
104. _____, R. Brown, V. Burenkov, and S. Clark, "Second order opial inequalities in L^p spaces and applications, " in Analytic and Geometric Inequalities and Applications, T.M. Rassias and H. M. Srivastara (eds.), pp. 37-52, Kluwer, Dordrecht, 1999.
105. _____, R. Brown, and M. Shaw, "Some separation criteria and inequalities associated with linear second order differential equations, " in Function Spaces and Applications, D.E. Edmunds, et. al. editors, pp. 7-35, Narosa Publishing House, New Delhi, 2000.
106. ______, and R. Brown, "Two separation criteria for second order ordinary or partial differential operators," Mathematica Bohemica 124 (1999), 273-292.
107. _____, R. Brown, and A. M. Fink, "Some Opial and Lyapunov inequalities with non-homogeneous boundary conditions, " J. Inequalities and Applications 5 (2000), 11-37.
108. _____ and R. Brown, "Lyapunov inequalities and their applications, " Survey on Classical Inequalities, R. Themistocles (ed.), Kluwer Academic Publishers, Dordrecht, 2000, pp. 1-25.
109. _____ and S. Collier-Melescue, "Relative boundedness-compactness inequalities for a second order differential operator," Mathematical Inequalities and Appl., 4 (2001), 35-52.
110. ______, H. Behncke, and C. Remling, "The spectrum of differential operators of order 2n with almost constant coefficients, " J. Diff. Eqs., to appear.
111. ______ and S Clark, "Positive eigenvalues of second order boundary value problems and a theorem of M. G. Krein, " Proc. AMS, to appear.
INVITED TALKS (1), COLLOQUIA (2), OTHER TALKS:
1 "Some aspects of pre-calculus mathematics," NCTM Meeting, Knoxville, Tennessee, November, 1972.
"Limit point criteria for positive definite fourth order differential operators, Amer. Math. Soc., Chapel Hill, NC, November, 1972.
1 "Teaching qualitative properties of solutions differential equations," TMTA Meeting, Chapel Hill, Tennessee, May, 1973.
"Continuous spectra of an even order differential equations," Amer. Math. Soc., Atlanta, GA, November, 1973.
1 "Limit point-limit circle criteria for (py')' + qy = ky ,"Dundee Conference
on Differential Equations, Dundee, Scotland, March,
1974.
1 "Discrete spectra criteria for differential operators," Murray State Conference of Differential Equations, October 1974.
2 "Deficiency indices of differential operators," a series of four lectures presented to Wake Forrest Mathematics Faculty, March 1975.
1 "Principal solutions of positive linear Hamiltonian systems," Amer. Math. Soc., St. Louis, MO, April 1975.
2 "Prediction of behavior of solutions of differential equations," East Tenn. State., Feb., 1975.
1 "Spectral theory of second-order difference equations," Midwest regional
conference in differential equations, Carbondale, Ill. Fall,
1976.
2 "Square roots of differential operators," Penn. State University, March, 1977.
2 "Qualitative theory of difference equations," Murray State University, January, 1978.
"Eigenvalue problems with eigenvalue parameter," Winter AMS Meeting, 1978.
2 "The deficiency index problem," University of Alabama in Birmingham, Fall, 1978.
1 "Oscillation theory at a finite singularity," Winter AMS Meeting, 1979.
1 "The deficiency index problem for ordinary differential equations," Symposium on applied mathematics, Oklahoma State, March, 1979.
2 "Discrete spectra criteria," North Texas State, April, 1979.
1 "Discrete spectra criteria for singular differential operators,"Can. Math Seminar, University of Toronto, July, 1979.
2 "The deficiency index problem, VPI, December 1980.
1 "Titchmarsh-Weyl theory for Hamiltonian systems, 1981, International Conference on Spectral Theory, Birmingham, March 1981.
1 "Titchmarsh's -dependent boundary conditions for Hamiltonian systems," Dundee, Scotland, March, 1982.
2 "The Weyl approach to singular boundary value problems," University of Missouri, Columbia, Missouri, August 1982.
1 "Singular boundary value problems for linear differential equations,"
Southeastern-Atlantic Conference on differential
equations, N.C. State, October 1982.
1 "The asymptotic behavior of solutions of disconjugate differential
equations," International Conference on Spectral Theory, Birmingham,
March 1983.
2 "On absolutely continuous spectrum of 2nd order ordinary differential equations," VPI, May 1983.
1 "On a Dirac System of Titchmarsh," Argonne workshop on spectral theory
of Sturm-Liouville Differential Operators", Argonne National
Lab., June 1984.
"Spectral properties of a separated Dirac operator," Southeastern-Atlantic
Conference on Differential Equations, Wake
Forest, October, 1984.
"Sufficient conditions for weighted Gabushin Inequalities,"
Southeastern - Atlantic Conference on Differential Equations, Atlanta, October, 1985.
1"Spectral concentration and spectral functions," International Conference
on Differential Equations and Math Physics, Birmingham,
March, 1986.
1"On the number of eigenvalues in the spectral gap of a Dirac system,"
Southeastern-Atlantic Conference on Differential Equations,
Clemson, October, 1986.
1"One variable interpolation inequalities," Seminar, Argonne National Lab., April, 1987.
1"Levinson's theorem and Titchmarsh-Weyl theory for Dirac systems" Colloquium Lecture Series, Birmingham, May, 1987.
1"Series representations and asymptotics for Titchmarsh-Weyl functions"
Spectral theory conference at Mathematisches
Forschungsinstitut Oberwolfach, Germany, April, 1989.
1 "Halfbound states and Levinson's theorem for discrete systems," UAB
International conference on differential equations and mathematical
physics, Birmingham, AL, March, 1990.
1 "Interpolation theorems and non-oscillatory differential equations,"
Nineteenth midwest differential and integral equations
conference, Rolla, MO, October, 1990.
1 "Inverse problems for the Dirac equation on a half line," University of Munich, Munich, Germany, January, 1991.
1 "Interpolation inequalities and Lp nonoscillation criteria," Spectral
theory conference at Mathematisches Forschungsinstitut
Oberwolfach, Germany, January, 1991. 1 "Absolutely continuous spectra
of Sturm-Liouville equations," AMS special session, Tuscaloosa, AL,
March, 1992.
2 "Eigenfunction expansions for self-adjoint systems of differential equations," University of Groningen, Holland, June, 1993.
1 "Interpolation inequalities and applications to spectral theory, "University
of Osnabrück, University of Munich, and University of
Frankfurt, Germany, June, 1993.
1 "The theory of subordinacy," University of Dortmund, Germany, June, 1993.
2 "The Titchmarsh-Weyl matrix for S-Hermitian systems," University of Essen, Germany, June, 1993.
1 "Interpolation inequalities," Conference on spectral theory, Gregynog, Wales, July, 1993.
2 "Sturmian Theory: Some developments and connections" University of Tennessee, October, 1993.
1 "Applications of a one dimensional Sobolev inequality to eigenvalue
problems," Symposium in honor of Norrie Everitt's 70th birthday.
Tuscaloosa, AL, March, 1994.
1 "Properties of Titchmarsh-Weyl M-matrices," UAB-Georgia Tech International
Conference of Differential Equations and Mathematical
Physics, Birmingham, AL, March, 1994.
1 "Some extremal properties of eigenvalue problems," Oberwolfach, Germany, November, 1995.
1 "Bounds on Spectral quantities," Gregynog Workshop on Computation
and analytic problems in spectral theory, Gregynog, Wales, July,
1996.
2 "Opial and other inequalities, " Math Dept. Knoxville, Tn, March , 1997.
2. "Some inequalities and their use in differential equations, " Math Dept., UT Chattanooga, April, 1997.
1 "Liapunov Inequalities," Southeastern conference on Differential Equations, Nashville, November, 1997.
2. "Second order Opial inequalities and applications, " AMS southeastern regional conference, Wake Forest, October, 1998.
1. "Liapunov and Opial inequalites with applications," UAB-Georgia Tech
International Conference of Differential Equations and Mathematical
Physics, Birmingham, AL, March, 1999.
1 " Perturbation theory for ordinary differential equations, " Gregynog
Workshop on Computation and analytic problems in spectral theory, Gregynog,
Wales, July, 1999.
2 "Some classical inequalities and their applications to ordinary differential equations," Math. Dept., University of Missouri-Rolla, October, 1999.
1 "The Zettl contribution to inequalities and Sturm-Liouville type theory," plenary lecture, Conference in honor of Tony Zettl, Northern Illinois University, DeKalb, Il, September 2000.
"Positive eigenvalues of second order BVPs and a theorem of M. G. Krein," SEARCDE conference on differential equations, Virginia Tech, Blacksburg, VA, October, 2000
PUBLIC SERVICE ACTIVITIES:
Review for Math Reviews and Zentralblatt fur Mathematik
Referee for NSF
Referee for Research Council of Canada
Referee for SWON (Dutch Math. Research Foundation)
REFEREE FOR THE FOLLOWING JOURNALS:
J. of Differential Equations
Proc. of AMS
Transactions of AMS
Pacific J. Math
SIAM J. Math Analysis
SIAM J. Applied Math
Canadian J. Math
Rocky Mt. J. Math
Proc. Royal Society Edinburgh
Houston J. Math.
J. Math Anal. Appl.
Canadian Math. Bull.
J. London Math. Soc.
Annali Di Matematica Pura ed Applicata
Journal of Natural Sciences and Mathematics
International Journal of Mathematics and Mathematical Sciences
Communications in Math Physics
Differential and Integral Equations
Proceedings of London Math Society
Journal of the Australian Mathematical Society
Applicable Analysis
Bulletin Malaysian Mathematical Society
Quaestiones Mathematicae
Mathematische Nachrichten
J. Difference Eqs. and Applications
Manuscripta Mathematica
Dynamics of Continuous, Discrete, and Impulsive Systems
Quarterly of Applied Mathematics
Mathematica Bohemica
ACM Transactions On Mathematical Software
Computers and Mathematics with Applications
Methods and Applications of Analysis
Mathematical Inequalities and Applications
Mathematical and Computer Modelling
J. Inequalities in Pure and Applied Math
Mathematik
RESEARCH FUNDING
NSF Grant, 1967-68, University of Georgia
NSF Grant for Summer Institute for College Teachers, 1970, University
of Georgia NSF Grant, 1973, University of Tennessee
NSF Grant, 1975, University of Tennessee
NSF Grant, 1978, University of Tennessee
NSF Grant, 1981, University of Tennessee
DFG Grant, 1993, University of Dortmund
TEACHING HISTORY--LIST OF PH.D. AND MASTERS STUDENTS:
Robert A. Leslie. "The zeros of solutions to certain linear homogeneous
differential equations of even order," Ph.D. in
Mathematics, June, 1968.
Philip W. Walker. "Asymptotica of the solutions to [(r")' - py']' +qy =y ," Ph.D. in Mathematics, June, 1969.
George W. Pfeiffer. "Asymptotic solutions of the equations y''' +qy' + ry = 0 ," Ph.D. in Mathematics, August, 1970.
Roger T. Lewis. "Oscillation criteria for fourth order linear differential operators," Ph.D. in Mathematics, August, 1972.
Robert L. Anderson. "Singular symmetric differential operators in a
hilbert space of vector valued functions," Ph.D. in Mathematics,
August, 1973.
Vishwavasu M. Sakhare. "Asymptotic and oscillation theorems for a second
order differential equation with delay," Ph.D. in Mathematics,
December, 1973.
Ruth Ann Lewis. "Introduction to non-linear differential equations," M.S. in Mathematics, June, 1974.
John W. McPherson. "Analysis of the behavior of solutions to a certain
non-linear, second, order, ordinary differential equation,"
M.S. in Mathematics, August, 1974.
Barbara Driggers. "Limit Cycle Behavior of the Op-Amp Wien-Bridge Oscillator," M.S. in Mathematics, June, 1975.
Thomas Womack. "Limit point-limit circle criteria for the separated Dirac Operator," M.A. in Mathematics, August, 1975.
Carol Wolf, "A comparison of eigenvalues of orthogonal systems," M.A. in Mathematics, August, 1976.
John Robinette. "On the dirichlet problem for ordinary differential equations," M.S. in Mathematics, August 1979.
Patricia Lynn Williams. "Limit point characteristics of even ordered differential operators," M.A. in Mathematics, August, 1979.
Maureen Smith. "A qualitative and quantitative analysis of second-order
difference equations," M.S. in Mathematics, December,
1979.
Mark Fortenberry. "Some numerical approximations of the Titchmarsh-Weyl
m-coefficient for certain second order ordinary
differential equations," M.S. in Mathematics, December, 1982.
Stephen L. Clark. "Some qualitative properties of the spectral density
function for Hamiltonian systems," Ph.D. in Mathematics,
August 1987.
Brenda Harrington. "Qualitative and quantitative properties of eigenvalue
problems with eigen parameter in the boundary conditions,"
M.S. in Mathematics, June 1988.
Terry G. Anderson. "A theory of relative boundedness and relative compactness
for ordinary differential operators," Ph.D. in
Mathematics, August, 1989.
James C. Smith. "On Lp solutions of 2nd order linear differential equations"
Ph.D. in Mathematics, May 1995.
Yoko Shioji. "The spectral properties of boundary value problems with
eigenvalue parameter in the boundary conditions," M.S. in
Mathematics, December 1995..
Suzanne Collier, "A theory on perturbations of the Dirac Operator,"
Ph.D in Mathematics, August 1997.
.
Charlotte Knotts-Zides, " Extremal properties of eigenvalues, " Ph.D
in Mathematics, August 1999.
Brenda Blevins, "Some mathematical models of cold pill concentration in the body," M.S. in Mathematics,August, 2000.
NON-THESIS MASTERS' PROJECTS DIRECTED:
Jim Vargo. "Combat models," August, 1985.
David Stark. "Conditionally integrable perturbations in the study of asymptotic differential equations," June 1988.
Nathan Coffey. "Qualitative behavior of the eigenvalues of a second-order problem with parameters in the ODE," June 1988.
Sterling Strevel. "Approximations of periodic solutions for nonlinear differential equations," May, 1996.
Charlotte Knotts, "Extremal properties of eigenvalues," May, 1997.
George Chailos, "Applications of Prufer transformations, " May, 1998.
Laurie Battle, "Maximum of Green's Functions for the Sturm-Liouville Problem," December, 2000
COURSES TAUGHT AND COMMITTEES LAST FIVE YEARS:
(subcommittees, thesis and orals committees not included)
2000-2001: Courses: Fall: 231, 531; Spring: 300, 532
Committees: Orientation committee (chair), ODE prelims, Teaching effectiveness
committee,
Post-Tenure Review committee (chair), math contest
1999-2000: Courses: Fall: 141, 141; Spring: 200, 142
Committees: Orientation committe (chair), ODE prelims, Advisory committee,
Graduate committee (chair), 231 text committee, Recommendation committee,
Husch's Post Tenure Review
1998-1999: Courses: Fall 231, 431; Spring 200, 431
Committees: Orientation committee (chair), ODE prelims (chair), Teaching
effectiveness committee (chair), Advisory committee,
GTA teaching awards (chair)
1997-1998: Courses: Fall 200, 435; Spring 141, 435
Committees: Orientation Committee (chair), Teaching effectiveness committee (chair), GTA teaching awards (chair), ODE prelims (chair)
1996-1997: Courses: Fall 141, 443; Spring 532
Committees: Advisory, Orientation, 231 textbook, calculus reform, GTA teaching awards, ODE prelim (chair)
1995-96: Courses: Fall - 241, 631
Spring - 231, 632
Committees: Calculus Committee, Graduate Student awards, ODE prelims
(chair), Barrett Lectures (chair).
1994-95: Courses: Fall - 531, 231
Spring - 532, 241
Committees: Advising new graduate students (chair), Calculus committee,
Advisory committee, GTA teaching awards, prelims: ODE
(chair), linear analysis, research committee for Freire, Teaching evaluations:
chair for Xiong, Collins, Feng.
1993-94: Courses: Fall - 141, 443 Spring - 431
Committees: Assistantship Committee (chair), Advising new graduate students
(chair), GTA teaching awards, calculus committee, prelims:
ODE (chair), linear analysis, Teaching evaluations: Jordan (chair-)
1992-93: Courses: Fall - 141, 531, Spring - 532
Committees: Assistanship Committee (chair), Orientation, Advising Graduate
Students, Teaching evaluations of Kuo, Serbin, Differential
equations search committee, GTA teaching awards, co-organizer of spring
AMS meeting, prelims: ODE (chair), Recommendation