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Refereed
Journals
1. A contribution
to the analytic theory of partial differential equations, J. Diff.
Eqns.
5 (l969), 117-135.
2. Jacobi polynomials of negative
index and a nonexistence theorem for the generalized axially symmetric
potential equation, SIAM J. Appl. Math. l6
(l968),
771-776.
3. Singularities of solutions to
elliptic partial differential equations with analytic coefficients, Quart.
J.
Math. 19 (l968), 391-396 (with R. P. Gilbert).
4. Jacobi series which converge
to zero, with applications to a class of singular partial differential
equations,
Proc. Camb. Phil. Soc. 65 (l969), 101-106 (with Jet
Wimp).
5. A priori estimates for
solutions of the Helmholtz equation in exterior domains and their
application, J.
Math. Anal. Appl. 27 (l969), 253-26l.
6. Uniqueness theorems for
axially symmetric partial differential equations, J. Math. Mech.
18
(1969), 921-930.
7. Analytic theory and uniqueness
problems for the generalized axially symmetric Schrodinger equation, J.
Diff.
Eqns. 6 (l969), 264-270.
8. Cauchy's problem for almost
linear elliptic equations in two independent variables, J. Approx.
Theory,
3 (l970), 66-71.
9. John's decomposition theorem
for generalized metaharmonic functions, J. London Math. Soc. 1
(l969), 737-742.
10. Nonlinear analytic partial
differential equations with generalized Goursat data, Duke Math. J.
37
(l970), 367-376. Corrigendum, 39 (l972), 823 (with R. P. Gilbert).
11. Applications of a class of
singular partial differential equations to Gegenbauer series which
converge to
zero, SIAM J. Math. Anal. 1 (l970), 90-95.
12. A contribution to
Vekua-Rellich theory of metaharmonic functions, Amer. J. Math.,
92
(l970), 525-540 (with R. P. Gilbert).
13. Decomposition theorems for
the generalized metaharmonic equation in several independent variables,
J.
Australian Math. Soc. 13 (l972), 35-46.
14. Cauchy's problem for a
singular parabolic partial differential equation, J. Diff. Eqns.
8
(l970), 250-257.
15. On the inverse scattering
problem for axially symmetric solutions of the Helmholtz equation, Quart.
J.
Math. 22 (1971), 125-130.
16. Cauchy's problem for almost
linear elliptic equations in two independent variables, II, J.
Approx.
Theory 4 (1971), 288-294.
17. An integral operator approach
to Cauchy's problem for 
, SIAM J. Math. Anal. 2
(1971), 113-132,
(with R. P. Gilbert).
18. Rapidly convergent
approximations to Dirichlet's problem for semi-linear elliptic
equations, Applicable
Analysis 2 (1972), 229-240 (with R. P. Gilbert).
19. Cauchy's problem for a class
of fourth order elliptic equations in two independent variables, Applicable
Analysis
1 (1971), 13-22.
20. Integral operators and
complete families of solutions for 
, Arch. Rat. Mech. Anal. 43
(1971),
62-78. Corrigendum, 48 (l972), 397 (with R. P. Gilbert).
21. Bergman operators for
elliptic equations in four independent variables, SIAM J. Math.
Anal. 3
(l972), 401-412.
22. Integral representations of
solutions to a class of fourth order elliptic equations in three
independent
variables, Mathematika 18 (1971), 283-290.
23. Integral operators for
elliptic equations in three independent variables I, Applicable
Analysis
4 (l974), 77-95.
24. Integral operators for
elliptic equations in three independent variables II, Applicable
Analysis
4 (l975), 283-295.
25. On the analytic theory of
pseudoparabolic equations, Quart. J. Math.23 (1972),
179-192.
26. Improperly posed initial
value problems for self-adjoint hyperbolic and elliptic equations, SIAM
J.
Math.
Anal. 4 (1973), 42-5l.
27. Pseudoparabolic equations in
one space variable, J. Diff. Eqns.12 (l972),
559-565.
28. Integral operators and the
first initial boundary value problem for pseudoparabolic equations with
analytic coefficients, J. Diff. Eqns. 13 (l973),
506-522.
29. Bergman operators for
parabolic equations in two space variables, Proc. Amer. Math. Soc.
38
(l973), ll9-l26.
30. The non-characteristic Cauchy
problem for parabolic equations in one space variable, SIAM J.
Math. Anal.
5 (l974), 263-272.
31. The non-characteristic Cauchy
problem for parabolic equations in two space variables, Proc. Amer.
Math.
Soc. 41 (l973), 55l-556.
32. Generalized reflection
principles for parabolic equations in one space variable, Duke
Math. J. 41
(l974), 547-553.
33. Integral operators and
reflection principles for parabolic equations in one space variable, J.
Diff.
Eqns. 15 (l974), 55l-559.
34. The approximation of
solutions to initial boundary value problems for parabolic equations in
one
space variable, Quart. Applied Math. 33 (l976),
377-386.
35. The inverse Stefan problem
for the heat equation in two space variables, Mathematika 21
(l974), 282-286.
36. Runge's theorem for parabolic
equations in two space variables, Proc. Roy. Soc. Edinburgh 73A
(l975), 307-3l5.
37. Complete families of
solutions for parabolic equations with analytic coefficients, SIAM
J. Math.
Anal. 6 (l975), 937-947.
38. The solution of
initial-boundary value problems for parabolic equations by the method
of
integral operators, J. Diff. Eqns., 26 (l977),
181-l90.
39. Constructive methods for
solving the exterior Neumann problem for the reduced wave equation in a
spherically symmetric medium, Proc. Roy. Soc. Edinburgh, 75A
(l976), 98-l07 (with W. Wendland).
40. An inverse scattering problem
for acoustic waves in a spherically symmetric medium, Proc.
Edinburgh Math.
Soc. 20 (l977), 257-263.
41. A reflection principle for
solutions to the Helmholtz equation and an application to the inverse
scattering problem, Glasgow Math. J., 18 (l977),
125-130.
42. Complete families of
solutions to the heat equation and generalized heat equation in 
, J. Diff. Eqns., 25
(l977), 96-l07
(with W. Watzlawek).
43. The scattering of acoustic
waves by a spherically stratified inhomogeneous medium, Proc. Roy.
Soc.
Edinburgh, 76A (l977), 345-350.
44. The exterior Dirichlet
problem for 
, Applicable Analysis, 7
(l978),
207-212.
45. The scattering of acoustic
waves by a spherically stratified medium and an obstacle, SIAM J.
Math.
Anal., 9 (l978), 935-942.
46. The solution of problems in
radiowave propagation by the method of parabolic equations and
transformation
operators, Applicable Analysis, 8 (l978), ll-22.
47. The numerical solution of
parabolic partial differential equations by the method of integral
operators, Int.
J. Computer Math., 6 (l977), 229-239 (with Y. F.
Chang).
48. On reflection principles for
parabolic equations in one space variable, Proc. Edinburgh Math.
Soc., 21
(l978), l43-l47.
49. The construction of solutions
to acoustic scattering problems in a spherically stratified medium, Quart.
J.
Mech.
Appl. Math., 31 (l978), 9-17 (with R. Kress).
50. Remarks on the representation
of zero by solutions of differential equations, Proc. Amer. Math.
Soc.,
74 (l979), 232-234 (with J.
Wimp).
51. The construction of solutions
to acoustic scattering problems in a spherically stratified medium II, Quart.
J.
Mech.
Appl. Math., 32
(l979), 53-62 (with R. Kress).
52. The construction of solutions
to the heat equation backward in time, Math. Methods Applied Science,
1
(l979), 32-39 (with J. Wimp).
53. Asymptotic behavior of the
fundamental solution to the equation of heat conduction in two
temperatures, J.
Math. Anal. Appl., 69
(l979), 4ll-4l8 (with J. Wimp).
54. The approximation of
solutions to the backwards heat equation in a nonhomogeneous medium, J.
Math.
Anal.
Appl., 72
(l979), 418-429.
55. The inverse scattering
problem for a cylinder, Proc. Roy. Soc. Edinburgh, 84A (l979),
l35-l43.
56. Arthur Erdelyi (Obituary
Notice), Bull. London Math. Soc., 11 (1979), 191-207.
57. The direct and inverse
scattering problems for an arbitrary cylinder: Dirichlet boundary
conditions, Proc.
Roy. Soc. Edinburgh, 86A
(l980), 29-42 (with R. Kleinman).
58. Schwarz reflection principles
for solutions of parabolic equations, Proc. Amer. Math. Soc.,
82 (l98l),
87-94.
59. Iterative methods for solving
the exterior Dirichlet problem for the Helmholtz equation with
applications to
the inverse scattering problem for low frequency acoustic waves, J.
Math.
Anal. Appl. 77 (l980),
60-72 (with R. Kress).
60. Remarks on the inverse
scattering problem for low frequency acoustic waves, J. Diff. Eqns.,
37
(l980), 374-38l.
61. The determination of the
surface impedance of an obstacle from measurements of the far field
pattern, SIAM
J. Appl. Math. 41 (l98l),
8-l5 (with A. Kirsch).
62. Stable methods for solving
the inverse scattering problem for a cylinder, Proc. Roy. Soc.
Edinburgh,
89A (l98l), l8l-l88 (with A.
Kirsch).
63. The impedance boundary value
problem for the time harmonic Maxwell equations, Math. Methods
Applied
Science, 3 (l98l), 475-487
(with R. Kress).
64. The inverse electromagnetic
scattering problem for a perfectly conducting cylinder, IEEE
Transactions on
Antennas and Propagation 29 (1981), 364-368.
65. The three dimensional inverse
scattering problem for acoustic waves, J. Diff. Eqns. 46
(1982), 46-58
(with T. S. Angell and A. Kirsch).
66. Runge's theorem and far field
patterns for the impedance boundary value problem in acoustic wave
propagation,
SIAM J. Math. Anal. 13
(l982), 970-977.
67. The unique solvability of the
null field equations of acoustics, Quart. J. Mech. Appl. Math.,
36
(l983), 87-95 (with R. Kress).
68. Stable methods for
determining the surface impedance of an obstacle from low frequency far
field
data, Applicable Analysis, 14
(l982), 6l-70.
69. Dense sets and far field
patterns in acoustic wave propagation, SIAM J. Math. Anal., 15
(l984),
996-l006 (with A. Kirsch).
70. Far field patterns for the
impedance boundary value problem in acoustic scattering, Applicable
Analysis,
16 (1983), 131-139.
71. The numerical solution of the
inverse Stefan problem in two space variables, SIAM J. Appl. Math.,
44
(1984), 996-1013 (with R. Reemtsen).
72. The inverse scattering
problem for time-harmonic acoustic waves, SIAM Review, 26
(1984),
323-350.
73. Uniqueness theorems for the
inverse problem of acoustic scattering, IMA J. Appl. Math. 31
(l983),
253-259 (with B. D. Sleeman).
74. Dense sets and far field
patterns in electromagnetic wave propagation, SIAM J. Math. Anal.,
16
(1985), 1049-1060, (with R. Kress).
75. Analytic solutions of the
heat equation and some formulas for Laguerre and Hermite polynomials, Complex
Variables 3 (l984), 397-412
(with J. Wimp).
76. The strong maximum principle
for the heat equation, Proc. Edinburgh Math. Soc., 27 (1984),
297-299.
77. A novel method for solving
the inverse scattering problem for time-harmonic acoustic waves in the
resonance region, SIAM J. Appl. Math., 45 (1985), 1039-1053
(with P.
Monk).
78. A novel method for solving
the inverse scattering problem for time-harmonic acoustic waves in the
resonance region II, SIAM J. Appl. Math., 46 (1986), 506-523
(with P.
Monk).
79. Generalized Herglotz domains,
Math. Methods Applied Sciences, 8
(1986), 451-457 (with J.
Wimp).
80. The numerical solution of the
three dimensional inverse scattering problem for time harmonic acoustic
waves, SIAM
J. Sci. Stat. Comp., 8
(1987), 278-291 (with P. Monk).
81. The inverse scattering
problem for time harmonic acoustic waves in a penetrable medium, Quart.
J.
Mech.
Appl.
Math., 40
(1987), 189-212 (with P. Monk).
82. The inverse scattering
problem for time harmonic acoustic waves in an inhomogeneous medium, Quart.
J.
Mech.
Appl. Math., 41
(1988), 97-125 (with P. Monk).
83. Dense sets and far field
patterns for acoustic waves in an inhomogeneous medium, Proc.
Edinburgh
Math. Soc., 31 (1988),
401-407.
84. Karp's theorem in acoustic
scattering theory, Proc. Amer. Math. Soc., 103 (1988), 783-788
(with A.
Kirsch).
85. Far field patterns and the
inverse scattering problem for electromagnetic waves in an
inhomogeneous
medium, Math. Proc. Camb. Phil. Soc., 103 (1988), 561-575 (with
L.
Päivärinta).
86. Karp's theorem in
electromagnetic scattering theory, Proc. Amer. Math. Soc., 104
(1988),
764-769 (with R. Kress).
87. Far field patterns and the
inverse scattering problem for acoustic waves in an inhomogeneous
medium, Quart.
J. Mech. Appl. Math., 42 (1989),
317-326.
88. Some preliminary observations
on an algorithm for the computation of moment integrals, J. Comp.
Applied
Math., 19 (1987), 117-124
(with A. Calardi, B. Kline and J.
Wimp).
89. Far field patterns for
acoustic waves in an inhomogeneous medium, SIAM J. Math. Anal.
20
(1989), 1472-1483 (with A. Kirsch and L. Päivärinta).
90. The inverse scattering
problem for time harmonic acoustic waves in an inhomogeneous medium:
numerical
experiments, IMA Jour. Appl. Math., 42 (1989), 77-95 (with P.
Monk).
91. A new method for solving the
inverse scattering problem for acoustic waves in an inhomogeneous
medium, Inverse
Problems 5 (1989),
1013-1026 (with P. Monk).
92. Far field patterns and
inverse scattering problems for imperfectly conducting obstacles, Math.
Proc.
Camb.
Phil. Soc. 106
(1989), 553-569 (with T.S. Angell and R.
Kress).
93. The scattering of
electromagnetic waves by a perfectly conducting infinite cylinder, Math.
Methods
Applied
Sciences, 12
(1990), 503-518 (with P. Monk).
94. Far field patterns for
electromagnetic waves in an inhomogeneous medium, SIAM J. Math.
Anal.,
21 (1990), 1537-1549 (with L.
Päivärinta).
95. Time harmonic electromagnetic
waves in an inhomogeneous medium, Proc. Roy. Soc. Edinburgh
116A (1990),
279-293 (with R. Kress).
96. A new method for solving the
inverse scattering problem for acoustic waves in an inhomogeneous
medium II, Inverse
Problems, 6 (1990),
935-947 (with P. Monk).
97. The use of polarization
effects in electromagnetic inverse scattering problems, Math.
Methods
Applied Science, 15
(1992), 1-10 (with A. Kirsch).
98. An approximation problem in
inverse scattering theory, Applicable Analysis, 41 (1991),
23-32 (with
A. Kirsch).
99. A comparison of two methods
for solving the inverse scattering problem for acoustic waves in an
inhomogeneous medium, J. Comp. Appl. Math. 42 (1992), 5-16
(with P.
Monk).
100. The uniqueness of a solution
to an inverse scattering problem for electromagnetic waves, Arch.
Rational
Mech. Anal. 119 (1992),
59-70 (with L. Päivärinta).
101. The numerical solution of an
inverse scattering problem for acoustic waves, IMA Journal Appl.
Math.
49 (1992), 163-184 (with P.
Monk).
102. On a class of integral equations
of the first kind in inverse scattering theory, SIAM J. Appl. Math.,
53
(1993), 847-860 (with P. Monk).
103. Modified far field operators
in inverse scattering theory, SIAM J. Math. Anal, 24 (1993),
365-389
(with P. Hahner).
104. Target signatures for
imperfectly conducting obstacles at fixed frequency, Quart. J.
Mech. Appl.
Math. 47 (1994), 1-15
(with A. Kirsch).
105. Eigenvalues of the far field
operator and inverse scattering theory, SIAM J. Math Anal., 26
(1995),
601-615 (with R. Kress).
106. Eigenvalues of the far field
operator for the Helmholtz equation in an absorbing medium, SIAM J.
Appl.
Math., 55 (1995),
1724-1735 (with R. Kress).
107. A modified dual space method
for solving the electromagnetic inverse scattering problem for an
infinite
cylinder, Inverse Problems, 10
(1994), 87-107 (with P.
Monk).
108. The detection and monitoring
of leukemia using electromagnetic waves: mathematical theory, Inverse
Problems 10 (1994),
1235-1251 (with P. Monk).
109. A new approach to detecting
leukemia: using computational electromagnetics, IEEE Comp. Science
and
Engineering, 2 (1995), 46-52 (with P. Monk).
110. The detection and monitoring
of leukemia using electromagnetic waves: numerical analysis, Inverse
Problems 11 (1995),
329-342 (with P. Monk).
111. A new algorithm in
electromagnetic inverse scattering theory with an application to
medical
imaging, Math Methods Applied Science, 20 (1997), 385-401 (with
R. Kress
and P. Monk).
112. A simple method for solving
inverse scattering problems in the resonance region, Inverse
Problems, 12
(1996), 383-393 (with A. Kirsch).
113. A linear sampling method for
the detection of leukemia using microwaves, SIAM J. Applied Math.,
58
(1998), 926-941 (with P. Monk).
114. A simple method using
Morozov's discrepancy principle for solving inverse scattering
problems, Inverse
Problems, 13 (1997), 1477-1493 (with M. Piana and R.
Potthast).
115. Inverse scattering from an
orthotropic medium, J. Comp. Appl. Math., 81 (1997),
269-298
(with R. Kress and P. Monk).
116. The simple method for
solving the electromagnetic inverse scattering problem: the case of TE
polarized waves, Inverse Problems, 14 (1998), 597-614
(with M.
Piana).
117. The inverse electromagnetic
scattering problem for an anisotropic medium, Quart. J. Mech. Appl.
Math.
52 (1999), 349-372 (with R. Potthast).
118. A regularized sampling
method for solving three dimensional inverse scattering problems, SIAM
J.
Scientific
Computation, 21 (2000), 2316-2330 (with K.
Giebermann and
P. Monk).
119. A linear sampling method for
the detection of leukemia using microwaves II, SIAM J. Applied
Math., 60
(1999), 241-255 (with P. Monk).
120. Transmission eigenvalues and
a problem of Hans Lewy, J. Comp. Appl. Math., 117
(2000), 91-104
(with L. Päivärinta).
121. Recent developments in
inverse acoustic scattering theory, SIAM Review, 42
(2000),
369-414 (with J. Coyle and P. Monk).
122. An approximation property of
importance in inverse scattering theory, Proc. Edinburgh Math. Soc.,
44
(2001), 449-454 (with B. D. Sleeman).
123. Inequalities for inverse
scattering problems in absorbing media, Inverse Problems, 17
(2001),
597-605 (with M. Piana).
124. The direct and inverse
scattering problems for partially coated obstacles, Inverse Problems,
17
(2001), 1997-2015 (with F. Cakoni and P. Monk).
125. On the denseness of Herglotz
wave functions and electromagnetic Herglotz pairs in Sobolev spaces, Math.
Methods
Applied
Science, 24 (2001), 1289-1303 (with R.
Kress).
126. Mathematical and numerical
methods in inverse acoustic scattering theory, Zeit. Ang. Math.
Mech., 81
(2001), 723-731 (with P. Monk).
127. The linear sampling method
for anisotropic media, J. Comp. Appl. Math., 146 (2002),
285-299
(with
F.
Cakoni and H. Haddar).
128. The linear sampling method
for solving the electromagnetic inverse scattering problem, SIAM J.
Scientific Computation, 24 (2002), 719-731 (with H.
Haddar and
P. Monk).
129. Combined far field operators
in electromagnetic inverse scattering theory, Math. Methods Applied
Science, 26 (2003), 413-429 (with F. Cakoni).
131. On the mathematical basis of the linear sampling method, Georgian
Mathematical
Journal, 10 (2003), 411-425 (with
F. Cakoni).
133. A uniqueness theorem for an
inverse electromagnetic scattering problem in inhomogeneous anisotropic
media, Proc.
Edinburgh Math. Soc. 46 (2003), 293-314 (with
F. Cakoni).
134. The linear sampling method in
inverse electromagnetic scattering theory, Inverse Problems, 19,
(2003),
105-137 (with H. Haddar
and M. Piana).
135. The determination of the surface impedance of a partially coated obstacle from far field data, SIAM J. Appl. Math., 64 (2004), 709-723 (with F. Cakoni).
136. The electromagnetic inverse
scattering problem for partially coated Lipschitz domains, Proc.
Royal Soc.
Edinburgh, 134A (2004),
661-682
(with
F. Cakoni and P. Monk).
137. A target signature for distinguishing perfect conductors from anisotropic media of finite conductivity, Math. Comp. Sim. 66 (2004), 325-335 (with F. Cakoni).
138. The determination of the surface conductivity of a partially
coated
dielectric, SIAM J. Appl. Math. 65 (2005), 767-789
(with F. Cakoni and
P.
Monk).
140. Open problems in the qualitative approach to inverse electromagnetic scattering theory, European Jour. Appl. Math. 16 (2005), 411- 425 (with F. Cakoni).
141. Target identification of coated objects, IEEE Transactions on Antennas and Propagation 54 (2006), 1232 - 1242 (with P. Monk).
142. Target identification of burried objects, Comp. Appl. Math., 25 (2006), 269-288 (with F. Cakoni).
143. Using fundamental solutions in inverse scattering, Inverse Problems 22 (2006), R49 - R66 (with R.Kress).
144. The inverse electromagnetic scattering problem for a partially coated dielectric, J. Comp. Appl. Math., 204 (2007), 256-267 (with F. Cakoni and P. Monk).
145. The interior transmission problem, Inverse Problems and Imaging, 1 (2007), 13-28 (with L. Paivarinta and J. Sylvester).
146. On the use of transmission eigenvalues to estimate the index of refraction from far field data, Inverse Problems, 23 (2007), 507-522 (with F. Cakoni and P. Monk).
147. Inequalities in inverse scattering theory, Inverse and Ill-posed Problems, 15 (2007), 483-491 (with F. Cakoni).
148. Transmission eigenvalues and the nondestructive testing of dielectrics, Inverse Problems, 24 (2008) 065016 (with F. Cakoni and M. Cayoren).
149. The computation of lower bounds for the norm of the index of refraction in an anisotropic media from far field data, Jour. Integral Equations and Applications, 21 (2009), 203-227 (with F. Cakoni and H. Haddar).
150. The determination of boundary coefficients from far field measurements, Jour. Integral Equations and Applications, 22 (2010), 167-191 (with F. Cakoni and P. Monk).
151. The interior transmission problem for regions with cavities, SIAM J. Math. Anal., 42 (2010), 145-162 (with F. Cakoni and H. Haddar).
152. On the determination of Dirichlet or transmission eigenvalues from far field data, Compte Rendues Mathematique, 348 (2010), 379-383 (with F. Cakoni and H. Haddar).
153. Analytical and computational methods for transmisson eigenvalues, Inverse Problems, 26 (2010), 045011 (with P. Monk and J. Sun).
154. The inverse electromagnetic scattering problem for anisostropic media, Inverse Problems, 26 (2010), 074004 (with F. Cakoni, P. Monk and J. Sun).
155. The inverse scattering problem for cavities, Applied Numerical Mathematics, to appear (with H. Qin).
156. The inverse scattering problem for cavities with impedance boundary condition, Advances in Computational Mathematics, to appear (with H. Qin).
157. The interior transmission eigenvalue problem, SIAM J. Math. Anal., 42 (2010), 2912-2921 (with F. Cakoni and D. Gintides).