A Personal Mathematical History I wasn’t always a mathematician
Institute for Fluid Dynamics and Applied Mathematics 1961-65
Assistant Professor and Associate Professor Indiana University
Bloomington, Professor 1966-75 Analytic Methods in Mathematical
Physics My First Monograph Generalized Hyperanalytic Function
Theory The Georgians Free University Berlin and the Hahn-Meitner
Institute 1974-75 University of Delaware, Unidel Professor 1975
Some Work in Elasticity, etc. I visit China for the First Time,
1984 Research in Underwater Acoustics The 65th Birthday Conference
in Graz The Cold War Ends: No More Underwater Acoustics The Birth
of ISAAC I am 63 and I begin to work in Homogenization My 70th
Birthday Conference in Frejus, France The
75thBirthdayConferenceinOrlando Medical Mathematics
A Personal Mathematical History
Robert Pertsch-Rusterholz Gilbert Department of Mathematics
A Personal Mathematical History I wasn’t always a mathematician
Institute for Fluid Dynamics and Applied Mathematics 1961-65
Assistant Professor and Associate Professor Indiana University
Bloomington, Professor 1966-75 Analytic Methods in Mathematical
Physics My First Monograph Generalized Hyperanalytic Function
Theory The Georgians Free University Berlin and the Hahn-Meitner
Institute 1974-75 University of Delaware, Unidel Professor 1975
Some Work in Elasticity, etc. I visit China for the First Time,
1984 Research in Underwater Acoustics The 65th Birthday Conference
in Graz The Cold War Ends: No More Underwater Acoustics The Birth
of ISAAC I am 63 and I begin to work in Homogenization My 70th
Birthday Conference in Frejus, France The
75thBirthdayConferenceinOrlando Medical Mathematics
I wasn’t always a mathematician
Originally I was a student of physics and obtained a BSc and MSc in
Physics before switching to mathematics. The cause was the
Heisenberg Uncertainty Principle, which led me to write to Albert
Einstein about my uncertainty about Uncertainty. After switching to
the Mathematics Department I worked on a project with Hirsh Cohen
and it resulted in a paper. Hirsh left Carnegie for Rennselaer. I
began working with Zeev Nehari, who had recently joined the
Department from Washington University. This was professionally a
good move, as Zeev Nehari was one of the preeminent complex
analysts during the 1950s.
A Personal Mathematical History I wasn’t always a mathematician
Institute for Fluid Dynamics and Applied Mathematics 1961-65
Assistant Professor and Associate Professor Indiana University
Bloomington, Professor 1966-75 Analytic Methods in Mathematical
Physics My First Monograph Generalized Hyperanalytic Function
Theory The Georgians Free University Berlin and the Hahn-Meitner
Institute 1974-75 University of Delaware, Unidel Professor 1975
Some Work in Elasticity, etc. I visit China for the First Time,
1984 Research in Underwater Acoustics The 65th Birthday Conference
in Graz The Cold War Ends: No More Underwater Acoustics The Birth
of ISAAC I am 63 and I begin to work in Homogenization My 70th
Birthday Conference in Frejus, France The
75thBirthdayConferenceinOrlando Medical Mathematics
A Personal Mathematical History I wasn’t always a mathematician
Institute for Fluid Dynamics and Applied Mathematics 1961-65
Assistant Professor and Associate Professor Indiana University
Bloomington, Professor 1966-75 Analytic Methods in Mathematical
Physics My First Monograph Generalized Hyperanalytic Function
Theory The Georgians Free University Berlin and the Hahn-Meitner
Institute 1974-75 University of Delaware, Unidel Professor 1975
Some Work in Elasticity, etc. I visit China for the First Time,
1984 Research in Underwater Acoustics The 65th Birthday Conference
in Graz The Cold War Ends: No More Underwater Acoustics The Birth
of ISAAC I am 63 and I begin to work in Homogenization My 70th
Birthday Conference in Frejus, France The
75thBirthdayConferenceinOrlando Medical Mathematics
This is the paper with Hirsh Cohen on free-boundary problems, an
area I would return to after many years.
A Personal Mathematical History I wasn’t always a mathematician
Institute for Fluid Dynamics and Applied Mathematics 1961-65
Assistant Professor and Associate Professor Indiana University
Bloomington, Professor 1966-75 Analytic Methods in Mathematical
Physics My First Monograph Generalized Hyperanalytic Function
Theory The Georgians Free University Berlin and the Hahn-Meitner
Institute 1974-75 University of Delaware, Unidel Professor 1975
Some Work in Elasticity, etc. I visit China for the First Time,
1984 Research in Underwater Acoustics The 65th Birthday Conference
in Graz The Cold War Ends: No More Underwater Acoustics The Birth
of ISAAC I am 63 and I begin to work in Homogenization My 70th
Birthday Conference in Frejus, France The
75thBirthdayConferenceinOrlando Medical Mathematics
For my PhD thesis I used Integral Operator Methods, a le Stefan
Bergman, which were used to determine the analytic and singular
behavior of various classes of elliptic partial differential
equations. The Bergman-Whittaker Operator generates harmonic
functions in R3,
H(X) = B3(f ) :=
ζ ,
from functions of two complex variable f (u, ζ), where X = (x1, x2,
x3), u = x1 (ζ − 1/ζ) + ix2 (ζ + 1/ζ) + x3 is an auxillary variable
and C is a contour in C1. I proved necessary and sufficient
conditions for H(X) to be singular in terms of its analytic
associate.
A Personal Mathematical History I wasn’t always a mathematician
Institute for Fluid Dynamics and Applied Mathematics 1961-65
Assistant Professor and Associate Professor Indiana University
Bloomington, Professor 1966-75 Analytic Methods in Mathematical
Physics My First Monograph Generalized Hyperanalytic Function
Theory The Georgians Free University Berlin and the Hahn-Meitner
Institute 1974-75 University of Delaware, Unidel Professor 1975
Some Work in Elasticity, etc. I visit China for the First Time,
1984 Research in Underwater Acoustics The 65th Birthday Conference
in Graz The Cold War Ends: No More Underwater Acoustics The Birth
of ISAAC I am 63 and I begin to work in Homogenization My 70th
Birthday Conference in Frejus, France The
75thBirthdayConferenceinOrlando Medical Mathematics
Theorem
Let the defining function for the set of singularities of f (u,
ζ)ζ−1
be a global function in C2. Then if h(u, ζ) := S(X; ζ) = 0 is such
a function we have that H(X) = B3f is regular for all points X
which may be reached by continuation along a curve Γ starting at an
initial point of definition X0, provided X and hence, the curve Γ,
do not lie on the intersection
S := {X : S(X; ζ) = 0} ∩ {X : Sζ(X; ζ) = 0} .
A Personal Mathematical History I wasn’t always a mathematician
Institute for Fluid Dynamics and Applied Mathematics 1961-65
Assistant Professor and Associate Professor Indiana University
Bloomington, Professor 1966-75 Analytic Methods in Mathematical
Physics My First Monograph Generalized Hyperanalytic Function
Theory The Georgians Free University Berlin and the Hahn-Meitner
Institute 1974-75 University of Delaware, Unidel Professor 1975
Some Work in Elasticity, etc. I visit China for the First Time,
1984 Research in Underwater Acoustics The 65th Birthday Conference
in Graz The Cold War Ends: No More Underwater Acoustics The Birth
of ISAAC I am 63 and I begin to work in Homogenization My 70th
Birthday Conference in Frejus, France The
75thBirthdayConferenceinOrlando Medical Mathematics
Figure: Zeev Nehari, nee Wili Weissbach
A Personal Mathematical History I wasn’t always a mathematician
Institute for Fluid Dynamics and Applied Mathematics 1961-65
Assistant Professor and Associate Professor Indiana University
Bloomington, Professor 1966-75 Analytic Methods in Mathematical
Physics My First Monograph Generalized Hyperanalytic Function
Theory The Georgians Free University Berlin and the Hahn-Meitner
Institute 1974-75 University of Delaware, Unidel Professor 1975
Some Work in Elasticity, etc. I visit China for the First Time,
1984 Research in Underwater Acoustics The 65th Birthday Conference
in Graz The Cold War Ends: No More Underwater Acoustics The Birth
of ISAAC I am 63 and I begin to work in Homogenization My 70th
Birthday Conference in Frejus, France The
75thBirthdayConferenceinOrlando Medical Mathematics
Figure: Graduation, Carnegie-Mellon 1958
A Personal Mathematical History I wasn’t always a mathematician
Institute for Fluid Dynamics and Applied Mathematics 1961-65
Assistant Professor and Associate Professor Indiana University
Bloomington, Professor 1966-75 Analytic Methods in Mathematical
Physics My First Monograph Generalized Hyperanalytic Function
Theory The Georgians Free University Berlin and the Hahn-Meitner
Institute 1974-75 University of Delaware, Unidel Professor 1975
Some Work in Elasticity, etc. I visit China for the First Time,
1984 Research in Underwater Acoustics The 65th Birthday Conference
in Graz The Cold War Ends: No More Underwater Acoustics The Birth
of ISAAC I am 63 and I begin to work in Homogenization My 70th
Birthday Conference in Frejus, France The
75thBirthdayConferenceinOrlando Medical Mathematics
Using the methods of projective differential geometry we were able
to prove, among other results,
Theorem
Let H(X) be a harmonic function given by H(X) = B3f where the
singulaities of f (u, ζ) have a global representation, h(u, ζ) :=
ζu − φ(ζ) = 0. Then the singularities of H(X) must lie on a
develople in P. Further, if φ(ζ) is a polynomial of degree n, n
> 2, then the singularities are twisted nth degree (complex)
space curves.
A Personal Mathematical History I wasn’t always a mathematician
Institute for Fluid Dynamics and Applied Mathematics 1961-65
Assistant Professor and Associate Professor Indiana University
Bloomington, Professor 1966-75 Analytic Methods in Mathematical
Physics My First Monograph Generalized Hyperanalytic Function
Theory The Georgians Free University Berlin and the Hahn-Meitner
Institute 1974-75 University of Delaware, Unidel Professor 1975
Some Work in Elasticity, etc. I visit China for the First Time,
1984 Research in Underwater Acoustics The 65th Birthday Conference
in Graz The Cold War Ends: No More Underwater Acoustics The Birth
of ISAAC I am 63 and I begin to work in Homogenization My 70th
Birthday Conference in Frejus, France The
75thBirthdayConferenceinOrlando Medical Mathematics
The above results were generalized to harmonic functions in
R4
using the operator
H(X) = G4f := − 1
η f (τ, ξ, η) X; = (x1, x2, x3, x4)
where f is a holomorphic function of three complex variables
and
τ := x1(1 + 1
1
ξ +
1
η ).
Here the curves Ck are homologous to zero. Kreyzig inverted this
operator and referred to G4 as Gilbert’s operator. Using Kreyzig’s
inversion the entire three-dimensional theory was carried over to
either R4 or C4.
A Personal Mathematical History I wasn’t always a mathematician
Institute for Fluid Dynamics and Applied Mathematics 1961-65
Assistant Professor and Associate Professor Indiana University
Bloomington, Professor 1966-75 Analytic Methods in Mathematical
Physics My First Monograph Generalized Hyperanalytic Function
Theory The Georgians Free University Berlin and the Hahn-Meitner
Institute 1974-75 University of Delaware, Unidel Professor 1975
Some Work in Elasticity, etc. I visit China for the First Time,
1984 Research in Underwater Acoustics The 65th Birthday Conference
in Graz The Cold War Ends: No More Underwater Acoustics The Birth
of ISAAC I am 63 and I begin to work in Homogenization My 70th
Birthday Conference in Frejus, France The
75thBirthdayConferenceinOrlando Medical Mathematics
Figure: Erwin Kreyzig
A Personal Mathematical History I wasn’t always a mathematician
Institute for Fluid Dynamics and Applied Mathematics 1961-65
Assistant Professor and Associate Professor Indiana University
Bloomington, Professor 1966-75 Analytic Methods in Mathematical
Physics My First Monograph Generalized Hyperanalytic Function
Theory The Georgians Free University Berlin and the Hahn-Meitner
Institute 1974-75 University of Delaware, Unidel Professor 1975
Some Work in Elasticity, etc. I visit China for the First Time,
1984 Research in Underwater Acoustics The 65th Birthday Conference
in Graz The Cold War Ends: No More Underwater Acoustics The Birth
of ISAAC I am 63 and I begin to work in Homogenization My 70th
Birthday Conference in Frejus, France The
75thBirthdayConferenceinOrlando Medical Mathematics
Institute for Fluid Dynamics and Applied Mathematics 1961-65
Assistant Professor and Associate Professor
We were supported by Alexander Weinstein’s AFOSR grant and our NSF
grant to make a systematic investigation of the analytic properties
of solutions to singular, elliptic partial differential equation of
the type blow
∂2u
∂x2 +
∂2u
∂y2 +
2µ
y +
∂ u
in two and higher dimensions.
A Personal Mathematical History I wasn’t always a mathematician
Institute for Fluid Dynamics and Applied Mathematics 1961-65
Assistant Professor and Associate Professor Indiana University
Bloomington, Professor 1966-75 Analytic Methods in Mathematical
Physics My First Monograph Generalized Hyperanalytic Function
Theory The Georgians Free University Berlin and the Hahn-Meitner
Institute 1974-75 University of Delaware, Unidel Professor 1975
Some Work in Elasticity, etc. I visit China for the First Time,
1984 Research in Underwater Acoustics The 65th Birthday Conference
in Graz The Cold War Ends: No More Underwater Acoustics The Birth
of ISAAC I am 63 and I begin to work in Homogenization My 70th
Birthday Conference in Frejus, France The
75thBirthdayConferenceinOrlando Medical Mathematics
We developed the so-called envelope method which was applied to
potential scattering and to quantum field theory by Gilbert with
Aks, Howard and Shieh.
A Personal Mathematical History I wasn’t always a mathematician
Institute for Fluid Dynamics and Applied Mathematics 1961-65
Assistant Professor and Associate Professor Indiana University
Bloomington, Professor 1966-75 Analytic Methods in Mathematical
Physics My First Monograph Generalized Hyperanalytic Function
Theory The Georgians Free University Berlin and the Hahn-Meitner
Institute 1974-75 University of Delaware, Unidel Professor 1975
Some Work in Elasticity, etc. I visit China for the First Time,
1984 Research in Underwater Acoustics The 65th Birthday Conference
in Graz The Cold War Ends: No More Underwater Acoustics The Birth
of ISAAC I am 63 and I begin to work in Homogenization My 70th
Birthday Conference in Frejus, France The
75thBirthdayConferenceinOrlando Medical Mathematics
Figure: Expansions of analytic functions
A Personal Mathematical History I wasn’t always a mathematician
Institute for Fluid Dynamics and Applied Mathematics 1961-65
Assistant Professor and Associate Professor Indiana University
Bloomington, Professor 1966-75 Analytic Methods in Mathematical
Physics My First Monograph Generalized Hyperanalytic Function
Theory The Georgians Free University Berlin and the Hahn-Meitner
Institute 1974-75 University of Delaware, Unidel Professor 1975
Some Work in Elasticity, etc. I visit China for the First Time,
1984 Research in Underwater Acoustics The 65th Birthday Conference
in Graz The Cold War Ends: No More Underwater Acoustics The Birth
of ISAAC I am 63 and I begin to work in Homogenization My 70th
Birthday Conference in Frejus, France The
75thBirthdayConferenceinOrlando Medical Mathematics
Indiana University Bloomington, Professor 1966-75
I am all of 34 and Full Professor at Indiana University. I have an
AFOSR grant which is supporting, in addition to me, David Colton,
Lucio Tavernini and Kendall Atkinson. I start the journal
Applicable Analysis.
Figure: Kendal Atkinson and Lothar Collatz. During the 1960s
Collatz was the premier numerical analyst in Germany.
A Personal Mathematical History I wasn’t always a mathematician
Institute for Fluid Dynamics and Applied Mathematics 1961-65
Assistant Professor and Associate Professor Indiana University
Bloomington, Professor 1966-75 Analytic Methods in Mathematical
Physics My First Monograph Generalized Hyperanalytic Function
Theory The Georgians Free University Berlin and the Hahn-Meitner
Institute 1974-75 University of Delaware, Unidel Professor 1975
Some Work in Elasticity, etc. I visit China for the First Time,
1984 Research in Underwater Acoustics The 65th Birthday Conference
in Graz The Cold War Ends: No More Underwater Acoustics The Birth
of ISAAC I am 63 and I begin to work in Homogenization My 70th
Birthday Conference in Frejus, France The
75thBirthdayConferenceinOrlando Medical Mathematics
Figure: Sketch of ”Owls” by L. Collatz. Collatz knew I liked owls
and gave me the sketch.
A Personal Mathematical History I wasn’t always a mathematician
Institute for Fluid Dynamics and Applied Mathematics 1961-65
Assistant Professor and Associate Professor Indiana University
Bloomington, Professor 1966-75 Analytic Methods in Mathematical
Physics My First Monograph Generalized Hyperanalytic Function
Theory The Georgians Free University Berlin and the Hahn-Meitner
Institute 1974-75 University of Delaware, Unidel Professor 1975
Some Work in Elasticity, etc. I visit China for the First Time,
1984 Research in Underwater Acoustics The 65th Birthday Conference
in Graz The Cold War Ends: No More Underwater Acoustics The Birth
of ISAAC I am 63 and I begin to work in Homogenization My 70th
Birthday Conference in Frejus, France The
75thBirthdayConferenceinOrlando Medical Mathematics
Figure: Max Schiffer visits us at IU.
A Personal Mathematical History I wasn’t always a mathematician
Institute for Fluid Dynamics and Applied Mathematics 1961-65
Assistant Professor and Associate Professor Indiana University
Bloomington, Professor 1966-75 Analytic Methods in Mathematical
Physics My First Monograph Generalized Hyperanalytic Function
Theory The Georgians Free University Berlin and the Hahn-Meitner
Institute 1974-75 University of Delaware, Unidel Professor 1975
Some Work in Elasticity, etc. I visit China for the First Time,
1984 Research in Underwater Acoustics The 65th Birthday Conference
in Graz The Cold War Ends: No More Underwater Acoustics The Birth
of ISAAC I am 63 and I begin to work in Homogenization My 70th
Birthday Conference in Frejus, France The
75thBirthdayConferenceinOrlando Medical Mathematics
Analytic Methods in Mathematical Physics
In June 1968 Roger Newton and I organized an AFOSR Conference named
Analytic Methods in Mathematical Physics
A Personal Mathematical History I wasn’t always a mathematician
Institute for Fluid Dynamics and Applied Mathematics 1961-65
Assistant Professor and Associate Professor Indiana University
Bloomington, Professor 1966-75 Analytic Methods in Mathematical
Physics My First Monograph Generalized Hyperanalytic Function
Theory The Georgians Free University Berlin and the Hahn-Meitner
Institute 1974-75 University of Delaware, Unidel Professor 1975
Some Work in Elasticity, etc. I visit China for the First Time,
1984 Research in Underwater Acoustics The 65th Birthday Conference
in Graz The Cold War Ends: No More Underwater Acoustics The Birth
of ISAAC I am 63 and I begin to work in Homogenization My 70th
Birthday Conference in Frejus, France The
75thBirthdayConferenceinOrlando Medical Mathematics
In his plenary address Maria v. Krzywoblocki presented a review of
the integral Operator Method as initiated by Bergman and others, me
included.
A Personal Mathematical History I wasn’t always a mathematician
Institute for Fluid Dynamics and Applied Mathematics 1961-65
Assistant Professor and Associate Professor Indiana University
Bloomington, Professor 1966-75 Analytic Methods in Mathematical
Physics My First Monograph Generalized Hyperanalytic Function
Theory The Georgians Free University Berlin and the Hahn-Meitner
Institute 1974-75 University of Delaware, Unidel Professor 1975
Some Work in Elasticity, etc. I visit China for the First Time,
1984 Research in Underwater Acoustics The 65th Birthday Conference
in Graz The Cold War Ends: No More Underwater Acoustics The Birth
of ISAAC I am 63 and I begin to work in Homogenization My 70th
Birthday Conference in Frejus, France The
75thBirthdayConferenceinOrlando Medical Mathematics
Figure: Paul Garabedian and David Widder
A Personal Mathematical History I wasn’t always a mathematician
Institute for Fluid Dynamics and Applied Mathematics 1961-65
Assistant Professor and Associate Professor Indiana University
Bloomington, Professor 1966-75 Analytic Methods in Mathematical
Physics My First Monograph Generalized Hyperanalytic Function
Theory The Georgians Free University Berlin and the Hahn-Meitner
Institute 1974-75 University of Delaware, Unidel Professor 1975
Some Work in Elasticity, etc. I visit China for the First Time,
1984 Research in Underwater Acoustics The 65th Birthday Conference
in Graz The Cold War Ends: No More Underwater Acoustics The Birth
of ISAAC I am 63 and I begin to work in Homogenization My 70th
Birthday Conference in Frejus, France The
75thBirthdayConferenceinOrlando Medical Mathematics
Figure: A. Wheeler and S. Abyankar
A Personal Mathematical History I wasn’t always a mathematician
Institute for Fluid Dynamics and Applied Mathematics 1961-65
Assistant Professor and Associate Professor Indiana University
Bloomington, Professor 1966-75 Analytic Methods in Mathematical
Physics My First Monograph Generalized Hyperanalytic Function
Theory The Georgians Free University Berlin and the Hahn-Meitner
Institute 1974-75 University of Delaware, Unidel Professor 1975
Some Work in Elasticity, etc. I visit China for the First Time,
1984 Research in Underwater Acoustics The 65th Birthday Conference
in Graz The Cold War Ends: No More Underwater Acoustics The Birth
of ISAAC I am 63 and I begin to work in Homogenization My 70th
Birthday Conference in Frejus, France The
75thBirthdayConferenceinOrlando Medical Mathematics
Figure: Bers, Garabedian, Erdelyi, Masani, me
A Personal Mathematical History I wasn’t always a mathematician
Institute for Fluid Dynamics and Applied Mathematics 1961-65
Assistant Professor and Associate Professor Indiana University
Bloomington, Professor 1966-75 Analytic Methods in Mathematical
Physics My First Monograph Generalized Hyperanalytic Function
Theory The Georgians Free University Berlin and the Hahn-Meitner
Institute 1974-75 University of Delaware, Unidel Professor 1975
Some Work in Elasticity, etc. I visit China for the First Time,
1984 Research in Underwater Acoustics The 65th Birthday Conference
in Graz The Cold War Ends: No More Underwater Acoustics The Birth
of ISAAC I am 63 and I begin to work in Homogenization My 70th
Birthday Conference in Frejus, France The
75thBirthdayConferenceinOrlando Medical Mathematics
My First Monograph
I summed up my work to this time with the Academic Press
monograph
Figure: My first monograph, 1969.
A Personal Mathematical History I wasn’t always a mathematician
Institute for Fluid Dynamics and Applied Mathematics 1961-65
Assistant Professor and Associate Professor Indiana University
Bloomington, Professor 1966-75 Analytic Methods in Mathematical
Physics My First Monograph Generalized Hyperanalytic Function
Theory The Georgians Free University Berlin and the Hahn-Meitner
Institute 1974-75 University of Delaware, Unidel Professor 1975
Some Work in Elasticity, etc. I visit China for the First Time,
1984 Research in Underwater Acoustics The 65th Birthday Conference
in Graz The Cold War Ends: No More Underwater Acoustics The Birth
of ISAAC I am 63 and I begin to work in Homogenization My 70th
Birthday Conference in Frejus, France The
75thBirthdayConferenceinOrlando Medical Mathematics
Before leaving the operator approach of Bergman I developed the
Method of Ascent MoA. The method of ascent maps a harmonic function
of two variables onto solutions of a metaharmonic-type
equation.
∂2u
This idea has had applications in potential scattering and
acoustical scattering. Robert Carroll referred to this as the
Bergman-Gilbert Transmutation.
A Personal Mathematical History I wasn’t always a mathematician
Institute for Fluid Dynamics and Applied Mathematics 1961-65
Assistant Professor and Associate Professor Indiana University
Bloomington, Professor 1966-75 Analytic Methods in Mathematical
Physics My First Monograph Generalized Hyperanalytic Function
Theory The Georgians Free University Berlin and the Hahn-Meitner
Institute 1974-75 University of Delaware, Unidel Professor 1975
Some Work in Elasticity, etc. I visit China for the First Time,
1984 Research in Underwater Acoustics The 65th Birthday Conference
in Graz The Cold War Ends: No More Underwater Acoustics The Birth
of ISAAC I am 63 and I begin to work in Homogenization My 70th
Birthday Conference in Frejus, France The
75thBirthdayConferenceinOrlando Medical Mathematics
A Personal Mathematical History I wasn’t always a mathematician
Institute for Fluid Dynamics and Applied Mathematics 1961-65
Assistant Professor and Associate Professor Indiana University
Bloomington, Professor 1966-75 Analytic Methods in Mathematical
Physics My First Monograph Generalized Hyperanalytic Function
Theory The Georgians Free University Berlin and the Hahn-Meitner
Institute 1974-75 University of Delaware, Unidel Professor 1975
Some Work in Elasticity, etc. I visit China for the First Time,
1984 Research in Underwater Acoustics The 65th Birthday Conference
in Graz The Cold War Ends: No More Underwater Acoustics The Birth
of ISAAC I am 63 and I begin to work in Homogenization My 70th
Birthday Conference in Frejus, France The
75thBirthdayConferenceinOrlando Medical Mathematics
Generalized Hyperanalytic Function Theory
I then turned away from the Bergman approach to function theoretic
methods for pde to that of Bers and Vekua. and to the introduction
of an entirely new function theory called Generalized Hyperanalytic
Function Theory GHA.
A Personal Mathematical History I wasn’t always a mathematician
Institute for Fluid Dynamics and Applied Mathematics 1961-65
Assistant Professor and Associate Professor Indiana University
Bloomington, Professor 1966-75 Analytic Methods in Mathematical
Physics My First Monograph Generalized Hyperanalytic Function
Theory The Georgians Free University Berlin and the Hahn-Meitner
Institute 1974-75 University of Delaware, Unidel Professor 1975
Some Work in Elasticity, etc. I visit China for the First Time,
1984 Research in Underwater Acoustics The 65th Birthday Conference
in Graz The Cold War Ends: No More Underwater Acoustics The Birth
of ISAAC I am 63 and I begin to work in Homogenization My 70th
Birthday Conference in Frejus, France The
75thBirthdayConferenceinOrlando Medical Mathematics
The generalized hyperanalytic theory was developed to handle
individual blocks of first order elliptic systems, ie those terms
belonging to a single complex eigenvalue. The GHA functions
satisfiedequations of the type
Du + Au + Bu = F , D := ∂
∂z + q(z)
ekak(z) etc. where e is a
nilpotent such that en = 0. A complete function theory was
developed for this system by Gilbert with Hile, Begehr, Buchanan,
Wendland etc. Bojarski also treated this problem using a different
approach. Gillbert with Buchanan and Wendland used this function
theory to investigate elastic plates and shells.
A Personal Mathematical History I wasn’t always a mathematician
Institute for Fluid Dynamics and Applied Mathematics 1961-65
Assistant Professor and Associate Professor Indiana University
Bloomington, Professor 1966-75 Analytic Methods in Mathematical
Physics My First Monograph Generalized Hyperanalytic Function
Theory The Georgians Free University Berlin and the Hahn-Meitner
Institute 1974-75 University of Delaware, Unidel Professor 1975
Some Work in Elasticity, etc. I visit China for the First Time,
1984 Research in Underwater Acoustics The 65th Birthday Conference
in Graz The Cold War Ends: No More Underwater Acoustics The Birth
of ISAAC I am 63 and I begin to work in Homogenization My 70th
Birthday Conference in Frejus, France The
75thBirthdayConferenceinOrlando Medical Mathematics
A Personal Mathematical History I wasn’t always a mathematician
Institute for Fluid Dynamics and Applied Mathematics 1961-65
Assistant Professor and Associate Professor Indiana University
Bloomington, Professor 1966-75 Analytic Methods in Mathematical
Physics My First Monograph Generalized Hyperanalytic Function
Theory The Georgians Free University Berlin and the Hahn-Meitner
Institute 1974-75 University of Delaware, Unidel Professor 1975
Some Work in Elasticity, etc. I visit China for the First Time,
1984 Research in Underwater Acoustics The 65th Birthday Conference
in Graz The Cold War Ends: No More Underwater Acoustics The Birth
of ISAAC I am 63 and I begin to work in Homogenization My 70th
Birthday Conference in Frejus, France The
75thBirthdayConferenceinOrlando Medical Mathematics
The Georgians
Ilya Vekua invites me to attend the Muskhelishvili Conference in
Tblisi. I meet Ladyshenskya, Mazya and Koshelev and Leray. I
already knew Fichera, Vekua and Oleinik from Maryland.
Figure: Gaetano Fichera with Galina Koshelev
A Personal Mathematical History I wasn’t always a mathematician
Institute for Fluid Dynamics and Applied Mathematics 1961-65
Assistant Professor and Associate Professor Indiana University
Bloomington, Professor 1966-75 Analytic Methods in Mathematical
Physics My First Monograph Generalized Hyperanalytic Function
Theory The Georgians Free University Berlin and the Hahn-Meitner
Institute 1974-75 University of Delaware, Unidel Professor 1975
Some Work in Elasticity, etc. I visit China for the First Time,
1984 Research in Underwater Acoustics The 65th Birthday Conference
in Graz The Cold War Ends: No More Underwater Acoustics The Birth
of ISAAC I am 63 and I begin to work in Homogenization My 70th
Birthday Conference in Frejus, France The
75thBirthdayConferenceinOrlando Medical Mathematics
Figure: Vladimir Mazya and Koshelev
A Personal Mathematical History I wasn’t always a mathematician
Institute for Fluid Dynamics and Applied Mathematics 1961-65
Assistant Professor and Associate Professor Indiana University
Bloomington, Professor 1966-75 Analytic Methods in Mathematical
Physics My First Monograph Generalized Hyperanalytic Function
Theory The Georgians Free University Berlin and the Hahn-Meitner
Institute 1974-75 University of Delaware, Unidel Professor 1975
Some Work in Elasticity, etc. I visit China for the First Time,
1984 Research in Underwater Acoustics The 65th Birthday Conference
in Graz The Cold War Ends: No More Underwater Acoustics The Birth
of ISAAC I am 63 and I begin to work in Homogenization My 70th
Birthday Conference in Frejus, France The
75thBirthdayConferenceinOrlando Medical Mathematics
Free University Berlin and the Hahn-Meitner Institute 1974-75
I spent a sabbatical semester Spring 1974 at the Hahn Meitner
Institute for Nuclear Research in Berlin. The Mathematics group was
headed up by Wolfgang Haack who happens to be Wolfgang Wendland’s
thesis advisor. The possibility to take over the Dinghas Chair at
the Free University opened up and I remained in Berlin for another
year. This time was spent developing the generalized hyperanalytic
function theory with Heinrich Begehr and Manfred Schneider. George
Hsiao and I carry on a midnight vigil writing papers, he in
Darmstadt and me in Berlin. I visit the Soviet Union and the
Georgian Republic again.
A Personal Mathematical History I wasn’t always a mathematician
Institute for Fluid Dynamics and Applied Mathematics 1961-65
Assistant Professor and Associate Professor Indiana University
Bloomington, Professor 1966-75 Analytic Methods in Mathematical
Physics My First Monograph Generalized Hyperanalytic Function
Theory The Georgians Free University Berlin and the Hahn-Meitner
Institute 1974-75 University of Delaware, Unidel Professor 1975
Some Work in Elasticity, etc. I visit China for the First Time,
1984 Research in Underwater Acoustics The 65th Birthday Conference
in Graz The Cold War Ends: No More Underwater Acoustics The Birth
of ISAAC I am 63 and I begin to work in Homogenization My 70th
Birthday Conference in Frejus, France The
75thBirthdayConferenceinOrlando Medical Mathematics
Figure: A paper of mine and George’s and Pat’s in
Rendiconti”.
A Personal Mathematical History I wasn’t always a mathematician
Institute for Fluid Dynamics and Applied Mathematics 1961-65
Assistant Professor and Associate Professor Indiana University
Bloomington, Professor 1966-75 Analytic Methods in Mathematical
Physics My First Monograph Generalized Hyperanalytic Function
Theory The Georgians Free University Berlin and the Hahn-Meitner
Institute 1974-75 University of Delaware, Unidel Professor 1975
Some Work in Elasticity, etc. I visit China for the First Time,
1984 Research in Underwater Acoustics The 65th Birthday Conference
in Graz The Cold War Ends: No More Underwater Acoustics The Birth
of ISAAC I am 63 and I begin to work in Homogenization My 70th
Birthday Conference in Frejus, France The
75thBirthdayConferenceinOrlando Medical Mathematics
I visit the Humboldt Universiy and Martin Luther University and
begin to lecture in German.
Figure: Christian Vidic, Hahn-Meitner Institute
Figure: Wolfgag Tutschke and Naas at Humboldt University
A Personal Mathematical History I wasn’t always a mathematician
Institute for Fluid Dynamics and Applied Mathematics 1961-65
Assistant Professor and Associate Professor Indiana University
Bloomington, Professor 1966-75 Analytic Methods in Mathematical
Physics My First Monograph Generalized Hyperanalytic Function
Theory The Georgians Free University Berlin and the Hahn-Meitner
Institute 1974-75 University of Delaware, Unidel Professor 1975
Some Work in Elasticity, etc. I visit China for the First Time,
1984 Research in Underwater Acoustics The 65th Birthday Conference
in Graz The Cold War Ends: No More Underwater Acoustics The Birth
of ISAAC I am 63 and I begin to work in Homogenization My 70th
Birthday Conference in Frejus, France The
75thBirthdayConferenceinOrlando Medical Mathematics
Figure: My father who is my present age visits me in Berlin in
Spring 1974.
A Personal Mathematical History I wasn’t always a mathematician
Institute for Fluid Dynamics and Applied Mathematics 1961-65
Assistant Professor and Associate Professor Indiana University
Bloomington, Professor 1966-75 Analytic Methods in Mathematical
Physics My First Monograph Generalized Hyperanalytic Function
Theory The Georgians Free University Berlin and the Hahn-Meitner
Institute 1974-75 University of Delaware, Unidel Professor 1975
Some Work in Elasticity, etc. I visit China for the First Time,
1984 Research in Underwater Acoustics The 65th Birthday Conference
in Graz The Cold War Ends: No More Underwater Acoustics The Birth
of ISAAC I am 63 and I begin to work in Homogenization My 70th
Birthday Conference in Frejus, France The
75thBirthdayConferenceinOrlando Medical Mathematics
University of Delaware, Unidel Professor 1975
I am 43 and Unidel Professor. The AFOSR allows me to transfer the
grant to Delaware. The grant supports my work on generalized
hyperanalytic functions and elasticity and David Colton’s work on
scattering. Alan Jeffrey and I had a DOE grant here also for a
while. I become interested in Underwater Acoustics after spending a
summer the Naval Underwater Systems Center in New London, CT. I had
served on David Wood’s PhD committee at the University of Rhode
Island. David had done work on the Function Theoretic Method for
his thesis. This leads to support from NOAH and NSF for this
research. David Wood and I wrote a paper on the use of
transmutations in underwater acoustics and provided some propagator
representations. These were representations in a stratified,
acoustic wave guide. This work was continued by me with Steve Xu
and published jointly in what now is a well cited set of
articles.
A Personal Mathematical History I wasn’t always a mathematician
Institute for Fluid Dynamics and Applied Mathematics 1961-65
Assistant Professor and Associate Professor Indiana University
Bloomington, Professor 1966-75 Analytic Methods in Mathematical
Physics My First Monograph Generalized Hyperanalytic Function
Theory The Georgians Free University Berlin and the Hahn-Meitner
Institute 1974-75 University of Delaware, Unidel Professor 1975
Some Work in Elasticity, etc. I visit China for the First Time,
1984 Research in Underwater Acoustics The 65th Birthday Conference
in Graz The Cold War Ends: No More Underwater Acoustics The Birth
of ISAAC I am 63 and I begin to work in Homogenization My 70th
Birthday Conference in Frejus, France The
75thBirthdayConferenceinOrlando Medical Mathematics
Some people at and passing through Delaware during my first few
years here.
Figure: Gary Roach and Sam Nadler Figure: Dick Weinacht
A Personal Mathematical History I wasn’t always a mathematician
Institute for Fluid Dynamics and Applied Mathematics 1961-65
Assistant Professor and Associate Professor Indiana University
Bloomington, Professor 1966-75 Analytic Methods in Mathematical
Physics My First Monograph Generalized Hyperanalytic Function
Theory The Georgians Free University Berlin and the Hahn-Meitner
Institute 1974-75 University of Delaware, Unidel Professor 1975
Some Work in Elasticity, etc. I visit China for the First Time,
1984 Research in Underwater Acoustics The 65th Birthday Conference
in Graz The Cold War Ends: No More Underwater Acoustics The Birth
of ISAAC I am 63 and I begin to work in Homogenization My 70th
Birthday Conference in Frejus, France The
75thBirthdayConferenceinOrlando Medical Mathematics
Figure: Pat Brown, David Colton, Alan Jeffrey
A Personal Mathematical History I wasn’t always a mathematician
Institute for Fluid Dynamics and Applied Mathematics 1961-65
Assistant Professor and Associate Professor Indiana University
Bloomington, Professor 1966-75 Analytic Methods in Mathematical
Physics My First Monograph Generalized Hyperanalytic Function
Theory The Georgians Free University Berlin and the Hahn-Meitner
Institute 1974-75 University of Delaware, Unidel Professor 1975
Some Work in Elasticity, etc. I visit China for the First Time,
1984 Research in Underwater Acoustics The 65th Birthday Conference
in Graz The Cold War Ends: No More Underwater Acoustics The Birth
of ISAAC I am 63 and I begin to work in Homogenization My 70th
Birthday Conference in Frejus, France The
75thBirthdayConferenceinOrlando Medical Mathematics
Figure: Tom Angell Figure: George Hsiao
A Personal Mathematical History I wasn’t always a mathematician
Institute for Fluid Dynamics and Applied Mathematics 1961-65
Assistant Professor and Associate Professor Indiana University
Bloomington, Professor 1966-75 Analytic Methods in Mathematical
Physics My First Monograph Generalized Hyperanalytic Function
Theory The Georgians Free University Berlin and the Hahn-Meitner
Institute 1974-75 University of Delaware, Unidel Professor 1975
Some Work in Elasticity, etc. I visit China for the First Time,
1984 Research in Underwater Acoustics The 65th Birthday Conference
in Graz The Cold War Ends: No More Underwater Acoustics The Birth
of ISAAC I am 63 and I begin to work in Homogenization My 70th
Birthday Conference in Frejus, France The
75thBirthdayConferenceinOrlando Medical Mathematics
Some Work in Elasticity, etc.
A reactive shock in a polytropic gas, J. Math. Analysis &
Applications 89 (1982), 193-202 (with A. Jeffrey).
Function theoretic solutions to problems of orthotropic elasticity
Journal of Elasticity 15 (1985) 143-154.(with Lin)
The two dimensional linear, orthotropic plate: The traction
problem, Math. Methods Appl. Scis. 8 (1986), 102-116 ( M.
Schneider). GSch= 11
The boundary integral method for two dimensional orthotropic
materials, Journal of Elasticity (with R. Magnanini) J. Elasticity
18 (1987) 61-82. GSch= 12
Nonisothermal, nonnewtonial Hele-Shaw flows, Part II: Asymptotics
and existence of weak solutions, Nonlinear Analysis 27(1996)
539-559. (with P. Shi).
A Personal Mathematical History I wasn’t always a mathematician
Institute for Fluid Dynamics and Applied Mathematics 1961-65
Assistant Professor and Associate Professor Indiana University
Bloomington, Professor 1966-75 Analytic Methods in Mathematical
Physics My First Monograph Generalized Hyperanalytic Function
Theory The Georgians Free University Berlin and the Hahn-Meitner
Institute 1974-75 University of Delaware, Unidel Professor 1975
Some Work in Elasticity, etc. I visit China for the First Time,
1984 Research in Underwater Acoustics The 65th Birthday Conference
in Graz The Cold War Ends: No More Underwater Acoustics The Birth
of ISAAC I am 63 and I begin to work in Homogenization My 70th
Birthday Conference in Frejus, France The
75thBirthdayConferenceinOrlando Medical Mathematics
Journal of Elasticity 15 (1985) 143-154. © 1985 Martinus Nijhoff
Publishers, Dordrecht. Printed in The Netherlands.
Function theoretic solutions to problems of orthotropic elasticity
* R O B E R T P. GILBERT 1,** and L I N W E I 2
J Department of Mathematics, University of Delaware, Newark, DE
19711, USA 2 Zhongshan University, Guangzhou, People's Republic of
China
(Received October 18, 1983)
Abstract The plane strain problem for a two dimensional orthotropic
elastic body is investigated. In particular analytic
representations for the solution of the displacement boundary value
problem and the stress boundary value problems are found. To this
end, the Navier equations are reducrd by means of composite
transformations to normal form. These are the so-called equations
for bianalytic function of the type (hk). The generalized Cauchy
integral formula for this function theory is used to obtain
representation formulae. A simplified method to solve these
problems by bianalytic function theory is given for certain
situations of plane strain for an orthotropic elastic body. AMS
(MOS): 35A20, 35CO5, 35G15, 35J55.
1. Introduction Funct ion theoretic methods for second order
elliptic systems have been investigated by H u a Loo Keng [1], [2]
and his coworkers. These results are well known in the east;
however, for the benefi t of western readers we shall present as
prel iminaries a short in t roduct ion to these ideas.
Let us consider the following second order system
32 32 C 3---~-2 ] ( u ] = 0 , (1.1) A ~ x 2 + 2B 3 - ~ y + 3 y 2 j
\ v l
where A, B, C are constant 2 × 2 real matrices. We shall refer to
this system as elliptic if the characterist ic equat ion IA~ 2 =
2B~ + C I = 0 possesses only complex eigenvalues. W h e n this
characterist ic equat ion has two mult iple (complex) eigenvalues
the system (1.1) m a y be reduced to the canonical fo rm El:
3 [ (1 0 ) ~ x + ( 0 0~)3_%][ i3_~+(0 1 3 0 0 ) ~ y ] ( U ) = 0,
(1.2)
for ~ 4= 0, - 1. This factors into the first-order system
1 0 ) ~ x + ( 0 - 1 ) ~ y ] ( U ) = ( O ) [ ( 0 1 1 0 ' (1.3)
[(01 -~)~x+( ° 0~)~y](0) = ° o
* Applied Mathematics Institute Technical Report No. 140A, July
1983. ** The work of this author was supported in part by grant no.
DE-AC01-81ER-10967 from the Department
of Energy.
143
A Personal Mathematical History I wasn’t always a mathematician
Institute for Fluid Dynamics and Applied Mathematics 1961-65
Assistant Professor and Associate Professor Indiana University
Bloomington, Professor 1966-75 Analytic Methods in Mathematical
Physics My First Monograph Generalized Hyperanalytic Function
Theory The Georgians Free University Berlin and the Hahn-Meitner
Institute 1974-75 University of Delaware, Unidel Professor 1975
Some Work in Elasticity, etc. I visit China for the First Time,
1984 Research in Underwater Acoustics The 65th Birthday Conference
in Graz The Cold War Ends: No More Underwater Acoustics The Birth
of ISAAC I am 63 and I begin to work in Homogenization My 70th
Birthday Conference in Frejus, France The
75thBirthdayConferenceinOrlando Medical Mathematics
A Personal Mathematical History I wasn’t always a mathematician
Institute for Fluid Dynamics and Applied Mathematics 1961-65
Assistant Professor and Associate Professor Indiana University
Bloomington, Professor 1966-75 Analytic Methods in Mathematical
Physics My First Monograph Generalized Hyperanalytic Function
Theory The Georgians Free University Berlin and the Hahn-Meitner
Institute 1974-75 University of Delaware, Unidel Professor 1975
Some Work in Elasticity, etc. I visit China for the First Time,
1984 Research in Underwater Acoustics The 65th Birthday Conference
in Graz The Cold War Ends: No More Underwater Acoustics The Birth
of ISAAC I am 63 and I begin to work in Homogenization My 70th
Birthday Conference in Frejus, France The
75thBirthdayConferenceinOrlando Medical Mathematics
Journal of Elasticity 22: 81-93, 1989. © 1989 Kluwer Academic
Publishers. Printed in the Netherlands. 81
A function theory for thin elastic shells
R O B E R T P. G I L B E R T & Y O N G Z H I XU Department of
Mathematical Sciences, University of Delaware, Newark, DE 19717,
USA
Received 16 November 1987
Abstract. It is well known in the theory of elastic shells that a
first order approximation using the shell thickness as an expansion
parameter leads to the membrane theory of shells. The membrane
equations have as solutions the generalized analytic functions.
These functions have been exhaus- tively studied by Ilya N. Vekua
[6], [7] and his students. R.P. Gilbert and J. Hile [3] introduced
an extension of these systems to include elliptic systems of 2n
equations in the plane and named the solutions of these systems
generalized hyperanalytic functions.
It is shown in this paper that the next order approximation to the
shell, which permits, moreover, the introduction of bending, may be
described in terms of the generalized hyperanalytic functions. It
is strongly suspected that the higher order approximations may also
be described in terms of corresponding hypercomplex systems.
1. Notation and formulation
In this work we follow the notation used by Dikmen [1]; we view a
shell as a
three dimensional body, which we try to reduce to two dimensional
consider-
ation by introducing a suitable reference surface. A set of
curvilinear coordi-
nates 0 i, (i = 1, 2, 3) are chosen so that a reference surface
within the shell may be represented by 0 3 = 0. For purposes of
defining our notation let a be a
surface embedded in R 3 which we represent in the form r = r(0~).
The vectors
a~ .'=r~ = (ar)/(O0 ~) are the base vectors. The first fundamental
form of the surface is given by a~p d0~d0 a where the a~a.-=a~ "ap
are the covariant
components of the metric tensor. I f the .4 ~p are the cofactors of
the a~p we define the contravariant metric tensor as a~a:=.4~a/a
where a is the determi-
nant of a~p. The second fundamental form of the surface is defined
through
b~ a dO ~ d0a:= a3 • a~,a dO ~ d0 a = - d r " da3, with a3 = (al ×
a2)/([al )< a2l). The Christoffel symbols are given as usual by
. i F~a ~ .= ~(a~,a + ap~,~ - a~a,~ ), and covariant
differentiation is defined by
, r'~ Tx. (1.1) T~I := T~ -
The position vector of a generic point on the shell at time t is
given by x = x(O ~, ~, t) where (0 l, 0 2) ~ i'~ is a point on the
reference surface and
~ [0, h], in particular x(O ~, O, t ) = r(O~, t). The methods of
Dikmen [1] and
A Personal Mathematical History I wasn’t always a mathematician
Institute for Fluid Dynamics and Applied Mathematics 1961-65
Assistant Professor and Associate Professor Indiana University
Bloomington, Professor 1966-75 Analytic Methods in Mathematical
Physics My First Monograph Generalized Hyperanalytic Function
Theory The Georgians Free University Berlin and the Hahn-Meitner
Institute 1974-75 University of Delaware, Unidel Professor 1975
Some Work in Elasticity, etc. I visit China for the First Time,
1984 Research in Underwater Acoustics The 65th Birthday Conference
in Graz The Cold War Ends: No More Underwater Acoustics The Birth
of ISAAC I am 63 and I begin to work in Homogenization My 70th
Birthday Conference in Frejus, France The
75thBirthdayConferenceinOrlando Medical Mathematics
A function theory for thin elastic shells, Journal of Elasticity
22:81-93, (1989). ( with Xu).
Wavelet solutions for time harmonic acoustic waves in a finite
ocean, J. Comp. Acoustics,1(1)(1993), 31-61. (with W. Lin)
Non-isothermal, non-Newtonial Hele-Shaw flows, Part II:
Asymptptotics and existence of weak solutions, Nonlinear Analysis
27(1996) 539-559. (with P. Shi).
An inverse problem for harmonic acoustics in stratified oceans, J.
Math. Anal. Appl.176(1)(1993),121-137 (with Y. Xu).
A Personal Mathematical History I wasn’t always a mathematician
Institute for Fluid Dynamics and Applied Mathematics 1961-65
Assistant Professor and Associate Professor Indiana University
Bloomington, Professor 1966-75 Analytic Methods in Mathematical
Physics My First Monograph Generalized Hyperanalytic Function
Theory The Georgians Free University Berlin and the Hahn-Meitner
Institute 1974-75 University of Delaware, Unidel Professor 1975
Some Work in Elasticity, etc. I visit China for the First Time,
1984 Research in Underwater Acoustics The 65th Birthday Conference
in Graz The Cold War Ends: No More Underwater Acoustics The Birth
of ISAAC I am 63 and I begin to work in Homogenization My 70th
Birthday Conference in Frejus, France The
75thBirthdayConferenceinOrlando Medical Mathematics
A Personal Mathematical History I wasn’t always a mathematician
Institute for Fluid Dynamics and Applied Mathematics 1961-65
Assistant Professor and Associate Professor Indiana University
Bloomington, Professor 1966-75 Analytic Methods in Mathematical
Physics My First Monograph Generalized Hyperanalytic Function
Theory The Georgians Free University Berlin and the Hahn-Meitner
Institute 1974-75 University of Delaware, Unidel Professor 1975
Some Work in Elasticity, etc. I visit China for the First Time,
1984 Research in Underwater Acoustics The 65th Birthday Conference
in Graz The Cold War Ends: No More Underwater Acoustics The Birth
of ISAAC I am 63 and I begin to work in Homogenization My 70th
Birthday Conference in Frejus, France The
75thBirthdayConferenceinOrlando Medical Mathematics
I visit China for the First Time, 1984
Nixon has opened up relations with China. I am in the first group
to visit China. They have translated my book into Chinese. 7, 500
copies are sold in China alone!
Figure: Acting like Nixon on the Great Wall.
Figure: 7,500 copies!!!
A Personal Mathematical History I wasn’t always a mathematician
Institute for Fluid Dynamics and Applied Mathematics 1961-65
Assistant Professor and Associate Professor Indiana University
Bloomington, Professor 1966-75 Analytic Methods in Mathematical
Physics My First Monograph Generalized Hyperanalytic Function
Theory The Georgians Free University Berlin and the Hahn-Meitner
Institute 1974-75 University of Delaware, Unidel Professor 1975
Some Work in Elasticity, etc. I visit China for the First Time,
1984 Research in Underwater Acoustics The 65th Birthday Conference
in Graz The Cold War Ends: No More Underwater Acoustics The Birth
of ISAAC I am 63 and I begin to work in Homogenization My 70th
Birthday Conference in Frejus, France The
75thBirthdayConferenceinOrlando Medical Mathematics
Research in Underwater Acoustics
Yongzhi Xu and I began our underwater research by extending the
Colton-Kirsch theory for R3 to a waveguide.
The propagation problem and far-field problem in a stratified
finite-depth ocean Math. Meth in Applied Sciences 12 (1990),
199-208 (with Xu, Yongzhi).
Dense sets and the projection theorem for acoustic harmonic waves
in homogeneous finite depth ocean, Math. Meth in Applied Sciences
12 (1990), 69-76 (with Xu, Yongzhi).
Starting fields and far fields in ocean acoustics, Wave Motion 11
(1989), 507-524 (with Xu, Yongzhi)
A Personal Mathematical History I wasn’t always a mathematician
Institute for Fluid Dynamics and Applied Mathematics 1961-65
Assistant Professor and Associate Professor Indiana University
Bloomington, Professor 1966-75 Analytic Methods in Mathematical
Physics My First Monograph Generalized Hyperanalytic Function
Theory The Georgians Free University Berlin and the Hahn-Meitner
Institute 1974-75 University of Delaware, Unidel Professor 1975
Some Work in Elasticity, etc. I visit China for the First Time,
1984 Research in Underwater Acoustics The 65th Birthday Conference
in Graz The Cold War Ends: No More Underwater Acoustics The Birth
of ISAAC I am 63 and I begin to work in Homogenization My 70th
Birthday Conference in Frejus, France The
75thBirthdayConferenceinOrlando Medical Mathematics
A Personal Mathematical History I wasn’t always a mathematician
Institute for Fluid Dynamics and Applied Mathematics 1961-65
Assistant Professor and Associate Professor Indiana University
Bloomington, Professor 1966-75 Analytic Methods in Mathematical
Physics My First Monograph Generalized Hyperanalytic Function
Theory The Georgians Free University Berlin and the Hahn-Meitner
Institute 1974-75 University of Delaware, Unidel Professor 1975
Some Work in Elasticity, etc. I visit China for the First Time,
1984 Research in Underwater Acoustics The 65th Birthday Conference
in Graz The Cold War Ends: No More Underwater Acoustics The Birth
of ISAAC I am 63 and I begin to work in Homogenization My 70th
Birthday Conference in Frejus, France The
75thBirthdayConferenceinOrlando Medical Mathematics
A Personal Mathematical History I wasn’t always a mathematician
Institute for Fluid Dynamics and Applied Mathematics 1961-65
Assistant Professor and Associate Professor Indiana University
Bloomington, Professor 1966-75 Analytic Methods in Mathematical
Physics My First Monograph Generalized Hyperanalytic Function
Theory The Georgians Free University Berlin and the Hahn-Meitner
Institute 1974-75 University of Delaware, Unidel Professor 1975
Some Work in Elasticity, etc. I visit China for the First Time,
1984 Research in Underwater Acoustics The 65th Birthday Conference
in Graz The Cold War Ends: No More Underwater Acoustics The Birth
of ISAAC I am 63 and I begin to work in Homogenization My 70th
Birthday Conference in Frejus, France The
75thBirthdayConferenceinOrlando Medical Mathematics
Armand Wirgin and I with Buchanan, Xu continued by developing the
Intersecting Canonical Domain Method for the Waveguide.
Identification of a 3D object in a shallow sea from scattered sound
Ondes et vibrations/ Waves and Vibrations,C. R. Sci. Paris, 325
(1997) 383-389. (with T. Scotti, A. Wirgin, and Y. Xu)
Identification of object in an acoustic wave guide inversion II:
Robin-Dirichlet conditions, Math. Methods. Appl. Scis. bf 14
(2)185-199 (2006). (with Doo-Sung Lee)
A Personal Mathematical History I wasn’t always a mathematician
Institute for Fluid Dynamics and Applied Mathematics 1961-65
Assistant Professor and Associate Professor Indiana University
Bloomington, Professor 1966-75 Analytic Methods in Mathematical
Physics My First Monograph Generalized Hyperanalytic Function
Theory The Georgians Free University Berlin and the Hahn-Meitner
Institute 1974-75 University of Delaware, Unidel Professor 1975
Some Work in Elasticity, etc. I visit China for the First Time,
1984 Research in Underwater Acoustics The 65th Birthday Conference
in Graz The Cold War Ends: No More Underwater Acoustics The Birth
of ISAAC I am 63 and I begin to work in Homogenization My 70th
Birthday Conference in Frejus, France The
75thBirthdayConferenceinOrlando Medical Mathematics
Figure: Armand Wirgin.
A Personal Mathematical History I wasn’t always a mathematician
Institute for Fluid Dynamics and Applied Mathematics 1961-65
Assistant Professor and Associate Professor Indiana University
Bloomington, Professor 1966-75 Analytic Methods in Mathematical
Physics My First Monograph Generalized Hyperanalytic Function
Theory The Georgians Free University Berlin and the Hahn-Meitner
Institute 1974-75 University of Delaware, Unidel Professor 1975
Some Work in Elasticity, etc. I visit China for the First Time,
1984 Research in Underwater Acoustics The 65th Birthday Conference
in Graz The Cold War Ends: No More Underwater Acoustics The Birth
of ISAAC I am 63 and I begin to work in Homogenization My 70th
Birthday Conference in Frejus, France The
75thBirthdayConferenceinOrlando Medical Mathematics
MATHEMATICAL METHODS IN THE APPLIED SCIENCES Math. Meth. Appl. Sci.
2006; 29:401–414 Published online 8 December 2005 in Wiley
InterScience (www.interscience.wiley.com). DOI: 10.1002/mma.687 MOS
subject classication: 35R 30; 73D 50
Identication of objects in an acoustic wave guide inversion II:
Robin–Dirichlet conditions
Doo-Sung Lee1 and R. P. Gilbert2;∗;†
1Department of Mathematics; College of Education; Konkuk
University; 1 Hwayang-Dong; Kwangjin-Gu; Seoul; Korea
2Department of Mathematical Sciences; University of Delaware;
Newark; DE 19716; U.S.A.
Communicated by W. Sproig
SUMMARY
In this paper we investigate the unknown body problem in a wave
guide where one boundary has a pressure release condition and the
other an impedance condition. The method used in the paper for
solving the unknown body inverse problem is the intersection
canonical body approximation (ICBA). The ICBA is based on the
Rayleigh conjecture, which states that every point on an
illuminated body radiates sound from that point as if the point
lies on its tangent sphere. The ICBA method requires that an
analytical solution be known exterior to a canonical body in the
wave guide. We use the sphere of arbitrary centre and radius in the
wave guide as our canonical body. We are lead then to analytically
computing the exterior solution for a sphere between two parallel
plates. We use the ICBA to construct solutions at points ranging
over the suspected surface of the unknown object to reconstruct the
unknown object using a least-squares matching of computed, acoustic
eld against the measured, scattered eld. Copyright ? 2005 John
Wiley & Sons, Ltd.
KEY WORDS: inverse problems; Helmholtz equation; special functions;
wave guide
1. INTRODUCTION
In this paper we investigate the localization and identication of a
three-dimensional object in an acoustic wave guide by inversion of
the scattered wave eld. This inverse problem is non-linear in terms
of position and shape parameters of the object and fundamentally
ill posed. Furthermore, because of the multiple scattering of sound
between the object and the top and bottom boundaries of the sea,
the associated direct problem is much more complicated than for a
body in space. This problem has important practical marine
applications such as identication of mineral deposits, submarines,
submerged navigational obstacles and wreckage,
∗Correspondence to: R. P. Gilbert, Department of Mathematical
Sciences, University of Delaware, Newark, DE 19716, U.S.A.
†E-mail:
[email protected]
Copyright ? 2005 John Wiley & Sons, Ltd. Received 13 June
2005
A Personal Mathematical History I wasn’t always a mathematician
Institute for Fluid Dynamics and Applied Mathematics 1961-65
Assistant Professor and Associate Professor Indiana University
Bloomington, Professor 1966-75 Analytic Methods in Mathematical
Physics My First Monograph Generalized Hyperanalytic Function
Theory The Georgians Free University Berlin and the Hahn-Meitner
Institute 1974-75 University of Delaware, Unidel Professor 1975
Some Work in Elasticity, etc. I visit China for the First Time,
1984 Research in Underwater Acoustics The 65th Birthday Conference
in Graz The Cold War Ends: No More Underwater Acoustics The Birth
of ISAAC I am 63 and I begin to work in Homogenization My 70th
Birthday Conference in Frejus, France The
75thBirthdayConferenceinOrlando Medical Mathematics
Inverse problems in a waveguide are numerically more difficult than
in R3 because of the attenuation of certain modes.
2 1
0 1
2 1
0 1
Figure: The reconstructed spindle
A Personal Mathematical History I wasn’t always a mathematician
Institute for Fluid Dynamics and Applied Mathematics 1961-65
Assistant Professor and Associate Professor Indiana University
Bloomington, Professor 1966-75 Analytic Methods in Mathematical
Physics My First Monograph Generalized Hyperanalytic Function
Theory The Georgians Free University Berlin and the Hahn-Meitner
Institute 1974-75 University of Delaware, Unidel Professor 1975
Some Work in Elasticity, etc. I visit China for the First Time,
1984 Research in Underwater Acoustics The 65th Birthday Conference
in Graz The Cold War Ends: No More Underwater Acoustics The Birth
of ISAAC I am 63 and I begin to work in Homogenization My 70th
Birthday Conference in Frejus, France The
75thBirthdayConferenceinOrlando Medical Mathematics
1 0.5
0 0.5
1
0.5
0
0.5
1
Figure: The reconstructed torus
A Personal Mathematical History I wasn’t always a mathematician
Institute for Fluid Dynamics and Applied Mathematics 1961-65
Assistant Professor and Associate Professor Indiana University
Bloomington, Professor 1966-75 Analytic Methods in Mathematical
Physics My First Monograph Generalized Hyperanalytic Function
Theory The Georgians Free University Berlin and the Hahn-Meitner
Institute 1974-75 University of Delaware, Unidel Professor 1975
Some Work in Elasticity, etc. I visit China for the First Time,
1984 Research in Underwater Acoustics The 65th Birthday Conference
in Graz The Cold War Ends: No More Underwater Acoustics The Birth
of ISAAC I am 63 and I begin to work in Homogenization My 70th
Birthday Conference in Frejus, France The
75thBirthdayConferenceinOrlando Medical Mathematics
The 65th Birthday Conference in Graz
Some of the people at my 65th birthday conference in GRAZ,
Austria.
Figure: Klaus Habetha, Rector University Aachen
Figure: Bogdan Bojarski, Dir. Stefan Banach Institute
A Personal Mathematical History I wasn’t always a mathematician
Institute for Fluid Dynamics and Applied Mathematics 1961-65
Assistant Professor and Associate Professor Indiana University
Bloomington, Professor 1966-75 Analytic Methods in Mathematical
Physics My First Monograph Generalized Hyperanalytic Function
Theory The Georgians Free University Berlin and the Hahn-Meitner
Institute 1974-75 University of Delaware, Unidel Professor 1975
Some Work in Elasticity, etc. I visit China for the First Time,
1984 Research in Underwater Acoustics The 65th Birthday Conference
in Graz The Cold War Ends: No More Underwater Acoustics The Birth
of ISAAC I am 63 and I begin to work in Homogenization My 70th
Birthday Conference in Frejus, France The
75thBirthdayConferenceinOrlando Medical Mathematics
Figure: Elena Obalishvili at Graz Figure: Okay Celebi
A Personal Mathematical History I wasn’t always a mathematician
Institute for Fluid Dynamics and Applied Mathematics 1961-65
Assistant Professor and Associate Professor Indiana University
Bloomington, Professor 1966-75 Analytic Methods in Mathematical
Physics My First Monograph Generalized Hyperanalytic Function
Theory The Georgians Free University Berlin and the Hahn-Meitner
Institute 1974-75 University of Delaware, Unidel Professor 1975
Some Work in Elasticity, etc. I visit China for the First Time,
1984 Research in Underwater Acoustics The 65th Birthday Conference
in Graz The Cold War Ends: No More Underwater Acoustics The Birth
of ISAAC I am 63 and I begin to work in Homogenization My 70th
Birthday Conference in Frejus, France The
75thBirthdayConferenceinOrlando Medical Mathematics
The Cold War Ends: No More Underwater Acoustics
We were happy to have funding from NOA, NSF and ONR for another 15
years for our research on Inverse Problems in an underwater
environment. We collected our research in the following ( my fifth
monograph):
A Personal Mathematical History I wasn’t always a mathematician
Institute for Fluid Dynamics and Applied Mathematics 1961-65
Assistant Professor and Associate Professor Indiana University
Bloomington, Professor 1966-75 Analytic Methods in Mathematical
Physics My First Monograph Generalized Hyperanalytic Function
Theory The Georgians Free University Berlin and the Hahn-Meitner
Institute 1974-75 University of Delaware, Unidel Professor 1975
Some Work in Elasticity, etc. I visit China for the First Time,
1984 Research in Underwater Acoustics The 65th Birthday Conference
in Graz The Cold War Ends: No More Underwater Acoustics The Birth
of ISAAC I am 63 and I begin to work in Homogenization My 70th
Birthday Conference in Frejus, France The
75thBirthdayConferenceinOrlando Medical Mathematics
The Birth of ISAAC
At the Hong Kong Complex Analysis meeting in 1997 I floated the
idea of starting an international society devoted to real and
complex analysis. The idea was strongly endorsed by the attendees.
In order to get the thing moving I agreed to hold the first meeting
at the University of Delaware. The turnout was impressive,
approximately 400 attendees and ISAAC the International Society for
Analysis, Applications and Computation was born. We decided to
elect officers, a board and to approve a constitution. Subsequent
meetings were held at Fukuoka University Japan, the Free University
Berlin, University of Catania, the Mideast Technical University
Ankara, York University Toronto and last year at Imperial College
London where we had 600 attendees. Pierre Lions gave a plenary talk
at this meeting along with Sir John Ball and Gunter Uhlmann. This
next summer the meeting will be at the Steklov Institute Moscow.
All are welcome to attend.
A Personal Mathematical History I wasn’t always a mathematician
Institute for Fluid Dynamics and Applied Mathematics 1961-65
Assistant Professor and Associate Professor Indiana University
Bloomington, Professor 1966-75 Analytic Methods in Mathematical
Physics My First Monograph Generalized Hyperanalytic Function
Theory The Georgians Free University Berlin and the Hahn-Meitner
Institute 1974-75 University of Delaware, Unidel Professor 1975
Some Work in Elasticity, etc. I visit China for the First Time,
1984 Research in Underwater Acoustics The 65th Birthday Conference
in Graz The Cold War Ends: No More Underwater Acoustics The Birth
of ISAAC I am 63 and I begin to work in Homogenization My 70th
Birthday Conference in Frejus, France The
75thBirthdayConferenceinOrlando Medical Mathematics
7th ISAAC Congress Imperial College London July 13-18, 2009
International
Society for Analysis, its Applications and Computation
Sir John Ball (Oxford) Louis Boutet de Monvel (Paris) Brian Davies
(London) Simon Donaldson (London) Carlos Kenig (Chicago) Vakhtang
Kokilashvili (Tbilisi)
Nicolas Lerner (Paris) Paul Malliavin (Paris) Vladimir Maz’ya
(Liverpool) Bert-Wolfgang Schulze (Potsdam) Gunther Uhlmann
(Seattle) Masahiro Yamamoto (Tokyo)
Confirmed Plenary Speakers
Sessions I.1. Complex variables and potential theory I.2.
Differential equations: complex methods, applications I.3.
Complex-analytical methods in applied sciences I.4. Value
distributions of functions II.1. Clifford and quaternion analysis
II.2. Methods in Clifford- and Cayley- Dickson algebras III.1.
Toeplitz operators and applications III.2. Reproducing kernels
III.3. Integral transforms III.4. Spaces of differentiable
functions III.5. Analytic function spaces
III.6. Spectral theory IV.1. Pseudo-differential operators IV.2.
Dispersive equations IV.3. Control and optimisation of evolutionary
systems IV.4. Nonlinear PDE IV.5. Asymptotic and multiscale
analysis V.1. Inverse problems V.2. Stochastic analysis V.3.
Coercivity and functional inequalities V.4. Dynamical systems V.5.
Functional differential equations V.6. Mathematical biology VI.
Others
Contact and Further Information Michael Ruzhansky, Department of
Mathematics, Imperial College London, 180 Queen’s Gate, London SW7
2AZ, UK http://www.isaac2009.org
[email protected]
Local Organisers Michael Ruzhansky (Chairman) Dan Crisan Brian
Davies Jeroen Lamb
Ari Laptev (President of the EMS) Jens Wirth Boguslaw
Zegarlinski
International Advisory Board H. Begehr (Berlin) A. Berlinet
(Montpellier) B. Bojarski (Warsaw) E. Bruning (Durban) V. Burenkov
(Padova) O. Celebi (Istanbul) R. Gilbert (Newark)
A. Kilbas (Minsk) M. Lanza (Padova) M. Reissig (Freiberg) L. Rodino
(Torino) M. Ruzhansky (London) J. Ryan (Fayetteville) S. Saitoh
(Aveiro)
B.-W. Schulze (Potsdam) J. Toft (Växjö) M.W. Wong (Toronto) Y. Xu
(Louisville) M. Yamamoto (Tokyo) S. Zhang (Newark)
European Math. Society
London Math. Society
International Math. Union
Public Lecture on Nonlinear PDEs (Monday 13 July) Pierre-Louis
Lions (Paris)
Figure: The announcement of the London meeting.
A Personal Mathematical History I wasn’t always a mathematician
Institute for Fluid Dynamics and Applied Mathematics 1961-65
Assistant Professor and Associate Professor Indiana University
Bloomington, Professor 1966-75 Analytic Methods in Mathematical
Physics My First Monograph Generalized Hyperanalytic Function
Theory The Georgians Free University Berlin and the Hahn-Meitner
Institute 1974-75 University of Delaware, Unidel Professor 1975
Some Work in Elasticity, etc. I visit China for the First Time,
1984 Research in Underwater Acoustics The 65th Birthday Conference
in Graz The Cold War Ends: No More Underwater Acoustics The Birth
of ISAAC I am 63 and I begin to work in Homogenization My 70th
Birthday Conference in Frejus, France The
75thBirthdayConferenceinOrlando Medical Mathematics
Figure: Lee Lorch, Victor Berenkov and Heinrich begehr.
A Personal Mathematical History I wasn’t always a mathematician
Institute for Fluid Dynamics and Applied Mathematics 1961-65
Assistant Professor and Associate Professor Indiana University
Bloomington, Professor 1966-75 Analytic Methods in Mathematical
Physics My First Monograph Generalized Hyperanalytic Function
Theory The Georgians Free University Berlin and the Hahn-Meitner
Institute 1974-75 University of Delaware, Unidel Professor 1975
Some Work in Elasticity, etc. I visit China for the First Time,
1984 Research in Underwater Acoustics The 65th Birthday Conference
in Graz The Cold War Ends: No More Underwater Acoustics The Birth
of ISAAC I am 63 and I begin to work in Homogenization My 70th
Birthday Conference in Frejus, France The
75thBirthdayConferenceinOrlando Medical Mathematics
I am 63 and I begin to work in Homogenization
I began to work in Homogenization on my sabbatical to Lyon and St.
Etienne in 1995. This work was supported by ONR, NATO and NSF. My
first paper is with Grisha Panasenko. My second paper is with Andro
Mikelic.
Figure: A. Bourgeat, G. Panaseko and the Gilberts
A Personal Mathematical History I wasn’t always a mathematician
Institute for Fluid Dynamics and Applied Mathematics 1961-65
Assistant Professor and Associate Professor Indiana University
Bloomington, Professor 1966-75 Analytic Methods in Mathematical
Physics My First Monograph Generalized Hyperanalytic Function
Theory The Georgians Free University Berlin and the Hahn-Meitner
Institute 1974-75 University of Delaware, Unidel Professor 1975
Some Work in Elasticity, etc. I visit China for the First Time,
1984 Research in Underwater Acoustics The 65th Birthday Conference
in Graz The Cold War Ends: No More Underwater Acoustics The Birth
of ISAAC I am 63 and I begin to work in Homogenization My 70th
Birthday Conference in Frejus, France The
75thBirthdayConferenceinOrlando Medical Mathematics
Homogenizing the acoustic properties of the seabed: Part I,
Nonlinear Analysis 40, 185-212, (2000), (with A. Mikelic)
(45)
Homogenizing the acoustic properties of the seabed, Part II,(with
Th. Clopeau, J.L. Ferrn, and A. Mikelic), Mathematical and Computer
Model. 33 (2001) 821-841.
Acoustics of a stratified poroelastic composite, Zeit. f. Analysis
u. i. Anwendungen 184 (1999), 977-1001. (1999)977-1001. (with A.
Panchenko)
Vibration of two bonded composites: effects of the interface and
distinct periodic structures,Int. J. Solids and Structures, 40
(2003), 3177-3193, (with Michael Harik and Alexander
Panchenko)
A Personal Mathematical History I wasn’t always a mathematician
Institute for Fluid Dynamics and Applied Mathematics 1961-65
Assistant Professor and Associate Professor Indiana University
Bloomington, Professor 1966-75 Analytic Methods in Mathematical
Physics My First Monograph Generalized Hyperanalytic Function
Theory The Georgians Free University Berlin and the Hahn-Meitner
Institute 1974-75 University of Delaware, Unidel Professor 1975
Some Work in Elasticity, etc. I visit China for the First Time,
1984 Research in Underwater Acoustics The 65th Birthday Conference
in Graz The Cold War Ends: No More Underwater Acoustics The Birth
of ISAAC I am 63 and I begin to work in Homogenization My 70th
Birthday Conference in Frejus, France The
75thBirthdayConferenceinOrlando Medical Mathematics
Figure: Chez le maison de Andro Milic a St. Etienne.
Figure: My second homogenization paper.
A Personal Mathematical History I wasn’t always a mathematician
Institute for Fluid Dynamics and Applied Mathematics 1961-65
Assistant Professor and Associate Professor Indiana University
Bloomington, Professor 1966-75 Analytic Methods in Mathematical
Physics My First Monograph Generalized Hyperanalytic Function
Theory The Georgians Free University Berlin and the Hahn-Meitner
Institute 1974-75 University of Delaware, Unidel Professor 1975
Some Work in Elasticity, etc. I visit China for the First Time,
1984 Research in Underwater Acoustics The 65th Birthday Conference
in Graz The Cold War Ends: No More Underwater Acoustics The Birth
of ISAAC I am 63 and I begin to work in Homogenization My 70th
Birthday Conference in Frejus, France The
75thBirthdayConferenceinOrlando Medical Mathematics
A Personal Mathematical History I wasn’t always a mathematician
Institute for Fluid Dynamics and Applied Mathematics 1961-65
Assistant Professor and Associate Professor Indiana University
Bloomington, Professor 1966-75 Analytic Methods in Mathematical
Physics My First Monograph Generalized Hyperanalytic Function
Theory The Georgians Free University Berlin and the Hahn-Meitner
Institute 1974-75 University of Delaware, Unidel Professor 1975
Some Work in Elasticity, etc. I visit China for the First Time,
1984 Research in Underwater Acoustics The 65th Birthday Conference
in Graz The Cold War Ends: No More Underwater Acoustics The Birth
of ISAAC I am 63 and I begin to work in Homogenization My 70th
Birthday Conference in Frejus, France The
75thBirthdayConferenceinOrlando Medical Mathematics
I begin to work with two of my students, Alex Panchenko and Yvonne
Ou, on homogenization.
Figure: Yvonne Ou
Figure: Alex Panchenko.
A Personal Mathematical History I wasn’t always a mathematician
Institute for Fluid Dynamics and Applied Mathematics 1961-65
Assistant Professor and Associate Professor Indiana University
Bloomington, Professor 1966-75 Analytic Methods in Mathematical
Physics My First Monograph Generalized Hyperanalytic Function
Theory The Georgians Free University Berlin and the Hahn-Meitner
Institute 1974-75 University of Delaware, Unidel Professor 1975
Some Work in Elasticity, etc. I visit China for the First Time,
1984 Research in Underwater Acoustics The 65th Birthday Conference
in Graz The Cold War Ends: No More Underwater Acoustics The Birth
of ISAAC I am 63 and I begin to work in Homogenization My 70th
Birthday Conference in Frejus, France The
75thBirthdayConferenceinOrlando Medical Mathematics
Figure: Gaetano and Mathilda Fichera with friends.
Figure: Heinrich Begehr, Wolfgang Wendland and friends..
A Personal Mathematical History I wasn’t always a mathematician
Institute for Fluid Dynamics and Applied Mathematics 1961-65
Assistant Professor and Associate Professor Indiana University
Bloomington, Professor 1966-75 Analytic Methods in Mathematical
Physics My First Monograph Generalized Hyperanalytic Function
Theory The Georgians Free University Berlin and the Hahn-Meitner
Institute 1974-75 University of Delaware, Unidel Professor 1975
Some Work in Elasticity, etc. I visit China for the First Time,
1984 Research in Underwater Acoustics The 65th Birthday Conference
in Graz The Cold War Ends: No More Underwater Acoustics The Birth
of ISAAC I am 63 and I begin to work in Homogenization My 70th
Birthday Conference in Frejus, France The
75thBirthdayConferenceinOrlando Medical Mathematics
My 70th Birthday Conference in Frejus, France
I was lucky that Armand Wirgin got CNRS funding from the French
Government for my 70th birthday celebration in FREJUS on the Cote
d’Azure. This resulted a collection of very nice papers
A Personal Mathematical History I wasn’t always a mathematician
Institute for Fluid Dynamics and Applied Mathematics 1961-65
Assistant Professor and Associate Professor Indiana University
Bloomington, Professor 1966-75 Analytic Methods in Mathematical
Physics My First Monograph Generalized Hyperanalytic Function
Theory The Georgians Free University Berlin and the Hahn-Meitner
Institute 1974-75 University of Delaware, Unidel Professor 1975
Some Work in Elasticity, etc. I visit China for the First Time,
1984 Research in Underwater Acoustics The 65th Birthday Conference
in Graz The Cold War Ends: No More Underwater Acoustics The Birth
of ISAAC I am 63 and I begin to work in Homogenization My 70th
Birthday Conference in Frejus, France The
75thBirthdayConferenceinOrlando Medical Mathematics
Figure: Armand Wirgin.
A Personal Mathematical History I wasn’t always a mathematician
Institute for Fluid Dynamics and Applied Mathematics 1961-65
Assistant Professor and Associate Professor Indiana University
Bloomington, Professor 1966-75 Analytic Methods in Mathematical
Physics My First Monograph Generalized Hyperanalytic Function
Theory The Georgians Free University Berlin and the Hahn-Meitner
Institute 1974-75 University of Delaware, Unidel Professor 1975
Some Work in Elasticity, etc. I visit China for the First Time,
1984 Research in Underwater Acoustics The 65th Birthday Conference
in Graz The Cold War Ends: No More Underwater Acoustics The Birth
of ISAAC I am 63 and I begin to work in Homogenization My 70th
Birthday Conference in Frejus, France The
75thBirthdayConferenceinOrlando Medical Mathematics
Figure: Mazya, Jenny and Lenny Schwarzt Figure: Lin Wei and Andro
Mikelic
A Personal Mathematical History I wasn’t always a mathematician
Institute for Fluid Dynamics and Applied Mathematics 1961-65
Assistant Professor and Associate Professor Indiana University
Bloomington, Professor 1966-75 Analytic Methods in Mathematical
Physics My First Monograph Generalized Hyperanalytic Function
Theory The Georgians Free University Berlin and the Hahn-Meitner
Institute 1974-75 University of Delaware, Unidel Professor 1975
Some Work in Elasticity, etc. I visit China for the First Time,
1984 Research in Underwater Acoustics The 65th Birthday Conference
in Graz The Cold War Ends: No More Underwater Acoustics The Birth
of ISAAC I am 63 and I begin to work in Homogenization My 70th
Birthday Conference in Frejus, France The
75thBirthdayConferenceinOrlando Medical Mathematics
Figure: Klaus Hackl Figure: Lou Fishman
A Personal Mathematical History I wasn’t always a mathematician
Institute for Fluid Dynamics and Applied Mathematics 1961-65
Assistant Professor and Associate Professor Indiana University
Bloomington, Professor 1966-75 Analytic Methods in Mathematical
Physics My First Monograph Generalized Hyperanalytic Function
Theory The Georgians Free University Berlin and the Hahn-Meitner
Institute 1974-75 University of Delaware, Unidel Professor 1975
Some Work in Elasticity, etc. I visit China for the First Time,
1984 Research in Underwater Acoustics The 65th Birthday Conference
in Graz The Cold War Ends: No More Underwater Acoustics The Birth
of ISAAC I am 63 and I begin to work in Homogenization My 70th
Birthday Conference in Frejus, France The
75thBirthdayConferenceinOrlando Medical Mathematics
Figure: The Mazyas and me Figure: Heinrich Begehr and Franco
Nicolosi
A Personal Mathematical History I wasn’t always a mathematician
Institute for Fluid Dynamics and Applied Mathematics 1961-65
Assistant Professor and Associate Professor Indiana University
Bloomington, Professor 1966-75 Analytic Methods in Mathematical
Physics My First Monograph Generalized Hyperanalytic Function
Theory The Georgians Free University Berlin and the Hahn-Meitner
Institute 1974-75 University of Delaware, Unidel Professor 1975
Some Work in Elasticity, etc. I visit China for the First Time,
1984 Research in Underwater Acoustics The 65th Birthday Conference
in Graz The Cold War Ends: No More Underwater Acoustics The Birth
of ISAAC I am 63 and I begin to work in Homogenization My 70th
Birthday Conference in Frejus, France The
75thBirthdayConferenceinOrlando Medical Mathematics
Figure: Richard Delanghe and jerry Hile
Figure: Jim Buchanan and Lenny Schwarzt
A Personal Mathematical History I wasn’t always a mathematician
Institute for Fluid Dynamics and Applied Mathematics 1961-65
Assistant Professor and Associate Professor Indiana University
Bloomington, Professor 1966-75 Analytic Methods in Mathematical
Physics My First Monograph Generalized Hyperanalytic Function
Theory The Georgians Free University Berlin and the Hahn-Meitner
Institute 1974-75 University of Delaware, Unidel Professor 1975
Some Work in Elasticity, etc. I visit China for the First Time,
1984 Research in Underwater Acoustics The 65th Birthday Conference
in Graz The Cold War Ends: No More Underwater Acoustics The Birth
of ISAAC I am 63 and I begin to work in Homogenization My 70th
Birthday Conference in Frejus, France The
75thBirthdayConferenceinOrlando Medical Mathematics
Some more recent papers:
An obstacle problem in non-isothermal and non-Newtonian Hele-Shaw
flows Comm. Applied Analysis 8 (4) (2004) 459-489 (with Ming
Fang).
Effective acoustic equations for a two-phase medium with
microstructure, Mathematical and Computer Model., 39, (2004)
1431-1448. (with A.Panchenko )
A two-dimensional nonlinear theory of anisotropic plates,
Mathematical and Computer Modeling 32 (2000) 855-857, (with T. S.
Vashakmadze)
Compression moulding II: Existance of a solution for a Hele Shaw
type model, Jour. Analysis and Applications 23 783–807 (2004).(with
M. Fang)
A Personal Mathematical History I wasn’t always a mathematician
Institute for Fluid Dynamics and Applied Mathematics 1961-65
Assistant Professor and Associate Professor Indiana University
Bloomington, Professor 1966-75 Analytic Methods in Mathematical
Physics My First Monograph Generalized Hyperanalytic Function
Theory The Georgians Free University Berlin and the Hahn-Meitner
Institute 1974-75 University of Delaware, Unidel Professor 1975
Some Work in Elasticity, etc. I visit China for the First Time,
1984 Research in Underwater Acoustics The 65th Birthday Conference
in Graz The Cold War Ends: No More Underwater Acoustics The Birth
of ISAAC I am 63 and I begin to work in Homogenization My 70th
Birthday Conference in Frejus, France The
75thBirthdayConferenceinOrlando Medical Mathematics
A Personal Mathematical History I wasn’t always a mathematician
Institute for Fluid Dynamics and Applied Mathematics 1961-65
Assistant Professor and Associate Professor Indiana University
Bloomington, Professor 1966-75 Analytic Methods in Mathematical
Physics My First Monograph Generalized Hyperanalytic Function
Theory The Georgians Free University Berlin and the Hahn-Meitner
Institute 1974-75 University of Delaware, Unidel Professor 1975
Some Work in Elasticity, etc. I visit China for the First Time,
1984 Research in Underwater Acoustics The 65th Birthday Conference
in Graz The Cold War Ends: No More Underwater Acoustics The Birth
of ISAAC I am 63 and I begin to work in Homogenization My 70th
Birthday Conference in Frejus, France The
75thBirthdayConferenceinOrlando Medical Mathematics
A Personal Mathematical History I wasn’t always a mathematician
Institute for Fluid Dynamics and Applied Mathematics 1961-65
Assistant Professor and Associate Professor Indiana University
Bloomington, Professor 1966-75 Analytic Methods in Mathematical
Physics My First Monograph Generalized Hyperanalytic Function
Theory The Georgians Free University Berlin and the Hahn-Meitner
Institute 1974-75 University of Delaware, Unidel Professor 1975
Some Work in Elasticity, etc. I visit China for the First Time,
1984 Research in Underwater Acoustics The 65th Birthday Conference
in Graz The Cold War Ends: No More Underwater Acoustics The Birth
of ISAAC I am 63 and I begin to work in Homogenization My 70th
Birthday Conference in Frejus, France The
75thBirthdayConferenceinOrlando Medical Mathematics
Yvonne Ou and Alex Panchenko decide to do something about my 75th
birthday.
I really like parties!
A Personal Mathematical History I wasn’t always a mathematician
Institute for Fluid Dynamics and Applied Mathematics 1961-65
Assistant Professor and Associate Professor Indiana University
Bloomington, Professor 1966-75 Analytic Methods in Mathematical
Physics My First Monograph Generalized Hyperanalytic Function
Theory The Georgians Free University Berlin and the Hahn-Meitner
Institute 1974-75 University of Delaware, Unidel Professor 1975
Some Work in Elasticity, etc. I visit China for the First Time,
1984 Research in Underwater Acoustics The 65th Birthday Conference
in Graz The Cold War Ends: No More Underwater Acoustics The Birth
of ISAAC I am 63 and I begin to work in Homogenization My 70th
Birthday Conference in Frejus, France The
75thBirthdayConferenceinOrlando Medical Mathematics
Figure: D. Khavinson, J. Ryan and G. Auchmutty at my 75th
A Personal Mathematical History I wasn’t always a mathematician
Institute for Fluid Dynamics and Applied Mathematics 1961-65
Assistant Professor and Associate Professor Indiana University
Bloomington, Professor 1966-75 Analytic Methods in Mathematical
Physics My First Monograph Generalized Hyperanalytic Function
Theory The Georgians Free University Berlin and the Hahn-Meitner
Institute 1974-75 University of Delaware, Unidel Professor 1975
Some Work in Elasticity, etc. I visit China for the First Time,
1984 Research in Underwater Acoustics The 65th Birthday Conference
in Graz The Cold War Ends: No More Underwater Acoustics The Birth
of ISAAC I am 63 and I begin to work in Homogenization My 70th
Birthday Conference in Frejus, France The
75thBirthdayConferenceinOrlando Medical Mathematics
Figure: Armand Wirgin and me at my 75th
A Personal Mathematical History I wasn’t always a mathematician
Institute for Fluid Dynamics and Applied Mathematics 1961-65
Assistant Professor and Associate Professor Indiana University
Bloomington, Professor 1966-75 Analytic Methods in Mathematical
Physics My First Monograph Generalized Hyperanalytic Function
Theory The Georgians Free University Berlin and the Hahn-Meitner
Institute 1974-75 University of Delaware, Unidel Professor 1975
Some Work in Elasticity, etc. I visit China for the First Time,
1984 Research in Underwater Acoustics The 65th Birthday Conference
in Graz The Cold War Ends: No More Underwater Acoustics The Birth
of ISAAC I am 63 and I begin to work in Homogenization My 70th
Birthday Conference in Frejus, France The
75thBirthdayConferenceinOrlando Medical Mathematics
Medical Mathematics
Since the cold war was over and there was no more funding for the
type of problems we were interested in we decided first to look
into another poroelastic material, namely bone. This has led to an
active research program and funding from NSF for the International
Program, NATO and the NSF Bio-Math Program. We have been interested
in determining the rigidity of bone, modeling the disease
osteoporosis and medical-mathematics in general.
A Personal Mathematical History I wasn’t always a mathematician
Institute for Fluid Dynamics and Applied Mathematics 1961-65
Assistant Professor and Associate Professor Indiana University
Bloomington, Professor 1966-75 Analytic Methods in Mathematical
Physics My First Monograph Generalize