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This volume presents the proceedings of the Seventh International
Colloquium on Finite or Infinite Dimensional Complex Analysis held
in Fukuoka, Japan. The contributions offer multiple perspectives
and numerous research examples on complex variables, Clifford
algebra variables, hyperfunctions and numerical analysis.
This book is the Proceedings of the Second ISAAC Congress. ISAAC is
the acronym of the International Society for Analysis, its
Applications and Computation. The president of ISAAC is Professor
Robert P. Gilbert, the second named editor of this book, e-mail:
[email protected]. The Congress is world-wide valued so highly
that an application for a grant has been selected and this project
has been executed with Grant No. 11-56 from *the Commemorative
Association for the Japan World Exposition (1970). The finance of
the publication of this book is exclusively the said Grant No.
11-56 from *. Thus, a pair of each one copy of two volumes of this
book will be sent to all contributors, who registered at the Second
ISAAC Congress in Fukuoka, free of charge by the Kluwer Academic
Publishers. Analysis is understood here in the broad sense of the
word, includ ing differential equations, integral equations,
functional analysis, and function theory. It is the purpose of
ISAAC to promote analysis, its applications, and its interaction
with computation. With this objective, ISAAC organizes
international Congresses for the presentation and dis cussion of
research on analysis. ISAAC welcomes new members and those
interested in joining ISAAC are encouraged to look at the web site
http://www .math. udel.edu/ gilbert/isaac/index.html vi and
http://www.math.fu-berlin.de/ rd/ ag/isaac/newton/index.html.
This volume consists of papers presented in the special sessions on
"Complex and Numerical Analysis," "Value Distribution Theory and
Complex Domains," and "Use of Symbolic Computation in Mathematics
Education" of the ISAAC'97 Congress held at the University of
Delaware, during June 2-7, 1997. The ISAAC Congress coincided with
a U.S.-Japan Seminar also held at the University of Delaware. The
latter was supported by the National Science Foundation through
Grant INT-9603029 and the Japan Society for the Promotion of
Science through Grant MTCS-134. It was natural that the
participants of both meetings should interact and consequently
several persons attending the Congress also presented papers in the
Seminar. The success of the ISAAC Congress and the U.S.-Japan
Seminar has led to the ISAAC'99 Congress being held in Fukuoka,
Japan during August 1999. Many of the same participants will return
to this Seminar. Indeed, it appears that the spirit of the
U.S.-Japan Seminar will be continued every second year as part of
the ISAAC Congresses. We decided to include with the papers
presented in the ISAAC Congress and the U.S.-Japan Seminar several
very good papers by colleagues from the former Soviet Union. These
participants in the ISAAC Congress attended at their own expense.
Let 8 be a Riemann surface of analytically finite type (9, n) with
29 - 2+n> O. Take two pointsP1, P2 E 8, and set 8 ,1>2= 8 \
{P1' P2}. Let PI Homeo+(8;P1,P2) be the group of all orientation
preserving homeomor- phismsw: 8 -+ 8 fixingP1, P2 and isotopic to
the identity on 8. Denote byHomeot(8;Pb P2) the set of all elements
ofHomeo+(8;P1, P2) iso- topic to the identity on 8 ,P2'
ThenHomeot(8;P1,P2) is a normal sub- pl group ofHomeo+(8;P1,P2). We
setIsot(8;P1,P2) =Homeo+(8;P1,P2)/ Homeot(8;p1, P2). The purpose of
this note is to announce a result on the Nielsen- Thurston-Bers
type classification of an element [w] ofIsot+(8;P1,P2). We give a
necessary and sufficient condition for thetypeto be hyperbolic. The
condition is described in terms of properties of the pure braid [b
] w induced by [w]. Proofs will appear elsewhere. The problem
considered in this note and the form ofthe solution are suggested
by Kra's beautiful theorem in [6], where he treats self-maps of
Riemann surfaces with one specified point. 2
TheclassificationduetoBers Let us recall the classification of
elements of the mapping class group due to Bers (see Bers [1]).
LetT(R) be the Teichmiiller space of a Riemann surfaceR, andMod(R)
be the Teichmtiller modular group of R. Note that an orientation
preserving homeomorphism w: R -+ R induces canonically an element
(w) EMod(R). Denote by&.r(R)(*,.) the Teichmiiller distance
onT(R). For an elementXEMod(R), we define a(x)= inf
&.r(R)(r,x(r)).
This volume consists of papers presented in the special sessions on
"Wave Phenomena and Related Topics," and "Asymptotics and
Homogenization" of the ISAAC'97 Congress held at the University of
Delaware, during June 2-7, 1997. The ISAAC Congress coincided with
a U.S.-Japan Seminar also held at the University of Delaware. The
latter was supported by the National Science Foundation through
Grant INT -9603029 and the Japan Society for the Promotion of
Science through Grant MTCS-134. It was natural that the
'participants of both meetings should interact and consequently
several persons attending the Congress also presented papers in the
Seminar. The success of the ISAAC Congress and the U.S.-Japan
Seminar has led to the ISAAC'99 Congress being held in Fukuoka,
Japan during August 1999. Many of the same participants will return
to this Seminar. Indeed, it appears that the spirit of the
U.S.-Japan Seminar will be continued every second year as part of
the ISAAC Congresses. We decided to include with the papers
presented in the ISAAC Congress and the U.S.-Japan Seminar several
very good papers by colleagues from the former Soviet Union. These
participants in the ISAAC Congress attended at their own expense.
This volume has the title Direct and Inverse Problems of
Mathematical Physics which consists of the papers on scattering
theory, coefficient identification, uniqueness and existence
theorems, boundary controllability, wave propagation in stratified
media, viscous flows, nonlinear acoustics, Sobolev spaces,
singularity theory, pseudo differential operators, and semigroup
theory.
Let 8 be a Riemann surface of analytically finite type (9, n) with
29 - 2+n> O. Take two pointsP1, P2 E 8, and set 8 ,1>2= 8 \
{P1' P2}. Let PI Homeo+(8;P1,P2) be the group of all orientation
preserving homeomor- phismsw: 8 -+ 8 fixingP1, P2 and isotopic to
the identity on 8. Denote byHomeot(8;Pb P2) the set of all elements
ofHomeo+(8;P1, P2) iso- topic to the identity on 8 ,P2'
ThenHomeot(8;P1,P2) is a normal sub- pl group ofHomeo+(8;P1,P2). We
setIsot(8;P1,P2) =Homeo+(8;P1,P2)/ Homeot(8;p1, P2). The purpose of
this note is to announce a result on the Nielsen- Thurston-Bers
type classification of an element [w] ofIsot+(8;P1,P2). We give a
necessary and sufficient condition for thetypeto be hyperbolic. The
condition is described in terms of properties of the pure braid [b
] w induced by [w]. Proofs will appear elsewhere. The problem
considered in this note and the form ofthe solution are suggested
by Kra's beautiful theorem in [6], where he treats self-maps of
Riemann surfaces with one specified point. 2
TheclassificationduetoBers Let us recall the classification of
elements of the mapping class group due to Bers (see Bers [1]).
LetT(R) be the Teichmiiller space of a Riemann surfaceR, andMod(R)
be the Teichmtiller modular group of R. Note that an orientation
preserving homeomorphism w: R -+ R induces canonically an element
(w) EMod(R). Denote by&.r(R)(*,.) the Teichmiiller distance
onT(R). For an elementXEMod(R), we define a(x)= inf
&.r(R)(r,x(r)).
This book is the Proceedings of the Second ISAAC Congress. ISAAC is
the acronym of the International Society for Analysis, its
Applications and Computation. The president of ISAAC is Professor
Robert P. Gilbert, the second named editor of this book, e-mail:
[email protected]. The Congress is world-wide valued so highly
that an application for a grant has been selected and this project
has been executed with Grant No. 11-56 from *the Commemorative
Association for the Japan World Exposition (1970). The finance of
the publication of this book is exclusively the said Grant No.
11-56 from *. Thus, a pair of each one copy of two volumes of this
book will be sent to all contributors, who registered at the Second
ISAAC Congress in Fukuoka, free of charge by the Kluwer Academic
Publishers. Analysis is understood here in the broad sense of the
word, includ ing differential equations, integral equations,
functional analysis, and function theory. It is the purpose of
ISAAC to promote analysis, its applications, and its interaction
with computation. With this objective, ISAAC organizes
international Congresses for the presentation and dis cussion of
research on analysis. ISAAC welcomes new members and those
interested in joining ISAAC are encouraged to look at the web site
http: //www .math. udel.edu/ gilbert/isaac/index.html vi and http:
//www.math.fu-berlin.de/ rd/ ag/isaac/newton/index.html."
This volume consists of papers presented in the special sessions on
"Wave Phenomena and Related Topics," and "Asymptotics and
Homogenization" of the ISAAC'97 Congress held at the University of
Delaware, during June 2-7, 1997. The ISAAC Congress coincided with
a U.S.-Japan Seminar also held at the University of Delaware. The
latter was supported by the National Science Foundation through
Grant INT -9603029 and the Japan Society for the Promotion of
Science through Grant MTCS-134. It was natural that the
'participants of both meetings should interact and consequently
several persons attending the Congress also presented papers in the
Seminar. The success of the ISAAC Congress and the U.S.-Japan
Seminar has led to the ISAAC'99 Congress being held in Fukuoka,
Japan during August 1999. Many of the same participants will return
to this Seminar. Indeed, it appears that the spirit of the
U.S.-Japan Seminar will be continued every second year as part of
the ISAAC Congresses. We decided to include with the papers
presented in the ISAAC Congress and the U.S.-Japan Seminar several
very good papers by colleagues from the former Soviet Union. These
participants in the ISAAC Congress attended at their own expense.
This volume has the title Direct and Inverse Problems of
Mathematical Physics which consists of the papers on scattering
theory, coefficient identification, uniqueness and existence
theorems, boundary controllability, wave propagation in stratified
media, viscous flows, nonlinear acoustics, Sobolev spaces,
singularity theory, pseudo differential operators, and semigroup
theory.
This volume consists of papers presented in the special sessions on
"Complex and Numerical Analysis," "Value Distribution Theory and
Complex Domains," and "Use of Symbolic Computation in Mathematics
Education" of the ISAAC'97 Congress held at the University of
Delaware, during June 2-7, 1997. The ISAAC Congress coincided with
a U.S.-Japan Seminar also held at the University of Delaware. The
latter was supported by the National Science Foundation through
Grant INT-9603029 and the Japan Society for the Promotion of
Science through Grant MTCS-134. It was natural that the
participants of both meetings should interact and consequently
several persons attending the Congress also presented papers in the
Seminar. The success of the ISAAC Congress and the U.S.-Japan
Seminar has led to the ISAAC'99 Congress being held in Fukuoka,
Japan during August 1999. Many of the same participants will return
to this Seminar. Indeed, it appears that the spirit of the
U.S.-Japan Seminar will be continued every second year as part of
the ISAAC Congresses. We decided to include with the papers
presented in the ISAAC Congress and the U.S.-Japan Seminar several
very good papers by colleagues from the former Soviet Union. These
participants in the ISAAC Congress attended at their own expense.
This volume presents the proceedings of the Seventh International
Colloquium on Finite or Infinite Dimensional Complex Analysis held
in Fukuoka, Japan. The contributions offer multiple perspectives
and numerous research examples on complex variables, Clifford
algebra variables, hyperfunctions and numerical analysis.
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