Japanese version
Hiroshima Complex Analysis Seminar

2015 academic year
No. 8
 Date: January 27 (Wed) 16:30  17:30
 Place: B707, Fac. Sci., Hiroshima University
 Speaker: Genki Shibukawa (Osaka University)
 Title: New elliptic function identities and an elliptic analogue of
reciprocity laws of generalized Dedekind sums
 Abstract:

We obtain new elliptic function identities, which are productto
sum type formulas for derivative of some elliptic functions.
Further, from specializations of our formulas, we derive not only
various known an elliptic analogue of reciprocity laws of generalized
Dedekind sums by FukuharaYui, Egami, but also new reciprocity laws of
an elliptic analogue of generalized Dedekind sums.
No. 7
 Date: Nobember 27 (Fri) 15:00  16:00
(This seminar starts at irregular time.)
 Place: B707, Fac. Sci., Hiroshima University
 Speaker: Yoko Umeta (Yamaguchi University)
 Title: Multiplescale analysis for some class of systems of
nonlinear differential equations
 Abstract:

T.Kawai and Y.Takei established structure theorem for
instantontype solutions of Painleve hierarchies (P_J)_m
(J =I, 34, II2 or IV) with a large parameter.
Instantontype solutions are formal solutions containing
sufficiently many free parameters. They explained the Stokes
phenomenon for instantontype solutions of (P_J)_m by the change
of parameters. In this talk, we study the construction of
instantontype solutions.
Multiplescale analysis is an effective method in obtaining
the concrete forms of instantontype solutions. In this talk,
we generally explain multiplescale analysis for some class of
systems of nonlinear differential equations. We consider a
question:@What kind of classes of differential equations is the
multiplescale analysis effective for ?
No. 6
 Date: Nobember 6 (Fri) 16:00  17:40
 Place: B707, Fac. Sci., Hiroshima University
 16:00  17:00
 Speaker: Seiji NISHIOKA (Yamagata University)
 Title: doubleangle formulae and algebraic independency
 Abstract:

Looking at the "doubleangle formulae" of the cosine function, Weierstrass function and the independent variable, we find polynomials and a rational function in themselves of degrees 2, 4 and 1, respectively. Since the degrees are distinct, the above three functions are algebraically independent over the field of complex numbers.
 17:10  17:40
 Speaker: Hiroshi OGAWARA (Kumamoto University)
 Title: A difference analogue of a theorem of Wallenberg
 Abstract:

Wallenberg showed that every common solution of both a linear differential equation of 2ndorder and an algebraic differential equation of 1storder over the rational function field is Liouvillian over the rational function field if the latter equation has at least two different homogeneous terms except for the constant term.
Here, we say that a function is Liouvillian when it is a composite function of a finite number of exponential functions, primitive functions, or roots of algebraic equations.
In this talk, we give a difference analogue of his result of higherorder in difference algebra.
As an application of the difference analogue, we consider reducibility of solutions for linear difference equations.
In particular, we will consider several linear qdifference equations as examples.
No. 5
 Date: July 31 (Fri) 15:00  16:00
(This seminar starts at irregular time.)
 Place: B707, Fac. Sci., Hiroshima University
 Speaker: Sampei HIROSE (Shibaura Institute of Technology)
 Title: On singular perturbed qdifference equations
 Abstract:

In this talk, we study singular perturbed qdifference equations.
We would like to explain the difference between singular perturbed qdifference equations and singular perturbed differential equations by using some examples.
No. 4
 Date: July 24 (Fri) 16:00  17:30
 Place: B707, Fac. Sci., Hiroshima University
 Speaker: Takuya WATANABE (Ritsumeikan University)
 Title: Molecular predissociation resonances at an energylevel crossing
 Abstract:

We study the resonances of a 2 x 2 semiclassical system of one dimensional Schrödinger operators near an energy where two potentials intersect transversally.
In a molecular predissociation coming from an energylevel crossing between bonding and antibonding, its quantum resonances appear as eigenvalues of the potential well are perturbed by the interaction of the crossing.
A connection of solutions around energy crossing is a main problem in our work and it is difficult to treat the energy crossing, where each simple turning point joins together, not only in a complex WKB analysis but also in a microlocal analysis.
In this talk, we would like to show our result on the semiclassical distributions of resonances near the crossing energylevel and introduce constructions and connections of solutions.
This is a joint work with Setsuro Fujiié (Ritsumeikan University) and André Martinez (Università di Bologna).
No. 3
 Date: May 22 (Fri) 16:00  17:30
 Place: B707, Fac. Sci., Hiroshima University
 Speaker: Yusaku TIBA (The University of Tokyo)
 Title: A minimum principle of a maximum plurisubharmonic function and its application to the complex MongeAmpère equation
 Abstract:

In this talk, we study a geometric property of a plurisubharmonic function which is a solution of the MongeAmpère equation and has a convex level set by using our minimum principle of a maximal plurisubharmonic function. We also show a relation between the supports of the MongeAmpère currents and complex extreme points of closed balls for the Kobayashi distance in a bounded convex domain in ℂ^{n}.
No. 2
 Date: May 8 (Fri) 16:00  17:00

May 9 (Sat) 10:00  11:30
 Place: B707, Fac. Sci., Hiroshima University
 Speaker: Hiroshi YAMAZAWA (Shibaura Institute of Technology)
 Title: qanalogue of the multisummability of formal solutions for a differencedifferential equation —example version—
 Abstract:

We have results of the multisummability of formal solutions for some partial differential equations by S. Ouchi.
In this talk the lecturer will introduce about the multisummability of formal solutions on one example.
Key words are qdiscrete, qGevrey estimate and qmultisummability etc.
No. 1
 Date: April 24 (Fri) 16:00  17:00
 Place: B707, Fac. Sci., Hiroshima University
 Speaker: Ahmed Sebbar (Bordeaux University, France)
 Title: Critical points of Green's functions
 Abstract:

Let D a bounded and multiply connected domain, of connectivity p. The Green's function of D of pole w has p critical points z_{i} (w), 1≤i≤p. The main result is that there is a compact set K⊂D, independent of w and containing all these critical points: The critical points will never see the boundary ∂D of D.
We will discuss in detail the case of a doubly connected domain. We also discuss some possible developments: Cartan geometry, Casimir effect.
The main result is a joint work with Björn Gustafsson (KTH, Stockholm).
How to access to our department is Here.
Past seminars
Organizers
Makoto ABE (Graduate School of Science, Hiroshima University)
Yoshikatsu SASAKI (Graduate School of Science, Hiroshima University)
Tetsu SHIMOMURA (Graduate School of Education, Hiroshima University)
Kazuhiro TAKIMOTO (Graduate School of Science, Hiroshima University)
Kentaro HIRATA (Graduate School of Science, Hiroshima University)
Yoshihiro MIZUTA (Faculty of Engineering, Hiroshima Institute of Technology)
Masafumi YOSHINO (Graduate School of Science, Hiroshima University)
Contact
Last update: October 13, 2015
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