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 product-to- 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 Fukuhara-Yui, 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: Multiple-scale analysis for some class of systems of non-linear differential equations

Abstract:

    T.Kawai and Y.Takei established structure theorem for instanton-type solutions of Painleve hierarchies (P_J)_m (J =I, 34, II-2 or IV) with a large parameter.
    Instanton-type solutions are formal solutions containing sufficiently many free parameters. They explained the Stokes phenomenon for instanton-type solutions of (P_J)_m by the change of parameters. In this talk, we study the construction of instanton-type solutions.
    Multiple-scale analysis is an effective method in obtaining the concrete forms of instanton-type solutions. In this talk, we generally explain multiple-scale analysis for some class of systems of non-linear differential equations. We consider a question:�@What kind of classes of differential equations is the multiple-scale 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: double-angle formulae and algebraic independency

Abstract:

    Looking at the "double-angle 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 2nd-order and an algebraic differential equation of 1st-order 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 higher-order 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 q-difference 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 q-difference equations

Abstract:

    In this talk, we study singular perturbed q-difference equations. We would like to explain the difference between singular perturbed q-difference 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 energy-level 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 energy-level crossing between bonding and anti-bonding, 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 energy-level 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 Monge-Ampère equation

Abstract:

    In this talk, we study a geometric property of a plurisubharmonic function which is a solution of the Monge-Ampère 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 Monge-Ampère currents and complex extreme points of closed balls for the Kobayashi distance in a bounded convex domain in ℂⁿ.

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: q-analogue of the multi-summability of formal solutions for a difference-differential equation —example version—

Abstract:

    We have results of the multi-summability of formal solutions for some partial differential equations by S. Ouchi. In this talk the lecturer will introduce about the multi-summability of formal solutions on one example. Key words are q-discrete, q-Gevrey estimate and q-multi-summability 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).

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