Updated on 2022/01/28

写真a

 
NOBE, Atsushi
 
Affiliation
Faculty of Political Science and Economics, School of Political Science and Economics
Job title
Professor

Concurrent Post

  • Faculty of Political Science and Economics   Graduate School of Economics

Education

  • 1999.04
    -
    2002.03

    The University of Tokyo   Graduate School of Mathematical Sciences  

  • 1997.04
    -
    1999.03

    The University of Tokyo   Graduate School of Mathematical Sciences  

  • 1994.04
    -
    1996.03

    The University of Tokyo   The Graduate School of Engineering   Department of Quantum Engineering and Systems Science  

  • 1990.04
    -
    1994.03

    Nagoya University   School of Science  

Degree

  • 2002.03   東京大学   博士(数理科学)

  • 1999.03   東京大学   修士(数理科学)

  • 1996.03   東京大学   修士(工学)

  • 1994.03   名古屋大学   学士(理学)

Research Experience

  • 2021.04
    -
    Now

    Waseda University   Faculty of Political Science and Economics   Professor

  • 2010.04
    -
    2021.03

    Chiba University   Graduate School of Science

  • 2009.10
    -
    2021.03

    Chiba University   Faculty of Education

  • 2007.04
    -
    2009.09

    Osaka University   Graduate School of Engineering Science

  • 2004.04
    -
    2007.03

    Osaka University   Graduate School of Engineering Science

  • 2003.09
    -
    2004.03

    The University of Tokyo   Graduate School of Mathematical Sciences   Postdoctoral Researcher

  • 2011.04
    -
    Now

    気象大学校   大学部   非常勤講師

    線形代数学、数学演習

  • 2018.11
    -
    2021.03

    津田塾大学   学芸学部   非常勤講師

  • 2013.04
    -
    2021.03

    日本大学   生産工学部   非常勤講師

    線形代数学、微分積分学

▼display all

Professional Memberships

  •  
     
     

    THE JAPAN SOCIETY FOR INDUSTRIAL AND APPLIED MATHEMATICS

  •  
     
     

    日本数学会

  •  
     
     

    日本物理学会

 

Research Areas

  • Mathematical analysis

  • Applied mathematics and statistics

  • Basic mathematics

Research Interests

  • Ultradiscrete system

  • ソリトン

  • クラスター代数

  • セルオートマトン

  • トロピカル幾何

  • 可積分系

  • Cellular automata

  • Tropical geometry

  • Integrable systems

▼display all

Papers

  • Periodicity, linearizability and integrability in seed mutations of type $A^{(1)}_N$

    Atsushi Nobe, Junta Matsukidaira

    Journal of Mathematical Physics   62 ( 1 ) 013510 - 013510  2021.01  [Refereed]  [International journal]

    Authorship:Lead author, Corresponding author

     View Summary

    In the network of seed mutations arising from a certain initial seed, an
    appropriate path emanating from the initial seed is intendedly chosen, noticing
    periodicity of the exchange matrices in the path each of which is assigned to
    the generalized Cartan matrix of type $A^{(1)}_N$. Then dynamical property of
    the seed mutations along the path, which is referred to as of type $A^{(1)}_N$,
    is intensively investigated. The coefficients assigned to the path form certain
    $N$ monomials that posses periodicity with period $N$ under the seed mutations
    and enable to obtain the general terms of the coefficients. The cluster
    variables assigned to the path of type $A^{(1)}_N$ also form certain $N$
    Laurent polynomials possessing the same periodicity as the monomials generated
    by the coefficients. These Laurent polynomials lead to sufficiently number of
    conserved quantities of the dynamical system derived from the cluster mutations
    along the path. Furthermore, by virtue of the Laurent polynomials with
    periodicity, the dynamical system is non-autonomously linearized and its
    general solution is concretely constructed. Thus the seed mutations along the
    path of type $A^{(1)}_N$ exhibit discrete integrability.

    DOI

  • A family of integrable and non-integrable difference equations arising from cluster algebras

    Atsushi Nobe, Junta Matsukidaira

    RIMS Kokyuroku Bessatsu   B78   99 - 120  2020.04  [Refereed]  [Invited]

    Authorship:Lead author, Corresponding author

     View Summary

    The one-parameter family of second order nonlinear difference equations each
    of which is given by $$ x_{n-1}x_nx_{n+1}=x_{n-1}+(x_n)^{\beta-1}+x_{n+1}
    \qquad(\beta\in\mathbb{N}) $$ is explored. Since the equation above is arising
    from seed mutations of a rank 2 cluster algebra, its solution is periodic only
    when $\beta\leq3$. In order to evaluate the dynamics with $\beta\geq4$,
    algebraic entropy of the birational map equivalent to the difference equation
    is investigated; it vanishes when $\beta=4$ but is positive when $\beta\geq5$.
    This fact suggests that the difference equation with $\beta\leq4$ is integrable
    but that with $\beta\geq5$ is not. It is moreover shown that the difference
    equation with $\beta\geq4$ fails the singularity confinement test. This fact is
    consistent with linearizability of the equation with $\beta=4$ and reinforces
    non-integrability of the equation with $\beta\geq5$.

  • Generators of rank 2 cluster algebras of affine types via linearization of seed mutations

    Atsushi Nobe

    Journal of Mathematical Physics   60 ( 7 ) 072702 - 072702  2019.07  [Refereed]  [International journal]

    Authorship:Lead author, Corresponding author

    DOI

  • Group actions on the tropical Hesse pencil

    Atsushi Nobe

    JAPAN JOURNAL OF INDUSTRIAL AND APPLIED MATHEMATICS   33 ( 3 ) 537 - 556  2016.12  [Refereed]

    Authorship:Lead author, Corresponding author

     View Summary

    Addition of points on the tropical Hesse curve is realized via its intersections with two tropical lines. Then the addition formula for the points on the curve is reduced from the one for the level-three theta functions through the ultradiscretization procedure. In addition, a tropical analogue of the Hessian group , the group of linear automorphisms acting on the Hesse pencil, is investigated; it is shown that the dihedral group of degree three is the group of linear automorphisms acting on the tropical Hesse pencil.

    DOI

  • Mutations of the cluster algebra of type $A^{(1)}_1$ and the periodic discrete Toda lattice

    Atsushi Nobe

    JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL   49 ( 28 )  2016.07  [Refereed]  [International journal]

    Authorship:Lead author, Corresponding author

     View Summary

    A direct connection between two sequences of points, one of which is generated by seed mutations of the cluster algebra of type A(1)((1)) and the other by time evolutions of the periodic discrete Toda lattice, is explicitly given. In this construction, each of them is realized as an orbit of a QRT map, and specialization of the parameters in the maps and appropriate choices of the initial points relate them. The connection with the periodic discrete Toda lattice enables us a geometric interpretation of the seed mutations of the cluster algebra of type A(1)((1)) as an addition of points on an elliptic curve.

    DOI

  • A geometric realization of the ultradiscrete periodic Toda lattice via tropical plane curves

    NOBE Atsushi

    RIMS Kokyuroku Bessatsu   B47   55 - 76  2014.12  [Refereed]  [Invited]

    Authorship:Lead author, Corresponding author

     View Summary

    This is a review article on a tropical geometric realization of the<br />
    ultradiscrete periodic Toda lattice (UD-pTL). Time evolution of the UD-pTL is<br />
    translated into an addition on the Picard group of its spectral curve, which is<br />
    a tropical hyperelliptic curve of arbitrary genus depending on the system size.<br />
    The addition on the Picard group can be realized by using intersection of<br />
    several tropical plane curves, one of which is the spectral curve. In addition,<br />
    the tropical eigenvector map, which maps a point in the phase space of the<br />
    UD-pTL into a set of points on the spectral curve, can also be realized by<br />
    using intersection of tropical curves. Thus, if the initial values are given<br />
    then the time evolution of the UD-pTL is completely translated into a motion of<br />
    intersection points of tropical plane curves. Moreover, all tropical plane<br />
    curves appearing in the curve intersection are explicitly given in terms of the<br />
    conserved quantities of the UD-pTL.

  • A geometric realization of the periodic discrete Toda lattice and its tropicalization

    Atsushi Nobe

    Journal of Physics A: Mathematical and Theoretical   46 ( 46 )  2013.11  [Refereed]

     View Summary

    An explicit formula concerning curve intersections equivalent to the time evolution of the periodic discrete Toda lattice (pdTL) is presented. First, the time evolution is realized as a point addition on a hyperelliptic curve, which is the spectral curve of the pdTL, then the point addition is translated into curve intersections. Next, it is shown that the curves which appear in the curve intersections are explicitly given by using the conserved quantities of the pdTL. Finally, the formulation is lifted to the framework of tropical geometry and a tropical geometric realization of the periodic box-ball system is constructed via tropical curve intersections. © 2013 IOP Publishing Ltd.

    DOI

  • Addition in Jacobians of tropical hyperelliptic curves

    NOBE Atsushi

    RIMS Kokyuroku Bessatsu   B30   25 - 51  2012.11  [Refereed]  [Invited]

    Authorship:Lead author, Corresponding author

     View Summary

    We show that there exists a surjection from the set of effective divisors of<br />
    degree $g$ on a tropical curve of genus $g$ to its Jacobian by using a tropical<br />
    version of the Riemann-Roch theorem. We then show that the restriction of the<br />
    surjection is reduced to the bijection on an appropriate subset of the set of<br />
    effective divisors of degree $g$ on the curve. Thus the subset of effective<br />
    divisors has the additive group structure induced from the Jacobian. We finally<br />
    realize the addition in Jacobian of a tropical hyperelliptic curve of genus $g$<br />
    via the intersection with a tropical curve of degree $3g/2$ or $3(g-1)/2$.

  • An ultradiscrete integrable map arising from a pair of tropical elliptic pencils

    Atsushi Nobe

    PHYSICS LETTERS A   375 ( 47 ) 4178 - 4182  2011.11  [Refereed]

     View Summary

    We present a tropical geometric description of a piecewise linear map whose invariant curve is a concave polygon. In contrast to convex polygons, a concave one is not directly related to tropical geometry; nevertheless the description is given in terms of the addition formula of a tropical elliptic curve. We show that the map arises from a pair of tropical elliptic pencils, each member of which is the invariant curve of an ultradiscrete QRT map. (C) 2011 Elsevier B.V. All rights reserved.

    DOI

  • Constructing two-dimensional integrable mappings that possess invariants of high degree

    Hironori Tanaka, Junta Matsukidaira, Atsushi Nobe, Teruhisa Tsuda

    RIMS Kokyuroku Bessatsu   B13   75 - 84  2009.10  [Refereed]  [Invited]

  • ULTRADISCRETIZATION OF A SOLVABLE TWO-DIMENSIONAL CHAOTIC MAP ASSOCIATED WITH THE HESSE CUBIC CURVE

    Kenji Kajiwara, Masanobu Kaneko, Atsushi Nobe, Teruhisa Tsuda

    KYUSHU JOURNAL OF MATHEMATICS   63 ( 2 ) 315 - 338  2009.09  [Refereed]

     View Summary

    We present a solvable two-dimensional piecewise linear chaotic mail that arises from the duplication map of a certain tropical cubic curve. Its general solution is constructed by means of the ultradiscrete theta function. We show that the map is derived by the ultradiscretization of the duplication map associated with the Hesse cubic curve. We also show that it is possible to obtain the non-trivial ultradiscrete limit of the solution in spite of a problem known as 'the minus-sign problem'

    DOI J-GLOBAL

  • Ultradiscretization of solvable one-dimensional chaotic maps

    Kenji Kajiwara, Atsushi Nobe, Teruhisa Tsuda

    JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL   41 ( 39 )  2008.10  [Refereed]

     View Summary

    We consider the ultradiscretization of a solvable one-dimensional chaotic map which arises from the duplication formula of the elliptic functions. It is shown that the ultradiscrete limit of the map and its solution yield the tent map and its solution simultaneously. A geometric interpretation of the dynamics of the tent map is given in terms of the tropical Jacobian of a certain tropical curve. Generalization to the maps corresponding to the mth multiplication formula of the elliptic functions is also discussed.

    DOI J-GLOBAL

  • Ultradiscrete QRT maps and tropical elliptic curves

    Atsushi Nobe

    JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL   41 ( 12 )  2008.03  [Refereed]

     View Summary

    It is shown that the polygonal invariant curve of the ultradiscrete QRT (uQRT) map, which is a two-dimensional piecewise linear integrable map, is the complement of the tentacles of a tropical elliptic curve on which the curve has a group structure in analogy to classical elliptic curves. Through the addition formula of a tropical elliptic curve, a tropical geometric description of the uQRT map is then presented. This is a natural tropicalization of the geometry of the QRT map found by Tsuda. Moreover, the uQRT map is linearized on the tropical Jacobian of the corresponding tropical elliptic curve in terms of the Abel- Jacobi map. Finally, a formula concerning the period of a point in the uQRT map is given, and an exact solution to its initial-value problem is constructed by using the ultradiscrete elliptic theta function.

    DOI J-GLOBAL

  • Linearizable cellular automata

    Atsushi Nobe, Fumitaka Yura

    JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL   40 ( 26 ) 7159 - 7174  2007.06  [Refereed]

     View Summary

    The initial value problem for a class of reversible elementary cellular automata with periodic boundaries is reduced to an initial- boundary value problem for a class of linear systems on a finite commutative ring Z(2). Moreover, a family of such linearizable cellular automata is given.

    DOI

  • Soliton-antisoliton collision in the ultradiscrete modified KdV equation

    S. Isojima, M. Murata, A. Nobe, J. Satsuma

    PHYSICS LETTERS A   357 ( 1 ) 31 - 35  2006.08  [Refereed]

     View Summary

    The discrete modified Korteweg-de Vries equation admits exact solutions with nondefinite sign, which describe interaction among solitons with positive and negative amplitude. In this Letter a transformation of hyperbolic sine type is proposed in order to ultradiscretize this equation and solutions. (c) 2006 Elsevier B.V. All rights reserved.

    DOI J-GLOBAL

  • Ultradiscretization of elliptic functions and its applications to integrable systems

    A Nobe

    JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL   39 ( 20 ) L335 - L342  2006.05  [Refereed]

     View Summary

    It is shown that there exist three kinds of ultradiscrete analogues of Jacobi's elliptic functions. In this process, the asymptotic behaviour of the poles and the zeros of the functions plays a crucial role. Using the ultradiscrete analogues and an addition formula, exact solutions to the ultradiscrete KP equation are constructed, and their relation to the ultradiscrete QRT system is discussed.

    DOI J-GLOBAL

  • Exact solutions for discrete and ultradiscrete modified KdV equations and their relation to box-ball systems

    M Murata, S Isojima, A Nobe, J Satsuma

    JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL   39 ( 1 ) L27 - L34  2006.01  [Refereed]

     View Summary

    A new class of solutions is proposed for discrete and ultradiscrete modified KdV equations. These are directly related to solutions of the box and ball system with a carrier. Moreover, an extended box and ball system and its exact solutions are discussed.

    DOI J-GLOBAL

  • Periodic multiwave solutions to the Toda-type cellular automaton

    A Nobe

    JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL   38 ( 43 ) L715 - L723  2005.10  [Refereed]

     View Summary

    An ultradiscretization of the Riemann theta function is proposed. The ultradiscretization satisfies an addition formula, which is an ultradiscrete analogue of an addition formula for the Riemann theta function. Using the addition formula, periodic multiwave solutions to the Toda-type cellular automaton are obtained.

    DOI J-GLOBAL

  • An ultradiscretization of the sine-Gordon equation

    S Isojima, M Murata, A Nobe, J Satsuma

    PHYSICS LETTERS A   331 ( 6 ) 378 - 386  2004.11  [Refereed]

     View Summary

    An ultradiscrete system corresponding to the sine-Gordon equation is proposed. A new dependent variable for the discrete sine-Gordon equation is introduced in order to apply the procedure of ultradiscretization. The ultradiscrete system possesses exact solutions which are directly related to soliton solutions of the discrete equation. (C) 2004 Elsevier B.V. All rights reserved.

    DOI J-GLOBAL

  • On reversibility of cellular automata with periodic boundary conditions

    A Nobe, F Yura

    JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL   37 ( 22 ) 5789 - 5804  2004.06  [Refereed]

     View Summary

    Reversibility of one-dimensional cellular automata with periodic boundary conditions is discussed. It is shown that there exist exactly 16 reversible elementary cellular automaton rules for infinitely many cell sizes by means of a correspondence between elementary cellular automaton and the de Bruijn graph. In addition, a sufficient condition for reversibility of three-valued and two-neighbour cellular automaton is given.

    DOI J-GLOBAL

  • On periodic mappings arising from the QRT system

    NOBE Atsushi

    Theoretical and Applied Mechanics Japan   52   229 - 237  2003.12  [Refereed]

     View Summary

    An eight-parameter family of two-dimensional piecewise linear mappings is discussed. Since the dynamical system is obtained from the QRT system through the ultradiscretization, the dynamical system is called the ultradiscrete QRT system. The ultradiscrete QRT system is considered to be integrable because it has an eight-parameter family of invariant curves which fills the plane. It is shown that, for particular parameters, the dynamical system can be regarded as a dynamical system on a fan associated with the conserved quantity. It is also shown that such a dynamical system has periodic solutions for any initial value. Therefore we call such a dynamical system the ultradiscrete periodic QRT system. From the ultradiscrete periodic QRT system, the periodic QRT system is obtained in terms of the inverse ultradiscretization.

    DOI J-GLOBAL

  • Stable Difference Equations Associated with Elementary Cellular Automata

    Atsushi Nobe, Junkichi Satsuma, Tetsuji Tokihiro

    Japan Journal of Industrial and Applied Mathematics   18 ( 2 ) 293 - 305  2001  [Refereed]

     View Summary

    We construct a difference equation which preserves any time evolution pattern of the rule 90 elementary cellular automaton. We also demonstrate that such difference equations can be obtained for any elementary cellular automata.

    DOI

  • From cellular automaton to difference equation: A general transformation method which preserves time evolution patterns

    A. Nobe, J. Satsuma, T. Tokihiro

    Journal of Physics A: Mathematical and General   34 ( 25 ) L371 - L379  2001  [Refereed]

     View Summary

    We propose a general method to construct a partial difference equation which preserves any time evolution patterns of a cellular automaton. The method is based on inverse ultradiscretization with filter functions. © 2001 IOP Publishing Ltd.

    DOI J-GLOBAL

  • Numerical analysis of breaking waves using the moving particle semi-implicit method

    S Koshizuka, A Nobe, Y Oka

    INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS   26 ( 7 ) 751 - 769  1998.04  [Refereed]

     View Summary

    The numerical method used in this study is the moving particle semi-implicit (MPS) method, which is based on particles and their interactions. The particle number density is implicitly required to be constant to satisfy incompressibility. A semi-implicit algorithm is used for two-dimensional incompressible non-viscous flow analysis. The particles whose particle number densities are below a set point are considered as on the free surface. Grids are not necessary in any calculation steps. It is estimated that most of computation time is used in generation of the list of neighboring particles in a large problem. An algorithm to enhance the computation speed is proposed. The MPS method is applied to numerical simulation of breaking waves on slopes. Two types of breaking waves, plunging and spilling breakers, are observed in the calculation results. The breaker types are classified by using the minimum angular momentum at the wave front. The surf similarity parameter which separates the types agrees well with references. Breaking waves are also calculated with a passively moving float which is modelled by particles. Artificial friction due to the disturbed motion of particles causes errors in the flow velocity distribution which is shown in comparison with the theoretical solution of a cnoidal wave. (C) 1998 John Wiley & Sons, Ltd.

    DOI J-GLOBAL

  • $A^{(1)}_N$型ミューテーションの可積分性について

    野邊厚, 松木平淳太

    応用力学研究所研究集会報告   No. 2019 ( AO-S2 ) 45 - 50  2020.03

    Authorship:Lead author

  • Cluster algebras and cellular automata

    野邊 厚

    数理解析研究所講究録   2071 ( 2071 ) 141 - 159  2018.04  [Invited]

     View Summary

    連続的なクイバーの変異とある群の台グラフへの作用が可換になる場合, 対応するクラスター変数の列はその台グラフ上の離散力学系とみることができる. このような離散力学系の解は正値性とLaurent性をもつため, 超離散化の手法を適用してセルオートマトンを導出することが可能である. 本稿においては, 平行移動群T(2)の作用と可換なクイバーの変異から離散KdV方程式や離散戸田格子などの離散可積分系を導出し, これらに超離散化を適用して箱玉系を構成する. さらに, 同様の手法を用いてA_{infty}型クイバーの変異から離散力学系を導出し, 適当な仮定の下で, その時間発展はルール204 ECAと見なせることを示す. また, このような離散力学系の一般解を構成する. 本研究は, 黒田謙吾氏(千葉大学), 問田潤氏(日本大学), 中田庸一氏(東京大学)との共同研究に基づいている.

    CiNii

  • ランク2ミューテーションの不変曲線について

    野邊 厚

    応用力学研究所研究集会報告   No.29AO-S7   69 - 74  2018.03  [Refereed]

  • Birational maps conjugate to the rank 2 cluster mutations of affine types and their geometry

    Atsushi Nobe

      1801.10320v1  2018.01

     View Summary

    Mutations of the cluster variables generating the cluster algebra of type
    $A^{(2)}_2$ reduce to a two-dimensional discrete integrable system given by a
    quartic birational map. The invariant curve of the map is a singular quartic
    curve, and its resolution of the singularity induces a discrete integrable
    system on a conic governed by a cubic birational map conjugate to the cluster
    mutations of type $A^{(2)}_2$. Moreover, it is shown that the conic is also the
    invariant curve of the quadratic birational map arising from the cluster
    mutations of type $A^{(1)}_1$ and the two birational maps on the conic are
    commutative. Finally, the commutative birational maps are reduced as singular
    limits of additions of points on an elliptic curve arising as the spectral
    curve of the discrete Toda lattice of type $A^{(1)}_1$.

  • $A^{(1)}_1$型クラスター代数の変異と離散戸田格子

    野邊 厚

    応用力学研究所研究集会報告   No.28AO-S6   25 - 30  2017.03  [Refereed]

  • 一般化戸田格子の超離散化

    野邊 厚

    応用力学研究所研究集会報告   No.26AO-S   1 - 7  2015.03  [Refereed]

  • 超離散周期戸田格子の幾何学的実現

    野邊 厚

    応用力学研究所研究集会報告   No.25AO-S2   114 - 120  2014.03  [Refereed]

  • 超楕円曲線に付随する倍角写像力学系

    野邊 厚

    応用力学研究所研究集会報告   No.24AO-S3   77 - 82  2013.03  [Refereed]

  • Addition in Jacobians of hyperelliptic curves and the periodic discrete Toda lattice

    NOBE Atsushi

    RIAM Report   No.23AO-S7   84 - 89  2012.03  [Refereed]

  • Successes and Challenges of a Training Program for Scientists Aiming to Open Up the Future with a Spirit of Independence and Perseverance

    NOMURA Jun, YAMASHIDA Shuichi, ARAKI Fumiyo, KATO Tetsuya, HORNE Beverley, NAKAZAWA Jun, IIZUKA Masaaki, ITAKURA Yoshiya, KATO Osamu, KINOSHITA Ryu, SUGITA Katsuo, SUZUKI Takashi, TOZAKI Kenichi, SEO Yasuhiko, NOZAKI Tomoko, NOBE Atsushi, HAYASHI Hideko, YONEDA Chie, TOMOKIYA Satomi, KAWAKAMI Kikuko

    Journal of Science Education in Japan   36 ( 2 ) 122 - 130  2012

     View Summary

    With the support of JST we carried out research into developing a study program, "Fostering Next-Generation Scientists". This program for fostering talented young scientists, which was created by Chiba University, selects and trains participants in two stages. The program offers its participants the opportunity to experience advanced lectures and conduct experiments in the fields of Physics, Chemistry, Mathematics, Engineering, and Life Sciences. We are currently carrying out courses from the first to the third stage. There were 470 applicants for the program, of which 28 have completed the whole curriculum. Those who completed the program have given presentations on their research. They have also entered scientific essay competitions and won various awards such as a prize for excellence. Chiba University's program for fostering talented young scientists has been effective in selecting and developing the talents of students with a spirit of independence and perseverance.

    DOI CiNii

  • The group law on the tropical Hesse pencil

    Atsushi Nobe

      1111.0131v1  2011.11

     View Summary

    We show that the addition of points on the tropical Hesse curve can be
    realized via the intersection with a tropical line. Then the addition formula
    for the tropical Hesse curve is reduced from those for the level-three theta
    functions through the ultradiscretization procedure. A tropical analogue of the
    Hessian group, the group of linear automorphisms acting on the Hesse pencil, is
    also investigated; it is shown that the dihedral group of degree three is the
    group of linear automorphisms acting on the tropical Hesse pencil.

    DOI

  • On the addition formula for the tropical Hesse pencil (Diversity of the Theory of Integrable Systems)

    NOBE Atsushi

    RIMS Kokyuroku   1765   188 - 208  2011.09  [Invited]

    Authorship:Lead author, Corresponding author

     View Summary

    We give the addition formula for the tropical Hesse pencil, which is the<br />
    tropicalization of the Hesse pencil parametrized by the level-three theta<br />
    functions, via those for the ultradiscrete theta functions. The ultradiscrete<br />
    theta functions are reduced from the level-three theta functions through the<br />
    procedure of ultradiscretization by choosing their parameters appropriately.<br />
    The parametrization of the level-three theta functions firstly introduced in<br />
    \cite{KKNT09} gives an explicit correspondence between the amoeba of the real<br />
    part of the Hesse cubic curve and the tropical Hesse curve. Moreover, through<br />
    the parametrization, we obtain the subtraction-free forms of the addition<br />
    formulae for the level-three theta functions, which lead to the addition<br />
    formula for the tropical Hesse pencil in terms of the ultradiscretization.<br />
    Using the parametrization, the tropical counterpart of the Hesse configuration<br />
    is also given.

    CiNii

  • A tropical analogue of the Hessian group

    Atsushi Nobe

    RIAM Report No.22AO-S8 (2011) 37-42    2011.04

     View Summary

    We investigate a tropical analogue of the Hessian group $G_{216}$, the group
    of linear automorphisms acting on the Hesse pencil. Through the procedure of
    ultradiscretization, the group law on the Hesse pencil reduces to that on the
    tropical Hesse pencil. We then show that the dihedral group $\mathcal{D}_3$ of
    degree three is the group of linear automorphisms acting on the tropical Hesse
    pencil.

  • 周期写像を用いた高次保存量を持つ可積分方程式の生成

    田中 宏典, 津田 照久, 野邊 厚, 松木平 淳太

    応用力学研究所研究集会報告   No.21ME-S7   166 - 172  2010.03

  • QRT系から生成される高次保存量を持つ2階差分方程式

    田中 宏典, 野邊 厚, 松木平 淳太

    応用力学研究所研究集会報告   No.20ME-S7   175 - 181  2009.03

  • ブラウン写像について

    応用力学研究所研究集会報告   20ME-S7 35-42  2009

  • トロピカル楕円曲線と超離散QRT系

    九州大学応用力学研究所研究集会報告   19ME-S2 Article No.6  2008

  • 可逆エレメンタリーセルオートマトンの可積分性について(可積分系数理の眺望)

    野邊 厚, 由良 文孝

    数理解析研究所講究録   1541   178 - 191  2007.04  [Invited]

    CiNii

  • リーマンテータ関数の超離散化とその可積分系への応用

    九州大学応用力学研究所研究集会報告   No.17ME-S2  2006

  • Sine-Gordon方程式のある超離散化

    九州大学応用力学研究所研究集会報告   15ME-S3 88-93  2004

  • 周期境界をもつセルオートマトンの可逆性について

    野邊厚

    九州大学応用力学研究所研究集会報告   15ME-S3 82-87  2004

  • 超離散QRT系と扇について

    九州大学応用力学研究所研究集会報告   14ME-S7 165-170  2003

  • Stable dynamical systems associated with cellular automata

    Doctoral thesis, Univ. of Tokyo    2002

  • セルオートマトンと微分方程式 (離散可積分系の応用数理)

    野辺 厚

    数理解析研究所講究録   1098   14 - 22  1999.04  [Invited]

    Authorship:Lead author, Corresponding author

     View Summary

    RIMS研究集会「離散可積分系の応用数理」

    CiNii

▼display all

Books and Other Publications

  • ``Reversibility of Cellular Automata'' in Cellular Automata, ed. Thomas M. Li

    Atsushi Nobe, Fumitaka Yura( Part: Contributor)

    Nova Science Publishers  2011

  • Expansion of Integrable Systems, RIMS Kokyuroku Bessatsu B13

    Atsushi Nobe( Part: Edit)

    Research Institute for Mathematical Sciences, Kyoto University  2009  [Refereed]

Misc

  • アフィン型ミューテーションの可積分性について

    野邊厚, 松木平淳太

    日本応用数理学会年会講演予稿集(CD-ROM)   2019   560‐561  2019.08

    J-GLOBAL

  • A2(2)型クラスター代数の生成元について

    野邊厚

    日本応用数理学会年会講演予稿集(CD-ROM)   2018   241‐242  2018.09

    J-GLOBAL

  • A2(2)型マトリックスミューテーションの幾何学

    野邊厚

    日本応用数理学会年会講演予稿集(CD-ROM)   2017   467‐468  2017.09

    J-GLOBAL

  • クラスター代数とセルオートマトン

    野邊厚, 間田潤

    日本応用数理学会年会講演予稿集(CD-ROM)   2016   ROMBUNNO.9GATSU13NICHI,09:30,1A,3  2016

    J-GLOBAL

  • 離散戸田格子とQRT系

    野邊厚

    日本応用数理学会年会講演予稿集(CD-ROM)   2015   ROMBUNNO.9GATSU9NICHI,09:30,E,4  2015.09

    J-GLOBAL

  • C(1)N型超離散戸田格子と戸田型セルオートマトン

    野邊厚

    日本応用数理学会年会講演予稿集(CD-ROM)   2014   ROMBUNNO.9GATSU4NICHI,09:30,D,2  2014.08

    J-GLOBAL

  • 周期箱玉系の幾何学的実現

    野邊厚

    日本物理学会講演概要集   68 ( 2 ) 238  2013.08

    J-GLOBAL

  • 周期箱玉系の幾何学的実現

    野邊厚

    日本応用数理学会年会講演予稿集(CD-ROM)   2013   ROMBUNNO.9051  2013

    J-GLOBAL

  • A geometric realization of the periodic box-ball system

    Nobe Atsushi

    Meeting Abstracts of the Physical Society of Japan   68 ( 0 )  2013

    CiNii

  • 1A-05 「未来の科学者養成講座」と「キャリア教育」 : 理数学習支援における人材育成(一般研究発表(口頭発表))

    若月 聡, 野村 純, 中澤 潤, 飯塚 正明, 板倉 嘉哉, 加藤 修, 加藤 徹也, 塩田 瑠美, 鈴木 隆司, 妹尾 裕彦, 東崎 健一, 野崎 とも子, 野邊 厚, 林 英子, 米田 千恵, 川上 喜久子

    日本理科教育学会全国大会要項   ( 60 ) 119 - 119  2010

    CiNii

  • 周期写像を用いた高次保存量を持つ可積分方程式の生成

    田中宏典, 津田照久, 野邊厚, 松木平淳太

    日本応用数理学会年会講演予稿集   2009   251 - 252  2009.09

    J-GLOBAL

  • On the Brown map

    Reports of RIAM symposium   20ME-S7 35-42  2009

  • 27aQC-3 Two-dimensional integrable maps which possess invariants of high degree

    Nobe A., Matsukidaira J., Tanaka H., Tsuda T.

    Meeting Abstracts of the Physical Society of Japan   64 ( 0 ) 201 - 201  2009

    DOI CiNii

  • Tropical elliptic curves and ultradiscrete QRT maps

    Reports of RIAM Symposium   19ME-S2 Article No.6  2008

  • 24pWD-4 超離散QRT写像とトロピカル楕円曲線(古典・量子可積分系(数値計算アルゴリズムを含む),領域11,統計力学,物性基礎論,応用数学,力学,流体物理)

    野邊 厚

    日本物理学会講演概要集   63 ( 0 )  2008

    CiNii

  • 18aWB-3 Linearizable cellular automata

    Nobe Atsushi, Yura Fumitaka

    Meeting Abstracts of the Physical Society of Japan   62 ( 0 )  2007

    CiNii

  • Ultradiscretization of the Riemann theta functions and its applications to integrable systems

    RIAM Symposium "Phenomena and Mathematical Theory of Nonlinear Waves and Nonlinear Dynamical Systems"   No.17ME-S2  2006

  • 27aXE-5 Ultradiscretization of elliptic functions and its applications to integrable systems

    Nobe Atsushi

    Meeting Abstracts of the Physical Society of Japan   61 ( 0 )  2006

    CiNii

  • 東京大学大学院数理科学研究科平成15年度研究成果報告書

    野邊厚

        133 - 134  2004.03

    Authorship:Lead author, Corresponding author

  • Ultradiscrete QRT system and fans

    NOBE Atsushi

    NCTAM papers, National Congress of Theoretical and Applied Mechanics, Japan   52 ( 0 ) 149 - 149  2003

     View Summary

    超離散QRT系とは、8個のパラメータを含む区分線形写像で与えられる二次元の力学系である。この力学系はQRT系とよばれる二次元の離散可積分系から超離散化により得られ、一つの保存量をもつので可積分である。保存量を与える区分線形方程式から平面の分割が定まるが、パラメータがある関係を満たすときにはその分割から扇を得ることが出来る。このような場合、時間発展は扇の写像となるので超離散QRT系は扇の力学系とみなすことができ、任意の初期値に対して一定周期の解をもつことが示せる。扇の力学系となる場合は全部で24通りあり、それらの解の周期は2,3,4,5,6,7,8および無限大のいずれかである。

    CiNii

  • Ultradiscrete QRT System

    Nobe Ataushi

    Meeting Abstracts of the Physical Society of Japan   57 ( 0 )  2002

    CiNii

  • Cellular Automata and Differencial Equations

    SATSUMA Junkichi, TOKIHIRO Tetsuji, NOBE Atsushi

    Meeting Abstracts of the Physical Society of Japan   53 ( 0 )  1998

    CiNii

  • Cellular Automata and Diffution Equations

    NOBE A, SATSUMA J, TOKIHIRO T, OHTA Y

    Meeting Abstracts of the Physical Society of Japan   53 ( 0 )  1998

    CiNii

▼display all

Research Projects

  • Integrability of dynamical systems that exhibit Laurent phenomena and positivity and their algebraic entropy

    Japan Society for the Promotion of Science  Grants-in-Aid for Scientific Research Grant-in-Aid for Scientific Research (C)

    Project Year :

    2020.04
    -
    2023.03
     

    Atsushi Nobe

  • Studies on discrete integrable systems via tropical algebraic curves

    Japan Society for the Promotion of Science  Grants-in-Aid for Scientific Research Grant-in-Aid for Scientific Research (C)

    Project Year :

    2014.04
    -
    2018.03
     

    Nobe Atsushi

     View Summary

    First we considered Lie-algebraic generalizations of the Toda lattice. We realized the generalized Toda lattices of types A(2)2N, C(1)N and D(2)N as the sub-dynamical systems of the Toda lattices of types A(1)2N-1, A(1)2N, A(1)2N+1, respectively. We also obtained their tropical analogues.
    Next we studied a tropical analogue of the Hessian group, which is the group of linear automorphisms acting on the Hesse pencil. We then obtained the dihedral group of degree 3 as the group of linear automorphisms acting on the tropical analogue of the Hesse pencil.
    We moreover investigated the cluster algebras of rank 2 from the view point of discrete integrable systems. We gave the conserved quantities of the dynamical systems arising from the cluster algebras of types A1*A1, A2, B2, G2, A(1)1 and A(2)2. We also showed direct connections between the dynamical systems and the Mordell-Weil groups of the elliptic curves arising via the conserved quantities of the dynamical systems.

  • Studies on the geometry of discrete integrable systems and solvable chaotic systems

    Japan Society for the Promotion of Science  Grants-in-Aid for Scientific Research Grant-in-Aid for Young Scientists (B)

    Project Year :

    2010.04
    -
    2014.03
     

    NOBE Atsushi

     View Summary

    We establish a geometric realization of the periodic discrete Toda lattice of an arbitrary system size by using the intersection of its spectral curve and other two curves. This realization is reduced from the addition of points on the symmetric product of the spectral curve, and the curves in the realization are concretely given by using the conserved quantities of the periodic discrete Toda lattice.
    We also establish a geometric realization of the ultradiscrete periodic Toda lattice of an arbitrary system size, which is an ultradiscrete analogue of the periodic discrete Toda lattice, via tropical plane curves. The tropical curves in the realization, one of which is the spectral curve of the ultradiscrete periodic Toda lattice (a tropical hyperelliptic curve), are also given by using the conserved quantities of the ultradiscrete periodic Toda lattice.

  • Tropical geometry and integrable systems

    Japan Society for the Promotion of Science  Grants-in-Aid for Scientific Research Grant-in-Aid for Young Scientists (B)

    Project Year :

    2007.04
    -
    2010.03
     

    NOBE Atsushi

     View Summary

    We construct an 8-parameter family of two-dimensional bi-piecewise linear maps in terms of the addition of the points on tropical elliptic curves, and obtain the general solution for each member of the family. Through the ultradiscretization procedure, we associate the family with an 18-parameter family of two-dimensional birational maps called the QRT map including its general solutions. Similarly, applying such technique to solvable chaotic maps induced from the duplication of points on tropical elliptic curves, we obtain their general solution and clarify the correspondence to the rational maps induced from the duplication of points on elliptic curves. Moreover, we show that there exists a family of cellular automata each of which has a property called the linearizability. Then we obtain a formula concerning the fundamental period with respect to the time evolution of the family imposing periodic boundary conditions.

  • ソリトン方程式の超離散解析

    日本学術振興会  科学研究費助成事業 若手研究(B)

    Project Year :

    2005.04
    -
    2007.03
     

    野邊 厚

     View Summary

    平成18年度は次に挙げる研究を行った.
    (1)Jacobiの楕円関数の超離散化およびその可積分系への応用
    (2)双曲型sin関数を用いた変形KdV方程式の超離散化
    (3)可逆エレメンタリーセルオートンマトンの可積分性
    Jacobiの楕円関数の超離散化については既に先行する研究があったが,そこでは母数の超離散極限値が1の場合しか考慮されていなかった.そこで,(1)において,母数の超離散極限値全て(0,1,∞)について考察し,それぞれの場合におけるJacobiの楕円関数の超離散化を求めた.いずれの場合にもいても三つの楕円関数のうちの二つのみ周期関数となり,残りの一つは定数関数となることが示された.また,このようにして得られた超離散sn関数を用いて超離散QRT系の解を構成した.
    これまでの超離散化手法では零点を含むような関数を直接超離散化することはできなかった.しかし,(2)において,双曲型sin関数を用いた新しい超離散化手法を導入し,零点を含むような関数も超離散化可能であることを示した.さらに,この超離散化手法を用いて,変形KdV方程式のソリトンと反ソリトンの衝突が超離散系においても再現されることを示した.
    これまで箱玉系以外の可積分セルオートマトンはほとんど発見されていなかった.そこで,可逆セルオートマトンの中から可積分セルオートマトンを発見すべく,(3)において,可逆エレメンタリーセルオートマトンについて詳しく調べ,その中に線形化可能なセルオートマトンが存在することを示した.すなわち,初期状態を適切に分割することにより,周期境界をもつある非線形可逆セルオートマトンの初期値問題が,ある線形系の初期値境界値問題に帰着されることを示した.また,そのような線形化可能セルオートマトンの基本周期の明示公式を得た.

  • グラフ上のchip-firingと可積分系

    千葉大学  研究費獲得促進プログラム(多様型B)

    Project Year :

    2019.04
    -
    2020.03
     

  • 量子群の表現論と可積分系

    日本学術振興会  科学研究費補助金 基盤研究(C)

    Project Year :

    2008.04
    -
    2011.03
     

    尾角 正人

  • 8th International Conference on ``Symmetry and Integrability of Difference Equations (SIDE8)'

    日本学術振興会  国際学会等派遣事業

    Project Year :

    2008.04
    -
    2009.03
     

    野邊 厚

  • 可積分系と組合せ論的表現論

    日本学術振興会  科学研究費補助金 基盤研究(C)

    Project Year :

    2006.04
    -
    2009.03
     

    尾角 正人

  • 統計力学に現れる非線形偏微分方程式の数学的研究

    日本学術振興会  科学研究費補助金 基盤研究(B)

    Project Year :

    2004.04
    -
    2009.03
     

    鈴木 貴

  • 脈管形成の数理モデルに関する解析的研究

    日本学術振興会  科学研究費補助金 萌芽研究

    Project Year :

    2004.04
    -
    2006.03
     

    鈴木 貴

  • クリスタル基底の組合せ論的研究と離散可積分系への応用

    日本学術振興会  科学研究費補助金 基盤研究(C)

    Project Year :

    2004.04
    -
    2005.03
     

    尾角 正人

▼display all

Presentations

  • A family of integrable and non-integrable difference equations arising from cluster algebras

    NOBE Atsushi  [Invited]

    Cluster Algebras 2019  (Research Institute for Mathematical Science) 

    Presentation date: 2019.06

    Event date:
    2019.06
     
     
  • クラスター代数とカオス

    野邊 厚  [Invited]

    研究集会「離散力学系と組合せ論」  (津田塾大学小平キャンパス)  津田塾大学 数学・計算機科学研究所

    Presentation date: 2019.02

    Event date:
    2019.02
     
     
  • Chaos in cluster algebras

    NOBE Atsushi  [Invited]

    Presentation date: 2018.09

    Event date:
    2018.09
     
     
  • Mutations of cluster algebras and discrete integrable systems

    NOBE Atsushi  [Invited]

    The Tenth IMACS International Conference on Nonlinear Evolution Equations and Wave Phenomena: Computation and Theory  (Georgia Center for Continuing Education University of Georgia, Athens, GA) 

    Presentation date: 2017.03

    Event date:
    2017.03
    -
    2017.04
  • Tropical elliptic curves and discrete integrable systems

    NOBE Atsushi  [Invited]

    Workshop on Tropical geometry - basic and applications 

    Presentation date: 2017.01

  • Ultradiscretization of generalized Toda lattices

    NOBE Atsushi  [Invited]

    Workshop on Integrable and nonintegrable lattice models: theory and computation 

    Presentation date: 2016.07

  • セルオートマトンの幾何学 -- トロピカル超楕円曲線とソリトンセルオートマトン --

    野邊 厚  [Invited]

    早稲田大学理工学術院 数物コロキウム 

    Presentation date: 2013.10

  • 周期離散戸田格子の幾何学的実現とそのトロピカル化

    野邊 厚  [Invited]

    RIMS研究集会「非線形離散可積分系の新展開」 

    Presentation date: 2013.09

  • A geometric realization of the periodic discrete Toda lattice and its tropicalization

    NOBE Atsushi

    China-Japan Joint Workshop on Integrable Systems 2013 

    Presentation date: 2013.03

  • Integrable maps arising from the addition on tropical elliptic curves

    NOBE Atsushi  [Invited]

    Mini-Workshop: Tropical geometry and ultradiscrete integrable systems, NEEDS 2012 

    Presentation date: 2012.07

  • Tropical Jacobian of a hyperelliptic curve

    NOBE Atsushi  [Invited]

    International Workshop on Tropical and Quantum Geometries 

    Presentation date: 2012.02

  • トロピカル超楕円曲線のJacobi多様体における加法

    野邊 厚  [Invited]

    RIMS研究集会「可積分系数理の進化」 

    Presentation date: 2011.08

  • セルオートマトンとトロピカル幾何学

    野邊 厚  [Invited]

    明治大学 第9回現象数理若手シンポジウム「セルオートマトンは現象数理学の武器となりうるか?」 

    Presentation date: 2011.02

  • トロピカルHesse曲線の加法公式について

    野邊 厚  [Invited]

    RIMS研究集会「可積分系数理の多様性 - Diversity of the Theory of Integrable Systems -」 

    Presentation date: 2010.08

  • Tropicalization of a solvable chaotic map associated with the Hesse cubic curve

    野邊 厚  [Invited]

    研究集会「離散・超離散系の課題」 

    Presentation date: 2010.03

  • non-QRT mappingについて

    野邊 厚  [Invited]

    龍谷数理科学セミナー 

    Presentation date: 2009.12

  • トロピカル楕円曲線の加法の定める力学系について

    野邊 厚  [Invited]

    語ろう数理解析 第74回セミナー 

    Presentation date: 2009.12

  • 超離散可積分系とトロピカル楕円曲線

    野邊 厚  [Invited]

    デジタル解析学セミナー 

    Presentation date: 2009.07

  • Hesseの3次曲線のトロピカル化と可解カオス写像

    野邊 厚  [Invited]

    研究集会「トロピカル幾何と超離散系の展開」 

    Presentation date: 2009.03

  • Tropical curves, integrable maps and solvable chaos

    NOBE Atsushi  [Invited]

    Workshop ``Crystals and Tropical Combinatorics'' 

    Presentation date: 2008.08

  • トロピカル楕円曲線と超離散QRT系

    野邊 厚  [Invited]

    九州可積分系セミナー 

    Presentation date: 2007.12

  • トロピカル楕円曲線と超離散QRT系

    野邊 厚  [Invited]

    古典解析セミナー 

    Presentation date: 2007.11

  • 可逆エレメンタリーセルオートマトンの可積分性について

    野邊 厚  [Invited]

    RMS研究集会「可積分系数理の眺望」 

    Presentation date: 2006.08

  • 離散非線形Schr\"odinger方程式のソリトン解について

    野邊 厚  [Invited]

    研究集会「シミュレーションの数理科学」 

    Presentation date: 2004.05

  • セルオートマトンと微分方程式

     [Invited]

    短期共同研究「離散可積分系の応用数理」 

    Presentation date: 1998.07

  • アフィン型ミューテーションの周期性と線形化

    野邊厚, 松木平淳太

    日本応用数理学会2020年度年会  (オンライン)  日本応用数理学会

    Presentation date: 2020.09

    Event date:
    2020.09
     
     
  • $A^{(1)}_N$型ミューテーションの線形化

    野邊厚, 松木平淳太

    第16回日本応用数理学会研究部会連合発表会  (中央大学)  日本応用数理学会

    Presentation date: 2020.03

    Event date:
    2020.03
     
     
  • $A^{(1)}_N$型ミューテーションの可積分性について

    野邊厚, 松木平淳太

    応用力学研究所研究集会「非線形波動研究の多様性」  (九州大学応用力学研究所) 

    Presentation date: 2019.11

    Event date:
    2019.10
    -
    2019.11
  • アフィン型ミューテーションの可積分性について

    野邊厚, 松木平淳太

    日本応用数理学会2019年度年会  (東京大学駒場キャンパス)  日本応用数理学会

    Presentation date: 2019.09

    Event date:
    2019.09
     
     
  • クラスター代数とカオス

    野邊 厚

    第15回日本応用数理学会研究部会連合発表会 

    Presentation date: 2019.03

  • $A^{(2)}_2$型クラスター代数の生成元について

    野邊 厚

    日本応用数理学会 2018年度年会 

    Presentation date: 2018.09

  • ランク2ミューテーションの不変曲線について

    野邊 厚

    九州大学応用力学研究所研究集会「非線形波動研究の新潮流 -- 理論とその応用 -- 」  (九州大学応用力学研究所) 

    Presentation date: 2017.11

  • A2(2)型マトリックスミューテーションの幾何学

    野邊厚

    日本応用数理学会2017年度年会  (武蔵野大学有明キャンパス)  日本応用数理学会

    Presentation date: 2017.09

    Event date:
    2017.09
     
     
  • $A^{(1)}_1$型クラスター代数の変異と離散戸田格子

    野邊 厚

    九州大学応用力学研究所研究集会「非線形波動研究の深化と展開」  (九州大学応用力学研究所) 

    Presentation date: 2016.11

    Event date:
    2016.11
     
     
  • $A^{(1)}_1$型クラスター代数の変異と離散戸田格子

    野邊 厚

    日本数学会 2016年度秋季総合分科会 

    Presentation date: 2016.09

  • クラスター代数とセルオートマトン

    野邊厚, 間田潤

    Presentation date: 2016.09

    Event date:
    2016.09
     
     
  • クラスター代数とセルオートマトン

    野邊厚  [Invited]

    RIMS研究集会「可積分系数理の現状と展望」  (京都大学数理解析研究所) 

    Presentation date: 2016.09

    Event date:
    2016.09
     
     
  • クラスター代数とQRT系

    野邊厚, 間田潤

    第12回 日本応用数理学会 研究部会連合発表会  (神戸学院大学)  日本応用数理学会

    Presentation date: 2016.03

    Event date:
    2016.03
     
     
  • 戸田格子とクラスター代数

    野邊 厚

    2015年度 応用数学合同研究集会 

    Presentation date: 2015.12

  • Toda lattice, QRT maps, and cluster algebras

    野邊 厚

    MIMS共同研究集会「可積分系が拓く現象数理モデル」 

    Presentation date: 2015.11

  • 戸田格子とクラスター代数

    野邊厚  [Invited]

    数学教室談話会  (東京理科大学理工学部) 

    Presentation date: 2015.11

  • 離散戸田格子とQRT系

    野邊厚

    Presentation date: 2015.09

    Event date:
    2015.09
     
     
  • 周期戸田格子を用いて実現可能な一般化戸田格子について

    野邊 厚

    第11回 日本応用数理学会 研究部会連合発表会 

    Presentation date: 2015.03

  • 一般化戸田格子の超離散化

    野邊 厚

    九州大学応用力学研究所研究集会「非線形波動研究の現状—課題と展望を探る—」 

    Presentation date: 2014.10

  • C(1)N型超離散戸田格子と戸田型セルオートマトン

    野邊厚

    Presentation date: 2014.09

    Event date:
    2014.09
     
     
  • $C^{(1)}_N$型離散戸田格子の幾何学的実現

    野邊 厚

    第10回 日本応用数理学会 研究部会連合発表会 

    Presentation date: 2014.03

  • 周期離散戸田格子の幾何学的実現とトロピカル化

    野邊 厚

    九州大学応用力学研究所研究集会「非線形波動研究の拡がり」 

    Presentation date: 2013.11

  • 周期箱玉系の幾何学的実現

    野邊厚

    Presentation date: 2013.09

    Event date:
    2013.09
     
     
  • 周期箱玉系の幾何学的実現

    野邊 厚

    日本数学会 2013年度秋季総合分科会 

    Presentation date: 2013.09

  • 周期箱玉系の幾何学的実現

    野邊 厚

    日本応用数理学会 2013年度年会  (アクロス福岡)  日本応用数理学会

    Presentation date: 2013.09

    Event date:
    2013.09
     
     
  • 超楕円曲線に付随する可解カオス系

    野邊 厚

    九州大学応用力学研究所研究集会「非線形波動研究の最前線 -- 構造と現象の多様性 -- 」 

    Presentation date: 2012.11

  • 離散周期戸田格子の幾何学的実現

    野邊 厚

    第9回日本応用数理学会 研究部会連合発表会 

    Presentation date: 2012.03

  • 超楕円曲線の加法と可積分系 -- 差分および超離散 --

    野邊 厚

    九州大学応用力学研究所研究集会「非線形波動研究の進展 -- 現象と数理の相互理解 -- 」 

    Presentation date: 2011.10

  • トロピカルHesse曲線の加法公式について

    野邊 厚

    日本数学会2011年度年会 

    Presentation date: 2011.03

  • The group law on the tropical Hesse pencil

    野邊 厚

    九州大学応用力学研究所研究集会「非線形波動研究の新たな展開 -- 現象とモデル化 -- 」 

    Presentation date: 2010.10

  • Hesseの3次曲線に附随する可解カオス力学系の超離散化

    梶原 健司, 金子 昌信, 野邊 厚, 津田 照久

    超幾何方程式研究会2010 

    Presentation date: 2010.01

  • 高次保存量を持つ2階可積分方程式について

    松木平淳太, 田中宏典, 野邊厚, 津田照久

    九州大学応用力学研究所研究集会「非線形波動研究の現状と将来 -- 次の10年への展望」  (九州大学応用力学研究所) 

    Presentation date: 2009.11

    Event date:
    2009.11
     
     
  • カオス系の超離散化

    梶原 健司, 金子 昌信, 野邊 厚, 津田 照久

    九州大学応用力学研究所研究集会「非線形波動研究の現状と将来 -- 次の10年への展望」 

    Presentation date: 2009.11

  • 周期写像を用いた高次保存量を持つ可積分方程式の生成

    田中宏典, 津田照久, 野邊厚, 松木平淳太

    日本応用数理学会2009年度年会  (大阪大学豊中キャンパス)  日本応用数理学会

    Presentation date: 2009.09

    Event date:
    2009.09
     
     
  • 高次保存量をもつ2次元可積分写像

    野邊厚, 松木平淳太, 田中宏典, 津田照久

    Presentation date: 2009.09

    Event date:
    2009.09
     
     
  • Hesseの3次曲線に附随する2次元可解カオス系の超離散化

    梶原 健司, 金子 昌信, 野邊 厚, 津田 照久

    日本数学会2009年秋季総合分科会  (大阪大学豊中キャンパス)  日本数学会

    Presentation date: 2009.09

    Event date:
    2009.09
     
     
  • Ultradiscretization of solvable chaotic maps and the tropical geometry

    Kenji Kajiwara, Atsushi Nobe, Teruhisa Tsuda

    Workshop ``Geometric aspects of discrete and ultra-discrete integrable systems''  (University of Glasgow, Glasgow) 

    Presentation date: 2009.04

  • QRT系から生成される高次保存量を持つ2階差分方程式

    田中宏典, 松木平淳太, 野邊厚, 津田照久

    第5回日本応用数理学会研究部会連合発表会  (京都大学)  日本応用数理学会

    Presentation date: 2009.03

  • Hesseの3次曲線のトロピカル化と可解カオス写像

    野邊 厚

    第4回非線形テクノサイエンス講演会 

    Presentation date: 2009.03

  • QRT系から生成される高次保存量を持つ2階差分方程式

    田中 宏典, 野邊 厚, 松木平 淳太

    九州大学応用力学研究所研究集会「非線形波動の数理と物理」 

    Presentation date: 2008.11

  • ブラウン写像について

    野邊 厚

    九州大学応用力学研究所研究集会「非線形波動の数理と物理」 

    Presentation date: 2008.11

  • 1次元可解カオス系の超離散化とトロピカル幾何

    梶原 健司, 野邊 厚, 津田 照久

    日本数学会2008年秋季総合分科会 

    Presentation date: 2008.09

  • Ultradiscretization of one-dimensional solvebale chaotic systems and tropical geometry

    KAJIWARA Kenji, NOBE Atsushi, TSUDA Teruhisa

    Presentation date: 2008.09

    Event date:
    2008.09
     
     
  • 超離散QRT写像とトロピカル楕円曲線

    野邊 厚

    日本物理学会2008年春季大会 

    Presentation date: 2008.03

  • トロピカル楕円曲線と超離散QRT系

    野邊 厚

    研究集会「ソリトンの数理とその応用」  (湯田簡易保険保養センター) 

    Presentation date: 2007.12

  • トロピカル楕円曲線と超離散QRT系

    野邊 厚

    九州大学応用力学研究所研究集会「戸田格子40周年 非線形波動研究の歩みと展望」 

    Presentation date: 2007.11

  • 線形化可能セルオートマトン

    野邊 厚, 由良 文孝

    日本物理学会2007年春季大会 

    Presentation date: 2007.03

  • 楕円関数の超離散化とその可積分系への応用

    野邊 厚

    日本物理学会2006年春季大会 

    Presentation date: 2006.03

  • リーマンテータ関数の超離散化とその可積分系への応用

    野邊 厚

    九州大学応用力学研究所研究集会「非線形波動および非線形力学系の現象と数理」 

    Presentation date: 2005.11

  • Ultradiscrete Theta Functions

    野邊 厚

    研究集会「離散・超離散可積分系の数理とその応用」  (ホテル大佐渡) 

    Presentation date: 2005.10

  • 戸田型セルオートマトンの周期波解

    野邊 厚

    日本数学会秋季総合分科会 

    Presentation date: 2005.09

  • 非正値変数の超離散化

    礒島 伸, 村田 実貴生, 野邊 厚, 薩摩 順吉

    日本数学会秋季総合分科会 

    Presentation date: 2004.09

  • 周期境界をもつセルオートマトンの可逆性について

    野邊 厚

    九州大学応用力学研究所研究集会「非線形波動および非線形力学系の数理とその応用」 

    Presentation date: 2003.11

  • Sine-Gordon方程式のある超離散化

    礒島 伸, 村田 実貴生, 野邊 厚, 薩摩 順吉

    九州大学応用力学研究所研究集会「非線形波動および非線形力学系の数理とその応用」 

    Presentation date: 2003.11

  • Ultradiscrete QRT system and fans

    NOBE Atsushi

    National Congress of Theoretical and Applied Mechanics, Japan 

    Presentation date: 2003.01

     View Summary

    超離散QRT系とは、8個のパラメータを含む区分線形写像で与えられる二次元の力学系である。この力学系はQRT系とよばれる二次元の離散可積分系から超離散化により得られ、一つの保存量をもつので可積分である。保存量を与える区分線形方程式から平面の分割が定まるが、パラメータがある関係を満たすときにはその分割から扇を得ることが出来る。このような場合、時間発展は扇の写像となるので超離散QRT系は扇の力学系とみなすことができ、任意の初期値に対して一定周期の解をもつことが示せる。扇の力学系となる場合は全部で24通りあり、それらの解の周期は2,3,4,5,6,7,8および無限大のいずれかである。

  • 超離散QRT系と扇について

    野邊 厚

    九州大学応用力学研究所研究集会「非線形波動および非線形力学系に関する最近の話題」 

    Presentation date: 2002.11

  • 超離散QRT系

    野邊 厚

    日本物理学会2002年秋季大会  (中部大学)  日本物理学会

    Presentation date: 2002.09

  • Stable difference equations associated with elementary cellular automata

    NOBE Atsushi, SATSUMA Junkichi, TOKIHIRO Tetsuji

    4th International Interdisciplinary Meeting on ``Symmetries and Integrability of Difference Equations (SIDE4)" 

    Presentation date: 2000.11

  • フラクタル構造を示すある安定な差分方程式

    野邊 厚, 薩摩 順吉, 時弘 哲治

    日本応用数理学会2000年秋の分科会 

    Presentation date: 2000.10

  • Cellular Automata and Differencial Equations

    SATSUMA Junkichi, TOKIHIRO Tetsuji, NOBE Atsushi

    Meeting Abstracts of the Physical Society of Japan 

    Presentation date: 1998.09

  • Cellular Automata and Diffution Equations

    NOBE A, SATSUMA J, TOKIHIRO T, OHTA Y

    Meeting Abstracts of the Physical Society of Japan 

    Presentation date: 1998.09

  • セルオートマトンと微分方程式の対応

    野辺厚

    日本応用数理学会1998年度年会  (早稲田大学)  日本応用数理学会

    Presentation date: 1998.09

    Event date:
    1998.09
     
     
  • 粒子法を用いた海岸での砕波の数値解析

    野邊 厚, 越塚 誠一, 岡 芳明

    第9回数値流体力学シンポジウム 

    Presentation date: 1995.12

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Syllabus

▼display all

Teaching Experience

  • Analysis (Differential Equations)

    Waseda University, School of Political Science and Economics  

    2021.04
    -
    Now
     

  • Convex Analysis

    Waseda University  

    2021.04
    -
    Now
     

  • Introduction to Mathematics for Economics

    Waseda University  

    2021.04
    -
    Now
     

  • 数学演習

    気象大学校大学部  

    2011.04
    -
    Now
     

  • 線形代数学

    気象大学校大学部  

    2011.04
    -
    Now
     

  • 幾何学発展

    千葉大学教育学部  

    2020.10
    -
    2021.03
     

  • 解析学発展

    千葉大学教育学部  

    2020.10
    -
    2021.03
     

  • 離散数学c

    津田塾大学学芸学部  

    2018.11
    -
    2021.03
     

  • 解析学研究II

    千葉大学教育学部  

    2011.10
    -
    2021.03
     

  • 大域解析学

    千葉大学大学院教育学研究科  

    2011.10
    -
    2021.03
     

  • 機械計算論

    千葉大学教育学部  

    2010.10
    -
    2021.03
     

  • 数値解析

    千葉大学教育学部  

    2009.10
    -
    2021.03
     

  • 微分積分学

    日本大学生産工学部  

    2017.09
    -
    2020.11
     

  • 解析学

    千葉大学教育学部  

    2020.04
    -
    2020.09
     

  • 解析学研究I

    千葉大学教育学部  

    2011.04
    -
    2020.09
     

  • 小学校算数

    千葉大学教育学部  

    2011.04
    -
    2020.09
     

  • 情報数学

    千葉大学大学院教育学研究科  

    2011.04
    -
    2020.09
     

  • 線形代数学

    日本大学生産工学部  

    2017.04
    -
    2020.06
     

  • 長さ・面積・体積

    千葉大学教育学部  

    2010.04
    -
    2019.08
     

  • 数値計算法

    千葉大学教育学部  

    2010.10
    -
    2018.02
     

  • コンピュータ概論

    千葉大学教育学部  

    2010.04
    -
    2017.08
     

  • 線形代数学II

    日本大学生産工学部  

    2013.09
    -
    2017.01
     

  • 線形代数学I

    日本大学生産工学部  

    2013.04
    -
    2016.08
     

  • 図形と画像の処理

    千葉大学教育学部  

    2010.10
    -
    2016.02
     

  • 数理モデルの解析

    千葉大学教育学部  

    2010.10
    -
    2011.02
     

  • 微積分学A

    千葉大学普遍教育  

    2010.04
    -
    2010.08
     

  • 計算数理A

    大阪大学基礎工学部  

    2004.04
    -
    2009.10
     

  • 基礎数理演習C

    大阪大学始祖工学部  

    2004.04
    -
    2009.09
     

  • 基礎数理演習A

    大阪大学基礎工学部  

    2004.04
    -
    2009.09
     

  • Advanced Mathematical Science A

    Graduate School of Engineering Scicence, Osaka University  

    2008.04
    -
    2008.09
     

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Committee Memberships

  • 2020.04
    -
    Now

    日本応用数理学会  応用可積分系研究部会主査

  • 2015.04
    -
    Now

    日本応用数理学会  JSIAM Letters編集委員

  • 2016.04
    -
    2020.03

    日本応用数理学会  応用可積分系研究部会幹事

  • 2009.10
    -
    2011.09

    日本物理学会  領域11役員

Social Activities

  • 逆関数について

    東京都立城東高等学校  ジョイントセミナー  (東京都立城東高等学校) 

    2019.06
     
     

  • 算数

    千葉県教育委員会  教員免許法認定講習  (千葉大学) 

    2016.08
     
     

  • 暦の数理〜木星のカレンダーを作ろう〜

    千葉大学  高大連携講座  (千葉県立木更津高等学校) 

    2016.06
     
     

  • 算数

    千葉県教育委員会  教員免許法認定講習  (千葉大学) 

    2013.08
     
     

  • 審査委員

    千葉大学  第6回高校生理科研究発表会 

    2012.09
    -
     

  • 楕円曲線のはなし

    千葉大学  高大連携講座  (千葉県立木更津高等学校) 

    2012.05
     
     

  • 箱と玉の数理実験~ソリトンを作ろう〜

    千葉大学  未来の科学者養成講座  (千葉大学) 

    2012.04
     
     

  • 数学の最先端

    千葉県教育委員会  教員免許状更新講習  (千葉大学) 

    2011.08
     
     

  • ソリトンのはなし

    千葉大学  高大連携講座  (千葉県立千葉女子高等学校) 

    2010.06
     
     

  • 箱と玉の数理実験~究極の波を調べる〜

    千葉大学  未来の科学者養成講座  (千葉大学) 

    2010.04
     
     

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Academic Activities

  • reviewer

    Peer review

    Japan Journal of Industrial and Applied Mathematics  

    2017.02
    -
    Now
  • reviewer

    Peer review

    Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)  

    2010.11
    -
    Now
  • reviewer

    Peer review

    Journal of the Physical Society of Japan  

    2010.09
    -
    Now
  • reviewer

    Peer review

    Journal of Physics A: Mathematical and Theoretical  

    2005.04
    -
    Now
  • 日本応用数理学会2021年研究部会連合発表会実行委員

    Academic society, research group, etc.

    日本応用数理学会   法政大学(オンライン)

    2021.03
     
     
  • 日本応用数理学会2020年度年会応用可積分系オーガナイズドセッション主催者

    Academic society, research group, etc.

    日本応用数理学会   愛媛大学(オンライン)

    2020.09
     
     
  • Organizer, RIMS Conference ``Expansion of Integrable systems"

    Academic society, research group, etc.

    京都大学数理解析研究所

    2008.08
     
     
  • reviewer

    Peer review

    Journal of Nonlinear Mathematical Physics  

    2020.03
    -
    Now
  • reviewer

    Peer review

    Journal of Algebraic Combinatorics  

    2019.06
    -
    Now
  • reviewer

    Peer review

    Hokkaido Mathematical Journal  

    2018.12
    -
    Now
  • 研究集会「非線形波動から可積分系へ」世話人

    Academic society, research group, etc.

    津田塾大学 数学計算機科学研究所   オンライン

    2020.11
     
     
  • reviewer

    Peer review

    Integrable Systems and Algebraic Geometry (Cambridge University Press)  

    2018.11
    -
    2019.02
  • reviewer

    Peer review

    IEICE Transactions  

    2015.12
    -
    2016.04
  • 日本応用数理学会2009年度年会実行委員

    Academic society, research group, etc.

    日本応用数理学会   大阪大学豊中キャンパス

    2009.09
     
     
  • Organizer, 5th East Asia Partial Differential Equations Conference

    Academic society, research group, etc.

    Takashi Suzuki   大阪大学中之島センター

    2005.01
    -
    2005.02

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