Updated on 2024/04/20

写真a

 
NAGAHATA Yukio
 
Organization
Academic Assembly Institute of Science and Technology JOUHOU DENSHI KOUGAKU KEIRETU Professor
Faculty of Engineering Department of Engineering Professor
Title
Professor
External link

Degree

  • 博士（理学） ( 2001.3   東京工業大学 )

Research Interests

  • stochastic process

  • probability theory

Research Areas

  • Natural Science / Basic analysis  / probability theory

Research History (researchmap)

  • Niigata University   Faculty of Engineering Department of Engineering   Professor

    2017.4

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  • Niigata University   Graduate School of Science and Technology Electrical and Information Engineering   Associate Professor

    2011.10 - 2013.10

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  • Niigata University   Faculty of Engineering Department of Information Engineering Mathematical Information Division   Associate Professor

    2011.10 - 2013.10

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Research History

  • Niigata University   Faculty of Engineering Department of Engineering   Professor

    2017.4

  • Niigata University   Abolition organization Mathematical Information Division   Professor

    2013.11 - 2017.3

  • Niigata University   Abolition organization Mathematical Information Division   Associate Professor

    2011.10 - 2013.10

  • Niigata University   Graduate School of Science and Technology Electrical and Information Engineering   Associate Professor

    2011.10 - 2013.10

  • Niigata University   Graduate School of Science and Technology Electrical and Information Engineering   Associate Professor

    2011.10 - 2013.10

 

Papers

  • A remark on equivalence of ensembles for surface diffusion model Reviewed

    Yukio NAGAHATA

    RIMS Kôkyûroku Bessatsu B59   B59   23 - 30   2016

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    Language：English   Publishing type：Research paper (scientific journal)  

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  • TAGGED PARTICLE DYNAMICS IN STOCHASTIC RANKING PROCESS Reviewed

    Yukio Nagahata

    KODAI MATHEMATICAL JOURNAL   36 ( 3 )   397 - 408   2013.10

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    Language：English   Publishing type：Research paper (scientific journal)   Publisher：KINOKUNIYA CO LTD  

    We consider a stochastic ranking process, which is a mathematical model of the ranking in the web page of online bookstores or posting web pages. We give a scaling limit of tagged particle dynamics. In this limit the scaled tagged particles jumps to the top of the list when its own Poisson clock rings and moves deterministically along a curve otherwise. This curve is characteristic curve of a system of quasi linear PDE, which is mentioned in [11, 14]. We also give a scaling limit of multi-tagged particle dynamics, in which the motion of the particles are independent.

    DOI： 10.2996/kmj/1383660688

    Web of Science

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  • Functional central limit theorem for tagged particle dynamics in stochastic ranking process Reviewed

    Yukio Nagahata

    Kodai Mathematical Journal   36 ( 3 )   409 - 427   2013

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    Language：English   Publishing type：Research paper (scientific journal)  

    In this paper we consider "parabolically" scaled centered tagged particle dynamics for a stochastic ranking process (regarded as a particle system), which is driven according to an algorithm for self-organizing linear list of a finite number of items. We let the number of items to infinity and show that the scaled tagged particle weakly converges to a "diffusion" processes with occasional jumps, in which the particle jumps to 0 when its own Poisson clock rings and behaves as a "diffusion" process otherwise. The "diffusion" is decomposed into a sum of independent continuous Markov Gaussian processes with a random covariance. Intuitively, each component process is constructed by infinitely many particles having the same intensity behind the tagged particle. This random covariance depends only on its own last Poisson time. In multi-tagged particle system, "hyperbolically" scaled tagged particles decompose [0,1] interval into L + 1 layers, where L is a number of tagged particles. Intuitively, infinitely many particles in each layer construct a "diffusion" processes, which is interpreted as a shrunk version of that in the single tagged particle case. Each "parabolically" scaled centered tagged particle holds in common these "diffusion" processes if the corresponding layer is behind the corresponding "hyperbolically" scaled tagged particle.

    DOI： 10.2996/kmj/1383660689

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  • Lower bound estimate of the spectral gap for simple exclusion process with degenerate rates Reviewed

    Yukio Nagahata

    ELECTRONIC JOURNAL OF PROBABILITY   17 ( 92 )   1 - 19   2012.10

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    Language：English   Publishing type：Research paper (scientific journal)   Publisher：UNIV WASHINGTON, DEPT MATHEMATICS  

    We consider exclusion process with degenerate rates in a finite torus with size n. This model is a simplified model for some peculiar phenomena of the "glassy" dynamics. We prove that the spectral gap is bounded below by C rho(4)/n(2), where rho = k/n denotes the density of particle and C does not depend on n nor rho.

    DOI： 10.1214/EJP.v17-1916

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  • Spectral Gap for Multi-species Exclusion Processes Reviewed

    Yukio Nagahata, Makiko Sasada

    JOURNAL OF STATISTICAL PHYSICS   143 ( 2 )   381 - 398   2011.4

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    Language：English   Publishing type：Research paper (scientific journal)   Publisher：SPRINGER  

    We consider a multi-species generalization of the symmetric simple exclusion process in homogeneous and non-homogeneous hypercubes of Z (d) . In this model, the hyperplanes of configurations with given numbers of particles of each species are not necessarily irreducible. We give a sufficient condition of the dynamics to make them irreducible. In addition, assuming the irreducibility of them, we show some estimates of the spectral gap (the absolute value of the second largest eigenvalue of the generator), which plays an important role in the study of hydrodynamic limit.

    DOI： 10.1007/s10955-011-0176-0

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  • STOCHASTIC RANKING PROCESS WITH TIME DEPENDENT INTENSITIES Reviewed

    Yuu Hariya, Kumiko Hattori, Tetsuya Hattori, Yukio Nagahata, Yuusuke Takeshima, Takahisa Kobayashi

    TOHOKU MATHEMATICAL JOURNAL   63 ( 1 )   77 - 111   2011.3

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    Language：English   Publishing type：Research paper (scientific journal)   Publisher：TOHOKU UNIVERSITY  

    We consider the stochastic ranking process with the jump times of the particles determined by Poisson random measures. We prove that the joint empirical distribution of scaled position and intensity measure converges almost surely in the infinite particle limit. We give an explicit formula for the limit distribution and show that the limit distribution function is a unique global classical solution to an initial value problem for a system of a first order non-linear partial differential equations with time dependent coefficients.

    DOI： 10.2748/tmj/1303219937

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  • Localization for a class of linear systems Reviewed

    Y.Nagahata, Nobuo Yoshida

    Electronic Journal of Probability   15   636 - 653   2010.12

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  • A Note on the diffusive scaling limit for a class of linear systems Reviewed

    Y.Nagahata, Nobuo Yoshida

    Electronic Communications in Probability   15   68 - 78   2010.8

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  • Spectral gap for zero-range processes with jump rate g(x) = x(gamma) Reviewed

    Yukio Nagahata

    STOCHASTIC PROCESSES AND THEIR APPLICATIONS   120 ( 6 )   949 - 958   2010.6

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    Language：English   Publishing type：Research paper (scientific journal)   Publisher：ELSEVIER SCIENCE BV  

    We consider zero-range processes with jump rate g(x) = x(gamma) for 0 < gamma <= 1. We obtain that for the local process confined to a cube in Z(d) of width n, the spectral gap is bounded below by positive multiple of (n(2)(1 + rho)(1-gamma))(-1), where rho = k/(2n + 1)(d) and k is the total number of particles in the cube. (C) 2010 Elsevier B.V. All rights reserved.

    DOI： 10.1016/j.spa.2010.01.019

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  • Central Limit Theorem for a Class of Linear Systems Reviewed

    Yukio Nagahata, Nobuo Yoshida

    ELECTRONIC JOURNAL OF PROBABILITY   14   960 - 977   2009.5

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    Language：English   Publishing type：Research paper (scientific journal)   Publisher：UNIV WASHINGTON, DEPT MATHEMATICS  

    We consider a class of interacting particle systems with values in [0,8)(Zd), of which the binary contact path process is an example. For d >= 3 and under a certain square integrability condition on the total number of the particles, we prove a central limit theorem for the density of the particles, together with upper bounds for the density of the most populated site and the replica overlap.

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  • Regularity of the diffusion coefficient matrix for lattice gas reversible under gibbs measures with mixing condition Reviewed

    Yukio Nagahata

    COMMUNICATIONS IN MATHEMATICAL PHYSICS   273 ( 3 )   637 - 650   2007.8

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    Language：English   Publishing type：Research paper (scientific journal)   Publisher：SPRINGER  

    In this paper we obtain that the diffusion coefficient matrix for lattice gas reversible under Gibbs measures with mixing condition is continuously differentiable with respect to order parameter.

    DOI： 10.1007/s00220-007-0247-x

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  • Regularity of the diffusion coefficient matrix for generalized exclusion process Reviewed

    Yukio Nagahata

    STOCHASTIC PROCESSES AND THEIR APPLICATIONS   116 ( 6 )   957 - 982   2006.6

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    Language：English   Publishing type：Research paper (scientific journal)   Publisher：ELSEVIER SCIENCE BV  

    In this paper we obtain the smoothness of the diffusion coefficient matrix for the generalized exclusion process. (C) 2006 Elsevier B.V. All rights reserved.

    DOI： 10.1016/j.spa.2006.01.009

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  • Regularity of the diffusion coefficient matrix for the lattice gas with energy Reviewed

    Y Nagahata

    ANNALES DE L INSTITUT HENRI POINCARE-PROBABILITES ET STATISTIQUES   41 ( 1 )   45 - 67   2005

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    Language：English   Publishing type：Research paper (scientific journal)   Publisher：GAUTHIER-VILLARS/EDITIONS ELSEVIER  

    In this paper we obtain the smoothness of the diffusion coefficient matrix for the lattice gas with energy. Furthermore we also obtain the smoothness of the central limit theorem variances. for certain functions. (C) 2004 Elsevier SAS. All rights reserved.

    DOI： 10.1016/j.anihpb.2004.03.006

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  • An estimate of the spectral gap for zerorange-exclusion dynamics Reviewed

    Y.Nagahata, K.Uchiyama

    Osaka Journal of Mathematics   41 ( 4 )   961 - 975   2004.10

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  • Fluctuation Dissipation Equation for Lattice Gas with Energy Reviewed

    Yukio Nagahata

    Journal of Statistical Physics   110 ( 1-2 )   219 - 246   2003.1

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    In this paper we introduce a "lattice gas with energy," and obtain the "fluctuation dissipation equation" for it. The system has two conserved quantities, the number of particles and the total energy. Once the "fluctuation dissipation equation" is established, the hydrodynamic limit is easily deduced from it by using the methods found in ref. 1 for this model.

    DOI： 10.1023/A:1021022829221

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  • The gradient condition for one-dimensional symmetric exclusion process Reviewed

    Y.Nagahata

    Journal of Statistical Physics   91   587 - 602   1998.9

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    Language：English   Publishing type：Research paper (scientific journal)  

    DOI： 10.1023/A:1023025510497

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Presentations

  • On scaling limit of a cost in adhoc network model International conference

    Yukio NAGAHATA

    The 12th AIMS Conference on Dynamical Systems, Differential Equations and Applications  2018.7 

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    Language：English   Presentation type：Oral presentation (invited, special)  

    Venue：Taiwan National University  

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  • On scaling limit of a cost in adhoc network model

    永幡幸生

    第10回福島応用数学研究集会  2018.3 

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    Language：Japanese   Presentation type：Oral presentation (invited, special)  

    Venue：コラッセふくしま  

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  • On scaling limit of a cost in adhoc network model International conference

    Yukio NAGAHATA

    15th workshop on Stochastic Analysis on Large Scale Interacting Systems  2016.11 

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    Language：English   Presentation type：Oral presentation (invited, special)  

    Venue：東京大学  

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  • An estimate of spectral gap for surface diffusion International conference

    永幡幸生

    マルコフ過程とその周辺  2016.1 

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    Language：Japanese   Presentation type：Oral presentation (general)  

    Venue：ヴェルクよこすか  

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  • On scaling limit of a cost in an adhoc network model

    永幡幸生

    無限粒子系、確率場の諸問題XI  2015.12 

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    Language：Japanese   Presentation type：Oral presentation (general)  

    Venue：奈良女子大学  

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  • An estimate of spectral gap for surface diffusion International conference

    Yukio NAGAHATA

    Stochastic Analysis on Large Scale Interacting Systems  2015.10 

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    Language：English   Presentation type：Oral presentation (invited, special)  

    Venue：京都大学  

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  • Spectral gap for surface diffusion International conference

    Yukio NAGAHATA

    Stochastic Analysis and Applications  2015.8 

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    Language：English   Presentation type：Oral presentation (invited, special)  

    Venue：東北大  

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  • An estimate of spectral gap for surface diffusion International conference

    Yukio NAGAHATA

    13th workshop on Stochastic Analysis on Large Scale Interacting Systems  2014.11 

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    Language：English   Presentation type：Oral presentation (invited, special)  

    Venue：東京大学  

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  • On hydrodynamic limit for simple exclusion process with degenerate rates International conference

    Yukio NAGAHATA

    Stochastic processes, Analysis and Mathematical Phisics  2014.8 

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    Language：English   Presentation type：Oral presentation (invited, special)  

    Venue：関西大学  

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  • Central Limit Theorem for Additive Funcionals of Reversible Markov Processes and Applications to Simple Exclusions の紹介

    永幡幸生

    確率論早春セミナー  2014.3 

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    Language：Japanese   Presentation type：Oral presentation (invited, special)  

    Venue：関西大学  

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  • On hydrodynamic limit for simple exclusion process with degenerate rates International conference

    Yukio NAGAHATA

    Dirichlet Forms and Applications  2013.9 

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    Language：English   Presentation type：Oral presentation (invited, special)  

    Venue：Universitat Leipzig  

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  • 流体力学極限について International conference

    永幡幸生

    確率論早春セミナー  2013.3 

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    Language：Japanese   Presentation type：Oral presentation (invited, special)  

    Venue：関西大学  

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  • 流体力学極限について

    永幡幸生

    計算材料科学と数学の協働によるスマート材料デザイン手法の探索  2013.3 

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    Language：Japanese   Presentation type：Oral presentation (invited, special)  

    Venue：東北大学  

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  • Lower bound estimate of spectral gap for simple exclusion process with degenerate rates International conference

    Yukio NAGAHATA

    Markov chains on graphs and related topics  2013.2 

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    Language：English   Presentation type：Oral presentation (invited, special)  

    Venue：京都大学  

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  • Functional central limit theorem for tagged particle dynamics in stochastic ranking process International conference

    Yukio NAGAHATA

    Dirichlet Forms and Applications  2013.1  マルコフ過程と確率解析

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    Language：English   Presentation type：Oral presentation (invited, special)  

    Venue：京都大学  

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  • Functional central limit theorem for tagged particle dynamics in stochastic ranking process

    Yukio NAGAHATA

    無限粒子系、確率場の諸問題VIII  2012.10 

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    Language：Japanese   Presentation type：Oral presentation (general)  

    Venue：奈良女子大  

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  • Lower bound estimate of spectral gap for simple exclusion process with degenerate rates International conference

    Yukio NAGAHATA

    11th workshop on Stochastic Analysis on Large Scale Interacting Systems  2012.7 

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    Language：English   Presentation type：Oral presentation (invited, special)  

    Venue：東京大学  

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  • Scaling limit for multi-species exclusion processes International conference

    Yukio NAGAHATA

    The 2nd Institute of Mathematical Statics Asian Pacific Rim Meeting  2012.7 

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    Language：English   Presentation type：Oral presentation (invited, special)  

    Venue：Tsukuba International Congress Center  

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  • An estimate of spectral gap for simple exclusion process with degenerate rates

    永幡幸生

    数理物理と確率解析  2012.3 

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    Language：Japanese   Presentation type：Oral presentation (general)  

    Venue：湘南国際村センター  

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  • Hydrodynamic limit of lattice gas with two conserved quantities

    Yukio NAGAHATA

    2011.11 

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    Language：Japanese   Presentation type：Oral presentation (general)  

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  • An estimate of spectral gap for simple exclusion process with degenerate rates

    Yukio NAGAHATA

    2011.11 

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    Language：Japanese   Presentation type：Oral presentation (general)  

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  • An estimate of spectral gap for simple exclusion process with degenerate rates

    Yukio NAGAHATA

    2011.10 

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    Language：Japanese   Presentation type：Oral presentation (general)  

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Research Projects

  • 多種粒子系の格子気体の流体力学極限

    2011.4 - 2014.3

    System name：科学研究費助成事業

    Research category：基盤研究(C)

    Awarding organization：日本学術振興会

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    Grant type：Competitive

    Grant amount：\2500000 （ Direct Cost: \1750000 、 Indirect Cost：\750000 ）

    （例えば）２種類の粒子からなる気体の簡略化モデルとして、空間を離散かして各点にはたかだか１つの粒子しか入れなく、各粒子はランダムウォークをしているものとします。このとき時間ー空間に関して適切なスケールを保って極限をとれば決定論的な方程式（系）が出てくることが予想されます。この極限を数学的に厳密に導出することを目指しています。

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  • Scaling limit of stochastic processes

    2003.5

    System name：Basic Science Research Program

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    Grant type：Competitive

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Teaching Experience (researchmap)

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Teaching Experience

  • 応用数理C

    2018
    Institution name：新潟大学

  • 基礎数理B

    2017
    Institution name：新潟大学

  • 情報工学特定研究Ⅱ

    2014
    -
    2015
    Institution name：新潟大学

  • 情報工学研究発表(外部発表)

    2014
    -
    2015
    Institution name：新潟大学

  • 情報工学セミナーⅡ

    2014
    -
    2015
    Institution name：新潟大学

  • 情報工学文献詳読Ⅱ

    2014
    Institution name：新潟大学

  • 数理解析学

    2013
    Institution name：新潟大学

  • 情報工学特定研究Ⅰ

    2013
    -
    2014
    Institution name：新潟大学

  • 情報工学発表演習(中間発表)

    2013
    -
    2014
    Institution name：新潟大学

  • 情報工学セミナーⅠ

    2013
    -
    2014
    Institution name：新潟大学

  • 情報工学文献詳読Ⅰ

    2013
    -
    2014
    Institution name：新潟大学

  • 情報数理特論

    2012
    Institution name：新潟大学

  • 応用数理E

    2012
    Institution name：新潟大学

  • 基礎数理A I

    2012
    Institution name：新潟大学

  • 基礎数理A II

    2012
    -
    2022
    Institution name：新潟大学

  • 応用数理B

    2012
    -
    2017
    Institution name：新潟大学

  • 工学リテラシー入門(情報工学科)

    2012
    -
    2016
    Institution name：新潟大学

  • アドバンススキルズ

    2012
    -
    2013
    Institution name：新潟大学

  • 力学系理論

    2012
    Institution name：新潟大学

  • 代数解析学

    2012
    Institution name：新潟大学

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