Preface

Published (free access before August 18, 2018)

Differential transcendence of solutions of difference Riccati equations and Tietze's treatment

学生向けの情報

専門分野: 差分代数(と微分代数)
どんな研究? 差分方程式や微分方程式が解けるかどうかを判定する。

卒研ページに卒研で使った本のリストがあります。

Research interests

quadrature and reduction of algebraic difference/differential equations, difference/differential algebra, discrete/continuous Painlevé equations.

Articles

Preprints

Accepted

  1. Nishioka, S., Irreducibility of discrete Painlevé equation of type $D_7^{(1)}$, To appear in Funkcialaj Ekvacioj.

Published

  1. Nishioka, S., Differential transcendence of solutions of difference Riccati equations and Tietze's treatment, J. Algebra, 511 (2018), 16--40. DOI: 10.1016/j.jalgebra.2018.06.008. Preprint(outdated).
  2. Nishioka, S., Transcendence of solutions of q-Airy equation, Josai Mathematical Monographs, Vol. 10 (2017), 129--137.
  3. Nishioka, S., Proof of unsolvability of q-Bessel equation using valuations, J. Math. Sci. Univ. Tokyo, Vol. 23 (2016), No. 4, Page 763--789.
  4. Nishioka, K., Nishioka, S., Autonomous equations of Mahler type and transcendence, Tsukuba Journal of Mathematics, Vol. 39, No. 2 (2015), 251--257.
  5. Nishioka, S., Functions satisfying Poincaré's multiplication formula, Osaka Journal of Mathematics, 51 (2014), 141--160.
  6. Nakazono, N., Nishioka, S., Solutions to a q-analog of Painlevé III equation of type $D_7^{(1)}$. Funkcialaj Ekvacioj, 56 (2013), 415--439.
  7. Nishioka, S., Approximation of Poincaré's new functions by rational functions, Journal of Difference Equations and Applications, Volume 19, Issue 9 (2013), 1452--1462.
    doi:10.1080/10236198.2012.755963
    (Available online: 2013-02-06)
  8. Nishioka, S., Algebraic independence of solutions of first-order rational difference equations, Results in Mathematics, Volume 64, Issue 3 (2013), 423--433.
    doi:10.1007/s00025-013-0324-8
  9. Nishioka, S., Non-elementary solutions of difference equations, J. Differ. Equ. Appl., Volume 19, Issue 1 (2013), 54--58.
    doi:10.1080/10236198.2011.618498
  10. Nishioka, K., Nishioka, S., Algebraic theory of difference equations and Mahler functions, Aequationes Mathematicae, Volume 84, Issue 3 (2012), 245--259.
    doi:10.1007/s00010-012-0132-3
  11. Nishioka, S., Irreducibility of $q$-Painlevé equation of type $A_6^{(1)}$ in the sense of order, J. Differ. Equ. Appl., Volume 18, Issue 2 (2012), 313--333.
    doi:10.1080/10236198.2010.491824
  12. Nishioka, S., Transcendence of solutions of $q$-Painlevé equation of type $A_6^{(1)}$, Aequat. Math., 81 (2011), 121--134.
    doi:10.1007/s00010-010-0054-x
  13. Nishioka, S., Decomposable extensions of difference fields, Funkcial. Ekvac., 53 (2010), 489--501.
  14. Nishioka, S., Solvability of Difference Riccati Equations by Elementary Operations, J. Math. Sci. Univ. Tokyo, 17 (2010), 159--178.
  15. Nishioka, S., Transcendence of Solutions of $q$-Painlevé Equation of Type $A_7^{(1)}$, Aequat. Math., 79 (2010), 1--12.
    doi:10.1007/s00010-010-0007-4
  16. Nishioka, S., On Solutions of $q$-Painlevé Equation of Type $A_7^{(1)}$, Funkcial. Ekvac., 52 (2009), 41--51.
  17. Nishioka, S., Difference algebra associated to the $q$-Painlevé equation of type $A_7^{(1)}$, RIMS Kôkyûroku Bessatsu, Vol. B10 (2008), 167--176.

Not refereed

Proceedings

  1. 西岡斉治, 差分Riccati方程式の可解性, 数理解析研究所講究録1765「可積分系数理の多様性」 (2011), 64--71.

Lectures

International conferences

2015-10-19/23 Differential and Difference Equations: Analytic, Arithmetic and Galoisian Approaches, Lille (Laboratoire Paul Painlevé), France
[en] 「Double-angle formulae and algebraic independence」, 2015-10-20
2015-04-07/10 Model Theory, Difference/Differential Equations and Applications, CIRM, France
[en] 「Double-Angle Formulae and Algebraic Independence」, 2015-04-08
2014-11-17/21 Recent developments in differential equations in the complex domain, RIMS, Kyoto University, Japan
[en] 「Reducibility of algebraic difference equations」, 2014-11-18
2012-07-11 Nonlinear Evolution Equations and Dynamical Systems 2012, Orthodox Academy of Crete, Greece
[en] Nobutaka, N. (presenter), Nishioka, S., Study on a q-analog of the Painleve III equation of type D_7^{(1)}
2012-06-10/16 SIDE10 International Conference, 中華人民共和国(浙江省寧波市)・Yin Feng Holiday Resort
[en] Nakazono, N. (presenter), Nishioka, S., Study on a q-analog of the Painleve III equation of type D7, 2012-06-15
2012-01-04/07 Joint Mathematics Meetings, Boston, USA, AMS Special Session on Differential Algebraic Geometry and Galois Theory (in memory of Jerald Kovacic), 2012-01-05/06.
[en] Solvability of difference Riccati equations, 2012-01-05.
2010-06-24/25 Equations différentielles, équations fonctionnelles, Université d'Angers, France
[en] Irreducibility of q-Painlevé equation, 2010-06-25
2009-05-11/15 Algebraic Theory of Difference Equations, University of Leeds, UK
[en] Irreducibility of q-Painlevé equation of type $A_6^{(1)}$ in the sense of order, 2009-05-13.
2007-10-11 Differential Equations and Exact WKB Analysis, Research Institute for Mathematical Sciences, Kyoto University
[en, ja] Difference algebra associated to the $q$-Painlevé equation of type $A_7^{(1)}$

by poster

2016-07-03/09 SIDE 12, Quebec, Canada
[en] 「Irreducibility of difference Painleve equations」
2011-07-25/29 Infinite Analysis 11 ~ Frontier of Integrability ~, The University of Tokyo, Japan
[en] Approximation of solutions of Poincaré's multiplication formulas by rational functions, poster, 2011-07-27.
2008-06-09/13 From Painlevé to Okamoto, The University of Tokyo, Japan
[en] General Investigation On Decomposable Extension, poster, 2008-06-10/12

Domestic conferences

2018-02-02/04 可積分系ウィンターセミナー2018, KKR水上水明荘, 群馬県
[ja]「差分リッカチ方程式の解の超超越性」, 2018-02-03
2017-11-09/11 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, 福岡県
[ja] 「q-Airy方程式の解の超超越性」, 2017-11-09
2016-11-26/27 表現論と微分方程式, 城西大学, 東京都
[ja] 「反復差分リッカチ方程式の解の超越性」, 2016-11-27
2014-08-05/08 2014函数方程式論サマーセミナー, KKR伊豆長岡保養所「千歳荘」, 静岡県
[ja] 「超越古典関数がないこと(既約性)」, 2014-08-05
2013-09-14/15 Workshop on Galois point and related topics, 山形大学理学部
[ja] 差分代数と超越数論, 2013-09-15
2013-08-06/09 2013函数方程式論サマーセミナー, リゾートホテル阿蘇いこいの村, 熊本県
[ja] 倍角公式と代数的独立性, 2013-08-09
2013-01-26/28 ウィンターセミナー2013, KKR湯沢ゆきぐに, 新潟県
[ja] 差分リッカチ方程式の標準型, 2013-01-28
2012-09-18 日本数学会2012年度秋季総合分科会, 九州大学, 福岡県
[ja] Poincaréの新しい関数の有理関数による近似
2012-09-14/17 力学系勉強会, 九州大学九重共同研修所, 大分県
[ja] Picard-Vessiot理論(I)~(IV), 差分方程式と可解性
2012-08-07/10 2012函数方程式論サマーセミナー, 蔵王白銀荘, 山形市
[ja] q-P^{D_7^{(1)}}_{III}の代数関数解(II), 2012-08-10
2010-11-15/17 非線形数理若手の会(勉強会), 九州大学西新プラザ, 福岡市
[ja] 差分方程式の非初等的解, 2010-11-16
2010-08-18/20 RIMS研究集会2010「可積分系数理の多様性」 - Diversity of the Theory of Integrable Systems -, 京都大学
[ja] 差分Riccati方程式の可解性, 2010-08-19
2010-03-24/27 日本数学会2010年度年会, 慶應義塾大学
[ja] 中園信孝 (presenter), 西岡斉治, $\tilde{W}(A_4^{(1)})$から得られる $q$パンルヴェ方程式, 2010-03-27
2009-11-19/21 研究集会「非線形波動研究の現状と将来」, 応用力学研究所
[ja] 中園信孝 (presenter), 西岡斉治, $A_4$型アフィンワイル群対称性を持つ$q$-パンルヴェ方程式, 2009-11-20
2009-07-21/24 玉原特殊多様体研究集会, 玉原国際セミナーハウス
[ja] q-Bessel の非可解性, 2009-07-23.
2009-03-26/29 日本数学会2009年度年会(東京大学)
[ja] $q$-Painlevé II の irreducibility, 2009-03-28.
2007-09-21 日本数学会2007年度総合分科会 無限可積分系セッション(東北大学)
[ja] $A_7$型$q$-差分Painlevé方程式の解の超越性

by poster

2017-11-09/11 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, 福岡県
[ja] ○佐々木幹子(山形大), ○本郷史也(山形大), 西岡斉治(山形大), 村田実貴生(東京農工大), 「FitzHugh-Nagumo 方程式の超離散化」

Seminars

France

2013-02-12 Séminaire Equations fonctionnelles, Université de Strasbourg, France
[en] Approximation of Poincare's new functions by rational functions
2010-06-29 Séminaire Equations fonctionnelles, Université de Strasbourg, France
[en] Irreducibility of q-Painlevé equation

Japan

2015-11-06 広島複素解析セミナー, 広島大学
[ja] 「倍角公式と代数的独立性」
2012-12-12/13 つくば微分ガロア理論セミナー, 筑波大学
[ja] 差分方程式から見た関数の初等性, 2012-12-13
2012-07-11 古典解析セミナー, 東京大学
[ja] 中園信孝, 西岡斉治 (presenter), On a q-analog of Painlevé III (D_7^{(1)}) and its algebraic function solutions
2011-05-27 物理・数理コロキウム, 青山学院大学
[ja] 差分方程式の非可解性の簡易判定法
2011-05-18 古典解析セミナー, 大阪大学
[ja] 乗法公式を持つベキ級数の有理関数による近似
2011-02-16/18 古典解析セミナー・ミニ研究集会, The University of Tokyo, Japan
[en] Solvability of difference Riccati equations, 2011-02-16
2010-01-20 古典解析セミナー, 大阪大学
[ja] A_6^{(1)}型q-Painlevé方程式の解の超越性
2010-01-12 Lie群論・表現論セミナー, 東大
[ja] 代数的差分方程式の可解性と既約性
2008-12-06 古典解析セミナー(阪大)
[ja] q-Painlevé II の irreducibility
2007-05-30 古典解析セミナー(阪大)
[ja] $A_7$型$q$-パンルヴェ方程式の解の超越性と$A_6$型について
2007-01-19 九州可積分系セミナー(九州大学)
[ja] $q$-$P(A_7^{(1)})$の解の超越性