CONTENTS

1. Discrete hungry integrable systems related to matrix eigenvalue and their local analysis by center manifold theory (Expansion of Integrable Systems)---1

　　　　Graduate School of Science, Tokyo University of Science / Department of mathematical Information Science, Tokyo University of Science / Faculty of Life and Environmental Sciences, Kyoto Prefectural University / Graduate School of Informatics, Kyoto University　　　FUKUDA,Akiko / ISHIWATA,Emiko / IWASAKI,Masashi / NAKAMURA,Yoshimasa

　

2. A Discrete-State Spiking Neuron Model and its Learning Potential (Expansion of Integrable Systems)-------------------------------19

　　　　Graduate School of Engineering Science, Osaka University　　　TORIKAI,Hiroyuki

　

3. Remarks on collision manifolds and nonexistence of non self-similar collision solutions in the 3-vortex problem (Expansion of Integrable Systems)---35

　　　　Graudate School of Science, Hiroshima University　　　HIRAOKA,Yasuaki

　

4. Analytic solutions to the sixth $q$-Painleve equation around the origin (Expansion of Integrable Systems)------------------------45

　　　　Department of Mathematics, Osaka University　　　OHYAMA,Yousuke

　

5. Bilinearization and Casorati Determinant Solutions to Non-autonomous 1+1 Dimensional Discrete Soliton Equations (Expansion of Integrable Systems)---53

　　　　Faculty of Mathematics, Kyushu Unviersity / Department of Mathematics,Kobe University　　　KAJIWARA,Kenji / OHTA,Yasuhiro

　

6. Constructing two-dimensional integrable mappings that possess invariants of high degree (Expansion of Integrable Systems)--------75

　　　　Ryukoku University / Ryukoku University / Osaka University / Kyushu University　　　TANAKA,Hironori / MATSUKIDAIRA,Junta / NOBE,Atsushi / TSUDA,Teruhisa

　

7. On oscillatory solutions in ultradiscrete system (Expansion of Integrable Systems)-----------------------------------------------85

　　　　Department of Physics and Mathematics, Aoyama Gakuin University / Department of Physics and Mathematics, Aoyama Gakuin University / Department of Physics and Mathematics, Aoyama Gakuin University　　　ISOJIMA,Shin / KONNO,Tomoyuki / SATSUMA,Junkichi

　

8. Ultradiscrete Analogue of the Identity of Pfaffians (Expansion of Integrable Systems)--------------------------------------------95

　　　　Waseda University　　　HIROTA,Ryogo

　

9. Riemann zeta function and the best constants of five series of Sobolev inequalities (Expansion of Integrable Systems)-----------125

　　　　Faculty of Engineering Science, Osaka University / Osaka University / Liberal Arts and Basic Sciences, College of Industrial Technology, Nihon University / Department of Computer Science,National Defense Academy / Liberal Arts and Basic Sciences, College of Industrial Technology, Nihon University　　　YAMAGISHI,Hiroyuki / KAMETAKA,Yoshinori / NAGAI,Atsushi / WATANABE,Kohtaro / TAKEMURA,Kazuo

　

10. Existence and stability of periodic solutions in the isosceles three-body problem (Expansion of Integrable Systems)------------141

　　　　Research Institute for Mathematical Sciences, Kyoto University　　　SHIBAYAMA,Mitsuru

　

11. The Periodic Box-ball System and Tropical Curves (Expansion of Integrable Systems)---------------------------------------------157

　　　　Graudate School of Mathematical Sciences, The University of Tokyo　　　IWAO,Shinsuke

　

12. Tropical Jacobian and the generic fiber of the ultra-discrete periodic Toda lattice are isomorphic (Expansion of Integrable Systems)---175

　　　　Faculty of Pharmaceutical Sciences, Suzuka University of Medical Science / Faculty of Marine Technology, Tokyo University of Marine Science and Technology　　　INOUE,Rei / TAKENAWA,Tomoyuki