㸱㸬ᣐⅬ࣓ࣥࣂ࣮࣭◊✲ᴫせࡢ⤂௓㸺2012 ᖺᗘ㸼ͤ⌜࣮ࣜࢲ࣮

ࣔࢹࣜࣥࢢ⌜୕ᮧ ᫀὈ㻌 䈜⮬ᕫ⤌⧊໬㞟ྜᙧᡂ䛾⌧㇟ᩘ⌮ᏛྥẊ ᨻ⏨Ᏻ඲Ꮫ䛾య⣔໬䛸䝇䝬䞊䝖䜾䝸䝑䝗Ᏻ඲ᛶ䜈䛾㐺⏝สᒇ Ṋ᫛Ḣᕞᅜമ䛾ᐇドศᯒ(Credit Risk Analysis on GBs of Euro Countries)᳃ ၨஅ䝇䝬䞊䝖䜾䝸䝑䝗䛻䛚䛡䜛䜲䞁䝔䝸䝆䜵䞁䝖ணᑠᯘ ுື≀䛾㐠ື䛻Ꮫ䜆⮬ᚊศᩓไᚚ䛾ᩘ⌮ⓗ◊✲Ⲩᕝ ⸅ே䛸㛵䜟䜛どぬ䞉⫈ぬ᝟ሗฎ⌮す᳃ ᣅ

䜖䜙䛠せ⣲⣔䛾䝎䜲䝘䝭䜽䝇䛾ゎᯒ㧗Ᏻ ⚽ᶞ㔠⼥ᕷሙ䛾㠀䝷䞁䝎䝮䜴䜷䞊䜽ᛶ䛾☜ㄆ䛸䛭䛾䝰䝕䝸䞁䜾ᰘ⏣ 㐩ኵ⣽⬊䜔⤌⧊ᙧᡂ䛾䝣䜱䝆䜹䝹䝞䜲䜸䝻䝆䞊⏣㔝಴ ⴥᏊ

Development of index construction for a financial market with heavy-tailed
distributionsⱝ㔝 ཭୍㑻

⏕≀㐍໬䛾◊✲䠖⌮ㄽ䛸ᛂ⏝䞉᭱㐺໬䛾◊✲

ᩘ⌮ゎᯒ⌜
◁⏣ ฼୍㻌 䈜

Topics on Mathematical Crystallography୕ᮧ ᫀὈ⮬ᕫ⤌⧊໬㞟ྜᙧᡂ䛾⌧㇟ᩘ⌮Ꮫ⋢ᮌ ஂኵ

Algorithms for directed pathwidthᑠᕝ ▱அ཯ᛂᣑᩓ⣔䛾䝟䝍䞊䞁䝎䜲䝘䝭䜽䝇 0:1:2 ከ㔜⮫⏺Ⅼ䛸䛭䛾ᶆ‽ᙧゎᯒ஧ᐑ ᗈ࿴䝟䝍䞊䞁ゎ䛾ᵓᡂ䛸䛭䛾ᶵ⬟ᛂ⏝ࢩ࣑࣮ࣗࣞࢩࣙࣥ⌜ⲡ㔝 ᏶ஓ㻌 䈜ኴ㝧㠃⇿Ⓨ⌧㇟䛾Ⓨ⏕ᶵᵓ䛸䛭䛾ணᮡཎ ཌྜྷ㘒ど䛾⌧㇟ᩘ⌮Ꮫ䛸❧య㘒どᅗᙧ䛾๰సୖᒣ ኱ಙᩘ⌮⏕≀Ꮫ䛻䛚䛡䜛ཝᐦゎ䛸䛭䛾ᛂ⏝◊✲༠ຊ⪅ụ⏣ ᖾኴ䠍䠊ᶋ⬻⢏䛻ぢ䜙䜜䜛㞟ᅋ㐠ື䛾ゎᯒ
䠎䠊IPMCActuator 䛻ぢ䜙䜜䜛ᒅ᭤㐠ື䛾ゎᯒᮎᯇ J. ಙᙪ⏕≀䞉↓⏕≀䛾㞟ᅋ䛜ᙧᡂ䛩䜛⛛ᗎ䝟䝍䞊䞁୰ᮧ ࿴ᖾ᫬⣔ิ䞉᫬✵㛫ゎᯒᡭἲ䛾㛤Ⓨ䛸♫఍䛻䛛䛛䜟䜛ᕤᏛ䞉⤒῭Ꮫศ㔝䜈䛾ᛂ⏝ᮌୗ ಟ୍㠀୍ᵝ⯆ዧሙ䛻䛚䛡䜛䝇䝟䜲䝷䝹Ἴ䛾Ⓨ⏕䝯䜹䝙䝈䝮ᒸᔲ ுᏊ⏕≀ᙧ㉁䞉୙㐃⥆ศᕸ䛾㐍໬䠖㐃⥆ⓗ㈨※䛻ᑐ䛩䜛㑅ዲᛶ䛜ཬ䜌䛩ᙳ㡪䛾᳨ド⏫⏣ ᣅஓ㔞Ꮚ䜴䜷䞊䜽䛾⌧㇟ᩘ⌮Ꮫⓗ◊✲ඵᓥ ೺ኴ䝣䝷䜽䝍䝹཯ᛂ⌮ㄽ䛾⏕ែᏛ䜈䛾㐺⏝12◊✲༠ຊ⪅
HUNG, Li-Chang

1. Exact solutions of a Morisita-Shigesada system: periodic stationary solutions
and sharp wavefront solutions
2. Blow-up in reaction-diffusion systems under Robin boundary conditions

SIEW, Hai䠉Yen

The earthquake prediction based on focal mechanismཧ⣡ ᘪᙪ⎔ቃ䛻౫Ꮡ䛧䛯⮬ᕫ㥑ື⢏Ꮚ䛾㐠ື䛾⌮ゎ䛸ไᚚすᮧ ಙ୍㑻

䜰䝯䞊䝞ᵝ⣽⬊䛾䝅䝭䝳䝺䞊䝅䝵䞁MIMS Ph.D.䝥䝻䜾䝷䝮Ꮫ⏕
䠄2009 ᖺᗘධᏛ䠅ᅵᒃ ⱥ୍ᐇドⓗ䛻᭷ຠ䛺 JGB ౯᱁௜䛡䝰䝕䝹䛸㔠⼥༴ᶵ᫬䛾㔠฼䛾ᮇ㛫ᵓ㐀ศᯒ⸨㛫 ┿ᙅᑠ✀䛾౵ධ䛻䜘䜛➇த⦆࿴ඹᏑ䛻㉳ᅉ䛩䜛䝟䝍䞊䞁ᙧᡂ䛻㛵䛩䜛◊✲䠄2010 ᖺᗘධᏛ䠅㟷㇂ ❶ᘯ䝞䜽䝔䝸䜰䝁䝻䝙䞊䝟䝍䞊䞁䛾ከᵝᛶ䛻䛴䛔䛶䛾⌮ゎྥẊ ࿴ᘯ䝬䞊䜿䝑䝖䝬䜲䜽䝻䝇䝖䝷䜽䝏䝱䞊䜢⏝䛔䛯ᕷሙゎᯒᒣཱྀ ᑗ኱⏕≀䛾ᙧែᙧᡂ䛾㐺ᛂᛶ䛻㛵䛩䜛ᩘ⌮ⓗ⌮ゎCHEN, Yan-Yu

Traveling spots in singular limit problems of reaction-diffusion systems

䠄2011 ᖺᗘධᏛ䠅ᒾᮏ ┿⿱Ꮚ

⭡㊊㢮䛾㏺⾜㐠ື䝯䜹䝙䝈䝮䛻㛵䛩䜛⤫୍ⓗ⌮ゎỌ⏣ ┿୍ὠἼᾐỈ㆙ሗ䛾ᐇ⌧䛻ྥ䛡䛯䠈㝣ୖᘓ㐀≀䛾䝰䝕䝸䞁䜾䛸䝟䝷䝯䞊䝍Ỵᐃᡭἲ䛾ᨵⰋ䝬䞊䜿䝑䝖䝬䜲䜽䝻䝇䝖䝷䜽䝏䝱䞊䛸䝅䝇䝔䝭䝑䜽䞉䝸䝇䜽䛻㛵䛩䜛ὶືᛶศᯒ䛸᪤Ꮡ䝰䝕䝹䛾ၥ㢟Ⅼ

IJIOMA, Ekeoma Rowland

Multiscale approach to pattern formation in reverse smoldering combustion

LUKITO, Adi Nugroho

Real Options Application on Franchise Financial Contract኱ᐙ ⩏Ⓩ

䠄2012 ᖺᗘධᏛ䠅㕥㔝 ᾈ኱⮬ᕫ㥑ືᩓ㐓⢏Ꮚ䛾㞟ᅋ㐠ື㧗ᶫ ಇ⸨䜲䞁䝍䞊䝛䝑䝖䝡䝆䝛䝇䛻䛚䛡䜛౯್ホ౯䝰䝕䝹䛾సᡂᆏෆ ඖẼ≧ែ✵㛫䝰䝕䝹䜢⏝䛔䛯᫬⣔ิ䝕䞊䝍䛾ゎᯒ

GANI, Mohammad Osman

Alternans and Spiral Breakup in a modified FitzHugh-Nagumo Model of
Cardiac Cell Dynamics

SCOTTI, Tommaso

Reaction-Diffusion Equations in Ecology

13␌⏱␔␝⏚ྰ‫ܤ‬μ‫ܖ‬ỉ˳ኒ҄ểᴾἋἰὊἚἂἼἕἛ‫ܤ‬μࣱồỉᢘဇᴾӼോ૎ဏ

MUKAIDONO, Masaoᴾ৑ ‫ ޓ‬ȷ ࢫ Ꮀ Ჴ έᇢૠྸᅹ‫ܖ‬ǤȳǹȆǣȆȥȸȈи৑ᧈ ଢ඙‫ܖ߻ྸܖٻ‬ᢿ૙੉‫ ᧉ ݦ‬ȷ ‫ ܖ‬ˮ Ჴ ‫ܤ‬μ‫ܖ‬Ღ߻‫ܖ‬Ҧٟȷଢ඙‫ܖٻ‬ᄂ ᆮ ϋ ܾ Ჴ ɧᄩ‫ܭ‬ƳǷǹȆȠƷȢȇȪȳǰƓǑƼᚐௌᄂᆮಒᙲ

Modeling GroupᏳ඲Ꮫ䜢య⣔໬䛩䜛䛸䛔䛖❧ሙ䛛䜙䚸ከ䛟䛾Ᏻ඲䛾ศ㔝䛻㛵䛧䛶䚸య⣔ⓗ䚸ᛮ᝿ⓗ䛺ほⅬ䛛䜙◊✲䜢⾜䛳䛯䚹䛣䛣䛷Ᏻ඲Ꮫ䠄Safenology䠅䛸䛿䚸䝅䝇䝔䝮䛾Ᏻ඲☜ಖ䛻㛵䛧䛶䚸⮬↛⛉Ꮫ䛷䛒䜛ᢏ⾡ⓗഃ㠃䠄≀⌮䚸໬Ꮫ䚸ᩘ⌮➼䠅䛸ඹ䛻䚸ேᩥ⛉Ꮫ䛷䛒䜛ே㛫ⓗഃ㠃䠄ே㛫ᕤᏛ䚸ㄆ▱⛉Ꮫ䚸ᚰ⌮Ꮫ䚸ព㆑➼䠅䚸ཬ䜃♫఍⛉Ꮫ䛷䛒䜛⤌⧊ⓗഃ㠃䠄ᇶ‽䚸ἲᚊ䚸⟶⌮䚸⤌⧊䚸♫఍ไᗘ➼䠅䛾୕ഃ㠃䛛䜙䚸⥲ྜⓗ䛻䚸㡿ᇦᶓ᩿ⓗ䛻⪃ᐹ䛩䜛᪂䛧䛔Ꮫၥ䛷䛒䜚䚸䛣䛣䛷䛿䚸୕ഃ㠃䜢⤫ྜ䛩䜛⌮ᛕⓗഃ㠃䠄ᛮ᝿䚸ဴᏛ䚸౯್ほ➼䠅䜢㔜ど䛧䛶䛔䜛䚹௒ᖺᗘ䛾◊✲䛿䚸ୖグ䛾Ᏻ඲Ꮫ䛾どⅬ䛛䜙䚸ཎᏊຊⓎ㟁䜢౛䛻䛧䛶䝸䝇䜽䛜ᴟ䜑䛶㧗䛔䝅䝇䝔䝮䛻ᑐ䛩䜛Ᏻ඲タィᛮ᝿䛻䛴䛔䛶䚸䝻䝪䝑䝖䜢౛䛻䛧䛶ே㛫䛸ᶵᲔ䛜ඹᏑ䛩䜛ሙྜ䛻䛚䛡䜛Ᏻ඲ᢏ⾡䛾ᅾ䜚᪉䛻䛴䛔䛶䚸ཬ䜃䚸䜶䝛䝹䜼䞊䜢౛䛻䛧䛶♫఍䛻䛚䛡䜛ᢏ⾡䝸䝇䜽䛾ᤊ䛘᪉䛻䛴䛔䛶䚸⪃ᐹ䜢䛧䛯䚹≉䛻䚸௒ᚋ䛾♫఍Ᏻ඲䛻䛸䛳䛶᭱䜒㔜せ䛸䛺䜛䛸ᛮ䜟䜜䜛䝇䝬䞊䝖䜾䝸䝑䝗䜢౛䛻䛧䛶䚸䝉䜻䝳䝸䝔䜱䛻㛵䛩䜛ဴᏛⓗ䛺⪃ᐹ䚸ཬ䜃䝉䜻䝳䝸䝔䜱䛻㛵䛩䜛୍⯡ᾘ㈝⪅䛾せᮃ䛻䛴䛔䛶䚸⪃ᐹ䜢⾜䛳䛯䚹ཧ⪃ᩥ⊩
䠄1䠅ྥẊᨻ⏨䚸䝸䝇䜽䛜ᴟ䜑䛶㧗䛔䝅䝇䝔䝮䛻ᑐ䛩䜛Ᏻ඲タィᛮ᝿䛻䛴䛔䛶䡚ཎᏊຊⓎ㟁䛻ᑐ䛩䜛୍⪃
ᐹ䡚䚸SE 䝉䞊䝣䝔䜱䜶䞁䝆䝙䜰䝸䞁䜾䚸No.170, pp.10-15,⥲ྜᏳ඲ᕤᏛ◊✲ᡤ䚸2013-3
䠄2䠅ྥẊᨻ⏨䚸䝻䝪䝑䝖䛾Ᏻ඲ᢏ⾡䛾ᴫせ䛸᭱᪂ືྥ䚸䝻䝪䝑䝖㻌 No. 211䚸pp.1-7,᪥ᮏ䝻䝪䝑䝖ᕤᴗ఍䚸
2013-3䠄3䠅ྥẊᨻ⏨䚸♫఍䛻䛚䛡䜛ᢏ⾡䝸䝇䜽䛾ᤊ䛘᪉䚸䜶䝛䝹䜼䞊䝺䝡䝳䞊䚸2013 ᖺ 3 ᭶ྕ䚸 pp.18-21,䜶䝛䝹䜼䞊䝺䝡䝳䞊䝉䞁䝍䞊䚸 2013䠉2
䠄4䠅Amy Poh Ai Ling, Sugihara Kokichi, Mukaidono Masao, Enhancing Smart Grid System Processes via
Philosophy of Security - Case Study based on Information Security Systems -, Journal of Wireless Mobile
Networks, Ubiquitous Computing, and Dependable Applications, Vol. 3, No. 3, pp. 94-112, 2012
䠄5䠅Amy Poh Ai Ling, Chen Yan Yu, Sugihara Kokichi, and Mukaidono Masao, The Essential Identified
Consumer Requirements Derived through Descriptive Analysis on the Information Security in a Smart
Grid System, International Journal of Modern Engineering Research, Vol. 2, Issue. 5, pp-3347-3366,2012-9䠄 6 䠅 Amy Poh Ai Ling, Sugihara Kokichi, Masao Mukaidono, The Japanese Smart Grid-Initiatives,
Investments, and Collaborations, International Journal of Advanced Science and Applications, Vol. 3, No.
7: pp. 44-54, 201214

KARIYA, TakeakiᴾА‫ދ‬നଯ

␌⏱␔␝⏚ྰ

഑߸‫׎‬ͺ ỉܱᚰЎௌCredit Risk Analysis on GBs
of Euro Countries৑ ‫ ޓ‬ȷ ࢫ Ꮀ Ჴ έᇢૠྸᅹ‫ܖ‬ǤȳǹȆǣȆȥȸȈ৑Ճ ଢ඙‫ܖٻܖٻ‬ᨈέᇢૠྸᅹ‫ܖ‬ᄂᆮᅹᲦǰȭȸȐȫȷȓ Ǹȍǹᄂᆮᅹ૙੉ ɟ೛‫ܖٻ‬Ӹᛎ૙੉‫ ᧉ ݦ‬ȷ ‫ ܖ‬ˮ Ჴ ᣿ᗡ߻‫ܖ‬Ღ2J&ȷȟȍǽǿ‫ܖٻ‬Ღྸ‫ܖ‬Ҧٟȷʋ߸‫ܖٻ‬ᄂ ᆮ ϋ ܾ Ჴ ᣿ᗡƷȢȇȪȳǰƓǑƼᚐௌIn this research we make a comprehensive credit risk analysis on government bonds(GBs) of Germany, France, Italy, Spain, Greece and Germany over the period
2007.4-2012.3, where interest rate (IR) differential, government bond (GB) pricedifferential, default probability (DP) and CDS are considered. First, applying the
GB-pricing model in Kariya et al. (2012) to these GB prices, we first derive the term
structures of interest rates (TSIRs) and discuss on the Maastricht convergence condition
for IR-differentials among these states relative to the German TSIRs and make someobservations on divergent tendencies. The results are associated with business cycles andbudgetary condition of each state.














㻌 Fig. Term structure of default probabilities of France and Italy

In the second part, we derive term structures of default probabilities (DPs) for French,
Italy, Spanish and Greek Government Bonds (GBs) relative to German GBs. In the periodof the Euro Crisis, the DPs are higher than 30 % in case of Italian GBs of 10 year maturity,
while those of French GBs of 10 year are high enough to hit 10%.

15

Modeling Groupᄂᆮಒᙲ␌⏱␔␝⏚ྰἋἰὊἚἂἼἕἛỆấẬỦᴾ
ỶὅἘἼἊỹὅἚʖยὉஇᢘ҄ỉᄂᆮౕ գʂ

MORI, Hiroyukiᴾ৑ ‫ ޓ‬ȷ ࢫ Ꮀ Ჴ έᇢૠྸᅹ‫ܖ‬ǤȳǹȆǣȆȥȸȈ৑Ճ ଢ඙‫ܖ߻ྸܖٻ‬ᢿ૙੉‫ ᧉ ݦ‬ȷ ‫ ܖ‬ˮ Ჴ ჷᏡऴ‫ܖإ‬Ღ߻‫ܖ‬Ҧٟȷଔᆖဋ‫ܖٻ‬ᄂ ᆮ ϋ ܾ Ჴ ǤȳȆȪǸǧȳȈǷǹȆȠƷȢȇȪȳǰƓǑƼᚐௌᄂᆮಒᙲ

Modeling Groupᮏᖺᗘࡢࠕࢫ࣐࣮ࢺࢢࣜࢵࢻ࡟࠾ࡅࡿ࢖ࣥࢸࣜࢪ࢙ࣥࢺண ࣭᭱㐺໬ࡢ◊✲ࠖ࡜ࡋ࡚ࠊ㸱ࡘࡢࡇ࡜࡟ࡘ࠸࡚◊✲ࡋࡓࠋࡲࡎࠊẼ㇟᮲௳࡟ࡼࡗ࡚ฟຊኚືࡍࡿ෌⏕ྍ⬟࢚ࢿࣝࢠ࣮㟁※ࢆᣢ
ࡘࢫ࣐࣮ࢺࢢࣜࢵࢻ⎔ቃୗࡢ㏦㟁ࢿࢵࢺ࣮࣡ࢡ࡟࠾࠸࡚㟁ຊไᚚᶵჾ࡛࠶ࡿ㹄㸿㹁T㹑
㸦Flexible AC Transmission System㸧ࡢ᭱㐺㓄⨨࡜᭱㐺ฟຊࡢࢥ࣮ࢹ࢕ࣥࢢ᪉ᘧ࡟ࡘ࠸࡚◊✲ࡋࡓࠋࡇࡢ FACTS 㓄⨨ၥ㢟ࡣ㠀⥺ᙧΰྜᩚᩘィ⏬ၥ㢟࡜ࡋ࡚⾲⌧ࡉࢀࠊࡑࢀࢆ㧗㏿࡟ゎࡃࡓࡵ࡟ࠊࣁ࢖ࣈࣜࢵࢻࢥ࣮ࢹ࢕ࣥࢢࢆ⪃᱌ࡋࡓ[1]ࠋ
 ḟ࡟ࢫ࣐࣮ࢺࢢࣜࢵࢻ⎔ቃୗࡢ㓄㟁ࢿࢵࢺ࣮࣡ࢡ࡟࠾࠸࡚㟁ᅽ೫ᕪࢆ᭱ᑠ໬ࡍࡿ┠ⓗࡢ࢟ࣕࣃࢩࢱ㓄⨨ၥ㢟࡛ࠊ୪ิ཮ᑐࢱࣈࢧ࣮ࢳࢆ⪃᱌ࡋࡓࠋ࢟ࣕࣃࢩࢱ㓄⨨ၥ㢟ࡣ஦๓࡟ᐃࡵࡽࢀ
ࡓࣀ࣮ࢻ࡟࠾࠸࡚㟁ᅽㄪᩚ࡟ᚲせ࡞᭱㐺࡞ࣂࣥࢡᩘࢆỴᐃࡍࡿ⤌ྜࡏ᭱㐺໬ၥ㢟࡛࠶ࡿࠋࡑࡢ
ၥ㢟ࢆゎỴࡍࡿࡓࡵ࡟ࠊࢱࣈࢧ࣮ࢳࡢ㏆ഐ⏕ᡂ࡟࠾࠸࡚㏆ഐศ๭ࠊࢱࣈࣜࢫࢺ࡟࠾ࡅࡿከᵝ໬ࢆᑟධࡋࡓ୪ิࢱࣈࢧ࣮ࢳࡢึᮇ್࡟ᑐࡋ࡚཮ᑐࢥ࣮ࢻࢆ⪃៖ࡋࡓ᪉ᘧࢆ㛤Ⓨࡋࠊᚑ᮶ἲ࡜ẚ࡭࡚Ⰻዲ࡞⤖ᯝࢆᚓࡓ[2]ࠋ
 ࡉࡽ࡟ࠊኴ㝧ගⓎ㟁ࡢ▷ᮇண ࡟࠾࠸࡚ᚑ᮶ࡢࢽ࣮ࣗࣛࣝࢿࢵࢺ࡛࠶ࡿ RBFN(Radial Basis
Function Network)ࢆᨵၿࡍࡿࡓࡵ࡟ࠊRBFN ࢆ୍⯡໬ࡋࡓ GRBFN ࡢ฼⏝ࠊ࣓ࢱࣄ࣮ࣗࣜࢫࢸ
࢕ࢡࢫࡢ EPSO(Evolutionary Particle Swarm Optimization)࡟ࡼࡿࢽ࣮ࣗࣟࣥࡢ㔜ࡳ᭱㐺໬ࠊ㐣Ꮫ⩦㜵Ṇࡢࡓࡵࡢࢽ࣮ࣗࣟࣥࡢ㔜ࡳῶ⾶ἲࠊGRBFN ࡢึᮇ୰ᚰࢆỴᐃࡍࡿࡓࡵࡢ DeterministicAnnealing ࡟ࡼࡿࢹ࣮ࢱࢡࣛࢫࢱࣜࣥࢢࢆ⼥ྜࡋࡓᡭἲࢆᥦ᱌ࡋࠊࡑࡢᡭἲࡢ᭷ຠᛶࢆ♧၀ࡋ
ࡓ[3]ࠋ
ཧ⪃ᩥ⊩
[1] H. Fujita and H. Mori, “Development of Hybrid-Coded EPSO for Optimal Allocation of FACTS
Devices in Uncertain Smart Grids,” Procedia Computer Science (Elsevier), Vol. 12, pp.429-434, Nov.
2012.
[2] Y. Ogita and H. Mori, “Parallel Dual Tabu Search for Capacitor Placement in Smart Grids,”
Procedia Computer Science (Elsevier), Vol. 12, pp.307-313, Nov. 2012.
[3] 㧗ᶫᨻே, ᳃ၨஅ:ࠕEPSO ࢆ⏝࠸ࡓ GRBFN ࡟ࡼࡿኴ㝧ගⓎ㟁ฟຊண ࠖ, 㟁ẼᏛ఍ㄽᩥㄅ
B, Vol. 133, No.1, pp. 72-78 (2013-1)16ѣཋỉᢃѣỆ‫ܖ‬ốᴾᐯࢷЎ૝Сࣂỉૠྸႎᄂᆮ

␌⏱␔␝⏚ྰ‫ݱ‬௎ʰᴾ

KOBAYASHI, RyoиȪȸȀȸ৑ ‫ ޓ‬ȷ ࢫ Ꮀ Ჴ έᇢૠྸᅹ‫ܖ‬ǤȳǹȆǣȆȥȸȈ৑Ճ ࠼޽‫ܖٻܖٻ‬ᨈྸ‫ܖ‬ᄂᆮᅹ૙੉‫ ᧉ ݦ‬ȷ ‫ ܖ‬ˮ Ჴ ྵᝋૠྸ‫ܖ‬ᲦҦٟ ૠྸᅹ‫ ܖ‬ȷிʮ‫ܖٻ‬ᄂ ᆮ ϋ ܾ Ჴ ဃཋƷನᡯ࢟঺ȷᢃѣȷऴ‫إ‬ϼྸƷૠྸႎᄂᆮ ື≀ࡢࣟࢥ࣮ࣔࢩࣙࣥ࡟Ꮫࡪࡇ࡜࡟ࡼࡾࠊື≀୪ࡳ࡟ࡋ࡞ࡸ࠿࡟ࣟࣂࢫࢺ࡟ࠊ」㞧࡛୙☜ᐃ࡞⌧ᐇࡢ⎔ቃࡢ୰ࢆືࡁᅇࢀࡿࣟ࣎ࢵࢺࢆసࡿࡇ࡜ࢆ┠ᣦࡋ࡚ࠊ⏕≀Ꮫ⪅࣭ᩘᏛ⪅࣭ᕤᏛ⪅࠿ࡽ࡞ࡿࢳ࣮࣒࡛◊✲ࢆ⾜࡞ࡗ࡚࠸ࡿࠋᡃࠎࡣࠊ⢓⳦ࡢ㐠ືࡢᩘ⌮ࣔࢹࣝ࠿ࡽࠕ㱈㱒㛵ᩘࠖ࡜࠸࠺ᴫᛕࢆᢳฟࡋࠊࡑࢀࢆ⏝࠸ࡓ⮬ᚊศᩓไᚚ᪉⟇ࢆᥦ᱌ࡋࠊࡑࢀࢆᵝࠎ࡞ࢱ࢖ࣉࡢࣟ࣎ࢵࢺ࡟
㐺⏝ࡍࡿࡇ࡜࡛ࠊࡑࡢ᭷ຠᛶࢆ♧ࡋ࡚ࡁࡓࠋᮏᖺᗘࡣࣄ࣒ࣛࢩࢆ࣓࢖ࣥࡢࢱ࣮ࢤࢵࢺ࡜ࡋ࡚ࠊ
ࡑࡢ㐠ືࡢゎᯒࢆ⾜࠸ࠊࣄ࣒ࣛࢩࣟ࣎ࢵࢺࡢ〇సࢆ⾜ࡗࡓࠋࡲࡓࠊ⭡㊊㢮ࡢ㏺⾜࡟࠾ࡅࡿᦶ᧿
ไᚚࡢᢸ࠸ᡭ࡜ࡋ࡚ࡢ⢓ᾮ࡟㛵ࡍࡿ◊✲ࢆ⾜ࡗࡓࠋࡉࡽ࡟ࠊどぬඹ᭷࡟ᇶ࡙ࡃࣟ࣎ࢵࢺࡢࢼࣅ
ࢤ࣮ࢩࣙࣥࢩࢫࢸ࣒ࢆᵓ⠏ࡋࡓࠋ㸨ࣄ࣒ࣛࢩࡢ㐠ືࡢィ ࡜ࣔࢹࣝ໬ཬࡧࣟ࣎ࢵࢺ〇స㻌 䝠䝷䝮䝅䛾ᣢ䛴ከᵝ䛺㐠ືᙧែ䛾୰䛷䚸㏺⾜䛸㐟Ὃ䛾㐠ືゎᯒ䜢⾜䛳䛯䚹㏺⾜䛾㐠ືィ 䛻ᇶ䛵䛝䚸䝠䝷䝮䝅䛾䠎ḟඖⓗ㏺⾜䛾ᩘ⌮䝰䝕䝹䜢ᵓ⠏䛧䛯䚹㐟Ὃ䛻㛵䛧䛶䛿䚸䝠䝷䝮䝅䛿䛭䛾యഃ䛻䚸๓᪉䛛䜙ᚋ᪉䛻ྥ䛛䛳䛶Ἴ䜢ὶ䛩䛸ྠ᫬䛻䚸య㍈䜢᣺ືⓗ䛻ᢡ䜚᭤䛢䛶䛔䜛䚹ᡃ䚻䛿䚸䛣䛾㐟Ὃ䝟䝍䞊䞁䜢෌⌧䛩䜛䝋䝣䝖䝻䝪䝑䝖䜢〇స䛧䚸ຠᯝⓗ䛺㐟Ὃ䜢⾜䛖䛯䜑䛾యഃἼ䛸య㍈䛾ᢡ䜜᭤䛜䜚᣺ື䛾఩┦㛵ಀ䜢᫂䜙䛛䛻䛧䛯䚹㸨⭡㊊㢮➼ࡢ㏺⾜㐠ື࡟࠾ࡅࡿ⢓ᾮࡢຊᏛⓗᙺ๭ࡢゎ᫂㻌 ⢓ᾮ䛾䝺䜸䝻䝆䞊䛜䛒䜛✀䛾䝠䝇䝔䝸䝅䝇䜢ᣢ䛴䛸䛔䛖ᐇ㦂஦ᐇ䛻ᇶ䛵䛝䚸Direct wave ᆺ䛸Retrograde wave ᆺ䛾୧㏺⾜ᵝᘧ䛜䚸⢓ᾮ䛻䜘䜚⮬↛䛻ᐇ⌧䛥䜜䜛䛣䛸䜢䚸ᩘ⌮䝰䝕䝹䛻䜘䛳䛶♧䛧䛯䚹㸨ど⏺ඹ᭷ࢆ⏝࠸ࡓ┤ឤⓗ࣊ࣅᆺࣟ࣎ࢵࢺ᧯⦪ࢩ࣑࣮ࣗࣞࢱࡢ㛤Ⓨ㻌 䝻䝪䝑䝖䛾᧯⦪䜢㧗ᗘ䛺䝺䝧䝹䛷⾜䛖䛯䜑䛻䛿䚸䛷䛝䜛䛰䛡ከ䛟䛾ឤぬ䜢䚸䝻䝪䝑䝖䛸᧯⦪⪅䛾㛫䛷ඹ᭷䛩䜛䛣䛸䛜ᮃ䜎䛧䛔䚹䛭䛾䛯䜑䛾➨୍Ṍ䛸䛧䛶䚸䝦䝡ᆺࣟ࣎ࢵࢺ࡜᧯⦪⪅ࡢど⏺ඹ᭷࡟ࡼࡿ┤ឤⓗ࡞ࣟ࣎ࢵࢺࢼࣅࢤ࣮ࢩࣙࣥࢩࢫࢸ࣒ ”Snake Vision Simulator” ࢆᵓ⠏ࡋࡓࠋ᧯⦪⪅࡜ࣔࢹࣝࢆࡘ࡞ࡄ࢖ࣥࢱ࣮ࣇ࢙࣮ࢫ࡜ࡋ࡚ࠊゅᗘ᳨▱ࡀྍ⬟࡞࣊ࢵࢻ࣐࢘ࣥࢺࢹ࢕ࢫࣉࣞ࢖ࢆᑟධࡋࠊ
ࡇࢀ࡟ࡼࡾどぬඹ᭷࡜ྠ᫬࡟᧯⦪⪅ࡢど⥺࡟ࡼࡿ᪉ྥไᚚࢆྍ⬟࡟ࡋࡓࠋ

17

Modeling Groupᄂᆮಒᙲ␌⏱␔␝⏚ྰʴể᧙ỪỦᙻᙾὉᎮᙾऴ‫إ‬ϼྸᒰ߷ᕣ

ARAKAWA, Kaoruᴾ৑ ‫ ޓ‬ȷ ࢫ Ꮀ Ჴ έᇢૠྸᅹ‫ܖ‬ǤȳǹȆǣȆȥȸȈ৑Ճ ଢ඙‫ܖ߻ྸܖٻ‬ᢿ૙੉‫ ᧉ ݦ‬ȷ ‫ ܖ‬ˮ Ჴ ဒ΂ȷ᪦٣̮ӭϼྸᲦ߻‫ܖ‬Ҧٟȷிʮ‫ܖٻ‬ᄂ ᆮ ϋ ܾ Ჴ ჷᙾǷǹȆȠƷȢȇȪȳǰƓǑƼᚐௌᄂᆮಒᙲ

Modeling Groupே䛸㛵䜟䜛どぬ䞉⫈ぬ᝟ሗฎ⌮䛻䛴䛔䛶௨ୗ䛾◊✲䜢⾜䛳䛯䚹䠄䠍䠅ᑐヰᆺ㐍໬ィ⟬䜢⏝䛔䛯❧యឤ䛾䛒䜛㢦⏬ീఝ㢦⤮సᡂ䠄䠎䠅䝇䝬䞊䝖䝣䜷䞁䜰䝥䝸䛻䜘䜛ᐇ⿦䛾䛯䜑䛾ᑐヰᆺ㢦⏬ീ⨾ほ໬ฎ⌮䛾᳨୍ウ䠄䠏䠅ᡂ㛗ᮇ䛾ᖺ㱋ኚ໬䜢క䛖㢦⏬ീ䛻䜘䜛ே≀ㄆド䠄䠐䠅᪉ྥᛶ䝯䝕䜱䜰䞁䝣䜱䝹䝍䜢⏝䛔䛯䜲䞁䝨䜲䞁䝔䜱䞁䜾ἲ䛻䜘䜛ྂ䛔ື⏬ീ䛾䝇䜽䝷䝑䝏㝖ཤ䠄䠍䠅䛷䛿䠈䛣䜜䜎䛷䛾ᖹ㠃ⓗ䛻௙ୖ䛜䜛ఝ㢦⤮䛻ᑐ䛧䠈㝜ᙳ䜢䛴䛡䜛䛣䛸䛻䜘䛳䛶❧యឤ䜢ᣢ䛯䛫䠈䜘䜚⾲⌧ຊ䛾䛒䜛ఝ㢦⤮సᡂ䛾᪉ᘧ䜢ᥦ᱌䛧䛯䚹䛣䜜䛿䠈ᮏே䛾㢦෗┿䛾㍤ᗘ್䜢䛒䜛๭ྜ䛷ᖹ㠃ⓗ䛺ఝ㢦⤮䛻ΰྜ䛥䛫䜛䛣䛸䛻䜘䜚ᐇ⌧䛩䜛䜒䛾䛷䛒䜛䚹䜎䛯䠈䛭䛾ΰྜ⋡䜢ᑐヰᆺ㐍໬ィ⟬䛷ே䛜୺ほⓗ䛻Ⰻዲ䛸ᛮ䛘䜛್䛻タᐃ䛩䜛䚹䛣䜜䛻䜘䜚䠈ே䛜ぢ䛶䜒⮬↛䛷ዲ䜎䛧䛔❧యឤ䛾䛒䜛ఝ㢦⤮䜢సᡂ䛷䛝䜛䛣䛸䛜♧䛥䜜䛯䚹䠄䠎䠅䛷䛿䠈ᑐヰᆺ㐍໬ィ⟬䜢⏝䛔䛯㢦⏬ീ⨾ほ໬䝅䝇䝔䝮䜢䝇䝬䞊䝖䝣䜷䞁䜔䝍䝤䝺䝑䝖➃ᮎ䛷ᐇ⿦䛩䜛䛻ᙜ䛯䜚䠈᫖ᖺᗘ䠈ෆศཬ䜃እศ䜢⏝䛔䜛䛣䛸䛻䜘䜚䠈ຠᯝⓗ䛻฼⏝⪅䛾ዲ䜏䛾㢦⏬ീ䛜ᚓ䜙䜜䜛䛸䛔䛖᪉ᘧ䜢ᥦ᱌䛧䛯䛜䠈䛭䛾᭷ຠᛶ䜢ᐃ㔞ⓗ䛻☜ㄆ䛧䛯䚹䝇䝬䞊䝖䝣䜷䞁䜰䝥䝸䛸䛧䛶䛣䛾㢦⏬
ീ⨾ほ໬䝅䝇䝔䝮䜢ᐇ⿦䛩䜛䛸䠈䛒䜎䜚ከ䛟䛾㢦⏬ീ䜢䝕䜱䝇䝥䝺䜲䛻⾲♧䛷䛝䛺䛔䛯䜑䠈ᑡ䛺䛔ೃ⿵㢦⏬ീ䛛䜙ຠ⋡䜘䛟ᮃ䜎䛧䛔⨾ほ໬㢦⏬ീ䛜ฟ⌧䛥䜜䜛ᚲせ䛜䛒䜛䚹ᮏ◊✲䛷䛿䠈ᚑ᮶䛾஺ཫἲ䛸ෆศ䞉እศ䜢ᑟධ䛧䛯஺ཫἲ䛾≉ᛶ䜢ᐃ㔞ⓗ䛻ẚ㍑䛧䠈ෆศ䞉እศ䜢ᑟධ䛩䜛䛣䛸䛻䜘䜚䠈䜘䜚᪩䛟⌮᝿䛾㢦⏬ീ䛜ᐇ⌧䛷䛝䜛䛣䛸䜢♧䛧䛯䚹䠄䠏䠅䛷䛿䠈ᑠᏛ⏕䛾䛸䛝䛻᧜ᙳ䛧䛯㢦෗┿䛛䜙䠈୰Ꮫ⏕䛻䛺䛳䛯᫬䛾ே≀ㄆド䜢⾜䛖᪉ᘧ䜢ᥦ᱌䛧䠈䛭䛾᭷ຠᛶ䜢♧䛧䛯䚹㢦⏬ീ䛻䜘䜛ே≀ㄆド䛻䛿䛔䜝䛔䜝䛺᪉ᘧ䛜ᥦ᱌䛥䜜䛶䛔䜛䛜䠈ᡂ㛗ᮇ䛻䛚䛡䜛ᖺ㱋ኚ໬䛜䛒䜛䛸䠈㢦䛾ᵓ㐀䛜ኚ䜟䜚ㄆド䛜㞴䛧䛔䚹ᮏ◊✲䛷䛿䠈䝤䝻䝑䜽䝬䝑䝏䞁䜾䜢᥇⏝䛧䠈ᡂ㛗䛻䜘䜚㢦䛾ྛ㒊఩䛜⛣ື䛧䛶䜒ᮏே≉᭷䛾㒊఩䛾ᙧ≧䜢ぢ䛴䛡䜛䜒䛾䛷䛒䜛䚹䜎䛯䠈≉䛻䠈┠䛾≉ᚩ䛜ᮏே䛾ㄆド䛻㔜せ䛺ᙺ๭䜢ᢸ䛖䛣䛸䛻╔┠䛧䠈┠䛻㔜䛝䜢⨨䛔䛯ㄆドἲ䜢ᥦ᱌䛧䠈⣙ 9 ๭䛾⢭ᗘ䛷ᮏே䜢ㄆド䛷䛝䜛䛣䛸䜢♧䛧䛯䚹䠄䠐䠅䛷䛿䠈ື⏬ീ䛾യ䜢ᾘ䛩䛣䛸䛻⏝䛔䜙䜜䛶䛔䜛䜲䞁䝨䜲䞁䝔䜱䞁䜾ἲ䛻᪉ྥᛶ䝯䝕䜱䜰䞁䝣䜱䝹䝍䜢⤌䜏ྜ䜟䛫䜛䛣䛸䛻䜘䜚ྂ䛔ᫎ⏬䛺䛹䛾ື⏬ീ䛻ྵ䜎䜜䜛䝇䜽䝷䝑䝏䛸࿧䜀䜜䜛ᆶ┤≧䛾യ䜢㝖ཤ䛩䜛᪉ᘧ䜢ᥦ᱌䛧䛯䚹᪉ྥᛶ䝯䝕䜱䜰䞁䝣䜱䝹䝍䜢⏝䛔䜛䛣䛸䛻䜘䜚䠈䜲䞁䝨䜲䞁䝔䜱䞁䜾ἲ䛾㝈⏺䜢⿵䛔䠈Ⰻዲ䛺⏬ീಟ᚟䜢⾜䛖䛣䛸䛜䛷䛝䜛䛣䛸䜢♧䛧䛯䚹

18

NISHIMORI, Hirakuᴾᙱౕਏ␌⏱␔␝⏚ྰ

ỡỤẫᙲእኒỉἒỶἜἱἁἋỉᚐௌᴾ৑ ‫ ޓ‬ȷ ࢫ ᎰᲴ έᇢૠྸᅹ‫ܖ‬ǤȳǹȆǣȆȥȸȈ৑Ճ ࠼޽‫ܖٻܖٻ‬ᨈྸ‫ܖ‬ᄂᆮᅹ૙੉‫ ᧉ ݦ‬ȷ ‫ ܖ‬ˮᲴ ᩼࠯ᘖཋྸ‫ܖ‬Ღྸ‫ܖ‬Ҧٟȷிʮ߻ಅ‫ܖٻ‬ᄂ ᆮ ϋ ܾᲴ ңӷྵᝋƷȢȇȪȳǰƓǑƼᚐௌᡃࠎࢆྲྀࡾᅖࡴ⮬↛ࡢ୰࡟ࡣᵝࠎ࡞ࢱ࢖ࣉࡢ⩌ࢀࡀ࠶ࡿࠋ㨶ࠊ㫽ࠊ᪻⹸ࡢ⩌ࢀ࡞࡝ࡀ㌟㏆
࡞౛࡛࠶ࡿࠋࡲࡓࠊ㌴ࡢ⩌ࢀ,ࠊṌ⾜⪅ࡢ⩌ࢀ࡞࡝ேᕤ≀ࡸே㛫⮬㌟࠿ࡽ࡞ࡿ⩌ࢀࡶ࠶ࡿࠋࡇ
ࢀࡲ࡛ࡢ⩌ࢀࡢ㞟ᅋ㐠ື࡟㛵ࡍࡿ⌮ㄽ◊✲ࡢከࡃࡣࠊ i)ಶࠎࡢᵓᡂせ⣲ࡢ㐠ືࢆ࡛ࡁࡿࡔࡅ
༢⣧໬ࡋࡓୖ࡛ࠊii)⩌ࢀ඲య࡜ࡋ࡚⾲ฟࡍࡿ」㞧࡞㐠ືࢆ෌⌧ࡋࠊiii)ࡑࡇ࠿ࡽ⩌ࢀࡢ㞟ᅋ㐠ືࡢᮏ㉁ࢆᢳฟࡍࡿࠊ࡜࠸࠺ὶࢀ࡟ἢࡗࡓ◊✲࡛࠶ࡗࡓࠋ୍᪉࡛ࠊෑ㢌࡛♧ࡋࡓᵝࠎ࡞⩌ࢀ࡟࠾࠸࡚ࡣࠊᵓᡂせ⣲ࡢᣢࡘ㸪ࡇࢀ௨ୖ༢⣧໬࡛ࡁ࡞࠸ෆ㒊⮬⏤ᗘࡇࡑࡀࠊ ⩌ࢀ඲యࡢ」㞧࡞᣺ࡿ⯙࠸࡟Ỵᐃⓗ࡞ᙳ㡪ࢆ୚࠼ࡿྍ⬟ᛶࡶ᤼㝖࡛ࡁ࡞࠸ࠋ
ࡑࡇ࡛, 2012 ᖺᗘࡢᡃࠎࡢ◊✲┠ᶆࡢ୍ࡘ࡜ࡋ࡚ࠊ࠸ࡃࡘ࠿ࡢ⩌ࢀࡢ㞟ᅋ㐠ື࡟࠾࠸࡚ࠊ
ᐇ㦂ⓗほ ࡜ࡑࡢゎᯒࢆࡇࢀࡲ࡛௨ୖ࡟ヲ⣽࡟㐍ࡵࠊಶࠎࡢせ⣲ࡢ༢⣧໬࡛ࡁ࡞࠸ෆ㒊⮬⏤ᗘࡢᏑᅾࢆྫྷ࿡ࡍࡿࡇ࡜࡛ࠊ⩌ࢀࡢ㞟ᅋ㐠ືࡢᶵᵓࡢ⌮ゎࢆࡵࡊࡋࡓࠋලయⓗ࡟ࡣࠊ1.

࢔ࣜࡢ㞟ᅋ᥇㣵⾜ື࡟࠾ࡅࡿ໬Ꮫ᝟ሗ࡜どぬ᝟ሗࡢ฼⏝ࡢඃඛ㡰఩Ỵᐃᶵᵓࡢゎ᫂

2.

෇⎔≧Ỉ㊰ෆࡢ๓ᚋᑐ⛠ᶋ⬻⯪㞟ᅋࡢ஺㏻ὶࡢᐇ㦂࡜ᩘ⌮ᶍᆺ࡟ࡼࡿゎᯒࢆ⾜ࡗࡓࠋ1 ࡟㛵ࡋ࡚ࡣࠊ๓ᖺᗘࡲ࡛ࡢ◊✲࡟ᘬࡁ⥆ࡁࠊ᥇㣵Ṍ⾜୰ࡢ࢔ࣜ(ࢺࣅ࢖ࣟࢣ࢔ࣜ)ࡢ
ᖐᕢ⤒㊰ᵓ⠏ࡢᐇ㦂ࢆ⾜࠸ࠊ࢔ࣜࡀࣇ࢙ࣟࣔࣥ࡟ࡼࡿ໬Ꮫ᝟ሗࡔࡅ࡛࡞ࡃ, ᥇ 㣵 ㏵ ୖ ࡟ ࠾ ࡅࡿࣛࣥࢻ࣐࣮ࢡ࡞࡝ࡢどぬ᝟ሗࡶ฼⏝ࡋ࡞ࡀࡽ᫬ࠎ้ࠎࡢ⮬ศࡢ఩⨨ࢆᢕᥱࡋࠊ᥇㣵⤒㊰ࢆᵓ⠏ࡋ࡚࠸ࡿࡇ࡜ࢆᐃ㔞ⓗ࡟♧ࡋࡓࠋࡲࡓࠊどぬ᝟ሗࡢ฼⏝ࡀࠊグ᠈ࡢಖᣢ࡜㛵㐃ࡋ࡚࠸ࡿࡇ࡜
ࡶ᫂ࡽ࠿࡟ࡋ࡚ࡁࡓࠋࡲࡓࠊᶋ⬻⯪㞟ᅋࡢ㐠ື࡟㛵ࡋ࡚ࡣࠊ᫂἞኱Ꮫ≉௵ㅮᖌࡢᮎᯇಙᙪẶࡸ㸪ᗈᓥ኱Ꮫ GCOE ◊✲ဨཧ⣡ᘪᙪẶࡽ࡜ඹྠࡋ, ⾲㠃ᙇຊᕪ࡛⮬ᕫ㥑ືࡍࡿ๓ᚋᑐ⛠࠾ࡼࡧ๓ᚋ㠀ᑐ⛠࡞ᶋ⬻⯪ࡢ㞟ᅋࢆ෇⎔≧Ỉ㊰࡟୪࡭ࠊࡑࡢᩘᐦᗘ࡟౫Ꮡࡋ࡚ࠊ㸰ࡘࡢ㞟ᅋ㐠ື࣮ࣔࢻ---ᐦᗘἼ๓᪉ఏᦙ࣮ࣔࢻ࡜ᐦᗘἼᚋ᪉ఏᦙ࣮ࣔࢻ---ࡢ㛫ࡢษࡾ᭰࠼ࡀ㉳ࡇࡿࡇ࡜ࢆ♧ࡋࡓࠋୖグࡢ⩌ࢀ㐠ື࡜ࡣ⊂❧ࡋ࡚ࠊᆅᙧᏛ࡟࠾ࡅࡿせ⣲⣔ࡢ㐠ື࡜ࡋ࡚
3. ◁ୣࡢࢲ࢖ࢼ࣑ࢡࢫࡢ᪂ࡋ࠸⦰⣙ࣔࢹࣝࡢᵓ⠏ࢆ⾜ࡗࡓࠋලయⓗ࡟ࡣࠊ◁ୣࡢᑿ᰿⥺ࢆ◁ୣࡢᙧ≧࡟࠾ࡅࡿᇶᮏせ⣲࡜ぢ࡚ࠊ◁ୣࡢࢲ࢖ࢼ࣑
ࢡࢫࢆࠕ⣣ࡢ㐠ືࠖ࡜ࡋ࡚⾲⌧ࡍࡿ೫ᚤศ᪉⛬ᘧ⣔ࢆᥦ᱌ࡋࠊࡇࢀࢆ⌮ㄽⓗ࡟ゎᯒࡍࡿࡇ࡜࡛ࠊ
◁ୣࡢ඾ᆺⓗᙧ≧ࡀࡺࡽࡂ࡟ᑐࡋ࡚Ᏻᐃ࠿ྰ࠿ࢆ㆟ㄽࡋࡓࠋ19

Modeling Groupᄂᆮಒᙲ␌⏱␔␝⏚ྰ᣿ᗡࠊ‫‒↝ئ‬᩼∏∙⇦∆⇌⇏∞⇕ࣱ↝ᄩᛐ↗‒ᴾ᭗‫ܤ‬ᅵ೔ TAKAYASU, Hideki↌↝∈⇭∐∙⇖‒৑ ‫ ޓ‬ȷ ࢫ Ꮀ Ჴ έᇢૠྸᅹ‫ܖ‬ǤȳǹȆǣȆȥȸȈ৑Ճ ଢ඙‫ܖٻ‬ᄂᆮȷჷᝠ৆ဦೞನܲՃ૙੉ ǽȋȸǳȳȔȥȸǿǵǤǨȳǹᄂᆮ৑ȷǷȋǢȪǵȸȁȣȸ‫ ᧉ ݦ‬ȷ ‫ ܖ‬ˮ Ჴ ᩼ዴ࢟ཋྸ‫ܖ‬Ღྸ‫ܖ‬ҦٟȷӸӞ‫ܖٻދ‬ᄂ ᆮ ϋ ܾ Ჴ ኺฎཋྸ‫ܖ‬ƷؕᄽƔǒࣖဇǇưModeling Groupᄂᆮಒᙲ㻌 㔠⼥ᕷሙ䛻䛚䛡䜛౯᱁䛾ኚື䛿䚸ఏ⤫ⓗ䛻䝷䞁䝎䝮䜴䜷䞊䜽䝰䝕䝹䛷グ㏙䛩䜛䜰䝥䝻䞊䝏䛜୺ὶ䛷䛒䜛䛜䚸㧗㢖ᗘ䛾ᐇ䝕䞊䝍䜢୎ᑀ䛻ゎᯒ䛩䜛䛸䚸䛣䛾ᶆ‽䝰䝕䝹䛷䛿ㄝ᫂䛷䛝䛺䛔䜘䛖䛺ᵝ䚻䛺≉ᛶ䛜ほ 䛥䜜䜛䚹௒ᖺᗘ䛿䚸䛣䛾Ⅼ䛻㛵䛧䛶ᵝ䚻䛺᪉ྥ䛛䜙ศᯒ䜢㐍䜑䚸⌧ᐇ䛾㠀䝷䞁䝎䝮䜴䜷䞊䜽ᛶ䛸ᩚྜ䛩䜛䜘䛖䛺ᕷሙ䛾䝰䝕䝹㛤Ⓨ䜢⾜䛳䛯䚹㻌㻌 ୗグㄽᩥ㼇㻝㼉䛷䛿䚸䝗䝹෇ᕷሙ䛾Ⅽ᭰䝺䞊䝖䛾⛊้䜏䛾䝕䞊䝍䜢ゎᯒ䛧䚸౯᱁䛾ኚ఩䛾ศᕸ䛜䠎䛴䛾ព࿡䛷㠀ᐃᖖᛶ䜢♧䛩䛣䛸䜢᫂䜙䛛䛻䛧䛯䚹୍䛴┠䛾㠀ᐃᖖᛶ䛿㻞㻠᫬㛫䛾࿘ᮇ䛷ኚື䛩䜛ᡂศ䛷䛒䜚䚸䜒䛖䜂䛸䛴䛿䚸䠍㐌㛫⛬ᗘ䛾᫬㛫䝇䜿䞊䝹䛾䝫䜰䝋䞁㐣⛬䛷㏆ఝ䛷䛝䜛䜘䛖䛺䝷䞁䝎䝮䛻Ⓨ⏕䛩䜛㠀ᐃᖖᡂศ䛷䛒䜛䚹㻌㻌 ㄽᩥ㼇㻞㼉䛷䛿䚸ྠ䛨䛟Ⅽ᭰ᕷሙ䛾ᕷሙ౯᱁䛾ୖ䛜䜚ୗ䛜䜚䛾Ⓨ⏕஦㇟䛜䚸┤㏆䛾㐣ཤ䛾ୖ䛜䜚ୗ䛜䜚䛾ᒚṔ䛻౫Ꮡ䛧䛶䛔䜛䛣䛸䜢᮲௳௜䛝☜⋡䛾ほ 䛻䜘䛳䛶ᐇド䛧䛯䚹䜎䛯䚸ㄽᩥ㼇㻟㼉䛷䛿䚸ୖ䛜䜚ୗ䛜䜚䛾᫬⣔ิ䛻ᑐ䛧䛶⥙⨶ⓗ䛺㐃᳨ᐃ䜢⾜䛔䚸୍᪥䜘䜚䜒▷䛔᫬㛫䝇䜿䞊䝹䛷䛿୍⯡䛻ୖୗኚື䛿┦㛵䜢᭷䛩䜛䛣䛸䜢᫂䜙䛛䛻䛧䛯䚹㻌㻌 䛣䜜䜙䛾㠀䝷䞁䝎䝮䜴䜷䞊䜽ⓗ䛺ほ ஦ᐇ䛸▩┪䛧䛺䛔䜘䛖䛺ᕷሙ䛾䝰䝕䝹䛸䛧䛶䚸௬᝿ⓗ䛺䝕䜱䞊䝷䞊䛾㞟ᅋ⾜ື䜢䝅䝭䝳䝺䞊䝖䛩䜛䝇䝥䝺䝑䝗䝕䜱䞊䝷䞊䝰䝕䝹䜢ᵓ⠏䛧䛯䚹䛣䛾䝰䝕䝹䛷䛿䚸䝕䜱䞊䝷䞊䛜䝖䝺䞁䝗䜢㏣㝶䛩䜛ຠᯝ䜢௜ຍ䛩䜛䛣䛸䛻䜘䜚౯᱁䛾ୖ䛜䜚ୗ䛜䜚䛾ᇶᮏ≉ᛶ䜢෌⌧䛷䛝䜛䛰䛡䛷䛺䛟䚸᪥㖟䛾௓ධ䛺䛹䛾ᴟ➃䛻㠀ᐃᖖ䛺ᕷሙ䛾≧ែ䜒䝟䝷䝯䞊䝍䜢ㄪᩚ䛩䜛䛣䛸䛻䜘䛳䛶෌⌧䛩䜛䛣䛸䛜䛷䛝䜛䚹㻌
ᖺᗘⓎ⾲ㄽᩥ㸦ᰝㄞ௜ࡁ㸧[1] Takaaki Ohnishi, Hideki Takayasu, Takatoshi Ito, Yuko Hashimoto, Tsutomu Watanabe, Misako
Takayasu: On the nonstationarity of the exchange rate process, International Review of Financial
Analysis 23, 30–34 (2012)[2] Y. Hashimoto, T. Ito, T. Ohnishi, M. Takayasu, H. Takayasu, T. Watanabe: Random walk or a run.
Market microstructure analysis of foreign exchange rate movements based on conditional probability,
Quantitative Finance, 12, 893-905 (2012)[3] Yoshihiro Yura, Takaaki Ohnishi, Kenta Yamada, Hideki Takayasu, Misako Takayasu: REPLICATIONOF NON-TRIVIAL DIRECTIONAL MOTION IN MULTI-SCALES OBSERVED BY THE RUNS TEST,International Journal of Modern Physics: Conference Series, Vol. 16, 136–148 (2012)[4] ᯇỌ೺ኴࠊᒣ⏣೺ኴࠊ㧗㧗Ᏻ⚽ᶞࠊ㧗Ᏻ⨾బᏊ: ࢫࣉࣞࢵࢻࢹ࢕࣮࣮ࣛࣔࢹࣝࡢᵓ⠏࡜ࡑࡢᛂ⏝,ேᕤ▱⬟Ꮫ఍ㄽᩥㄅ, 27, 365㸫375 (2012)
௚5⦅

20

ᴾ

௷ဋᢋ‫پ‬

␌⏱␔␝⏚ྰ

ኬᏘởኵጢ࢟঺ỉἧỵἊỽἽἢỶỼἿἊὊ
SHIBATA, Tatsuo

ᄂᆮಒᙲ
ィ

ᢏ⾡ࡢⓎ㐩࡛ࠊⓎ⏕ࡸ෌⏕࡟㛵ࢃࡿ⣽⬊ࡸ⤌⧊ࡢᵓ㐀ᙧᡂࡸ᝟ሗฎ⌮࡞࡝ࡢᶵ⬟Ⓨ⌧ࡢࢲ࢖ࢼ࣑ࢵࢡ࡞ࣉࣟࢭࢫࡀぢ࠼࡚ࡁࡲࡋࡓࠋ⏕ࡁࡓ⣽⬊ࡸ⣽⬊ࡢ㞟ᅋࡀ♧ࡍࠊ┿࡟⏕≀ࡽࡋ࠸ࢲ࢖ࢼ࣑ࢵࢡ࡞⌧㇟ࡣࠊศᏊࡸ㑇ఏᏊ࡞࡝ࡢከࡃࡢせ⣲ࡀ༠ຊࡋ࡚ാࡃࡇ࡜࡛⏕ࡳฟࡉࢀ࡚
࠸ࡲࡍࠋࡑࡢࡼ࠺࡞ࠊከࡃࡢせ⣲ࡀ༠ຊࡋ࡚⏕ࡳฟࡍࠊ⏕≀ࡢ」㞧࡞⌧㇟ࡢືసཎ⌮ࡸタィཎ⌮ࡢ⌮ゎࢆ┠ᣦࡍࠊ⤫ྜⓗ࡛ࢩࢫࢸ࣒ㄽⓗ࡞◊✲ࡢᚲせᛶࡀ㧗ࡲࡗ࡚࠸ࡲࡍࠋࡑࡢࡓࡵ࡟ࡣࠊ
㧗ᗘ࡞ィ ᢏ⾡࡜㐃ືࡍࡿᩘ⌮ⓗ࡞᪉ἲㄽࡢⓎᒎࡀᚲせ࡛ࡍࠋࡇ࠺ࡋࡓ᪂ࡋ࠸⏕࿨⛉Ꮫࡢㄢ㢟࡟ࠊ≀⌮Ꮫࡸᩘ⌮⛉Ꮫ࡞࡝ࡢᩘ⌮ⓗ࡞Ⓨ᝿ࡸ᪉ἲㄽࢆ⏝࠸࡚ゎ᫂ࡍࡿࡇ࡜ࢆ┠ᣦࡋ࡚࠸ࡲࡍࠋ
㏆ᖺ㸪⣽⬊ෆ㒊࡟࠾࠸࡚཯ᛂᣑᩓ⣔ⓗ࡞௙⤌ࡳ࡟ࡼࡗ࡚᫬㛫̽✵㛫ⓗᵓ㐀ᙧᡂࡢ㉳ࡇࡿࡇ࡜ࡀከᩘሗ࿌ࡉࢀ࡚࠸ࡲࡍࠋࡑࢀࡽ࡟ࡣ᫬㛫ⓗ᣺ື㸪✵㛫ࣃࢱࣥ㸪ከᏳᐃᛶ࡞࡝ࡀྵࡲࢀ㸪ࡑࢀࡒࢀࡢᩥ⬦࡛㔜せ࡞ᶵ⬟ࢆᢸࡗ࡚࠸ࡲࡍࠋ⣽⬊ࡢࢫࢣ࣮࡛ࣝࡣ཯ᛂࡢ☜⋡ⓗᛶ᱁ࡣ㢧ⴭࡔ࠿ࡽ㸪ࡑࢀࡽࡢᵓ㐀ᙧᡂࡢ௙⤌ࡳࡣ☜⋡ⓗ࡞ࣀ࢖ࢬ࡟ᑐࡋ࡚㡹ᙉ࡛࠶ࡿᚲせࡀ࠶ࡾࡲࡍࠋ୍᪉࡛ᵓ㐀ᙧᡂࡢ௙⤌ࡳࡣ㸪⣲㐣⛬ࡢ☜⋡ᛶࢆᕧどⓗࢫࢣ࣮ࣝ࡟ቑᖜࡋ⣽⬊ࡢ᣺ࡿ⯙࠸࡟ከᵝᛶࢆࡶࡓࡽ
ࡍ㸪୍ぢ┦཯ࡍࡿᛶ㉁ࢆවࡡഛ࠼࡚࠸ࡲࡍࠋࡇࢀࡽࡀ࡝ࡢࡼ࠺࡟ࡋ࡚ྍ⬟࡟࡞ࡿ࠿ࢆᐇ㝿ࡢ㸯⣽⬊⺯ග࢖࣓࣮ࢪࢹ࣮ࢱࡢゎᯒࡸᩘ⌮ࣔࢹࣝࡢᵓ⠏࣭ゎᯒࢆ㏻ࡌ࡚◊✲ࢆ㐍ࡵ࡚࠸ࡲࡍࠋ
ࡲࡓ㸪Ⓨ⏕㐣⛬࡛ࡣ⣽⬊ෆࡢ཯ᛂࣉࣟࢢ࣒ࣛࢆṇ☜࡟సືࡉࡏ࡚㸪㸯⣽⬊࠿ࡽᵝࠎ࡞✀㢮࠿ࡽ࡞ࡿ⣽⬊ࢆ⏕ᡂࡋ✵㛫ⓗ࡟ㄪ࿴ࡢ࡜ࢀࡓᵓ㐀ࢆᙧᡂࡍࡿ㐣⛬࡛࠶ࡾࡲࡍࠋ⤌⧊ࡢᵓ㐀ᙧᡂ࡟ࡣ⣽⬊ࢆᇶᮏ༢఩࡜ࡍࡿ⢓ᙎᛶయࡢࡼ࠺࡞ຊᏛ㐣⛬ࡀ㛵୚ࡋ࡚࠾ࡾࠊࡑࢀࡀࡉࡽ࡟㑇ఏᏊࡸࢩࢢࢼࣝ࡞࡝ࡢ཯ᛂᣑᩓ㐣⛬࡜┦஫࡟స⏝ࡋ࠶ࡗ࡚࠸ࡲࡍࠋ⣽⬊ࡸ⤌⧊ࡢᐇ㝿ࡢᙧែᙧᡂ࡛ࡣࠊ
ึᮇ᮲௳ࡸቃ⏺᮲௳ࡀࡋࡤࡋࡤᮏ㉁ⓗ࡟㔜せ࡞ᙺ๭ࢆᯝࡓࡍࡇ࡜ࡀ࠶ࡾࡲࡍࠋࡑࡋ࡚ࠊࡑࢀࡽ
ࡢึᮇ᮲௳ࡸቃ⏺᮲௳ࡶࡲࡓ௚ࡢ⏕࿨㐣⛬࡟ࡼࡗ࡚సࡽࢀ࡚࠸ࡿࡢ࡛ࡍࠋ඲యࡢ⌧㇟ࡢ࠺ࡕࠊ
࡝ࡢ㒊ศࢆࣔࢹࣝ࡜ࡋ࡚ษࡾฟࡋ࡚ࠊࡲࡓ࡝ࡢ㒊ศࢆึᮇ᮲௳ࡸቃ⏺᮲௳࡜ࡋ࡚グ㏙ࡍࡿࡢ࠿ࡣ⯆࿡῝࠸ၥ㢟࡛ࡍࠋࡇࢀࡽࡢၥ㢟ࢆⓎ⏕෌⏕⥲ྜ⛉Ꮫ◊✲ࢭࣥࢱ࣮ࡢࢢ࣮ࣝࣉ࡜༠ຊࡋ࡚ࠊ
ᩘ⌮ⓗࠊᐃ㔞ⓗ࡞ᡭἲࢆ⏝࠸࡚⌮ゎࡍࡿྲྀࡾ⤌ࡳࢆࡋ࡚࠸ࡲࡍࠋ

21

Modeling Group৑ ‫ ޓ‬ȷ ࢫ Ꮀ Ჴ έᇢૠྸᅹ‫ܖ‬ǤȳǹȆǣȆȥȸȈ৑Ճ ଢ඙‫ܖٻ‬ᄂᆮȷჷᝠ৆ဦೞನܲՃϱ૙੉Ტ཯Უྸ҄‫ܖ‬ᄂᆮ৑ ႆဃȷϐဃᅹ‫ܖ‬ዮӳᄂᆮǻȳǿȸȦȋȃȈȪȸ ȀȸᲦ‫ܖٻܖٻ᧵ٻ‬ᨈဃԡೞᏡᄂᆮᅹਔǁƍ૙੉Ღ࠼޽‫ܖٻܖٻ‬ᨈ ྸ‫ܖ‬ᄂᆮᅹܲՃ૙੉‫ ᧉ ݦ‬ȷ ‫ ܖ‬ˮ Ჴ ȕǣǸǫȫȐǤǪȭǸȸᲦҦٟ ‫ܖ‬ᘐ ȷிʮ‫ܖٻ‬ᄂ ᆮ ϋ ܾ Ჴ ኬᏘƓǑƼႆဃƷྸᛯႎȷ᬴ܱႎᄂᆮ

␌⏱␔␝⏚ྰDevelopment of index construction
for a financial market
with heavy-tailed distributionsဋ᣼̽ᓶ‫܇‬TANOKURA, Yoko

ᴾ
Modeling Group৑ ‫ ޓ‬ȷ ࢫ Ꮀ Ჴ έᇢૠྸᅹ‫ܖ‬ǤȳǹȆǣȆȥȸȈ৑Ճ ଢ඙‫ܖٻܖٻ‬ᨈέᇢૠྸᅹ‫ܖ‬ᄂᆮᅹཎ˓ϱ૙੉‫ ᧉ ݦ‬ȷ ‫ ܖ‬ˮ Ჴ ଺ኒЗᚐௌᲦҦٟ ‫ܖ‬ᘐ ȷዮӳᄂᆮ‫ܖٻ‬ᨈ‫ܖٻ‬ᄂ ᆮ ϋ ܾ Ჴ ᣿ᗡȷኺฎȷᅈ˟ྵᝋƷȢȇȪȳǰƓǑƼᚐௌᄂᆮಒᙲ
For making a financial market view, the movements of all prices or returns in the market
should be fully considered. Although their distributions should be reflected, they are often
heavy-tailed and possibly skewed and identifying them directly is not easy. To address these
difficulties, we proposed a statistical method of constructing a price index of a financial market
where the price distributions are skewed and heavy-tailed. Firstly, we apply the Box-Coxtransformation where the parameter is determined by minimizing the AIC with respect to theoriginal prices. Then, we estimate the long-term trend of the distributions by fitting a new
trend model with time-varying observation noises. Finally, we define the index by taking theinverse Box-Cox transformation of the optimal long-term trend. To show the effectiveness of
our method, we constructed the regional indices of the sovereign Credit Default Swap market
where the number of observations varies over time due to the immaturity. As a result, theworldwide spillover effects of the European debt crisis were detected. Applying our method tothe markets with insufficient information such as fast-growing or immature markets can beeffective.
This is the joint research with Hiroshi Tsuda (Doshisha University), Seisho Sato (The
University of Tokyo) and Genshiro Kitagawa (Research Organization of Information and
Systems).



22

ᴾ

ᒉ᣼Ӑɟᢹ

␌⏱␔␝⏚ྰ

ဃཋᡶ҄ỉᄂᆮᾉྸᛯểࣖဇ
WAKANO, Joe Yuichiroᄂᆮಒᙲᮏᖺᗘࡶᘬࡁ⥆ࡁࠊ⏕≀㐍໬⌧㇟࡟ᑐࡍࡿᩘ⌮ࣔࢹࣝ◊✲ࢆ⾜ࡗࡓࠋ2012 ᖺ࡟୺࡟㸰ࡘࡢ኱ࡁ࡞ࣉࣟࢪ࢙ࢡࢺࢆᐇ᪋ࡋࡓࠋ
⌮ㄽ㠃㸸JST ࡉࡁࡀࡅ㸦⏕࿨ࣔࢹࣝ㡿ᇦ㸧ࠕ⏕≀㐍໬ࡢ㸰኱⌮ㄽࡢ⤫୍ⓗ⌮ゎࠖᛂ⏝㠃㸸⛉Ꮫ◊✲㈝㸦᪂Ꮫ⾡㡿ᇦ◊✲㸧ࠕࢿ࢔ࣥࢹࣝࢱ࣮ࣝ࡜ࢧࣆ࢚ࣥࢫ஺᭰๻ࡢ┿┦ࠖ⌮ㄽ㠃ࣉࣟࢪ࢙ࢡࢺࡣࠊໟᣓ㐺ᛂᗘ⌮ㄽ(IFT㸧࡜ Adaptive Dynamics ⌮ㄽ(ADT)࡜ࡢ⤫୍ⓗ⌮ゎࡀ┠ᶆ࡛࠶ࡗࡓࠋ≉࡟㏆ᖺࡢ IFT ࡢ┠ぬࡋ࠸Ⓨᒎࡣࠊ୍᪉࡛⾑⦕㑅ᢥ࡜ࡣఱ࠿࡜࠸࠺ࡸࡸ
ဴᏛⓗ࡞ၥ㢟ࢆᥦ㉳ࡋࠊNature リୖ࡞࡝࡛άⓎ࡞㆟ㄽࡀ⾜ࢃࢀ࡚࠸ࡿࠋIFT ࡟ᑐࡍࡿㄗゎࡶࠊᮍࡔ࡟Ꮡᅾࡍࡿྍ⬟ᛶࡶ㧗࠸ࠋIFT ࡢṇయࢆ᫂ࡽ࠿࡟ࡋࠊࡑࡢ㛗ᡤ▷ᡤࢆ᫂ࡽ࠿࡟ࡍࡿࡓࡵࠊ
ᚑ᮶┤ឤⓗ࡞グ㏙ࡀࡉࢀ࡚ࡁࡓ IFT ࢆࠊᩘᏛ⌮ㄽ࡜ࡋ࡚෌ᵓ⠏ࡍࡿㄽᩥࢆⓎ⾲ࡋࡓࠋࡲࡓࠊ
ADT ࡟࠾࠸࡚㔜せ࡞⌧㇟࡛࠶ࡿ㐍໬ⓗศᒱࢆࠊIFT ⌮ㄽࡢほⅬ࠿ࡽゎ᫂ࡍࡿ◊✲ࢆࢫࢱ࣮ࢺࡋ
ࡓࠋᛂ⏝㠃࡛ࡣࠊே㢮㐍໬ࡢ኱ᆺࣉࣟࢪ࢙ࢡࢺ࡟ཧຍࡋ࡚࠸ࡿࠋࡇࢀࡣࠊ㸳୓ᖺ๓ࡈࢁ࡟㉳ࡁࡓࢿ࢔ࣥࢹࣝࢱ࣮ࣝ࠿ࡽࢧࣆ࢚ࣥࢫ࡬ࡢ஺᭰๻ࢆᢅ࠺ࣉࣟࢪ࢙ࢡࢺ࡛ࠊ໬▼ே㦵ࢆᢅ࠺⮬↛ே㢮Ꮫ⪅ࡔࡅ࡛࡞ࡃࠊ㑇㊧ㄪᰝࢆ⾜࠺⪃ྂᏛ⪅ࠊࢧࣆ࢚ࣥࢫ࡟≉᭷ࡢᏛ⩦⬟ຊࢆ᥈ࡿ⬻⛉Ꮫ⪅ࠊᙜ᫬ࡢ⎔ቃࢆィ⟬ࡍࡿྂẼೃᏛ⪅ࠊ⌧ᅾࡢ⊁⊟᥇㞟Ẹ᪘ࢆ◊✲ࡍࡿᩥ໬ே㢮Ꮫ⪅࡞࡝ࠊከᒱ࡟ࢃ
ࡓࡿ◊✲⪅ࡀཧຍࡍࡿᏛ㝿ⓗࣉࣟࢪ࢙ࢡࢺ࡛࠶ࡿࠋࡇࡢࣉࣟࢪ࢙ࢡࢺࡢ᱁Ꮚࡣࠊࠕࢧࣆ࢚ࣥࢫ
ࡣඃࢀࡓಶయᏛ⩦⬟ຊ࡟ࡼࡾࢿ࢔ࣥࢹࣝࢱ࣮ࣝࢆ㥑㏲ࡋࡓࠖ࡜࠸࠺Ꮫ⩦௬ㄝ࡛࠶ࡗ࡚ࠊࡇࢀࡣ
⌮ㄽ◊✲࠿ࡽ⏕ࡲࢀࡓ௬ㄝ࡛࠶ࡿࠋࡇࡢ௬ㄝࡣࠊࢧࣆ࢚ࣥࢫࡢ᫬௦௨㝆࡟▼ჾࡀᛴ㏿࡟ኚ໬㸦Ⓨᒎ㸧ࡍࡿࡇ࡜࠿ࡽࠊ㛫᥋ⓗ࡟ࡣᨭᣢࡉࢀ࡚࠸ࡿࡀࠊ࡛ࡣఱᨾࢧࣆ࢚ࣥࢫ࡟ࡔࡅ㧗࠸ಶయᏛ⩦⬟ຊࡀ㐍໬ࡋࡓࡢ࠿࡟ࡘ࠸࡚ࡣࠊ᫂ࡽ࠿࡛ࡣ࡞࠸ࠋ⚾ࡣࠊ㟷ᮌࡸ୰ᶫࠊLehmannࠊFeldman ࡽ࡜ඹྠ࡛ࠊᏛ⩦⬟ຊࡢ㐍໬ࣔࢹࣝࡢ◊✲ࢆ⥆ࡅ࡚ࡁ࡚࠸ࡿࠋ2012 ᖺࡣࠊ≉࡟ಶయࡢ⏕άྐᡓ␎࡜ࡋ࡚᭱㐺࡞Ꮫ⩦ࢫࢣࢪ࣮ࣗࣝ࡟࡜࠸࡚ࠊ᭱㐺ไᚚ⌮ㄽࢆ⏝࠸ࡓ◊✲ᡂᯝࢆ࠸ࡃࡘ࠿ᣲࡆࡿࡇ
࡜ࡀ࡛ࡁࡓࠋ
᭱⤊ⓗ࡟ 2012 ᖺ࡟බ⾲ࡋࡓᰝㄞ௜ᅜ㝿Ꮫ⾡ㄅ࡟࠾ࡅࡿㄽᩥᩘࡣࠊ㸴௳࡛࠶ࡗࡓࠋ

23

Modeling Group৑ ‫ ޓ‬ȷ ࢫ Ꮀ Ჴ έᇢૠྸᅹ‫ܖ‬ǤȳǹȆǣȆȥȸȈ৑Ճ ଢ඙‫ܖٻܖٻ‬ᨈέᇢૠྸᅹ‫ܖ‬ᄂᆮᅹཎ˓ϱ૙੉‫ ᧉ ݦ‬ȷ ‫ ܖ‬ˮ Ჴ ૠྸဃཋ‫ܖ‬ᲦҦٟ ྸ‫ ܖ‬ȷʮᣃ‫ܖٻ‬ᄂ ᆮ ϋ ܾ Ჴ Ȟǯȭဃཋኒȷဃ७ኒƷȢȇȪȳǰƓǑƼᚐௌૠྸᚐௌྰ

Topics on Mathematical Crystallographyίૠ‫ܖ‬ႎኽ୒ྸᛯὸ
ჿဋМɟSUNADA, ToshikazuૠྸᚐௌྰȪȸȀȸ৑ ‫ ޓ‬ȷ ࢫ Ꮀ Ჴ έᇢૠྸᅹ‫ܖ‬ǤȳǹȆǣȆȥȸȈ৑Ճ ଢ඙‫ܖ߻ྸܖٻ‬ᢿ૙੉‫ ᧉ ݦ‬ȷ ‫ ܖ‬ˮ Ჴ ᩉ૝࠹˴ᚐௌ‫ܖ‬Ღྸ‫ܖ‬Ҧٟȷிʮ‫ܖٻ‬ᄂ ᆮ ϋ ܾ Ჴ ȍȃȈȯȸǯǷǹȆȠƷᚐௌᄂᆮಒᙲMathematical Analysis GroupIn July 2012 the General Assembly of the United Nations resolved that 2014 should be theInternational Year of Crystallography, 100 years since the award of the Nobel Prize for the
discovery of X-ray diffraction by crystals. Towards this special occasion, I started to study
several topics in mathematical crystallography. Especially motivated by the recent
development in systematic design of crystal structures, I tried to find relationships among
seemingly irrelevant subjects; say, standard crystal models, tight frames in the Euclidean space,rational points on Grassmannian and quadratic Diophantine equations. Thus my view is quite abit different from the traditional one focusing mainly on crystallographic groups.
The central object in this study is what we call crystallographic tight frames, which are, in aloose sense, considered a generalization of root systems. We shall also pass a remark on therelations with tropical geometry, a relatively new area in mathematics, especially withcombinatorial analogues of Abel-Jacobi map and Abel's theorem.
As is well known, root systems are completely classified by means of Dynkin diagrams. I
have shown that similarity classes of crystallographic tight frames are parameterized byrational points on Grassmannians. Quadratic Diophantine equations show up when we
explicitly relate rational points to crystallographic tight frames. In the 2-dimensional caseespecially, we may parameterize the (oriented) congruence classes by ``rational points" on acertain complex projective quadric. A rational point we mean here is a point in a complex
projective space each of whose homogeneous coordinate is represented by a number in an
imaginary quadratic field.
[1] T. Sunada, Topological crystallography~---With a View Towards Discrete GeometricAnalysis---, Surveys and Tutorials in the Applied Mathematical Sciences, Vol. 6, Springer, 2012.
[2] T. Sunada, Lecture on topological crystallography, Japan. J. Math. 7 (2012), 1--39.
[3] T. Sunada, Standard 2D crystalline patterns and rational points in complex quadrics,
arXiv:submit/0620196 [math.CO] 23 Dec 2012.

24

ૠྸᚐௌྰ

ᐯࠁኵጢ҄ᨼӳ࢟঺ỉྵᝋૠྸ‫ܖ‬ɤ஭ଡ඲ MIMURA, Masayasu ȪȸȀȸᲢᄂᆮወਙᲣ
৑‫ޓ‬ȷࢫᎰ
‫ᧉݦ‬ȷ‫ܖ‬ˮᄂᆮϋܾᲴ έᇢૠྸᅹ‫ܖ‬ǤȳǹȆǣȆȥȸȈ৑ᧈ ଢ඙‫ܖٻܖٻ‬ᨈέᇢૠྸᅹ‫ܖ‬ᄂᆮᅹཎ˓૙੉Ჴ ྵᝋૠྸ‫ܖ‬Ღ߻‫ܖ‬Ҧٟȷʮᣃ‫ܖٻ‬Ჴ ᩼ዴ࢟᩼࠯ᘖྵᝋƷૠྸᚐௌ

ᄂᆮಒᙲ࡞࠺ࡇ࡜࡛࠶ࡗࡓ㸬ࡑࡢᡂᯝࢆࢸ࣮࣐ẖ࡟࡟ิᣲࡍࡿ㸸ձ ࡍࡍ⇞↝࡟⌧ࢀࡿ⇞↝ࣃࢱ࣮ࣥࡢࣔࢹࣝゎᯒ࠿ࡽࡢゎ᫂ ([1])ղ ቑṪࡍࡿ⭘⒆⣽⬊࡟⌧ࢀࡿ᥋ゐᢚไຠᯝࡢࣔࢹࣝゎᯒ࠿ࡽࡢゎ᫂ ([2])ճ ➇த—ᣑᩓ⣔࡟⌧ࢀࡿ➇த᤼௚࣭ඹᏑၥ㢟ࡢᩘ⌮ゎᯒ ([3], [5])մ ⮬ᕫ⤌⧊໬㞟ྜࡢࣔࢹࣝゎᯒ࠿ࡽࡢゎ᫂ ([4], [6])≉࡟ࠊմ࡟࠾࠸࡚ࡣࠊ⮬ᕫ⤌⧊໬㞟ྜᙧᡂ࡟ᑐࡋ࡚ࠊಶయࢆグ㏙ࡍࡿ࣑ࢡࣟࣞ࣋ࣝࣔࢹࣝ࡜
࣏ࣆ࣮ࣗࣞࢩࣙࣥࢆグ㏙ࡍࡿ࣐ࢡࣟࣞ࣋ࣝࣔࢹࣝࢆᥦ᱌ࡍࡿ࡜࡜ࡶ࡟ࠊ㸰ࡘࡢࣔࢹࣝ㛫ࡢࣜࣥࢡࢆ≉␗ᴟ㝈࡜ὶయຊᏛᴟ㝈࡜࠸࠺㸰ࡘࡢᴟ㝈ἲࡶࡕ࠸ࡿࡇ࡜࠿ࡽ᫂ࡽ࠿࡟ࡋࡓ㸬[1] K. Ikeda and M. Mimura: Traveling wave solutions of a 3-component reaction-diffusion modelin smoldering combustion, Communications on Pure and Applied Analysis, 11, 275-305 (2012)[2] M. Bertsch, D. Hilhorst, H. Izuhara and M. Mimura: A nonlinear parabolic-hyperbolic systemfor contact inhibition of cell-growth, Diff. Eqs. Appl. 4, 137-157 (2012)[3] D. Hilhorst, S. Martin and M. Mimura: Singular limit of a competition-diffusion system withlarge interspecific interaction, J. Math. Anal. Appl., 390, 488-513 (2012)[4] S.-I. Ei, H. Izuhara and M. Mimura: Infinite dimensional relaxation oscillation in aggregation-growth systems, Discrete and Continuous Dynamical Systems- Series B, 17, 1859-1887 (2012)[5] C.-C. Chen, L.-C. Hung, M. Mimura and D. Ueyama: Exact traveling wave solutions of three
species competition-diffusion systems, Discrete and Continuous Dynamical Systems- Series B,
17, 2653-2669 (2012)[6] T. Funaki, H. Izuhara, M. Mimura and C. Urabe: A link between microscopic and macroscopic
models of self-organized aggregation, Networks and Heterogeneous Media, 7, 705-740 (2012)25

Mathematical Analysis Groupᮏᖺᗘࡣ⮬ᕫ⤌⧊໬ࡢࡼࡿ㞟ྜᙧᡂࢆ཯ᛂᣑᩓ⣔ࣔࢹࣝ࡜ࡑࡢゎᯒ࡜࠸࠺⌧㇟ᩘ⌮Ꮫࢆ⾜ૠྸᚐௌྰ

Algorithms for directed pathwidthྚஙʁ‫پ‬TAMAKI, Hisao৑ ‫ ޓ‬ȷ ࢫ Ꮀ Ჴ έᇢૠྸᅹ‫ܖ‬ǤȳǹȆǣȆȥȸȈ৑Ճ ଢ඙‫ܖ߻ྸܖٻ‬ᢿ૙੉‫ ᧉ ݦ‬ȷ ‫ ܖ‬ˮ Ჴ ᚘምƷྸᛯᲦ2J&ȷȈȭȳȈ‫ܖٻ‬ᄂ ᆮ ϋ ܾ Ჴ ᚘምƱǢȫǴȪǺȠྸᛯ

Mathematical Analysis Groupᄂᆮಒᙲ

I have continued the research on directed pathwidth computation part of which was done inacademic year 2010. The algorithm obtained then that was claimed to run in n^{k + O(1)} time,
where n is the number of vertices and k is the pathwidth, has contained a serious flaw.

I havespent a large amount of time on fixing this flaw and succeeded in recovering an algorithm withrunning time n^{2k + O(1)}, but has not been able to retrieve the originally claimed running time.
My current plan is to publish this weakened result and continue working on the complete fix forsome extended period of time, as the problem appears really difficult.
On the other hand, this weakened result is sufficient for many theoretical applications.

Indeed,building on this result, I have developed, with my students Kenta Kitsunai, Yasuaki Kobayashi,
Keita Komuro, and Toshihiro Tano, a non-parameterized O(1.89^n) time algorithm for directed
pathwidth which improves the running time of O(1.996^n) the undirected pahtwidth algorithm
due to Suchan and Villanger.
I also continued the work on the two-layer graph drawing problem reported last year and haveobtained a non-trivial improvement to the one-sided crossing minimization algorithm due toYasuaki Kobayash and myself and obtained a kernel result for two-layer crossing minimization
with Yasuaki Kobayashi, Hirokazu Maruta, and Nakae Yusuke. The first result will appear in
Algorithmica and the second result has appeared in COCOON 2013 (The 19th Annual
International Computing and Combinatorics Conference).

26‫߷ݱ‬ჷʂ

OGAWA, ToshiyukiૠྸᚐௌྰӒࣖਘ૝ኒỉἣἑὊὅἒỶἜἱἁἋᴾ὿ᾉᾀᾉᾁᴾ‫ٶ‬᣻ᐮမໜểẸỉ೅แ࢟ᚐௌᴾ ৑ ‫ ޓ‬ȷ ࢫ Ꮀ Ჴ έᇢૠྸᅹ‫ܖ‬ǤȳǹȆǣȆȥȸȈ৑Ճ ଢ඙‫ܖ߻ྸܖٻ‬ᢿ૙੉‫ ᧉ ݦ‬ȷ ‫ ܖ‬ˮ Ჴ щ‫ܖ‬ኒྸᛯᲦҦٟ ྸ‫ ܖ‬ȷ࠼޽‫ܖٻ‬ᄂ ᆮ ϋ ܾ Ჴ ଺ᆰȑǿȸȳƷᚐௌȷЎ‫ޟ‬ᚐௌᄂᆮಒᙲ࣮ࣔࢻࡢ┦஫స⏝࠿ࡽ᣺ືࢱ࢖ࣉࡢ㸰ḟศᒱࡸ࣊ࢸࣟࢡࣜࢽࢵࢡࢧ࢖ࢡࣝࡀ⏕ࡌࡿࡇ࡜ࢆ᫂
ࡽ࠿࡟ࡋࡓࠋ ຊᏛ⣔ࡢศᒱ⌮ㄽࡣ≉␗Ⅼࡢࡲࢃࡾ࡛⣔ࡢ᣺ࡿ⯙࠸ࡀ࡝ࡢࡼ࠺࡟ኚࢃࡿ࠿ࢆグ㏙ࡍࡿࡶࡢ࡛࠶ࡿࠋ࡞࠿࡛ࡶ≉␗ᛶࡢ㧗࠸ከ㔜⮫⏺Ⅼࡢᵓ㐀࠿ࡽ඲ㇺࡀ᫂ࡽ࠿࡟࡞ࡿࡇ࡜ࡀከ࠸ࠋ୍⯡࡟ ḟඖࡢࣃࢱ࣮ࣥࡢၥ㢟࡞࡝࡛⏕ࡌࡿከ㔜≉␗Ⅼࡣ㞄ࡾྜ࠺ࣇ࣮࢚࣮ࣜࣔࢻࡀྠ᫬࡟⮫⏺࡟
࡞ࡿⅬ࡛࠶ࡿࠋࡲࡓ≉࡟࿘ᮇቃ⏺᮲௳ࡸࣀ࢖࣐ࣥቃ⏺᮲௳࡞࡝⮬↛࡞ቃ⏺᮲௳タᐃࡢሙྜࡣ⣔ࡀ 2  ᑐ⛠ᛶࢆࡶࡘࡢ࡛ࠊQ Q ࣮ࣔࢻࡀྠ᫬࡟⮫⏺࡟࡞ࡿ 2  ᑐ⛠࡞ຊᏛ⣔ࡀࣃࢱ࣮ࣥ
ࡢศᒱ࡟㛵ࡍࡿ୺せ࡞◊✲ᑐ㇟࡟࡞ࡿࠋQ!࡛࠶ࢀࡤᚓࡽࢀࡿ」⣲  ḟඖࡢᶆ‽ᙧࡣ㠀ᖖ࡟༢⣧࡛ゎᯒࡣᐜ࡛᫆࠶ࡿࠋࡋ࠿ࡋ၏୍࣮ࣔࢻࡀྠ᫬࡟⮫⏺࡟࡞ࡿⅬࡣ౛እ࡛ࠊ2  ᑐ⛠࡛࠶ࡗ࡚ࡶࠊ ḟࡢඹ㬆㡯ࡀ࠶ࡿࡓࡵ࡟⊂❧࡞᣺ᖜ᪉⛬ᘧࡀᑟࡅ࡞࠸ࡼ࠺࡞ᶆ‽ᙧࡀᚓࡽࢀࡿࠋ
ࡇࢀ࡟ᑐࡋ $UPEUXVWHU ࡓࡕ 3K\VLFD'௨ୗ $*+ ࡣ  ḟ㡯ࡢಀᩘࡢ✚ࡢ
ṇ㈇࡟ࡼࡾ⣔ࡀࡁࢃࡵ࡚≉ᚩⓗ࡞ࢲ࢖ࢼ࣑ࢡࢫࢆᣢࡘ஦ࢆ♧ࡋࡓࠋࡍ࡞ࢃࡕࡑࡢ✚ࡀ㈇࡛࠶ࢀ
ࡤࠊࡲࡓࡑࡢ࡜ࡁࡢࡳࠊ㐍⾜Ἴゎࡸ₞㏆Ᏻᐃ࡞࣊ࢸࣟࢡࣜࢽࢵࢡࢧ࢖ࢡࣝࢆᣢࡘ஦ࢆ♧ࡋࡓࠋ
୍᪉ࠊ6PLWK ࡓࡕ㸦3K\VLFD'㸧ࡣ  ࣮ࣔࢻࡀྠ᫬࡟⮫⏺࡟࡞ࡿ㸱㔜ࡢከ㔜⮫⏺Ⅼࢆ⪃࠼ࡿ࡜ᇶᮏⓗ࡟ $*+ ࢆෆໟࡍࡿࡼ࠺࡞  ḟࡢඹ㬆㡯ࢆᣢࡘᶆ‽ᙧࡀᚓࡽࢀ࡚ࠊࡸࡣࡾ  ḟ㡯ࡢಀᩘࡢ✚ࡀ㈇࡛࠶ࢀࡤࠊ㇏ᐩ࡞ゎᵓ㐀ࢆᣢࡘ஦ࢆ♧ࡋࡓࠋࡇࡢࡼ࠺࡞≧ἣୗ࡛ࠊᡃࠎࡣ཯ᛂᣑᩓ⣔࡟  ࣮ࣔࢻࡀྠ᫬࡟⮫⏺࡟࡞ࡿ  㔜ࡢከ㔜⮫⏺Ⅼࡀ࠶ࡿࡇ࡜ࢆ♧ࡋࠊࡉࡽ࡟ወ㛵ᩘᑐ⛠ᛶࢆㄢࡍ࡜  ḟ࡛࡞ࡃ  ḟࡢඹ㬆㡯ࢆࡶࡘᶆ‽ᙧࡀᚓࡽࢀࡿࡇ࡜ࡸࠊࡑࡇ࡛ࡣ ḟ㡯ࡢಀᩘࡢ✚ࡢṇ㈇࠸ࡎࢀࡢࢱ࢖ࣉࡢ $*+ ࡶෆໟࡍࡿࡼ࠺࡞ࢲ࢖ࢼ࣑ࢡࢫࡀ࠶ࡿࡇ࡜ࡶ᫂
ࡽ࠿࡟ࡋࡓࠋࡑࡇ࡛ࠊࡇࡢ  ḟࡢඹ㬆㡯ࢆࡶࡘᶆ‽ᙧࢆヲ⣽࡟ゎᯒࡋࡑࡢศᒱᵓ㐀ࢆỴᐃࡋࡓࠋT.Ogawa and T. Okuda, "Oscillatory dynamics in a reaction-diffusion system in the presence of
0:1:2 resonance", Networks and Heterogeneous Media, 893 - 926, Volume 7, Issue 4, December
2012

27

Mathematical Analysis Group ཯ᛂᣑᩓ⣔ࡢࣃࢱ࣮ࣥࢲ࢖ࢼ࣑ࢡࢫࡢศᒱࢆ኱ᇦࣇ࢕࣮ࢻࣂࢵࢡࡢほⅬ࠿ࡽᩚ⌮ࡋ㸪

数理解析班

パターン解の構成とその機能応用
二宮広和

NINOMIYA, Hirokazu

Mathematical Analysis Group

所 属 ・ 役 職 ： 先端数理科学インスティテュート所員
明治大学理工学部教授
専 門 ・ 学 位 ： 非線形偏微分方程式，博士 (理学)・京都大学
研 究 内 容 ： 拡散・伝播現象やパターン構造の数理

研究概要
パターンをもつ反応拡散系の解の構成をおこなっている。反応拡散系の特異極限問題の進行
スポット解の構成や自由境界問題の回転孤立波の構成，反応拡散近似による新しい自由境界問
題の導出を行った。また，心室細動は，活動電位のスパイラル波の発生が一つの原因と考えられている。スパイラル波の自発的発生メカニズムを調べている。

(a) 自由境界問題から表れる回転孤立波(b) 反応拡散系の進行スポット解業績
1.

H. Murakawa and H. Ninomiya: Fast reaction limit of a three-component reaction-diffusion
system, Journal of Mathematical Analysis and Applications, 379 (2011), No. 1,

2.

150-170

Y.Y. Chen, J.S. Guo and H. Ninomiya: Existence and uniqueness of rigidly rotating spiral waves
by a wave front interaction model, Physica D, Volume 241, Issue 20, (October 2012), 1758–176628ᒬ᣼‫ܦ‬ʍ

KUSANO, Kanya ǷȟȥȬȸǷȧȳྰȪȸȀȸ⏡␉␏␖␢⏡␑␝ྰ‫ٽ‬᩿ᨗ༪ႆྵᝋỉႆဃೞನểẸỉʖย৑ ‫ ޓ‬ȷ ࢫ Ꮀ Ჴ έᇢૠྸᅹ‫ܖ‬ǤȳǹȆǣȆȥȸȈ৑Ճ ӸӞ‫ٽܖٻދ‬ᨗ‫ྶע‬࿢‫ؾ‬ᄂᆮ৑૙੉
 ཯ᇌᘍ૎ඥʴෙබᄂᆮ᧏ႆೞನ ਔᎣɥࠗᄂᆮՃ ‫ྶע‬ϋᢿ ȀǤȊȟǯǹᄂᆮ᪸؏ ᨞‫ޖ‬ǷǹȆȠᄂᆮȁȸȠȪȸȀȸ ଢ඙‫ܖٻ‬ᄂᆮȷჷᝠ৆ဦೞನܲՃ૙੉‫ ᧉ ݦ‬ȷ ‫ ܖ‬ˮ Ჴ ǷȟȥȬȸǷȧȳᅹ‫ܖ‬Ღྸ‫ܖ‬Ҧٟȷ࠼޽‫ܖٻ‬ᄂ ᆮ ϋ ܾ Ჴ ‫ᙹٻ‬೉᨞‫ޖ‬ኒƷȢȇȪȳǰƓǑƼǷȟȥȬȸǷȧȳ䜛䚹䛭䛾䜶䝛䝹䜼䞊䛾୍㒊䛿䛧䜀䛧䜀⇿Ⓨⓗ䛻ゎᨺ䛥䜜䚸㧗 䝥䝷䝈䝬䛸኱つᶍ䛺ᨺฟ䜢ᘬ䛝㉳䛣䛩䛣䛸䛜䛒䜛䚹ኴ㝧䝣䝺䜰䜔䝁䝻䝘㉁㔞ᨺฟ䛸࿧䜀䜜䜛䛣䛾ኴ㝧㠃⇿Ⓨ⌧㇟䛿ᆅ⌫䛾⎔ቃ䜔⾨ᫍ䞉㏻ಙ䞉㟁ຊ䞉䜶䝛䝹䜼䞊䛻㛵䜟䜛♫఍䝅䝇䝔䝮䛻ከ኱䛺ᙳ㡪䜢୚䛘䜛䛣䛸䛜䛒䜛䚹䛭䜜ᨾ䚸䛭䛾Ⓨ⏕ᶵᵓ䜢⌮ゎ䛩䜛䛸ඹ䛻䛔䛴䚸䛹䛣䛷䚸䛹䜜䜋䛹䛾⇿Ⓨ䛜㉳䛝䜛䛛䜢ண 䛩䜛䛣䛸䛜ồ䜑䜙䜜䛶䛔䜛䚹㻌 ᡃ䚻䛿䝇䞊䝟䞊䝁䞁䝢䝳䞊䝍䛻䜘䜛䝅䝭䝳䝺䞊䝅䝵䞁䛸᪥ᮏ䛾㄂䜛᭱᪂䛾ኴ㝧ほ ⾨ᫍ䛂䜂䛾䛷䛃䛻䜘䜛ኴ㝧䝣䝺䜰䛾ほ䝕䞊䝍䛾ẚ㍑䛻ᇶ䛴䛔䛶䚸ኴ㝧⾲㠃䛾☢ሙ䛜≉Ṧ䛺ᵓ㐀䜢ᣢ䛴䛸䛝䛻ኴ㝧㠃

⇿Ⓨ䛜Ⓨ⏕䛩䜛䛣䛸䜢ぢฟ䛧䛯䚹䛣䛾ᵓ㐀䛿☢ሙ䛾䛂኱つᶍ䛺᤬䛨䜜䛃䛸䛂ᑠつᶍ䛺ᨐ஘䛃䛾┦஫స⏝䛻䜘䛳䛶⏕䜎䜜䜛䜒䛾䛷䛒䜛䚹䛣䛖䛧䛯䝇䜿䞊䝹䛾␗䛺䜛☢ሙᡂศ䛜☢Ẽ䝸䝁䝛䜽䝅䝵䞁䛸࿧䜀䜜䜛┦஫స⏝䜢㉳䛣䛩䛸☢ሙᵓ㐀඲య䛜୙Ᏻᐃ໬䛧䛶ୖ᪼䜢䛿䛨䜑䜛䚹䛭䛾⤖ᯝ䚸☢Ẽ䝸䝁䝛䜽䝅䝵䞁䛜ቑᖜ䛥䜜䜛䛸䛔䛖䝣䜱䞊䝗䝞䝑䜽䛜ാ䛝䚸⇿Ⓨⓗ䛻䜶䝛䝹䜼䞊䛜ゎᨺ䛥䜜䜛䛣䛸䛜⌮ゎ䛷䛝䛯䚹䛣䛾⤖ᯝ䛿ヲ⣽䛺ኴ㝧☢ሙほ 䛸䝁䞁䝢䝳䞊䝍䝅䝭䝳䝺䞊䝅䝵䞁䛾㐃ᦠ䛻䜘䛳䛶䚸ኴ㝧㠃⇿Ⓨ䜢ண 䛩䜛䛣䛸䛜ྍ⬟䛷䛒䜛䛣䛸䜢ព࿡䛧䛶䛔䜛䚹ᕥୖ䠖䜂䛾䛷⾨ᫍ䛜ほ 䛧䛯ኴ㝧䝣䝺䜰⇿Ⓨ䚹☢ሙ䠄䜾䝺䞊䝇䜿䞊䝹䠅䛸䝣䝺䜰Ⓨග䠄㉥⥺䠅䚹ᕥୗ䠖䝣䝺䜰㡿ᇦ䛾ᑠつᶍ䛺☢ሙᵓ㐀䛾ኚ໬䚹ྑ䠖䝁䞁䝢䝳䞊䝍䝅䝭䝳䝺䞊䝅䝵䞁䛷෌⌧䛥䜜䛯ኴ㝧䝣䝺䜰䛻䛚䛡䜛☢ຊ⥺䛾ᵓ㐀䚹㻌

29

Simulation Group㻌 㻌 ኴ㝧㯮Ⅼ䛿ኴ㝧⾲㠃䜢ᶓษ䜛ᕧ኱䛺☢᮰⟶䛷䛒䜚 1032 䜶䝹䜾䛾⭾኱䛺䜶䝛䝹䜼䞊䜢⵳✚䛧䛶䛔

ᴾ

ᄂᆮಒᙲ

⏡␉␏␖␢⏡␑␝ྰᥴᙻỉྵᝋૠྸ‫ܖ‬ểᇌ˳ᥴᙻ‫࢟׋‬ỉо˺னҾҽӴ

SUGIHARA, Kokichi৑ ‫ ޓ‬ȷ ࢫ Ꮀ Ჴ έᇢૠྸᅹ‫ܖ‬ǤȳǹȆǣȆȥȸȈи৑ᧈ ଢ඙‫ܖٻܖٻ‬ᨈέᇢૠྸᅹ‫ܖ‬ᄂᆮᅹཎ˓૙੉‫ ᧉ ݦ‬ȷ ‫ ܖ‬ˮ Ჴ ࠹˴ૠྸ߻‫ܖ‬Ღ߻‫ܖ‬Ҧٟȷிʮ‫ܖٻ‬ᄂ ᆮ ϋ ܾ Ჴ ཋྸྵᝋᲦဃ˳ྵᝋᲦᅈ˟ྵᝋƷᚘምૠྸ

ᴾ
ᄂᆮಒᙲ

Simulation Group୙ྍ⬟❧య䛾䛰䜎䛧⤮䛜ㄏⓎ䛩䜛㘒ど䛾ᩘ⌮䝰䝕䝹䜢ᚑ᮶䛛䜙◊✲䛧䛶䛔䜛䛜䠈䛭䛾䝰䝕䝹䛾⢭ᐦ໬䜢ᅗ䜚䠈䛭䜜䛻ᇶ䛵䛔䛶᪂䛧䛔㘒どసရ䜢๰స䛧䛯䚹௒䜎䛷䛿❧య䛸䛭䛾ᢞᙳീ䛾ᗄఱᙧ≧䛾䜏䛻ὀ┠䛧䛶䛝䛯䛜䠈ᮏᖺᗘ䛿❧య⾲㠃䛾ᶍᵝ䜔㝜ᙳ䛾ᙳ㡪䜒䝰䝕䝹䛻㏣ຍ䛧䛯䚹䛭䛧䛶䠈䛭䜜䛜䜒䛯䜙䛩᪂䛧䛔どぬຠᯝ䜢ண䛧䠈䛭䛾ண䛻ᇶ䛵䛔䛶᪂䛧䛔❧య䜢タィ䞉〇స䛧䠈ண䛹䛚䜚䛾㘒ど䛜⏕䛨䜛䛣䛸䜢☜ㄆ䛧䛯䚹ලయⓗ䛻ไస䛧䛯㘒どసရ䛻䛿ḟ䛾䜒䛾䛜䛒䜛䚹㻌㻔㻝㻕㻌 䜹䝣䜵䜴䜷䞊䝹䝡䝹㻌 㻌 䜹䝣䜵䜴䜷䞊䝹㘒ど䛸䛔䛖 㻞 ḟඖᅗᙧ䛜䜒䛯䜙䛩㘒ど䛿ᚑ᮶䛛䜙▱䜙䜜䛶䛔䛯䛜䠈䛭䜜䜢 㻟 ḟඖ䛻ᣑᙇ䛧䠈䝡䝹䛾ቨ㠃ᶍᵝ䛸䛧䛶ᐇ⌧䛧䛯䚹䜹䝣䜵䜴䜷䞊䝹㘒ど䛿䠈㛗᪉ᙧ䜢䛪䜙䛧䛶୪䜉䜛䛸䠈ቃ⏺䛾ᖹ⾜⥺䛜ഴ䛔䛶䜏䛘䜛㘒ど䛷䛒䜛䛜䠈㛗᪉ᙧ䜢ᖹ⾜ᅄ㎶ᙧ䛻⨨䛝䛛䛘䜛䛸㘒ど㔞䛜ቑ䛩䛣䛸䜢Ⓨぢ䛧䛯䚹䛭䛣䛷䛣䜜䜢䝡䝹䛾ቨ䛸䛔䛖❧య䛻ᥥ䛝䠈ぢ䜛᪉ྥ䛻䜘䛳䛶ᖹ⾜ᅄ㎶ᙧ䜈䛾䜂䛪䜏䛾⛬ᗘ䜢⮬⏤䛻ኚ䛘䜙䜜䜛䜘䛖䛻䛧䛯䚹䛣䜜䛻䜘䜚䠈୍䛴䛾సရ䛷䛔䜝䛔䜝䛺ᖹ⾜ᅄ㎶ᙧ䜢ヨ䛩䛣䛸䛜䛷䛝䠈㘒ど䛾ほᐹ䛜ᐜ᫆䛻䛺䛳䛯䚹㻌㻔㻞㻕㻌 䝣䝑䝖䝇䝔䝑䝥㘒ど䛾୍⯡໬䛸䜰䞊䝖໬㻌 㻌 䝣䝑䝖䝇䝔䝑䝥㘒ど䛻䛔䛟䛴䛛䛾䝞䝸䜶䞊䝅䝵䞁䛜䛒䜚䠈⫼ᬒ䛸ື䛟ᅗᙧ䛾┦ᑐⓗ䛺኱䛝䛥䛾㐪䛔䛛䜙䛹䛾䝞䝸䜶䞊䝅䝵䞁䛜䜘䛟㉳䛣䜛䛛䜢᫂䜙䛛䛻䛧䛯䚹䛭䜜䛻ᇶ䛵䛝䠈ከ䛟䛾㘒ど䜰䞊䝖䜢๰స䛩䜛䛸ྠ᫬䛻䠈䝁䞁䝢䝳䞊䝍⏬㠃䜢㞳䜜䛶䠈᫬ィ䛾⛊㔪䠈ᩳ㠃䜢㌿䛜䜛ྎ㌴䠈ே䛾ື䛝䜢฼⏝䛧䛯┳ᯈ䛺䛹䛾≀⌮ⓗᑐ㇟䛻䜘䛳䛶䜒ྠᵝ䛾㘒ど䜰䞊䝖䜢ᐇ⌧䛧䛯䚹䛭䛾䛔䛟䛴䛛䛿䠈ᅜෆ䛚䜘䜃ᾏእ䛾㘒ぬ䝁䞁䝔䝇䝖䛷ཷ㈹䜢ᯝ䛯䛧䛶䛔䜛䚹㻌㻔㻟㻕㻌 ྜᡂ⏬ീ㘒ど㻌 㻌 ⏬ീ䜢═䜑䜛どⅬ䜢᧯స䛩䜛䛣䛸䛻䜘䛳䛶䠈ぢ䜛ே䛻␗䛺䜛❧య䛾༳㇟䛜୚䛘䜙䜜䜛䛣䛸䜢ᩘ⌮ⓗ䛻ᩚ⌮䛧䛯䚹䛭䜜䛻ᇶ䛵䛔䛶䠈⫼ᬒ෗┿䛾୰䛻䝁䞁䝢䝳䞊䝍䜾䝷䝣䜱䝑䜽䝇⏬
ീ䜢ᇙ䜑㎸䜣䛷ᘓ≀䛺䛹䛾᏶ᡂண᝿ᅗ䜢స䜛㝿䛻䠈䜎䜟䜚䛾✵㛫䛾୰䛷䛾༳㇟䜢ពᅗⓗ䛻ኚ䛘䜛᪉ἲ䜢ᵓᡂ䛧䛯䚹䛣䜜䛿ᗈ࿌෗┿䛻䜘䜛ၟရ䛾༳㇟䛾᧯స䛻䛴䛺䛜䜛䛾䛷䠈௒ᚋ䛿ᗈ࿌෗┿つไ䛾ᣦ㔪䛸䛧䛶ᥦゝ䛧䛶䛔䛝䛯䛔䚹㻌㻔㻠㻕㻌 ୙つ๎㐠ື㘒ど䛾ᣑᙇ䛸❧య໬㻌 㻌 ᾋ㐟㘒ど䠈䝗䝸䝣䝖㘒ど䛺䛹䠈㟼Ṇ⏬䛜୙つ๎䛻䜖䜜䛶䜏䛘䜛㘒ど䛜䛒䜛䛜䠈䛭䛾௙⤌䜏䜢❆ᯟၥ㢟䛾ほⅬ䛛䜙䝰䝕䝹໬䛧䠈䛭䜜䛻ᇶ䛵䛔䛶䠈ྠᵝ䛾㘒ど䜢䜒䛯䜙䛩ከ䛟䛾ᇶᮏᅗᙧ䜢ᵓᡂ䛧䛯䚹ḟ䛻䛭䜜䜢 㻟 ḟඖ❧య䛻㈞䜚௜䛡䜛䛣䛸䛻䜘䜚䠈䜖䜜䜛㝵ẁ䛺䛹䛾❧యసရ䜢స䛳䛶䠈㘒どຠᯝ䜢☜ㄆ䛧䛯䚹

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UEYAMA, Daishinᴾɥ‫̮ٻޛ‬⏡␉␏␖␢⏡␑␝ྰૠྸဃཋ‫ܖ‬ỆấẬỦӈ݅ᚐểẸỉࣖဇ৑ ‫ ޓ‬ȷ ࢫ Ꮀ Ჴ έᇢૠྸᅹ‫ܖ‬ǤȳǹȆǣȆȥȸȈ৑Ճ ଢ඙‫ܖ߻ྸܖٻ‬ᢿϱ૙੉ȷ҅ෙᢊ‫ܖٻ‬‫ ᧉ ݦ‬ȷ ‫ ܖ‬ˮ Ჴ ྵᝋૠྸ‫ܖ‬ᲦҦٟᲢྸ‫ܖ‬Უᄂ ᆮ ϋ ܾ Ჴ ǷȟȥȬȸǷȧȳૅੲᚐௌ

࠶ࡿ㝈ࡽࢀࡓ㡿ᇦ࡟ఱࡽ࠿ࡢ⏕≀ࡀඛఫ✀࡜ࡋ࡚⏕ᜥࡋ࡚࠸ࡓ࡜ࡋࡼ࠺ࠋ౛࠼ࡤே㛫࡟ࡼࡗ࡚ඖ᮶ࡑࡇ࡟ࡣᏑᅾࡋ࡞࠿ࡗࡓ✀ࡀࡶࡓࡽࡉࢀ㸪ඛఫ✀࡜౵ධ✀ࡢ㛫࡟⏕άሙᡤࡸ㣵ࢆࡵࡄࡗࡓ➇தࡀ⏕ࡌ㸪ሙྜ࡟ࡼࡗ࡚ࡣ౵ධ✀࡟ࡼࡗ࡚ඛఫ✀ࡀ⤯⁛ࡉࡏࡽࢀࡿࡇ࡜ࡀ࠶ࡿࡔࢁ࠺ࠋ➇த㛵ಀ࡟࡝ࡢࡼ࠺࡞᮲௳ࡀ࠶ࢀࡤ㸪ඛఫ✀ࡢ⤯⁛ࡀ⏕ࡌࡿࡢ࡛࠶ࢁ࠺࠿ࠋ୍᪉㸪⏕≀ࡣ➇த㛵ಀ࡟࠶ࡾ࡞ࡀࡽࡶ㸪㝈ࡽࢀࡓ㡿ᇦෆ࡟ඹᏑࡋ࡚࠸ࡿሙྜࡶぢཷࡅࡽࢀࡿࠋඹᏑࡢࡓࡵࡢ᮲௳࡜
ࡣఱ࡛࠶ࢁ࠺࠿ࠋ౵ධ࡜ఏ᧛࡟㛵ࡍࡿᩘ⌮⏕ែᏛ࡟ࡣࡑࡢ௚ᵝࠎ࡞ࢺࣆࢵࢡࢫࡀ࠶ࡿࡀ㸪ᮏ◊✲࡛ࡣ≉࡟➇தᣑᩓ⣔࡜ࡼࡤࢀࡿ᪉⛬ᘧ࡟࠾࠸࡚ồࡲࡿ㐍⾜Ἴゎࡢཝᐦゎࢆ⤂௓ࡋ㸪ᩘ⌮⏕ែᏛ࡟࠾ࡅࡿཝᐦゎࡢ᭷ຠᛶࢆ♧ࡋࡓࠋz

Semi-exact equilibrium solutions for three-species competition-diffusion systems, C.-C. Chen,
L.-C. Hung, T. Tohma, D. Ueyama, and M. Mimura, Hiroshima Mathematical Journal
43(2)(2013), pp.179-206.

z

Exact traveling wave solutions of three species competition-diffusion systems, C.-C. Chen, L.-C.
Hung, M. Mimura, and D. Ueyama, DCDS-B 17(8) (2012), pp.2653-2669.

zᩘ⌮⏕ែᏛ࡟࠾ࡅࡿཝᐦゎ㸪ᩘ⌮⛉Ꮫ ᖺ  ᭶ྕࢧ࢖࢚ࣥࢫ♫

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Simulation Groupᄂᆮಒᙲ