• 検索結果がありません。

球磨川のシカ食害と斜面崩壊について

N/A
N/A
Protected

Academic year: 2021

シェア "球磨川のシカ食害と斜面崩壊について"

Copied!
5
0
0

読み込み中.... (全文を見る)

全文

(1)

球磨川のシカ食害と斜面崩壊について

著者

森山 聡之, つる 詳子

雑誌名

福岡工業大学総合研究機構研究所所報

3

ページ

35-38

発行年

2020-12-25

URL

http://hdl.handle.net/11478/00001587

(2)

⌫☻ᕝࡢࢩ࢝㣗ᐖ࡜ᩳ㠃ᔂቯ࡟ࡘ࠸࡚



᳃ᒣ ⪽அ

♫఍⎔ቃᏛ㒊♫఍⎔ቃᏛ⛉



ࡘࡿヲᏊ

⮬↛ほᐹᣦᑟဨ⇃ᮏ┴㐃⤡఍



Feeding Damage Caused by Deer and Slope Collapse on Kumagawa River Basin

MORIYAMA Toshiyuki㸦Department of Socio-Environmental Studies , Facuity of Socio-Environmental Studies㸧 TSURU Shoko 㸦Nature interpreter association in Kumamoto㸧

Abstract

In the middle of the Kuma River, which runs through the southern part of Kumamoto Prefecture, deer damage has been notice- able in recent years. This time, among them, the Sakamoto district in Yatsushiro City (formerly Sakamoto Village) was damaged, to confirm the fact with visiting the same district.

As a result, it is expected that sediment production will increase, so flood risk will increase in the near future. Immediately, it is necessary comprehensive measures including engineering are considered. First of all, it was concluded that a survey of deer dynamic and a food damage were necessary as basic data for next step.

Keywords㸸IoT-DRR, Feeding Damage with Deer, River Network

 ࡣࡌࡵ࡟ ⇃ᮏ┴༡㒊ࢆὶࢀࡿ⌫☻ᕝࡢ୰ὶᇦ࡛ࡣࠊࡇࡇᩘᖺࢩ࢝ ࡢ㣗ᐖࡀ┠❧ࡗ࡚ࡁࡓࠋ௒ᅇࡣࠊࡑࡢ୰࡛ࡶࠊඵ௦ᕷᆏᮏᆅ ༊㸦ᪧᆏᮏᮧ㸧࡛⿕ᐖࡀ኱ࡁ࠸ࡇ࡜࠿ࡽࠊྠᆅ༊ࢆᅇࡗ࡚ࡑ ࡢ஦ᐇࢆ☜ㄆࡋࡓࠋ  ᪉ἲ  ᩥ⊩ㄪᰝ ከࡃࡢᩥ⊩ࡀ࠶ࡗࡓࡀࠊ࢖ࣥࢱ࣮ࢿࢵࢺ(㸯)()()᭩⡠ 㸲 ࠊ 㸳 ࡛⾜ࡗࡓࠋ  ⌧ᆅ㋃ᰝ 2019 ᖺ 6 ᭶ 2 ᪥࡟ᆏᮏᆅ༊ࡢඵ❳ᒣࡸ❳ᓠᒣ࡛ணഛㄪᰝࢆ ⾜࡞ࡗࡓࠋᅗ㸯࡟ᑐ㇟ᆅ༊ࡢᆅᅗࢆ♧ࡍࠋඵ❳ᒣࡸ❳ᓠᒣࡣ ᅗ㸯ࡢᕥୖ࡟࡞ࡿࠋ  ⫈ࡁྲྀࡾ ➨ 2 ⴭ⪅ࡀࠊࢩ࢝ࡢ㣗ᐖ࡟㛵ࡋࠊ⇃ᮏ┴ᆏᮏ⊟཭఍ᆏ ᮏ᱈ᏊẶ , す㢪ᑎఫ⫋ ᒣᮏ㝯ⱥẶ , ࡸࡗࡕࢁࢺࣞ࢖ࣝࣛ ࣥࢽࣥࢢ࣓ࣥࣂ࣮,NPO ἲேỈ࡜࠸ࡁࡶࡢࢿࢵࢺ࣮࣡ࢡࡃࡲ ࡶ࡜ ḷᒸᏹಙẶ࠿ࡽ⫈ࡁྲྀࡾࢆ⾜ࡗࡓࠋ ᅗ㸯⌫☻ᕝ୰ୗὶ㒊 ࠕࣛ࢖ࢺ࣐ࢵࣉࣝ⇃ᮏ┴㐨㊰ᆅᅗࠖ᫛ᩥ♫ࠊ ࢆ࣮࣋ࢫ࡟฼⏝

Fig.1, Middle and lower Catchment Area of the Kuma-gawa River (Map is based on light Mapple road mao for Kumamoto pref.2011 published by Obunsha Co.Ltd)

(3)

᳃ᒣ ⪽அ㸪ࡘࡿ ヲᏊ



ᅗᔂቯࢆࡣࡌࡵ࡚࠸ࡿᩳ㠃㸦ᪧᆏᮏᮧ㸧 Fig.2, Slope which begin to collaspe.(Sakamoto town)



ᅗࢩ࢝ࡢ㣗ᐖ⑞㸦ᪧᆏᮏᮧ㸧 ࡇࡇࡣࡲࡔ᰿ࡇࡑࡂ㣗࡭ࡽࢀ࡚࠸࡞࠸ Fig.4, Mark of deer feeding.(Sakamoto town)

This place is not yet uprooted.

 ᅗࢩ࢝ࡢ㣗ᐖᚋࠊ⾲ᅵࡀὶฟࡋ࡚᰿ࡀ㟢ฟࡋ࡚࠸ࡿ

ᗈⴥᶞ㸦ඵ❳ᒣ㸧

Fig.6, Broad-leaved tree with exposed roots due to outflow of topsoil after the damage of deer feeding.(Mt.Hachiryu-zan)

 ⤖ᯝ  ᩥ⊩ㄪᰝ ࢩ࢝ၥ㢟ࡣ඲ᅜⓗ࡞ㄢ㢟࡛࠶ࡿࡀࠊ⌧≧࡛ࡣ㎰స≀ࢆⲨࡽ ࡋ࡚࠸ࡿࠊ㔪ⴥᶞࡢ๤⓶⿕ᐖ(㸯)ࡸᩳ㠃ᔂቯ࡛ὶධࡋࡓᅵ◁ ࡟ࡼࡾࠊἙᕝࡢ㨶㢮ࡢ⏕ែ⣔ࡀᙳ㡪ࢆཷࡅ࡚࠸ࡿ(㸰)ࣞ࣋ࣝ ࡟Ṇࡲࡗ࡚࠸ࡿ࡜ᛮࢃࢀ࡚࠸ࡿࡼ࠺࡛࠶ࡿࠋ ୍᪉ࠊࢩ࢝ࡢ㢌ᩘ࡟㛵ࡋ࡚ࡣ⣅⢏ἲ࡛㢌ᩘࡢᢕᥱࡣ⾜ࢃࢀ   ᅗࢩ࢝ࡀዲࡲ࡞࠸ࢼࢳࢩࢲࡔࡅࡀ⦾ⱱࡋࠊ⏕ែ⣔ࡀᔂࢀ ࡚࠸ࡿ㸦ᪧᆏᮏᮧ㸧

Fig.3, Only pteris wallsichiana,which deer do not like,are overgrown and the ecosystem is collapsing.(Sakamoto Town)





ᅗࢩ࢝ࡢ㣗ᐖ࡟ࡼࡾᔂቯࡋࡓ㐨㊰ࡂࢃࡢᩳ㠃 ❳ᓠᒣ 

Fig.5, Roadside slopethat collapsed due to the damage of deer feeding. (Mt.Ryuho-san)

ᅗࢩ࢝ࡢཱྀࡀᒆࡃୗⲡ࡜పᮌࢆ඲࡚㣗࡭࡚⌧ࢀࡓ'HHU /LQH ❳ᓠᒣ  ྜ┠ 

Fig.7, Deer Line appeared by eating the all of undergrowth and shrubs.(Mt.Ryuho-san 5th station) ࡚࠾ࡾࠊ⌫☻ᕝ࿘㎶࡛ࡣ⣙27,000 㢌ࡢࢽ࣍ࣥࢪ࢝ࡀ⏕ᜥࡋ ࡚࠾ࡾࠊࡇࢀࢆ9,000 㢌࡟ῶࡽࡍィ⏬࡟࡞ࡗ࡚࠸ࡿ(㸱)ࠋࡲࡓࠊ 㣗ᐖ࡟㛵ࡋ࡚ࡣࠊබⓗ࡞ㄪᰝࡣ࡞ࡉࢀ࡚࠸ࡿ(㸯)ࡀࠊ୺࡟㔪ⴥᶞᯘ ࡟࠾ࡅࡿ๤⓶⿕ᐖㄪᰝ࡛࠶ࡾࠊᗈⴥᶞᯘࡣ⾜ࢃࢀ࡚࠸࡞࠸ ࡼ࠺࡛࠶ࡿࠋ

(4)

  '\QDPR'%   



 ؽփָसͶΓΖ  ؽփָसͶΓΖ  $UF*,6RQOLQH ɦɋɜɻȸ   ౖ੶ླྀ৾ಊ 61  ࢝ࢱࣟࢢ໬ $UF*,6RQOLQH ؂ڧ '1$  ؂ڧ '1$ ࢹ࣮ࢱࣂࣥࢡ໬    



 



       



      ⌧ᆅ㋃ᰝ ᅗ㹼࡟㣗ᐖࡢᵝᏊࢆ♧ࡍࠋ࠸ࡓࡿ࡜ࡇࢁ࡛ぢࡽࢀࡓ㣗 ᐖ࡜ࠊᗈⴥᶞᯘෆࡢ㝆㞵࡟ࡼࡾ⾲ᅵࡀὶฟࡋࠊ᰿ࡀ㟢ฟࡋࠊ ❧ᮌࡀಽࢀࡿ࡜࡜ࡶ࡟ᩳ㠃ࡀᔂቯࡋ࡚࠸ࡿࡢࡀࢃ࠿ࡿࠋࡲ ࡓࠊࢩ࢝ࡀዲࡲ࡞࠸ࢼࢳࢩࢲࡸ࢔ࢭࣅ࡞࡝ࡀ㏫࡟⦾ⱱࡋ࡚ ࠸ࡿࠋ   ⫈ࡁྲྀࡾ ⌫☻ᕝࡢࡑࡤࢆ㉮ࡿJR ⫧⸃⥺࡛ࡣᗘࠎ❧ᮌࡀಽࢀ࡚࠸ࡿ࡜ ࡢࡇ࡜࡛ࠊ⫧⸃⥺111 ᖺࡢṔྐࡢ୰࡛ࡇࡇᩘᖺ㢧ⴭࡔ࡜࠸࠺ࠋࡋ ࠿ࡋࠊࢩ࢝ࡢ⏕ᜥᩘㄪᰝࡣࠊࣛ࢖ࣥࢭࣥࢧࢫ࢝࢘ࣥࢺἲ࡜⣅⢏ἲ ࡛࠶ࡾࠊືែ࡜ࡋ࡚౑࠼ࡿࡶࡢ࡛ࡣ࡞࠸࡜ࡢࡇ࡜࡛࠶ࡿࠋ ୍᪉ࠊࢩ࢝ࡢᤕ⋓࡟㛵ࡋ࡚ࡣ⊟ᖌࡀ㧗㱋໬ࡋ࡚ῶᑡࡋ࡚࠸ࡿ ୖ࡟ࠊᆏᮏᆅ༊ࡣᩳ㠃ࡀᛴᓧ࡛ᤕ⋓ࡋࡓࢩ࢝ࡀୗࢁࡏ࡞࠸ࡓࡵࠊ ᩳ㠃ࡀ⦆ࡸ࠿࡞௚ࡢᆅ༊࡛⊟ࢆࡋ࡚࠸ࡿ࡜࠸࠺ࡇ࡜ࡀࢃ࠿ࡗ ࡓࠋ ࡲࡓࠊFacebook ࡛ඵ௦ࡢᒣ㝿ࡢᕷ⾤ᆅ࡟ࢩ࢝ࡀฟἐࡍࡿ ࡼ࠺࡟࡞ࡗࡓ࡜ࡢሗ࿌ࡶ࠶ࡗࡓࠋ                                     ⪃ᐹ ㄪᰝࡋ࡚ࢃ࠿ࡗࡓࡇ࡜ࡣࠊ⇃ᮏ┴࡟ࡼࡾᐃ㔞ⓗ࡞ࢩ࢝ࡢ ᖺẖࡢ㢌ᩘㄪᰝࡣ⾜ࢃࢀ࡚࠸ࡿࡀࠊ⟶⌮ࡍ࡭ࡁ㢌ᩘࡣỴࡵ ࡽࢀ࡚࠸࡚ࡶᐇ㝿࡟ᤕ⋓ࡉࢀࡓࡢ࠿࡝࠺࠿ࡣ୙࡛᫂࠶ࡿࠋ   ࡝ࡢࡼ࠺࡞⩌ࢀࡀ࡝࠺⛣ືࡋ࡚࠸ࡿ࡜࠸ࡗࡓືែㄪᰝࡣ ⾜ࢃࢀ࡚࠾ࡽࡎࠊ⌧ᅾ≉࡟ၥ㢟࡟࡞ࡗ࡚࠸ࡿᗈⴥᶞᯘෆࡢ 㣗ᐖࡶㄪᰝࡉࢀ࡚࠸࡞࠸ࡼ࠺࡛࠶ࡿ(㸱) ᚑ᮶ࡣࠊࢩ࢝ࡢ㑅ዲ࡟ࡼࡾ≉ᐃࡢୗⲡࡀቑ࠼࡚⏕ែ⣔ࡢ ࣂࣛࣥࢫࡀᔂࢀࡿࡇ࡜ࠊࢩ࢝ࡢ㣗ᐖࡣ㔪ⴥᶞࡢ๤⓶㣗ᐖ࡟ ࡼࡿ❧ࡕᯤࢀࡸࠊ㎰స≀࡬ࡢ⿕ᐖ࡞࡝㝈ᐃⓗ࡜⪃࠼ࡽࢀ࡚ ࠸ࡓࡀࠊ௒ᅇࡢㄪᰝ࡛ࡣࠊࢩ࢝ࡀ㔪ⴥᶞᯘෆࡢࡳ࡞ࡽࡎᗈⴥ ᶞᯘෆࡢୗⲡࡸపᮌࢆ㣗࡭ᑾࡃࡍࡇ࡜࡟ࡼࡾࠊ኱ࡁ࡞⢏ᚄ ࡢᯘෆ㞵ࡢ㞵⁲ࡀⴠୗࡋࠊࡑࡢ⾪ᧁ࡛A ᒙࡀ◚ቯࡉࢀࠊᩳ㠃ᔂ ቯ࡟ࡼࡾ❧ᮌࡀಽࡉࢀ࡚࠸ࡿࠋ᪤࡟Ἑᕝࡢ㨶㢮࡟୚࠼ࡿᙳ㡪ࡣ኱ࡁ࠸࡜ ゝࢃࢀ࡚࠸ࡿ(㸰)ࡀࠊ㐲ࡃ࡞࠸ᑗ᮶࡟ࡉࡽ࡟ᅵ◁⏕⏘㔞ࡀቑ࠼࡚ ὥỈࣜࢫࢡࡀ㧗ࡲࡿࡇ࡜ࡀ᥎ ࡉࢀࡿࡇ࡜࠿ࡽࠊ᪩ᛴ࡟ᕤ Ꮫࢆྵࡴ⥲ྜⓗ࡞ᑐ⟇ࡀᚲせ࡜⪃࠼ࡽࢀࡿࠋࡲࡎࡣᑐ⟇࡟ ஌ࡾฟࡍᇶ♏ⓗࢹ࣮ࢱ࡜ࡋ࡚ࢩ࢝ࡢືែㄪᰝ࡜㣗ᐖㄪᰝࡀ ᚲせ࡛࠶ࢁ࠺ࠋ ਦ  ླྀҮϠωνϨϱήεητϞͳླྀҮϜρϒϱήϏʖτΡ ਦ  ླྀҮϠωνϨϱήεητϞͳླྀҮϜρϒϱήϏ τΡ Fig.8, Monitoring system and basin mapping party for river basin.

(5)

᳃ᒣ ⪽அ㸪ࡘࡿ ヲᏊ   ௒ᚋࡢணᐃ ௒ᚋࡢணᐃ࡜ࡋ࡚ࡣࠊ㉥እ⥺┘ど࣓࢝ࣛࢆ⋇㐨࡟ከᩘ㓄 ⨨ࡋࠊ࡝ࡢࡼ࠺࡞⩌ࢀࡀ࡝ࡢ⛬ᗘᏑᅾࡋࠊ࡝ࡢࡼ࠺࡟⾜ືࡋ ࡚࠸ࡿ࠿ࢆ‽ࣜ࢔ࣝࢱ࢖࣒࡟ᢕᥱࡍࡿࡇ࡜ࡀ⪃࠼ࡽࢀࡿࠋ ࡲࡓ㣗ᐖ࡟㛵ࡋ࡚ࡶࠊࢻ࣮ࣟࣥ➼ࢆά⏝ࡋࠊ࡛ࡁࡿࡔࡅᗈ࠸ ⠊ᅖࢆ▷᫬㛫࡛⡆᫆ⓗ࡟㣗ᐖㄪᰝࡍࡿᚲせࡀ࠶ࡿࡀࠊࢻࣟ ࣮ࣥࢆᯘෆ࡛㣕ࡤࡍࡢࡣ *36 ࡢ㟁Ἴࡀධࡽ࡞࠸ࡓࡵࠊᢏ⾡ ⓗ࡞㛤Ⓨࡶᚲせ࡛࠶ࡾࠊᇶ♏ࢹ࣮ࢱࢆᥞ࠼ࡘࡘࠊᑐᛂ⟇ࢆ⦎ ࡿᚲせࡀ࠶ࢁ࠺ࠋ ලయⓗ࡟ࡣࠊ ࢩ࢝ࡢ⏬ീࢆ஦๓࡟ᶵᲔᏛ⩦ࡋ࡚ࠊ࣓࢝ࣛື⏬࡛ࢩ࢝ࢆ ᳨ฟࡋࡓሙྜ࡟ప㏿ࡢ ,R7 ᅇ⥺࡛▱ࡽࡏࡿࠕ࢚ࢵࢪࢥࣥ ࣆ࣮ࣗࢸ࢕ࣥࢢࠖࡢά⏝ࠋ ࢻ࣮࡛ࣟࣥ᧜ᙳࡋࡓ⏬ീ࠿ࡽ᳜⏕ࢆࢸࢡࢫࢳ࣮ࣕゎᯒࡉ ࡏ࡚ࠊ᳜⏕ࡢኚືࢆㄪ࡭ࡿࠋ 㣗ᐖࡢ≧ἣࢆ 95 ࡛᧜ᙳࡋࠊࣜ࢔ࣝ࡟ఏ࠼ࡿࠋ ࢩ࢝࡟ⱞ῰㡢㸦ᷦ࡞࡝࡟㛢ࡌ㎸ࡵࡽࢀࡓ᫬ࡢኌ㸧ࢆࢫࣆ ࣮࣮࢝࠿ࡽ⪺࠿ࡏ࡚཯ᛂࢆぢࡿ 㸳 ࠋ ࢩ࢝࡟≟ࡢྭ࠼ࡿኌࢆࠊ」ᩘࡢࢫࣆ࣮࢝࠿ࡽḟࠎ࡟ὶࡋ ࡚ࠊ㏣࠸࠿ࡅ࡚࠸ࡿຠᯝࢆฟࡍࠋ ࡞࡝ࠊྛ✀ࡢ᪉ἲࡀ⪃࠼ࡽࢀࡿࠋࡇࢀࡽࡣ࠸ࡎࢀࡶせ⣲ᢏ ⾡࡜ࡋ࡚ࡣ࠶ࡿ⛬ᗘ㛤Ⓨࡉࢀ࡚࠸ࡿࡀࠊᅗࡢࡼ࠺࡞,R7ᢏ ⾡ࡸ*,6ࢆᛂ⏝ࡋࡓࢫ࣐࣮ࢺࣜࣂ࣮ࡢ୍㈏࡜⪃࠼ࠊ6WUHDP 9LHZ95ࡸఫẸཧຍࡢ࣐ࢵࣆࣥࢢࣃ࣮ࢸ࢕࠶ࡿ࠸ࡣ⎔ቃ'1$ ࡜⤌ࡳྜࢃࡏ࡚ࠊᆅᇦఫẸࡢព㆑ࢆ⎔ቃࡸ㜵⅏࡟ྥࡅࡿᚲ せࡀ࠶ࡿ࡜⪃࠼ࡿࠋ   ㅰ㎡ ⪺ࡁྲྀࡾࡢ⫈ྲྀ⪅࡜ࡋ࡚ࡣࠊ⇃ᮏ┴ᆏᮏ⊟཭఍ᆏᮏ᱈Ꮚ Ặす㢪ᑎఫ⫋ᒣᮏ㝯ⱥẶࡸࡗࡕࢁࢺࣞ࢖ࣝࣛࣥࢽࣥࢢ ࣓ࣥࣂ࣮132ἲேỈ࡜࠸ࡁࡶࡢࢿࢵࢺ࣮࣡ࢡࡃࡲࡶ࡜ḷ ᒸᏹಙẶ࡛࠶ࡿࠋࡑࡢ௚࡟ࡶ࣏ࢫࢱ࣮ࢭࢵࢩࣙࣥࡢⓎ⾲ 㸴 ࡟࠾࠸࡚ከࡃࡢ᪉ࠎࡢࡈពぢࢆ㡬࠸ࡓࠋࡲࡓࠊ᳃ᯘ⥲ྜ◊✲ ᡤ⇃ᮏᨭᡤࡢᏳ⏣㞞ಇẶ࡟ࡶ᭷┈࡞ຓゝࢆ࠸ࡓࡔ࠸ࡓࠋࡇ ࡢሙࢆ೉ࡾ࡚῝ㅰࡍࡿࠋ ᩥ   ⊩ (㸯) ᐑᓥ῟஧ࠊⲡ㔝㟼௦ ࠕ⇃ᮏ┴࡟࠾ࡅࡿࢩ࢝⿕ᐖࡢᐇែࠖࠊ஑ᕞ᳃ᯘ◊✲ㄅࠊ 56:pp.222-224ࠊ2003ࠊ http://ffpsc.agr.kyushu-u.ac.jp/kfs/kfr/56/bin090526114017009.pdf, 2019.9.27 㜀ぴ

(㸰) Hikaru Nakagawa, Habitat changes and population dynamics of fishes in a stream with forest floor degradation due to deer overconsumption in its catchment area, J. of the Society for Biology, 2019.7,

https://conbio.onlinelibrary.wiley.com/doi/full/10.1111/csp2.71 , 2019.9.27 㜀ぴ (㸱) ⇃ᮏ┴ࠊ➨஧✀≉ᐃ㫽⋇⟶⌮ィ⏬㸦ࢽ࣍ࣥࢪ࢝㸧➨㸳ᮇࠊ2018.03 https://www.pref.kumamoto.jp/common/UploadFileOutput.ashx?c_id=3&id= 22917&sub_id=2&flid=154088, 2019.9.27 㜀ぴ (㸲)  㧗ᵳᡂ⣖ࠊࠕࢩ࢝ၥ㢟ࢆ⪃࠼ࡿ ࣂࣛࣥࢫࢆᔂࡋࡓ⮬↛ࡢ⾜᪉ࠖࠊ ࣐ࣖࢣ࢖᪂᭩ࠊ2015 (㸳㸧 ⁽㇂ṇ⩏㸸ࠕື≀࡟࡛ࡁࡿࡔࡅࡸࡉࡋ࠸ᧁ㏥ᶵࢆసࡿࠖࠊ࢖ࣥࢱ࣮ࣇ࢙࣮ࢫ 2019 ᖺ 9 ᭶ྕࠊpp.76-89ࠊ2019 (㸴㸧 ᳃ᒣ⪽அ࣭ࡘࡿヲᏊ㸸ࠕ⌫☻ᕝᆏᮏᆅ༊࿘㎶࡟࠾ࡅࡿࢩ࢝ࡢ㣗ᐖ࡜ᩳ㠃ᔂቯ࡟ࡘ ࠸࡚ࠖࠊᛂ⏝⏕ែᕤᏛ఍➨23 ᅇ◊✲Ⓨ⾲఍ㅮ₇㞟ࠊᗈᓥࠊ2019.9

参照

関連したドキュメント

All (4 × 4) rank one solutions of the Yang equation with rational vacuum curve with ordinary double point are gauge equivalent to the Cherednik solution.. The Cherednik and the

Ulrich : Cycloaddition Reactions of Heterocumulenes 1967 Academic Press, New York, 84 J.L.. Prossel,

Keywords: continuous time random walk, Brownian motion, collision time, skew Young tableaux, tandem queue.. AMS 2000 Subject Classification: Primary:

Analogs of this theorem were proved by Roitberg for nonregular elliptic boundary- value problems and for general elliptic systems of differential equations, the mod- ified scale of

Then it follows immediately from a suitable version of “Hensel’s Lemma” [cf., e.g., the argument of [4], Lemma 2.1] that S may be obtained, as the notation suggests, as the m A

Definition An embeddable tiled surface is a tiled surface which is actually achieved as the graph of singular leaves of some embedded orientable surface with closed braid

Our method of proof can also be used to recover the rational homotopy of L K(2) S 0 as well as the chromatic splitting conjecture at primes p > 3 [16]; we only need to use the

Correspondingly, the limiting sequence of metric spaces has a surpris- ingly simple description as a collection of random real trees (given below) in which certain pairs of