On a coefficient concerning an ill-posed Cauchy problem and the singularity detection with the wavelet transform

We study the Cauchy problem for 2nd order weakly hyperbolic equations. F. Colombini, E. Jannelli and S. Spagnolo showed a coefficient degenerating at an infinite number of points, with which the Cauchy problem is ill-posed Gevrey classes. Moreover, we olso report numerical results of the singularity detection with wavelet trasform for coefficient functions

休眠程度の異なるブドウ‘ピオーネ’の発芽に及ぼす温度の影響

The effects of temperature on budbreak of cuttings obtained at different stages of dormancy from 'Pione' grapevines (Vitis labrusca × V. vinifera) grown in open field were investigated. Cuttings were collected at monthly intervals from July to March. Judging from the number of days to initial and 60% budbreak after treatment, indicating promotion and the uniformity of budbreak, respectively, 30℃ was the most effective in budbreak, followed by 25 and 20℃ in that order in all treatment times. However, the effect of temperature on budbreak was markedly affected by treatment time. The number of days to initial budbreak (NDIB) increased gradually from July to October, peaked in December and thereafter decreased gradually towards March. The periods from July to September, from October to December, and from January to March were assumed to correspond to paradormancy, endodormancy, and ecodormancy of 'Pione' grapevines, respectively. Final percentage of budbreak was less than 100% until endodormancy for all temperatures. It was below 60% at 20℃ treatments of July to September. On the other hand, a uniform budbreak was observed in the treatments after the middle of endodormancy for all temperatures, resulting in almost 100% of final percentage of budbreak. There was a significant negative correlation between NDIB and cumulative chilling hour (CCH) of exposure to below 7.2℃ in the treatments after November, and also between NDIB and cumulative temperature (CT, ℃･h), a summation of temperature and hours of exposure to above 0°C from November 1 to each treatment time and hours of exposure to 20, 25, or 30℃ from start of treatment to budbreak in each plot. The results suggest that besides CCH, CT can also be used to estimate the completion of dormancy in 'Pione' grapevine bud.露地栽培されているブドウ‘ピオーネ’について，休眠の深さが異なる7月から翌年3月まで約1か月間隔で枝を採取し，1芽を有す挿し穂を調整した後，20，25および30℃に制御したインキュベーター（いずれも14時間日長）に入れ，経時的に発芽を調査した．発芽の早さを示す発芽所要日数と発芽の揃いを示す60%発芽所要日数から発芽に及ぼす温度の影響を評価した．実験期間中の温度を測定し，休眠完了と温度との関係を考察した．いずれの処理時期においても30℃の発芽が最も優れ，次いで25℃，20℃の順であった．しかし，発芽に及ぼす温度の影響は処理時期によって大きく異なった．すなわち，発芽所要日数は7月から10月までは徐々に増加し，11月に最大に達した後，3月に向けて少しずつ減少した．このことから，‘ピオーネ’では7月から9月が条件的休眠期，10月から12月が自発休眠期，1月から3月が他発休眠期と推察された．自発休眠期までの最終発芽率はいずれの温度も100%未満であり，また7月～9月の20℃処理では60%未満の発芽率であった．一方，自発休眠期の中期以降の処理ではいずれの温度とも均一な発芽を示し，最終発芽率はほぼ100%であった．11月以降の処理において，発芽所要日数と7.2℃以下の温度に遭遇した時間数（CCH）との間に有意な負の相関があった．また，11月１日から各処理時期までの0℃以上の温度に遭遇した時間数と20，25または30℃で処理を始めた日から各処理区の発芽までの時間数との積算（CT, ℃・h）との間にも有意な負の相関が認められた．以上のことから，‘ピオーネ’の芽の休眠完了の予測には低温遭遇量だけでなく，0℃以上の積算温度による方法も有効と考えられた

ブドウの芽の休眠打破に及ぼす化学物質の種類と濃度の影響

　The effects of various chemicals and their concentrations on budbreak of ‘Pione’ grapevine (Vitis labrusca L. x V. vinifera L.) were studied by using single-bud cuttings obtained in endodormancy. When seven chemicals were applied to the upper half of cuttings, including bud, 2% hydrogen cyanamide (H2CN2) was most effective in budbreak, judging from acceleration and uniformity of budbreak. However, neither 10 % suspension of calcium cyanamide (CaCN2) nor 5% diallyl disulfide (C6H10S2) had any effect in breaking bud dormancy of ‘Pione’ cuttings. Budbreak in cuttings treated with 10 % hydrogen peroxide (H2O2) was inhibited slightly compared to the control cuttings. No effect of 2% potassium chlorate (KClO3), 2% sodium chlorate (NaClO3) or 2% paclobutrazol (PBZ) on breaking bud dormancy in ‘Pione’ cuttings was observed. The effects of CaCN2, H2CN2 and C6H10S2 on breaking bud dormancy in ‘Pione’ cuttings were compared at three to four concentrations. With CaCN2, a 20 % suspension significantly promoted budbreak, but a 5% suspension resulted in no effect. Both 5% and 2% of H2CN2 accelerated budbreak significantly and resulted in uniform budbreak, especially at 5 %, whereas at 0.5% H2CN2 no effect was observed. Of three concentration of C6H10S2, only a 10 % solution showed any effectiveness in budbreak. The results indicated that H2CN2 is most effective in breaking bud dormancy of ‘Pione’ grapevine cuttings, followed by CaCN2 and C6H10S2 in that order, although their effectiveness varied largely according to the concentrations for all chemicals.自発休眠期に採取したブドウ'ピオーネ'の挿し穂を用い，芽の休眠打破に及ぼす化学物資の種類と濃度の影響を調査した．７種類の化学物質について休眠打破の効果を比較したところ，発芽の促進と揃いからみて，２%シアナミド （H2CN2）の効果が最も大きかった．一方，10%石灰窒素（CaCN2）と５%２ 硫化ジアリル（C6H10S2）には休眠打破の効果は認められなかった．10%過酸化水素（H2O2）では発芽がやや抑制された．２%の塩素酸カリウ（KClO3）， 塩素酸ナトリウム（NaClO3）およびパクロブトラゾール（PBZ）はいずれも休眠打破の効果を示さなかった．石灰窒素，シアナミドおよび２硫化ジアリルの濃度を３～４段階に変え，'ピオーネ' 挿し穂の休眠打破に及ぼす影響を調査した．石灰窒素では，20%区の発芽が著しく促進されたが，５ｵ 区では発芽の揃いがよくなかった．シアナミドでは，５%区と２%区の休眠打破効果が著しかったのに対し，0.5%区では休眠打破の効果は認められなかった．２硫 化ジアリルでは，10%区で休眠打破効果がみられただけであった．以上の結果から，ブドウの芽の休眠打破に及ぼす化学物質の効果はシアナミドで最も大きく，次いで石灰窒素，２硫化ジアリルの順であったが，効果の程度は濃度によって異なった

ブドウの芽の休眠打破に伴う生理的変化

Changes in CO2 and C2H4 production and water content of bud associated with breaking in ‘Pione’ grapevine (Vitis labrusca ×V. vinifera) were investigated throughout dormancy. Buds were collected monthly from August to December, during dormancy induction and maintenance, and CO2 and C2H4 production were determined by GC after incubation. Both CO2 and C2H4 production, especially for the latter, were low throughout the experiment. Water content of bud gradually increased until October ; thereafter it was constant. When CO2 and C2H4 production was determined from December to April, during dormancy maintenance to release, CO2 production was low from beginning of experiment to early April, prior to bursting, then rapidly increased to April 13, the bursting date. C2H4 production was almost undetectable throughout the experiment. Cuttings obtained at 3 different stages of dormancy were applied with 2% H2CN2 or distilled water (control), and budbreak was monitored in a plastic house kept at 20℃ or more. The CO2 and C2H4 production of bud were also determined weekly until budbreak. Regardless of treatment time H2CN2 significantly promoted budbreak compared to the control. Significantly higher production of CO2 was observed in cuttings treated with H2CN2 at 3 to 9 days before bursting for all the treatment times. C2H4 production was very low throughout the experiment for all the treatments. Irrespective of chemical application and treatment time, water content of bud decreased to the bursting stage, H2CN2 treatment especially showing a large decline. When dormant cuttings were treated with ACC, GSH (reduced glutathione) and GSSG (oxidized glutathione), only ACC promoted budbreak. Budbreak in cuttings treated with cyanamides such as CaCN2 and H2CN2 and cyanides such as KCN and NaCN was significantly accelerated except for H2CN2. Based on these results, the relationship between budbreak of grapevine buds and physiological changes in buds, and the roles of substances related to ethylene biosynthesis on breaking bud dormancy are discussed.ブドウ‘ピオーネ’について，休眠の導入と覚醒の過程における芽の生理的変化を調査した．休眠導入期の8月から覚醒初期の12月まで露地で栽培されている個体から芽を採取し，呼吸量，エチレン生成量および含水率を測定し た．調査期間を通して呼吸量は低く，エチレンもほとんど検出されなかった．芽の含水率は8月から10月まで僅かに上昇し，その後は変化がみられなかった．休眠覚醒初期の12月から発芽期の4月中旬まで，芽の呼吸量とエチレン生成量を測定した．呼吸量は4月上旬までは低く推移し，発芽（4月13日）の直前に急上昇した．エチレンは測定期間を通して低かった．休眠期の12月，1月および2月に採取した穂木を2% H2CN2 または蒸留水（対照）で処理し，25℃以上に保ったプラスチックハウスに入れて発芽を調査するとともに，経時的に芽の呼吸量，エチレン生成量および含水率を測定した．両時期とも対照区よりも H2CN2 処理区の発芽が早く，しかも休眠の深い12月処理で区による差が大きかった．両区いずれの時期とも，芽の呼吸量は発芽直前に急上昇したのに対し，エチレン生成量は調査期間を通して低いままであった．芽の含水率は，いずれの時期および処理区とも発芽期に低下し，特に H2CN2 処理区の低下が大きかった．休眠最深期の10月に採取した穂木に ACC，GSH（還元型グルタチオン）および GSSG（酸化型グルタチオン）を処理し，発芽に及ぼす影響を調査したところ，ACC だけが発芽を促進した．同様に，4種のシアン化合物（CaCN2，H2CN2，KCN，NaCN）を処理したところ，H2CN2を除き有意に発芽を促した．これらの結果を基に，ブドウの発芽と生理的変化との関係および休眠覚醒に及ぼすエチレン生合成関連物質の作用性について考察した

インドネシア，西ジャワのマンゴスチン園における気象環境と葉のC-N 率の樹冠部位および樹齢による違い

Productivity and quality of mangosteen fruit is markedly affected by tree age and sector (position in canopy). The objective of this study was to make clear seasonal changes in meteorological conditions of mangosteen orchard, and C-N ratio of leaves in relation to tree age and sector. The experiment was conducted using mangosteen trees grown in commercial orchard in Bogor, Indonesia during May to October 2010. Mangosteen trees of 3 different ages, young (20-year-old), middle (35-year-old), and old (50-year-old), each of five trees, were selected for study, and the canopy of each tree was divided into 9 sectors based on height (bottom, middle, top) and width (inner, center, outer). The light intensity on sunny days was higher in Sector 9, it was 8.1, 7.5, and 7.7 μmol・M(−2)・s(−1) in young, middle-aged and old trees, respectively, whereas in Sector 1 it was low, resulting 0.5, 0.4, and 0.5 μmol・M(−2)・s(−1) in young, middle-aged and old trees, respectively. Regardless of tree age, light intensity in outer position in canopy was higher than in the inner, and also it was higher in taller than in lower positions in canopy. In 2010, the phenological aspects of mangosteen orchard markedly changed because of irregular rainfall. In spite of tree age, SPAD value of leaves in upper parts such as Sectors 5-9 was high comparing with lower ones such as Sectors 1-4. In young trees, carbohydrate content of leaves was higher in top positions such as Sectors 7-9 than in bottom ones such as Sectors 1-3, whereas in middle-aged and old trees, no significant difference of carbohydrate content was observed among sectors. Regardless of month and tree age measured, nitrogen content of leaves was higher in lower positions in canopy such as Sectors 1-4 than in upper ones such as Sectors 5-9. Consequently, the C-N ratio of leaves was higher in the upper part of canopy compared to the lower. Based on the results, the relationships between meteorological status and C-N ratio of leaves and fruit productivity and quality of mangosteen are discussed in relation to position in canopy and tree age.マンゴスチンの果実生産性や果実品質が樹冠部位や樹齢によって異なる点について，インドネシア西ジャワの商業的マンゴスチン園で照度と降雨量を調査するとともに，20，35および50年生樹を５個体ずつ選び，各個体樹冠の高さと幅から9つのセクター（樹冠部位）に分け，葉の葉色値（SPAD値），クロロフィル含量，炭水化物含量，窒素含量およびC-N率を比較した．晴天日の照度は，樹齢による差は小さくセクター9（各樹齢7.5～8.1μmol・M(-2)・S(-1)）が最も高く，一方セクター1（各樹齢0.4～0.5μmol・M(-2)・S(-1)）で最も低かった．樹冠外部の照度はいずれの樹齢も樹冠内部よりも高く，またセクター1，2，3のような下部よりも7，8，9のような上部で高かった．調査を行った2010年は雨季の開始が例年よりも2～3か月早く，このため樹体の生育相が例年とは大きく異なった．葉色値は樹齢に関係なくセクター1～4のような下部の葉よりもセクター5～9のような上部の葉で高かった．葉の炭水化物含量は，20年生樹ではセクター1～3の下部よりも7～9の上部で高かったが，35年生と50年生樹ではそれぞれ50.7～53.0%と51.3～52.6%で大差なかった．一方，葉の窒素含量は樹齢や測定時期に関係なくセクター5～9の上部よりもセクター1～4の下部で高かった．このため，葉のC-N率は樹冠の下部よりも上部で高かった．この結果をもとにマンゴスチンの果実生産性と品質および樹冠部位と樹齢との関係を考察した

モモ'紅清水'における落果および種子発育に及ぼす種子への障害およびジベレリンとプクロブトラゾールの注入の影響

The relationsships between fruit drop induced by seed injury and seed development were investigated in “Beni Shimizu” peach. Seed injury(Injury) was done by drilling from opposite side of suture line upto seed coat using an electric drill(outre diameter of 2.5mm) at 40, 50, 60, 72 and 80 days after full bloom(DAFB). Injections of gibberellic acid(GA) and paclobutrazol(PBZ) (Injection), which relate to fruit drop and seed development were carried out just after the injury for seed. In all of the Injury and Injection treatments, treated fruit dropped in 40, 50 and 60 DAFB treatments but not in 72 and 80 DAFB treatments. Weight of fruit and seed debreased rapidly at 3 days after treatment(DAT) in 60 DAFB treatment. Morphology of endosperm and embryo was compared among 60, 72 and 80 DAFB treatments. Growth of endosperm and embryo stopped from 3 DAT in 60 DAFB treatment but embryo continued to grow until 5 DAT in 72 DAFB treatment. Collapsed cell nucleus in endosperm and embryo occurred at 3 DAT in 60 DAFB treatment. On the other hend, in 72 DAFB treatment cell nuclei in endosperm collapsed in a similar manner as in 60 DAFB treatment although the cell nuclei in embryo did not collapse. When morphology of chalazal haustorium in 60 DAFB treatment was examined, chalazal haustorium began to shrink just after the treatment and percentage of seed with normal chalazal haustorium decreasedrapidly in all treatments. Based on these results, the process of seed abortion as a result of seed injury and its relationship between embryo growth and fruit drop is discussed.モモ‘紅清水’において種子への傷害が誘起する落果と種子発育との関係を検討した．種子への傷害（傷害処理）と して果実の縫合線と逆の位置から種皮まで外径2.5㎜のドリルを満開後40，50，60，72および80日に挿入した．落果や 種子発育と関係するジベレリンとパクロブトラゾールの種子への注入（注入処理）も傷害処理後に行った．傷害処理， 注入処理ともに，満開後40～60日処理には処理した果実が全て落下したのに対し，72および80日処理では，いずれも 落下しなかった．60日処理では，果実および種子の新鮮重がともに処理３日後に減少し始めた．胚乳と胚の形態を満 開後60，72および80日処理間で比較した．胚乳および胚の成長は60日処理では処理３日後に停止したが，72日処理で は胚が処理５日後まで成長し続けた．胚乳と胚の細胞核の崩壊は，処理時の胚長が５㎜未満であった60日処理では， 処理３日後に生じた．一方，処理時の胚長が約８㎜であった72日処理では，胚乳における細胞核の崩壊は60日処理と 同様の傾向で生じたが，胚の細胞核は崩壊しなかった．60日処理において合点側吸器の形態を観察したところ，吸器 は傷害処理や注入処理によって直ちに収縮し始め，正常な合点側吸器を持つ種子の割合は急速に低下した．これらの 結果に基づいて，種子への傷害による種子の退化過程ならびに胚の成長と落果との関係を考察し

Effects of Pruning Levels on Physiological Fruit Drop and Fruit Development in 'Shimizuhakuto' Peach

Using 'Shimizuhakuto' peach trees maintained by light (LP) and heavy (HP) prunings, fruit development and shoot growth were investigated in relation ro physiological fruit drop. The rate of split-pit fruits was significantly lower in LP trees than in HP trees, and the rate of dropped fruit in the former was also lower than in the latter although there was no significant. In LP trees shoot growth ceased by the end of May, while in HP trees the shoots continued to elongate until the end of June, corresponding to the end of stage 2 of fruit development. There was no significant difference in enlargement of normal and pit-split fruits between HP and LP trees. However, the enlargement of dropped fruits was more vigorous than those of pit-split fruit in HP and was by contrast inferior in LP trees. The growth of embryo in the fruits of HP trees was smaller than in those of LP trees from the beginning of stage 2, and the size of embryos of pit-split fruit were less than 50% in size compared to normal fruits in HP trees during stage 3. On the other hand, embryo of pit-split fruits in LP trees showed a similar growth to normal fruits until the end of stage 2. There was no difference in the size of endosperm and embryo of dropped fruit between HP and LP trees. Based on these results, ther possible causes whereby light pruning might decrease physiological fruit drop in peach are discussed.モモ‘清水白桃’について，生理的落果の軽減に有効とされている弱剪定樹の果実発育や新梢生長の様相を慣行剪定樹と比較した．弱剪定樹では核割れの発生程度が慣行剪定樹よりも有意に低く，落果率も低い傾向であった．新梢生長は，弱剪定樹では５月末までにほぼ停止したのに対し，慣行剪定樹では果実発育第２期末の６月末まで続いた．正常果と核割れ果の果実肥大には両剪定樹間に差がなかったが,落下した果実の肥大は，慣行剪定樹では核割れ果よりも旺盛であったのに対し，弱剪定樹では逆に劣った．胚乳の生長には両剪定樹間に違いがなかった．胚の生長は，慣行剪定樹では第２期初め以降弱剪定樹よりも劣り，また核割れ果の胚は正常果の半分以下の大きさであった．一方，弱剪定樹では核割れ果の胚も第２期末までは正常果と同様の生長を示した．落果した果実の胚乳と胚の大きさには両剪定樹間に差がなかった．これらの結果から，弱剪定樹で生理的落果が少ない理由について考察した