Bifurcation phenomena associated to a class of p-Laplacian like operators

 Global bifurcation of positive solutions for some degenerate quasilinear elliptic problems is considered. The uniform estimate of the gradient of weak solutions is given. This estimate is crucial in our arguments. Received: 10 August 2001 Supported in part by Grant-in-Aid for Scientific Research (No. 11640207), Ministry of Education, Science, Sports and Culture, Japan. Mathematics Subject Classification (2000): 35B32, 35J25, 35J70     

Crystal structure of the clathrate of 5,12-dihydro-5,12-o-benzenonaphthacene-1,4-dione with benzene (2:1).

In the crystal of the title compound, the quinone fragment of the host (1) participates in weak D-A interactions with a neighboring naphthalene moiety of 1 and with the guest molecule via fairly short intermolecular face-to-face contacts. An intermolecular electrostatic interaction between a quinone-oxygen atom and a neighboring quinone ring is suggested by short O...C contacts. There exist several C-H...O hydrogen bonds, one of which seems to contribute to the formation of a centrosymmetric dimer of 1.     

13C-NMR studies on the cevanine alkaloids : the application of 13C-NMR spectrum for structure elucidation of new alkaloids,baimonidine and isoverticine

The ¹³C-NMR spectra of seven cavanine alkaloids isolated from Veratrum and Fritillaria plants were measured and their signals were assigned, and these results were applicated for structure elucidation of two new cevanine alkaloids, baimonidine and isoverticine, isolated from mature Fritillaria verticillata.     

Dioxopyrrolines. LXII. Diels-Alder reaction of 1-Aryl-4- and 5-methoxycarbonyl-1H-pyrrole-2,3-diones with various 1,3-dienes

Two new dioxopyrrolines (1-aryl-4-methoxycarbonyl-1H-pyrrole-2,3-dione 6 and the 5-methoxycarbonyl isomer 8) behaved as good dienophiles to some kind of 1,3-dienes examined. In most cases, the products were explained by the reaction where the largest lobe of HOMO of dienes reacted to the larger LUMO of dienophiles in an expected cis-endo manner. However, in the reactions of 8 with alkylbutadienes, piperylene and isoprene, abnormality in the reaction was observed, which was well explained by taking account of steric factors.     

Synthesis of 1,8- and 2,8-dihydrocycloheptapyrazol-8-one derivatives by the reactions of 3-acetyltropolone and its methyl ethers with phenylhydrazine

3-Acetyltropolone ( 1 ) reacted with phenylhydrazine to give 3-acetyltropolone phenylhydrazone ( 3 ) and 3-methyl-1-phenyl-1,8-dihydrocycloheptapyrazol-8-one ( 4 ). The former ( 3 ) cyclized to afford the latter ( 4 ). The reaction of 3-acetyl-2-methoxytropone ( 2a ) with phenylhydrazine gave 4 , 3-methyl-2-phenyl-2,8-dihydrocyclo-heptapyrazol-8-one ( 5 ), and 3-methyl-2-phenyl-2,8-dihydrocycloheptapyrazol-8-one phenylhydrazone ( 6 ). The compound ( 5 ) reacted with phenylhydrazine to afford 6 . The reaction of 7-acetyl-2-methoxytropone ( 2b ) with phenylhydrazone gave 7-acetyl-2-methoxytropone phenylhydrazone ( 7 ), 7-acetyl-2-(N′-phenylhydrazino)-tropone phenylhydrazone ( 8 ), 3-methyl-1-phenyl-1,8-dihydrocycloheptapyrazol-8-one phenylhydrazone ( 9 ), and 6 . The compound ( 7 ) was heated to afford 4 and reacted with phenylhydrazine to afford 8 and 9 . The compound ( 8 ) was also refluxed to give 9 .     

Synthesis of 32‐phenyl‐substituted methyl E/Z‐pyropheophorbide‐a's from methyl E/Z‐pyropehophorbide‐a 131‐ketoximes

Methyl E/Z‐pyropheophorbide‐a 13¹‐ketoximes 2a,b and their O‐acetyl derivatives 3a,b were oxidized with osmium(VIII) oxide to give aldehydes 4a,b and 5a,b , respectively. The Wittig reactions of the aldehyde chlorines 4a,b and 5a,b with benzyltriphenylphosphonium chloride were performed to form the corresponding methyl (3¹E/Z,13¹E/Z)‐3²‐phenylpyropheophorbide‐a 13¹‐ketoximes 6aa‐bb and their O‐acetyl derivatives 7aa‐bb ; hydrolysis of these ketoximes 6aa,ba and 6ab,bb in formic acid produced methyl (E/Z)‐3²‐phenylpyropheophorbide‐a's 8a,b .     

An efficient novel synthesis of beta-(azuleno[1,2-b]benzothienyl)- and beta-(azuleno[2,1-b]benzothienyl)-alpha,beta-unsaturated ketones by the tropylium ion-mediated intramolecular furan ring-opening reaction and X-ray investigation of methyl ketone derivative

Intramolecular reaction of 2-tropylio-3-(5-substituted 2-furyl)benzothiophenes (3), prepared from the corresponding 2-cycloheptatrienyl-3-(5-substituted 2-furyl)benzothiophenes (2), afforded the beta-(azuleno[1,2-b]benzothienyl)-alpha,beta-unsaturated ketones (4), which are otherwise difficult to obtain, in moderate yields. The reaction involves a ring-opening process of the furan ring by intramolecular attack of the tropylium ion onto the 2-position of the furan ring. Similarly, beta-(azuleno[2,1-b]benzothienyl)-alpha,beta-unsaturated ketones (8) were obtained from the corresponding 3-tropylio-2-(5-substituted 2-furyl)benzothiophenes (7) albeit in lower yields. The molecular and crystal structures of the methyl ketone derivative, 8a, are discussed on the basis of X-ray structure analysis.     

A characteristic ribbon-like supramolecular structure and intermolecular D–A interactions in the crystals of triptycenequinones, triptycene-TCNQs and their clathrates as studied by X-ray investigations

A common ribbon-like structure was found in the crystals of triptycenequinones (TPQs), triptycene-TCNQs (TP-TCNQs) and their clathrates. The characteristic structure can be regarded as a supramolecular unit the formation of which is aided by weak intermolecular D–A interactions. This view is supported by the host–guest D–A interactions appeared in the crystals of the clathrates of 5,8-dimethyl-TPQ and 5,8-dimethoxy-TP-TCNQ. Intermolecular C–HO hydrogen bonds seem to be present in TPQ derivatives.     

Friedländer reaction of 3-acetyltropolones: Synthesis of naphthyridinyl- and allied heterocyclic-substituted tropolones

Five 3-acetyltropolones reacted with 2-amino-3-pyridinecarbaldehyde to afford the corresponding 3-(1,8-naphthyridin-2-yl)tropolones in excellent yields. In a similar manner, 1,6-naphthyridin-2-yl-,1,7-naphthyridin-2-yl-, 6-pyrido[2,3-b]pyrazinyl-, and 1-methyl-6-pyrazolo[5,4-b]pyridyl-substituted tropolones were prepared. Reactivities of amino-substituted heteroarenecarbaldehydes in these reactions and properties of the products are also discussed.