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.     

Fisher Information of Free-Electron Landau States

An electron in a constant magnetic field has energy levels, known as the Landau levels. One can obtain the corresponding radial wavefunction of free-electron Landau states in cylindrical polar coordinates. However, this system has not been explored so far in terms of an information-theoretical viewpoint. Here, we focus on Fisher information associated with these Landau states specified by the two quantum numbers. Fisher information provides a useful measure of the electronic structure in quantum systems, such as hydrogen-like atoms and under some potentials. By numerically evaluating the generalized Laguerre polynomials in the radial densities, we report that Fisher information increases linearly with the principal quantum number that specifies energy levels, but decreases monotonically with the azimuthal quantum number m. We also present relative Fisher information of the Landau states against the reference density with m=0, which is proportional to the principal quantum number. We compare it with the case when the lowest Landau level state is set as the reference.     

Synthesis and toxicity assay of ceramic nanophosphors for bioimaging with near-infrared excitation

Yttrium hydroxyl carbonate (Y(OH)CO₃) precursors were synthesized by the homogeneous co-precipitation method in the presence of polyacrylic acid (PAAc). Resultant precursor particle size is about 15–20 nm with narrow size distribution whereas the particle size is smaller than those acquired by the conventional homogeneous precipitation method. Effective decrease of Y(OH)CO₃ particle size was found to be higher for the presence of weak polyanionic ionomer such as PAAc than the presence of strong polyanionic ionomer such as sodium polystyrene sulfonate (PSS). It was observed that the morphology and size of the precursors are almost unchanged after the calcination process. Er³⁺ doped Y₂O₃ nanoparticles were synthesized by PAAc assisted homogeneous co-precipitation method showed bright green (550 nm) and red (660 nm) upconversion (UC) as well as near-infrared (NIR) fluorescence (1550 nm) under 980-nm excitation. UC and NIR fluorescence bioimaging and in-vitro cytotoxicity assay of Er³⁺ doped Y₂O₃ nanoparticles were successfully attempted with commercially available macrophages and B-cell hybridomas. Cellular uptake of nanoparticles is evidenced from bright field, UC and NIR fluorescence images of macrophages.     

Rhodium-Catalyzed Highly Diastereo- and Enantioselective Synthesis of a Configurationally Stable S-Shaped Double Helicene-Like Molecule

An S-shaped double helicene-like molecule (>99 % ee), possessing stable helical chirality, has been synthesized by the rhodium(I)/difluorphos complex-catalyzed highly diastereo- and enantioselective intramolecular double [2+2+2] cycloaddition of a 2-naphthol- and benzene-linked hexayne. The collision between two terminal naphthalene rings destabilizes the helical chirality of the S-shaped double helicene-like molecule, but the introduction of two additional fused benzene rings significantly increases the configurational stability. Thus, no epimerization and racemization were observed even at 100 °C. The enantiopure S-shaped double helicene-like molecule forms a trimer through the multiple C−H⋅⋅⋅π and C−H⋅⋅⋅O interactions in the solid-state. The trimers stack to form columnar packing structures, in which neighboring stacks have opposite dipole directions. The accumulation of helical structures in the same direction in the S-shaped double helicene-like molecule enhanced the chiroptical properties.