Nonlinear oscillations of fourth order quasilinear ordinary differential equations

We consider fourth order quasilinear ordinary differential equations. Firstly, we classify positive solutions into four types according to their asymptotic properties. Then we derive existence theorems of positive solutions belonging to each type. Using these results, we can obtain an oscillation criterion, which is our main objective. Moreover, applying such criteria for ordinary differential equations to binary elliptic systems, we establish nonexistence theorems for positive solutions.     

Significant substitution effects in dipolar and non-dipolar supercritical fluids

Vibrational Raman spectra of C=C stretching modes of ethylene derivates (cis-C(2)H(2)Cl(2), cis-stilbene, and trans-stilbene) were measured in supercritical fluids along an isotherm as functions of their densities. The substitution effect of the Raman shift is so significant that a difference among three solutes can be 20 times and is observed similarly in dipolar (CHF(3)) and non-dipolar (CO(2)) fluids. In particular, the shifts of trans-stilbene were enormously large among all systems for studies of vibrational spectroscopies of supercritical fluids and were equivalent to those of typical hydrogen-bonded fluids. Such large shifts arising from the significant attractive energy between solute and solvent molecules were attributed to a site-selective solvation around a phenyl group, which was driven by a dispersion force in the absence of steric hindrance. We found that the absence of steric hindrance causes the significant local density augmentation. To the best of our knowledge, Raman experiments and their theoretical analysis are the first ones quantifying how the difference of steric hindrance produces solvation structures in solution as well as supercritical solutions.     

Efficient synthesis of biazoles by aerobic oxidative homocoupling of azoles catalyzed by a copper(I)/2-pyridonate catalytic system

A highly efficient and convenient CuCl/2-pyridonate catalytic system for oxidative homocoupling of azoles affording a biazole product has been developed. With this system, a variety of biazoles have been effectively synthesized in good to excellent yields in the presence of a very small amount of copper catalyst (1.0 mol%). It was feasible to employ air as a green oxidant.     

Monitoring the aggregation processes of amyloid-β using a spin-labeled, fluorescent nitroxyl radical

Amyloid nitroxyl radical (nitroxide) ligands were used to detect amyloid-β fibrils, the main constituents of senile plaques in Alzheimer's disease, using anisotropic ESR spectra, and were found to affect the aggregation process due to the radical functionality. These compounds have great potential as novel and multifunctional probes, combining spin labels, spin probes, and fluorescence probes.     

Fluorescence studies on phenylene moieties embedded in a framework of periodic mesoporous organosilica

The excited state characteristics of phenylene (Ph)-bridged periodic mesoporous organosilica (PMO) powders with crystal-like and amorphous wall structures are investigated. Crystal-like Ph-PMO has a molecular ordering of the bridging organic moieties with intervals of 0.76 and 0.44 nm parallel and perpendicular to the mesochannel direction, respectively, whereas amorphous Ph-PMO has no molecular-level periodicity in the wall. Fluorescence from the exciton and excimer of the Ph moieties and the defect center in the silicate network were detected at room temperature, but fluorescence from the excimer and the defect center were not detected at 77 K for crystal-like Ph-PMO dispersed in a methanol/ethanol mixed solvent. The decay curve of the exciton fluorescence of crystal-like Ph-PMO at room temperature was analyzed successfully using a one-dimensional diffusion model quenched by the defect center and the excimer site. The results were discussed in comparison with those for the crystal-like biphenylene-bridged PMO reported in the preceding paper (Yamanaka et al., Phys. Chem. Chem. Phys., 2010, 12, 11688-11696). The existence of excited states with various conformations including ground state dimers or aggregates of the Ph moieties was suggested for amorphous Ph-PMO. It was clearly apparent that the differences in the excited state dynamics reflected the differences in the molecular-level structure in the wall.     

Synthesis and crystal structure of disiloxane-1,3-diols and disiloxane-1,1,3,3-tetraol

1,3-Dimethyl- or 1,3-divinyl-1,3-di-t-butoxydisiloxane-1,3-diol and 1,3-diphenyldisiloxane-1,1,3,3-tetraol were synthesized by hydrolysis of the corresponding diisocyanatodisiloxanes and tetrachlorodisiloxane. The disiloxanediols were soluble in common organic solvents and thermally very stable, therefore, they could be sublimed without decomposition. X-ray crystallography showed that the disiloxane-1,3-diols in the crystal feature a 1.21 nm diameter columnar array with intermolecular hydrogen bonding. The disiloxane-1,1,3,3-tetraol, on the other hand, revealed molecules with a gauche- and anti-conformation depending on crystallization method which formed a columnar array and a sheet-like array, respectively. It was confirmed that these silanols can be potential building blocks for ladder oligosilsesquioxanes.     

Vertices of Degree 5 in a Contraction Critically 5-connected Graph

An edge of a k-connected graph is said to be k-contractible if the contraction of the edge results in a k-connected graph. A k-connected graph with no k-contractible edge is said to be contraction critically k-connected. We prove that a contraction critically 5-connected graph on n vertices has at least n/5 vertices of degree 5. We also show that, for a graph G and an integer k greater than 4, there exists a contraction critically k-connected graph which has G as its induced subgraph.     

Acyclic stereocontrol via asymmetric [2,3]-Wittig rearrangement with high enantio- and erythro-selectivity and its use in the chiral synthesis of insect pheromones

Such an asymmetric [2,3]-Wittig variant that is both highly enantio- and erythro-selective is described within the context of the chiral synthesis of the insect pheromones, (3$\text{S}$, 4$\text{S}$)-4-methyl-3-heptanol and ($\text{S}$)-4-methyl-3-heptanone.     

s-channel discontinuities of reggeon diagrams with planar vertices

The mutual relations between s-channel discontinuities of reggeon diagrams with planar triple-Regge vertices are discussed. It is shown that, in general, contributions coming from different cuttings are not simply related to each other as certain vertices acquire non-trivial phase factors depending on the nature of the cutting. For diagrams with only triple-Regge vertices this phase may be related to the triple-Regge phase. The complete four-reggeon vertices are not known in general. An approximation is considered which amounts to preserving only the absorptive part of triple- or four-reggeon amplitudes in certain parts of the diagrams. This approximation turns out to be equivalent to a simple absorbed multiperipheral model. The problem of exchange degeneracy breaking within the dual unitarisation Scheme is briefly discussed as an example.