Nonlinear diffusion equations driven by the p(·)-Laplacian

This paper is concerned with nonlinear diffusion equations driven by the p(·)-Laplacian with variable exponents in space. The well-posedness is first checked for measurable exponents by setting up a subdifferential approach. The main purposes are to investigate the large-time behavior of solutions as well as to reveal the limiting behavior of solutions as p(·) diverges to the infinity in the whole or in a subset of the domain. To this end, the recent developments in the studies of variable exponent Lebesgue and Sobolev spaces are exploited, and moreover, the spatial inhomogeneity of variable exponents p(·) is appropriately controlled to obtain each result.     

Structures and Reaction Mechanism of Novel Metal-Carbene Complexes Derived from Hypervalent Diazadiselenathiapentalenes

Abstract

Novel metal-carbene complexes (4) with a metallapentalene framework have been obtained from hypervalent diazadiselenathiapentalenes (3) by treating with Pt(PPh₃)₄, Pd(PPh₃)₄ and RhCl(PPh₃)₃. X-Ray investigations revealed that the central hypervalent sulfur atom in 3 was substituted by a metal atom to form M-Se bonds in the resultant metallapentalene framework.     

Rapid reduction of titanium dioxide nano-particles by reduction with a calcium reductant

Micro-, submicron-, and nano-scale titanium dioxide particles were reduced by reduction with a metallic calcium reductant in calcium chloride molten salt at 1173 K, and the reduction mechanism of the oxides by the calcium reductant was explored. These oxide particles, metallic calcium as a reducing agent, and calcium chloride as a molten salt were placed in a titanium crucible and heated under an argon atmosphere. Titanium dioxide was reduced to metallic titanium through a calcium titanate and lower titanium oxide, and the materials were sintered together to form a micro-porous titanium structure in molten salt at high temperature. The reduction rate of titanium dioxide was observed to increase with decreasing particle size; accordingly, the residual oxygen content in the reduced titanium decreases. The obtained micro-porous titanium appeared dark gray in color because of its low surface reflection. Micro-porous metallic titanium with a low oxygen content (0.42 wt%) and a large surface area (1.794 m² g⁻¹) can be successfully obtained by reduction under optimal conditions.     

Rational Design for Cooperative Recognition of Specific Nucleobases Using β‐Cyclodextrin‐Modified DNAs and Fluorescent Ligands on DNA and RNA Scaffolds

We propose a binary fluorimetric method for DNA and RNA analysis by the combined use of two probes rationally designed to work cooperatively. One probe is an oligonucleotide (ODN) conjugate bearing a β‐cyclodextrin (β‐CyD). The other probe is a small reporter ligand, which comprises linked molecules of a nucleobase‐specific heterocycle and an environment‐sensitive fluorophore. The heterocycle of the reporter ligand recognizes a single nucleobase displayed in a gap on the target labeled with the conjugate and, at the same time, the fluorophore moiety forms a luminous inclusion complex with nearby β‐CyD. Three reporter ligands, MNDS (naphthyridine–dansyl linked ligand), MNDB (naphthyridine–DBD), and DPDB (pyridine–DBD), were used for DNA and RNA probing with 3′‐end or 5′‐end modified β‐CyD – ODN conjugates. For the DNA target, the β‐CyD tethered to the 3′‐end of the ODN facing into the gap interacted with the fluorophore sticking out into the major groove of the gap site ( MNDS and DPDB ). Meanwhile the β‐CyD on the 5′‐end of the ODN interacted with the fluorophore in the minor groove ( MNDB and DPDB ). The results obtained by this study could be a guideline for the design of binary DNA/RNA probe systems based on controlling the proximity of functional molecules.     

Synthetic study of kosinostatin aglycone: synthesis of BCDE rings using alkoxycarbonylmethylation of diazonaphthoquinone

A synthetic study of kosinostatin aglycone is reported. Synthesis of key intermediate lactone 3, which corresponds to the BCDE ring fragment, was accomplished, and the precursor BCD ring fragment 5 was synthesized via two routes. First, 5 was synthesized from 2,5-dimethoxybenzaldehyde 16 by the combination of typical known transformations including efficient application of non-aqueous OsO₄ oxidation in the presence of PhB(OH)₂. However the synthesis required 15 long steps, and its main difficulty was ortho-alkoxycarbonylmethylation of 1-naphthol. Next we attempted to apply our recently developed alkoxycarbonylmethylation of diazonaphthoquinone for the synthesis of 5, and 5 was successfully synthesized in 9 steps from the same starting compound 16. Finally, 5 was stereoselectively converted to lactone 3 via trifluoroacetic acid-mediated cyclization of the 3,4-epoxycylohexanecarboxylic acid derivative.     

Electrospinning of nylon-6,6 solutions into nanofibers: Rheology and morphology relationships

The relationship between the rheological properties of nylon-6,6 solutions and the morphology of their electrospun nanofibers was established. The viscosity of nylon-6,6 in formic acid(90%) was measured in the concentration range of 5 wt%-25 wt% using a programmable viscometer. Electrospinning of nylon-6,6 solutions was carried out under controlled parameters. The chemical structure, morphology and thermal properties of the obtained nanofibers were investigated using Fourier transform infrared spectroscopy(FTIR), scanning electron microscopy(SEM) and differential scanning calorimetry(DSC), respectively. Entanglement concentration(ce) was found to be 15 wt% and a power law relationship between specific viscosity and solution concentration was observed with exponents of 2.0 and 3.3 for semi-dilute unentangled(c ce) and semi-dilute entangled(c ce) regimes, respectively. The diameter and uniformity of the nanofibers were found to be dependent on the viscosity. Moreover, the average diameter of electrospun nanofibers was found to be dependent on zero shear rate viscosity and normalized concentration(c/ce) in a power law relationship with exponents of 0.298 and 0.816, respectively. For nylon-6,6 solutions, the entanglement concentration(ce = 15 wt%) provides the threshold viscosity required for the formation of a stable polymeric jet during electrospinning and producing uniform beadless fibers. For concentrations less than ce, beaded fibers with some irregularities are formed. DSC analysis showed an increase in crystallinity of all electrospun samples compared to original polymer. Furthermore, Based on FTIR spectroscopy, α phase is dominant in electrospun nanofibers and minor amount of β and γ phases is also available.     

Ultrasonic butt welding of aluminum,aluminum alloy and stainless steel plate specimens

Welding characteristics of aluminum, aluminum alloy and stainless steel plate specimens of 6.0 mm thickness by a 15 kHz ultrasonic butt welding system were studied. There are no detailed welding condition data of these specimens although the joining of these materials are required due to anticorrosive and high strength characteristics for not only large specimens but small electronic parts especially. These specimens of 6.0 mm thickness were welded end to end using a 15 kHz ultrasonic butt welding equipment with a vibration source using eight bolt-clamped Langevin type PZT transducers and a 50 kW static induction thyristor power amplifier. The stainless steel plate specimens electrolytically polished were joined with welding strength almost equal to the material strength under rather large vibration amplitude of 25 microm (peak-to-zero value), static pressure 70 MPa and welding time of 1.0-3.0 s. The hardness of stainless steel specimen adjacent to a welding surface increased about 20% by ultrasonic vibration.     

Phonon effects on oscillator strengths and ƒ-sum of a defect center

We first propose a simple method to deal with the electron-phonon interaction for all states involved in optical transitions and then use the results obtained to derive the equations of the oscillator strengths ? and ?-sum for a defect center including the phonon effects adequately. The derived results are applied to the F center in KCl and discussed in relation to those excluding the dynamical phonon effect.     

Photosensitized oxygenation of phenylpyruvic acid derivatives as a model for p-hydroxyphenylpyruvate dioxygenase

Dye-sensitized photooxygenation of enol ethers of methyl phenylpyruvates ($\text{3}$) produced diendoperoxides $\text{4}$ in aprotic solvents, whereas in methanol hydroxylated product $\text{6}$ was obtained. The reaction scheme is discussed in comparison uith that for the enzymic transformation.