Existence of infinitely many solutions for sublinear elliptic problems

Let N?2 and be a bounded domain. In the present paper, we show the existence of infinity many solutions of nonlinear Dirichlet boundary value problem

     

Internal Rotation of the Hydroxyl Group in Isopropanol and the Chirality of the Gauche Form: Fourier Transform Microwave Spectroscopy of (CH(3))(2)CHOD

The rotational spectrum of the deuterated isopropanol (CH(3))(2)CHOD has been observed by Fourier transform microwave spectroscopy and analyzed to yield tunneling splitting of 4431.4613 (17) MHz, between the antisymmetric and the symmetric gauche forms, which is much larger than the 2400 MHz estimated from the internal-rotation potential function reported in the literature. The potential function for the OH internal rotation has been examined in view of the discrepancy between the observed and estimated tunneling splitting, and it was accounted for by taking into account isotope effects on the potential constants. The deuterium quadrupole coupling effect has been included together with the Coriolis terms in the off-diagonal block of the Hamiltonian matrix for the gauche form. The deuterium quadrupole coupling constants obtained for the trans form were employed to calculate the components of the coupling constants as functions of the internal-rotation angle, and the components at around 120 degrees were compared with the values observed for the gauche form, thereby leading to unambiguous determination of the signs of the constants in the off-diagonal block; the signs are not obtainable from an ordinary analysis of the rotational spectra. The chirality of the gauche form was discussed by placing special emphasis on the effect of intermolecular interactions between two chiral molecules. Copyright 2001 Academic Press.     

Asymptotic stability of nonlinear wave for the compressible Navier-Stokes equations in the half space

In the present paper, we investigate the large-time behavior of the solution to an initial-boundary value problem for the isentropic compressible Navier-Stokes equations in the Eulerian coordinate in the half space. This is one of the series of papers by the authors on the stability of nonlinear waves for the outflow problem of the compressible Navier-Stokes equations. Some suitable assumptions are made to guarantee that the time-asymptotic state is a nonlinear wave which is the superposition of a stationary solution and a rarefaction wave. Employing the L²-energy method and making use of the techniques from the paper [S. Kawashima, Y. Nikkuni, Stability of rarefaction waves for the discrete Boltzmann equations, Adv. Math. Sci. Appl. 12 (1) (2002) 327-353], we prove that this nonlinear wave is nonlinearly stable under a small perturbation. The complexity of nonlinear wave leads to many complicated terms in the course of establishing the a priori estimates, however those terms are of two basic types, and the terms of each type are “good” and can be evaluated suitably by using the decay (in both time and space variables) estimates of each component of nonlinear wave.     

Magnetic dilution effect on the charge transfer phase transition and the ferromagnetic transition for an iron mixed-valence complex, (n-C3H7)4N[FeII1−xZnIIxFeIII(dto)3] (dto = C2O2S2)

Iron mixed-valence complex, (n-C₃H₇)₄N[Fe^IIFe^III(dto)₃] (dto = C₂O₂S₂) shows a new-type of phase transition coupled with spin and charge around 120 K, where the charge transfer between the Fe^II and Fe^III sites occurs reversibly, and shows the ferromagnetic transition at 7 K. To investigate the magnetic structure and its dimensionality of (n-C₃H₇)₄N[Fe^IIFe^III(dto)₃], we have synthesized a mixed crystal system, (n-C₃H₇)₄N[Fe^II_1?xZn^II_xFe^III(dto)₃], and measured its magnetic properties. In this system, the magnetic moment is reduced with increasing of Zn ratio. Moreover, the ferromagnetic interaction changes to the antiferromagnetic one and the remnant magnetization disappears between x = 0.48 and 0.96, while the charge transfer between the Fe^II and Fe^III sites disappears above x = 0.26. In this paper, we present the magnetic dilution effect on the charge transfer phase transition and the ferromagnetic transition by means of magnetic susceptibility measurement and ⁵⁷Fe Mössbauer spectroscopy.     

Mössbauer spectroscopic study of photo-sensitive organic–inorganic hybrid system, (SP)[Fe(II)Fe(III)(dto)3](dto = C2O2S2, SP = spiropyran)

A photo-sensitive organic–inorganic hybrid system (SP)[Fe^IIFe^III(dto)₃] (SP = spiropyran, dto = C₂O₂S₂), has recently been developed, where the photo-isomerization of the intercalated spiropyran in solid state triggers the change of the magnetic properties, including the ferromagnetic transition temperature from 5 to 22 K. We performed ⁵⁷Fe Mössbauer measurement in order to probe the microscopic states of iron ions in (SP)[Fe^IIFe^III(dto)₃] and have investigated the photo-induced effect on them. The sample without UV-irradiation shows the charge transfer phase transition between 200 and 70 K and the higher and lower temperature phases coexist below 70 K, whereas the UV-irradiated sample does not undergo the charge transfer phase transition and the higher temperature phase is stable between 200 and 6 K.     

Intensely Fluorescent Azobenzenes: Synthesis,Crystal Structures,Effects of Substituents,and Application to Fluorescent Vital Stain

2‐[Bis(pentafluorophenyl)boryl]azobenzenes bearing hydrogen, methoxy, dimethylamino, trifluoromethyl, fluoro, n‐butyl, and tert‐butyldimethylsiloxy groups at the 4′‐position or methoxy and bromo groups at the 4‐position have been synthesized. The 4‐bromo group of the 2‐boryl‐4‐bromoazobenzene derivative was converted to phenyl and diphenylamino groups by palladium‐catalyzed reactions. The absorption and fluorescence properties have been investigated using UV/Vis and fluorescence spectroscopy. The 2‐borylazobenzenes emitted an intense green, yellow, and orange fluorescence, in marked contrast to the usual azobenzene fluorescence. The 4′‐siloxy derivative showed the highest fluorescence quantum yield (0.90) among those reported for azobenzenes to date. The correlation between the substituent and the fluorescence properties was elucidated by studying the effect of the substituent on the relaxation process and from DFT and TD‐DFT calculations. An electron‐donating group at the 4′‐position was found to be important for an intense emission. Application of fluorescent azobenzenes as a fluorescent vital stain for the visualization of living tissues was also investigated by microinjection into Xenopus embryos, suggesting these compounds are nontoxic towards embryos.     

Synthesis of dihydroxyoligophenylenes containing π-deficient or π-excess hetero-aromatic rings and their solvatochromic behavior

Dihydroxyoligophenylenes (HO-ArPh(m)-OHs) with 9,9-dihexyl-2,7-fluorene (Ar=Flu), 2,5-dioctyloxy-1,4-benzene (Ar=Dob), pyridine (Ar=Py), or thiophene (Ar=Th) rings were synthesized by the Suzuki coupling reaction. Absorption maxima (λ_max) of HO-ArPh(m)-OHs shifted progressively toward long wavelengths due to the expansion of the π-conjugation system with an increase in the number of benzene rings. Deprotonation of the OH groups of HO-ArPh(m)-OHs by treatment with NaH caused a bathochromic shift of λ_max. The bathochromic shift of the deprotonated species increased with the donor numbers (DNs) of the solvents. The emission peak positions of NaO-ArPh(m)-ONas depended on the DNs of the solvents; therefore, the emission color could be tuned by changing the solvent.     

Structural Characterization of a Pentacoordinate Monohydrosilane with the Apical Si-H Bond

A pentacoordinate phenyldibenzosilazocine containing the apical Si-H bond has been prepared and characterized by ¹H and ²⁹Si NMR spectra and X-ray analysis.