Convergence of solutions for the fractional Cahn–Hilliard system

This paper deals with the Cauchy–Dirichlet problem for the fractional Cahn–Hilliard equation. The main results consist of global (in time) existence of weak solutions, characterization of parabolic smoothing effects (implying under proper condition eventual boundedness of trajectories), and convergence of each solution to a (single) equilibrium. In particular, to prove the convergence result, a variant of the so-called ?ojasiewicz–Simon inequality is provided for the fractional Dirichlet Laplacian and (possibly) non-analytic (but $C^1$) nonlinearities.     

PREPARATION AND CHARACTERIZATION OF SHISH-KEBAB TYPE LIQUID CRYSTALLINE POLY（p-PHENYLENEVINYLENE）

Novel shish-kebab type liquid crystalline poly（p-phenylenevinylene） derivatives were synthesized by Stille coupling reaction from 2,5-bis[（4-n-alkoxyl）benzoyloxy]1,4-dibromobenzene （monomer l） and 1,2-bis（tributylstannyl） ethylene （monomer 2）. The polymers with alkoxy groups are soluble in common organic solvents and exhibit blue fluorescence. Both the cast film and the annealed film have large red-shifts in fluorescence spectra and show yellow fluorescence. The polymers with CN and NO2 groups show poor solubility and green fluorescence. All the polymers possess liquid crystalline smectic phases. The melting point （Tm） of the polymers decreases when the length of the alkoxy tails of the mesogenic units increases. The polymers are easily aligned under a magnetic field of 10 Tesla. It is found that the conjugated backbone and LC side chain are aligned perpendicular and parallel to the magnetic field, respectively. The polymers show optical dichroism in fluorescence spectra, suggesting that they are available for advance materials with linear optical polarization.     

Trans-hydrometalation of alkynes by a combination of InCl3 and DIBAL-H: one-pot access to functionalized (Z)-alkenes

[reaction: see text] Triethylborane-induced hydrometalation of alkynes proceeds in an anti manner to afford the corresponding (Z)-alkenylmetal compounds stereoselectively, where dichloroindium hydride would play a key role. A variety of functional groups including hydroxy, carbonyl, and carboxy groups were tolerant under the reaction conditions. Following iodolysis and cross-coupling reaction of the (Z)-alkenylmetal species show the usefulness of this strategy.     

Stability of crown ether complexes: a mo theoretical study

Calculation using CNDO/2 method have been performed for the crown ethers and their cation complexes. The photoelectron spectra of 18-crown-6 and 12-crown-4 are well described by the present MO calculations. The orbital interactions between the crown ligand and the cation indicate the importance of the charge transfer interaction for the complex formation. The destabilization energy due to the ring-shrinking (~ 0.5 eV) is very small compared with the complexation energy (5–8 eV). The stability of the complex was reasonably explained by the considering the hydrated species of the cation and the complex, indicating the important role of the solvation effect in the selectivity of the crown ether to the cation.     

Radical alkenylation of alpha-halo carbonyl compounds with alkenylindiums

Alkenylation reaction of alpha-halo carbonyl compounds with alkenylindiums proceeded via a radical process in the presence of triethylborane. Unactivated alkene moieties as well as a styryl group could be introduced by this method. The geometry of the carbon-carbon double bonds of the alkenylindiums was retained. Preparation of an alkenylindium via a hydroindation of 1-alkyne followed by radical alkenylation established an efficient one-pot strategy. [reaction: see text]     

Chemical reaction dynamics of PeCB and TCDD decomposition: A tight‐binding quantum chemical molecular dynamics study with first‐principles parameterization

The decomposition reaction dynamics of 2,3,4,4′,5‐penta‐chlorinated biphenyl (2,3,4,4′,5‐PeCB), 3,3′,4,4′,5‐penta‐chlorinated biphenyl (3,3′,4,4′,5‐PeCB), and 2,3,7,8‐tetra‐chlorinated dibenzo‐p‐dioxin (2,3,7,8‐TCDD) was clarified for the first time at atomic and electronic levels, using our novel tight‐binding quantum chemical molecular dynamics method with first‐principles parameterization. The calculation speed of our new method is over 5000 times faster than that of the conventional first‐principles molecular dynamics method. We confirmed that the structure, energy, and electronic states of the above molecules calculated by our new method are quantitatively consistent with those by first‐principles calculations. After the confirmation of our methodology, we investigated the decomposition reaction dynamics of the above molecules and the calculated dynamic behaviors indicate that the oxidation of the 2,3,4,4′,5‐PeCB, 3,3′,4,4′,5‐PeCB, and 2,3,7,8‐TCDD proceeds through an epoxide intermediate, which is in good agreement with the previous experimental reports and consistent with our static density functional theory calculations. These results proved that our new tight‐binding quantum chemical molecular dynamics method with first‐principles parameterization is an effective tool to clarify the chemical reaction dynamics at reaction temperatures. © 2004 Wiley Periodicals, Inc. Int J Quantum Chem, 2005