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.     

Asymmetric synthesis of abietane diterpenoids via B-alkyl Suzuki-Miyaura coupling. Formal total asymmetric synthesis of 12-deoxyroyleanone and cryptoquinone

A convergent synthetic strategy for abietane diterpenoids via B-alkyl Suzuki-Miyaura coupling and Lewis acid-mediated cyclization reactions is established. Asymmetric total synthesis of 12-deoxyroyleanone, an antileishmanial diterpene, is described.     

Synthesis and absolute configuration of cordiaquinone K, antifungal and larvicidal meroterpenoid isolated from the Panamanian plant, Cordia curassavica

Total synthesis of cordiaquinone K, a new antifungal and larvicidal meroterpenoid, is reported. The absolute configuration of cordiaquinone K was confirmed by the synthesis.     

Synthesis of benzimidazole derivatives as potential H1-antihistaminic agents

Several types of benzimidazole derivatives were prepared and were screened for H ₁-antihistaminic activity. Most of the compounds showed potent antihistaminic activity in vitro. Among them 2-[(1-piperazinyl)methyl]-benzimidazoles 14 and 2-[(1-homopiperazinyi)methyl]benzimidazoles 15 exhibited potent activity also in vivo.     

Effect of the mobility of ligands in polyrotaxanes on order structure of water clusters

The effect of the mobility of ligands (maltose groups) in the polyrotaxanes (pRXs) on the structure of the surrounding water molecules was investigated. Raman spectra of collective OH stretching vibration of water molecules in aqueous solutions of maltose-pRX conjugates with different alpha-cyclodextrin (alpha-CD) threading on a poly(ethylene glycol) (PEG) chain was measured. The mobility of maltose groups was estimated by measuring the relaxation time T2 of the C1 protons in maltose groups bound on alpha-CD by NMR experiment. A positive correlation between the Raman intensity of the collective band and the relaxation time T2 was obtained. This result indicates that the degree of order of the water clusters is higher as the mobility of maltose groups increases in these conjugate solutions. It is suggested that rapid motion of maltose groups in the pRX conjugate can contribute to preserving ordered structure of the bulk water clusters.     

Regioselective Borylation of Porphyrins by C?H Bond Activation under Iridium Catalysis to Afford Useful Building Blocks for Porphyrin Assemblies

Highly regioselective and efficient borylation of a variety of porphyrins has been achieved by reaction with bis(pinacolato)diboron through C? H bond activation under iridium catalysis on the basis of the synthetic protocol developed by Miyaura, Hartwig, and Smith. A boryl group can be selectively introduced at sterically uncongested positions in the peripheral aryl groups of porphyrin substrates whose peripheral β‐positions are sterically hindered. Curiously, β substituents adjacent to the aryl group to be borylated have unexpectedly large effects on the regioselectivity, because the iridium catalyst can discriminate between subtle steric differences. Chemoselective borylation was also achieved for several functionalized porphyrins. This borylation protocol can be applied to various monomeric and oligomeric functional porphyrins, hence offering an efficient route to elaborate multiporphyrin‐based molecular constructs.     

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.     

A variational principle for doubly nonlinear evolution

The weighted energy-dissipation principle stands as a novel variational tool for the study of dissipative evolution and has already been applied to rate-independent systems and gradient flows. We provide here an example of its application to a specific yet critical doubly nonlinear equation featuring a super-quadratic dissipation.