Time periodic solutions to the Navier–Stokes equations in the rotational framework

We consider the Navier–Stokes equations in the rotational framework with the time periodic external force. We give sufficient conditions on the size of the external forces for the existence of time periodic solutions in terms of the Coriolis parameter. It follows from our conditions that the unique existence of time periodic solutions is guaranteed for large external forces provided the speed of rotation is sufficiently fast.     

Large-scale forcing with less communication in finite-difference simulations of stationary isotropic turbulence

This study proposes a new forcing scheme suitable for massively-parallel finite-difference simulations of stationary isotropic turbulence. The proposed forcing scheme, named reduced-communication forcing (RCF), is based on the same idea as the conventional large-scale forcing scheme, but requires much less data communication, leading to a high parallel efficiency. It has been confirmed that the RCF scheme works intrinsically in the same manner as the conventional large-scale forcing scheme. Comparisons have revealed that a fourth-order finite-difference model run in combination with the RCF scheme (FDM-RCF) is as good as a spectral model, while requiring less computational costs. For the range 80 < Re_λ < 540, where Re_λ is the Taylor microscale-based Reynolds number, large computations using the FDM-RCF scheme show that the Reynolds dependences of skewness and flatness factors have similar power-laws as found in previous studies.     

Comparisons of O-acylation and Friedel-Crafts acylation of phenols and acyl chlorides and Fries rearrangement of phenyl esters in trifluoromethanesulfonic acid: effective synthesis of optically active homotyrosines

Reactions involving phenol derivatives and acyl chlorides have to be controlled for competitive O-acylations and C-acylations (Friedel-Crafts acylations and Fries rearrangements) in acidic condition. The extent for these reactions in trifluoromethanesulfonic acid (TfOH), which is used as catalyst and solvent, is examined. Although diluted TfOH was needed for effective O-acylation, concentrated TfOH was required for effective C-acylations in mild condition. These results have been applied to the novel synthesis of homotyrosine derivatives. Both Fries rearrangement of N-TFA-Asp(OBn)-OMe and Friedel-Crafts acylation of phenol with N-TFA-Asp(Cl)-OMe in TfOH afforded the homotyrosine skeleton, followed by reduction and deprotection afforded homotyrosines maintaining stereochemistry of Asp as an optically pure form.     

Synthesis of plakevulin A and structure-activity relationships of its related compounds against DNA polymerases

Synthesis of plakevulin A and structure-activity relationships of its related compounds against DNA polymerases is described. We have achieved a total synthesis and revised the structure of plakevulin A. Several analogues including untenone A, manzamenone A, and optically active plakevulin A, were prepared and tested with an enzyme inhibition assay for mammalian DNA polymerases. The effect of the methyl ester moiety, and the substituents at the 1- and 4-positions of plakevulin A on DNA polymerase activities are discussed.     

Regioselective Nucleophilic Functionalization of Antiaromatic Nickel(II) Norcorroles

Treatment of antiaromatic nickel(II) norcorrole with potassium cyanide provided nickel(II) 3‐cyanonorcorrole with perfect regioselectivity without the help of a catalyst. The reaction of the nickel(II) norcorrole with phenol or thiophenol in the presence of a base also yielded substitution products. The antiaromatic 16π conjugation system in the norcorrole core was preserved in the functionalized products. Introduction of phenylthio groups significantly decreased the HOMO–LUMO gap and enhanced the near IR absorption property.