Guaranteed error bounds for finite element approximations of noncoercive elliptic problems and their applications

In this paper, we discuss with guaranteed a priori and a posteriori error estimates of finite element approximations for not necessarily coercive linear second order Dirichlet problems. Here, ‘guaranteed’ means we can get the error bounds in which all constants included are explicitly given or represented as a numerically computable form. Using the invertibility condition of concerning elliptic operator, guaranteed a priori and a posteriori error estimates are formulated. This kind of estimates plays essential and important roles in the numerical verification of solutions for nonlinear elliptic problems. Several numerical examples that confirm the actual effectiveness of the method are presented.     

Total synthesis of pyridomycin

The first total synthesis of pyridomycin is described including the stereocontrolled construction of the exocyclic (Z)-s-butylidene moiety in the 12-membered ring system.     

High-Pressure 19F NMR Measurements of a Series of Fluorinated Benzenes in Supercritical Carbon Dioxide

The high-pressure and high-resolution NMR cell method has been developed for precise measurements of supercritical carbon dioxide solutions. ¹⁹F NMR chemical shifts of a series of fluorinated benzenes, C₆H _n F _m (n = 6 ? m and m = 1 ～ 6) in CO₂ at dilute concentrations were measured over a wide pressure range up to 35 MPa at 314.3 K. The density dependence of the corrected chemical shift, where the bulk magnetic susceptibility contribution was subtracted, was well represented by a cubic function of CO₂ density for any fluorinated benzene. The linear coefficients, arising from pairwise intermolecular interactions, were found to be dependent on the numbers and positions of fluorine atoms in the fluorinated benzenes. The solute–solvent interaction between fluorine and CO₂ was discussed.     

Solution structures of 1-butyl-3-methylimidazolium hexafluorophosphate ionic liquid saturated with CO2: Experimental evidence of specific anion-CO2 interaction

X-ray diffraction measurements for 1-butyl-3-methylimidazolium hexafluorophosphate ionic liquid ([BMIM][PF6])-CO2 systems were carried out at high pressures with a newly developed polymer cell. The intermolecular distribution functions (g(inter)(r)) were obtained at 25 degrees C for neat [BMIM][PF6] and its solutions saturated with CO2 at 4 and 15 MPa, where the mole fractions (x) of CO2 correspond to 0.5 and 0.7, respectively. In g(inter)(r) for x = 0.5, two peaks appeared at around 2.8 and 3.2 A. These two peaks in g(inter)(r) appreciably increased for x = 0.7; moreover, there was another peak observed at approximately 3.8 A. Only assuming the correlations between CO2 and [PF6]-, it is reasonably determined that the nearest-neighbor P([PF6]-). . .C(CO2) distances are 3.57 and 3.59 A with the coordination numbers being 1.8 and 4.0 for x = 0.5 and 0.7, respectively. It is concluded that CO2 molecules are preferentially solvated to the [PF6]- anion.     

Michael and Acetal Aldol-Type Reactions on Solid-Phase. Use of the Swollen- Resin Magic Angle Spinning (SR-MAS) NMR Technique for the Development of the Solid-Phase Organic Reactions

Michael reactions of α,β-unsaturated ketones and aldol-type reactions of acetals with polymer- supported silyl enol ethers (PSSEEs) proceeded smoothly using a rare earth triflate as a catalyst. The Swollen-Resin Magic Angle Spinning (SR-MAS) NMR technique has been successfully used for the development of the reactions.     

Small-angle neutron-scattering study on a structure of microemulsion mixed with polymer networks

The structure of a microemulsion mixed with polymer networks was investigated by means of small-angle neutron scattering (SANS). The system consists of nonionic surfactant, polymer network, oil, and water. The microemulsion and the polymer network employed in this work are known to undergo temperature-induced structural transition and volume phase transition, respectively. Polymer solutions and gels were made by polymerizing monomer solutions in the presence of microemulsion droplets. In the case of a mixture of an N-isopropylacrylamide (NIPA) monomer solution and a microemulsion, the NIPA monomer was found to behave as a cosurfactant. However, polymerization resulted in a phase separation to polymer-rich and -poor phases. Interestingly, SANS results indicated that a well-developed ordered structure of oil domains was formed in polymer network and the structure was very different from its parent systems. Furthermore, the system underwent two different types of structural transitions with respect to temperature. One was originated from the structural transition of microemulsion due to the change of the spontaneous curvature and the other from the volume phase transition of the NIPA gel.     

Generation of bis(pentafluorophenyl)borane-dimethyl sulfide complex as a solution of hexane and its application to hydroboration of alk-1-yne with pinacolborane

A solution of bis(pentafluorophenyl)borane-dimethyl sulfide complex in hexane was generated by redistribution between tris(pentafluorophenyl)borane and borane-dimethyl sulfide complex. In the resulting solution a stoichiometric hydroboration of alk-1-yne with pinacolborane proceeded well at room temperature to afford (E)-alk-1-enylboronic acid pinacol ester in high yield. Bis(pentafluorophenyl)borane-dimethyl sulfide complex served as a mediator for the hydroboration.     

Intermolecular hydrophosphination of alkynes and related carbon[bond]carbon multiple bonds catalyzed by organoytterbiums

Intermolecular hydrophosphination of alkynes with diphenylphosphine is catalyzed by a Yb[bond]imine complex, [Yb(eta(2)-Ph(2)CNPh)(hmpa)(3)], to give alkenylphosphines and phosphine oxides after oxidative workup in good yields under mild conditions. This reaction is also applicable to various carbon[bond]carbon multiple bonds such as conjugated diynes and dienes, allenes, and styrene derivatives. Regio- and stereoselectivity and the scope and limitation of the present reaction clearly differ from those of the corresponding radical reaction. Instead, the reaction takes place through insertion of alkynes to a Yb[bond]PPh(2) species, followed by protonation. In fact, the Yb[bond]phosphido complex, [Yb(PPh(2))(2)(hmpa)(3)], is obtained from the imine complex and phosphine, which exhibits similar catalyst activity for the hydrophosphination. The empirical rate law is nu = k[catalyst](2) [alkyne](1)[phosphine](0) at least under the standard conditions.