Nonlinear Boundary Layers of the Boltzmann Equation: I. Existence

 We study the half-space problem of the nonlinear Boltzmann equation, assigning the Dirichlet data for outgoing particles at the boundary and a Maxwellian as the far field. We will show that the solvability of the problem changes with the Mach number ℳ^∞ of the far Maxwellian. If ℳ^∞<−1, there exists a unique smooth solution connecting the Dirichlet data and the far Maxwellian for any Dirichlet data sufficiently close to the far Maxwellian. Otherwise, such a solution exists only for the Dirichlet data satisfying certain admissible conditions. The set of admissible Dirichlet data forms a smooth manifold of codimension 1 for the case −1<ℳ^∞<0, 4 for 0<ℳ^∞<1 and 5 for ℳ^∞>1, respectively. We also show that the same is true for the linearized problem at the far Maxwellian, and the manifold is, then, a hyperplane. The proof is essentially based on the macro-micro or hydrodynamics-kinetic decomposition of solutions combined with an artificial damping term and a spatially exponential decay weight. Received: 20 April 2002 / Accepted: 4 December 2002 Published online: 21 March 2003 Communicated by H.-T. Yau     

Thermodynamic Insight into the Origin of a Calix[n]arene-[60]fullerene Interaction and its Application to a Porphyrin-[60]fullerene Energy Transfer System

The calixarene-fullerene interaction,which causes only a slight change in the absorptionspectra, has been substantiated by calorimetricmeasurements: the H° values arecomparable with those obtained from the associationconstants estimated by a spectroscopic method. Furthermore, we determined the association constantbetween homooxacalix[3]arene and [60]fullerenederivatives with a porphyrin moiety by fluorescencespectra.     

First thermally responsive supramolecular polymer based on glycosylated amino acid

In materials science, a dynamic property sensitive to an environmental change (heat, light, electric current, pH, and other chemical or physical changes) is indispensable for intelligent materials. Such organic materials, however, are very limited even in conventional polymers. This paper clearly demonstrates that, regardless of the low molecular weight, a glycosylated amino acid derivative newly screened by a combinatorial method forms a macroscopic supramolecular hydrogel that reversibly swells or shrinks in response to the external temperature. Using the unique thermal response of the present hydrogel, we carried out the controlled release of DNA and the perfect removal of bisphenol A from the polluted water. Recently, advanced supramolecular polymers, in which monomers are noncovalently connected, are expected to be highly advantageous over traditional polymers because of their tunable and recyclable characteristics. The present result newly confers a dynamic feature on the supramolecular polymers, which is desirable for the sophisticated application in many fields.     

Solubility of α-amino acids in water under high pressure: glycine, -alanine, -valine, -leucine, and -isoleucine

The solubility of glycine, -alanine, -valine, -leucine, and -isoleucine in water was measured at 298.15 K and pressures up to 400 MPa. The standard deviation of the logarithm of the solubility is 0.001–0.003, equal to or better than the accuracy of atmospheric pressure measurement in the literature (0.001–0.05). A variety of solubility phenomena were observed. The solubility of glycine decreased with increasing pressure, whereas that of -alanine increased. The -valine and -isoleucine have a solubility maximum at around 100 MPa, and -leucine seems to exhibit a solid-phase phase transition at around 200 MPa. Pressure coefficient of the solubilities at 0.10 MPa is compared with that thermodynamically estimated in reference to aqueous density measurements of glycine and -alanine at 298.15 K and 0.10 MPa, supporting a reliability of our high-pressure measurements.     

Heteroatom-guided torquoselective olefination of alpha-oxy and alpha-amino ketones via ynolates

Ynolates were found to react with alpha-alkoxy-, alpha-siloxy-, and alpha-aryloxyketones at room temperature to afford tetrasubstituted olefins with high Z selectivity. Since the geometrical selectivity was determined in the ring opening of the beta-lactone enolate intermediates, the torquoselectivity was controlled by the ethereal oxygen atoms. From experimental and theoretical studies, the high Z selectivity is induced by orbital and steric interactions rather than by chelation. In a similar manner, alpha-dialkylamino ketones provided olefins with excellent Z selectivity. These products can be easily converted into multisubstituted butenolides and gamma-butyrolactams in good yield.