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.     

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.     

A practical asymmetric synthesis of trans-4,5-benzhydrindan-1-ones as a precursor of A-nor B-aromatic steroidal compounds

The enantio-controlled synthesis of trans-4,5-benzhydrindan-1-ones was achieved by means of a stereoselective [4+2] cycloaddition of o-quinodimethanes generated by a thermal cleavage of benzocyclobutene derivatives as a key step. The chiral substrates of the thermal reaction were synthesized by a diastereoselective Grignard addition to the chiral O-isopropylideneglyceroketones connected to a benzocyclobutene ring, which were simply prepared from D-mannitol as a chiral source. This approach can provide a new efficient access to A-nor B-aromatic steroidal compounds.     

Vaporization and thermal decomposition of transition metal salts in flameless atomic absorption spectrometry with a carbon tube atomizer

Vaporization and thermal decomposition of Cr, Mn, Fe, Co, Ni and Cu salts were investigated by measuring the absorption spectra observed when aqueous solutions of these salts were heated in the carbon tube atomizer. Gaseous metal halides are vaporized in the atomizer at temperatures above 300–500° C. SO₂ and NO are produced by thermal decomposition of metal sulfates and nitrates, respectively. The vaporization of metal halides is also confirmed by the spectra for solutions of metals in hydrochloric acid and for mixtures of metal nitrates and ammonium halides.     

Radiation-induced emission from golden hamster embryo cells

Emission from high-energy-electron-irradiated golden hamster embryo (GHE) cells has been studied over the temperature range 12–300 K both by a one-shot-single-photon-counting method and by photocurrent measurements with an oscilloscope. Emission from the irradiated phosphate buffered saline (PBS) also has been studied. The emission spectra from PBS at 12 and 77 K show a maximum around 330 and 380 nm, respectively, which are the same spectra as those from irradiated pure H₂O. The emission from irradiated GHE consists of the new band at 480 nm in addition to the emission from H₂O. The 480 nm emission is observed at the temperature range of 12–300 K, though the emission at 300 K is much lower than that at low temperature. The 480 nm emission is ascribed to the transition from excited organic substances in GHE cells. The intensity of 480 nm emission at 300 K increases linearly with increasing irradiation-dose in the range of 11–600 Gy.     

Addition reactions of pendant epoxide group in poly(glycidyl methacrylate) with various active esters

Addition reactions of pendant epoxide groups in poly(glycidyl methacrylate) (PGMA) with various active esters such as 1-benzotriazolyl benzoate, S-(2-benzoxazolyl) thiobenzoate, S-(2-benzothiazolyl) thiobenzoate, 4-nitrophenyl benzoate (4NPB), and S-phenyl thiobenzoate (PTB) were carried out using quaternary salts as catalysts. The reactions of PGMA with those active esters proceeded in diglyme at 100°C for 24 h quantitatively without the formation of 2-hydroxyl pendant groups in the polymer when 10 mol % of tetraethylammonium bromide was used as a catalyst. Furthermore, it was found that the respective quaternary salts have higher catalytic activity than tertiary amines in the reaction of PGMA with the active esters, and the reaction of PGMA with 4NPB gave the corresponding polymer with the highest conversion by addition of tetrabutylammonium bromide as a catalyst, while tetraethylammonium chloride showed the highest activity for the reaction of PGMA with PTB. In addition, the rate of reaction of PGMA with 4NPB was proportional to third order kinetics of the epoxide concentration, the ester concentration and the catalyst concentration as follows: ?d[Epoxide]/dt = ?[Ester]/dt = k₃[Epoxide] [Ester] [Catalyst].     

Cation-pi interactions of a thiocarbonyl group and a carbonyl group with a pyridinium nucleus

Attractive interactions between a thiocarbonyl group and a pyridinium nucleus, and between a carbonyl group and a pyridinium nucleus have been proven by (1)H and (13)C NMR studies, UV-vis spectral analyses, and X-ray crystallographic analyses of nicotinic amides 1 and 3, and pyridinium salts 2 and 4. Comparison of the Deltadelta values, which are the differences in the chemical shifts with reference compounds 5 or 6, showed that the absolute Deltadelta values of 2 and 4 are much larger than those of 1 and 3. In the UV-vis spectra, the n-->pi absorption of the C=S group of 2a exhibited a significant blue shift in CHCl(3). X-ray crystallographic analysis of 1-4 clearly showed that the C=S group of 2a and the C=O group of 4 are very close to the pyridinium moiety compared to the case of 1 and 3. In addition, the X-ray crystal packing structure of 2a showed the C=S group is sandwiched between two pyridinium rings. These experimental results strongly suggested the existence of attractive (C=S)...Py(+) and (C=O)...Py(+) interactions in solution and in crystal. The optimized geometries of 1 and 2 calculated at the HF/6-311G level are in good agreement with their X-ray geometries. MP2/6-311G calculations for the model systems of pyridinium salts 2 and 4 predicted that the electrostatic and induction energies are the major source of the attractive interactions. Since the larger contribution of electrostatic and induction interactions are characteristic features of cation-pi interactions, the (C=S)...Py(+) and (C=O)...Py(+) interactions would be classified as a cation-pi interaction.     

Application of 1,2,3,5,6,7-hexahydropyrrolizinium perchlorate in the synthesis of 7a-substituted hexahydro-1h-pyrrolizines

The method for preparing 7a-substituted hexahydro-1H-pyrrolizines 2 from 1,2,3,5,6,7-hexahydropyrrol-izinium Perchlorate (3) was investigated, by which introduction of a wide variety of functionalities on C(7a) could be achieved easily.