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1.
2.
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 相似文献
3.
4.
Atsushi Ikeda Masaru Kawaguchi Yoshio Suzuki Tsukasa Hatano Munenori Numata Seiji Shinkai Akio Ohta Makoto Ohta 《Journal of inclusion phenomena and macrocyclic chemistry》2000,38(1-4):163-170
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. 相似文献
5.
Kiyonaka S Sugiyasu K Shinkai S Hamachi I 《Journal of the American Chemical Society》2002,124(37):10954-10955
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. 相似文献
6.
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. 相似文献
7.
Shindo M Yoshikawa T Itou Y Mori S Nishii T Shishido K 《Chemistry (Weinheim an der Bergstrasse, Germany)》2005,12(2):524-536
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. 相似文献
8.
Imahori H Fujimoto A Kang S Hotta H Yoshida K Umeyama T Matano Y Isoda S Isosomppi M Tkachenko NV Lemmetyinen H 《Chemistry (Weinheim an der Bergstrasse, Germany)》2005,11(24):7265-7275
Novel gold nanoparticles modified with a mixed self-assembled monolayer of porphyrin alkanethiol and short-chain alkanethiol were prepared (first step) to examine the size and shape effects of surface holes (host) on porphyrin-modified gold nanoparticles. The porphyrin-modified gold nanoparticles with a size of about 10 nm incorporated C60 molecules (guest) into the large, bucket-shaped holes, leading to the formation of a supramolecular complex of porphyrin-C60 composites (second step). Large composite clusters with a size of 200-400 nm were grown from the supramolecular complex of porphyrin-C60 composites in mixed solvents (third step) and deposited electrophoretically onto nanostructured SnO2 electrodes (fourth step). Differences in the porphyrin:C60 ratio were found to affect the structures and photoelectrochemical properties of the composite clusters in mixed solvents as well as on the SnO2 electrodes. The photoelectrochemical performance of a photoelectrochemical device consisting of SnO2 electrodes modified with the porphyrin-C60 composites was enhanced relative to a reference system with small, wedged-shaped surface holes on the gold nanoparticle. Time-resolved transient absorption spectroscopy with fluorescence lifetime measurements suggest the occurrence of ultrafast electron transfer from the porphyrin excited singlet states to C60 or the formation of a partial charge-transfer state in the composite clusters of supramolecular complexes formed between porphyrin and C60 leading to efficient photocurrent generation in the system. Elucidation of the relationship between host-guest interactions and photoelectrochemical function in the present system will provide valuable information on the design of molecular devices and machines including molecular photovoltaics. 相似文献
9.
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. 相似文献
10.
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. 相似文献