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921.
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
922.
923.
Two structure functions W1(x,Q2) and W2(x,Q2) are determined by using the cross sections measured in the deep inelastic electron-proton scattering experiments at Stanford Linac in the energy range of 5 to 20 GeV. In this paper an alternative mathematical approach have been used in such determination, resulting in a larger number of points in the graphs of the structure functions. 相似文献
924.
925.
The shape of lines in the radiospectroscopic (NMR and EPR) and dielectric spectra of materials formed by nanoparticles (hereafter, nanomaterials) is analyzed theoretically. The theory is developed in the framework of the core and shell model according to which a nanoparticle consists of two regions whose properties are affected and unaffected by the surface, respectively. The changes in the resonance frequency, the relaxation time, and the static permittivity due to the surface tension are taken into account, and the Gaussian and Lorentzian shapes of homogeneously broadened lines are considered. The inhomogeneous broadening of the spectral lines is examined for several types of nanoparticle size distributions. It is demonstrated that the splitting of the initial lines in the spectra of bulk systems into pairs of lines with a decrease in the particle size is a specific feature of the spectra of nanoparticles. The intensities and half-widths of the lines are investigated as functions of the parameters of the size distribution of nanoparticles. The results of theoretical calculations are compared with recent experimental data on the 17O and 25Mg NMR spectra of nanocrystalline MgO. The theoretical dependences of the intensity, the resonance frequency, and the half-width of the spectral lines are in good agreement with the experimental data. The proposed theory offers a satisfactory explanation of the behavior of the static permittivity in BaTiO3 ceramic materials with nanometer-sized grains. 相似文献
926.
A tight-binding (TB) hamiltonian for calcium is built with a high precision parametrization technique based on density functional calculations of the energy bands and the total energy at various lattice volumes. The new set of TB parameters is appropriate to study phenomena under pressures as high as 20 GPa. Specifically, both the metal to nonmetal transition at 4 GPa and the structural transition fcc to bcc at 19 GPa are well reproduced. These transitions and several static properties are in excellent agreement with experiments. Phonon frequencies, plasmon energy, melting temperature and the coefficient of thermal expansion were calculated with a molecular dynamics scheme of this TB hamiltonian. 相似文献
927.
Toshihiko Hoshiro 《Journal d'Analyse Mathématique》2003,91(1):211-230
This article discusses some smoothing estimates of the initial value problem for dispersive equations with constant coefficients.
In particular, it is shown that a certain condition for the principal part of the symbol (see the assumption (1.3) below,
which is equivalent to the one “of principal type” in the paper by Ben-Artzi and Devinatz [2]) is necessary and sufficient
for the maximal smoothing in space-time.
Dedicated to Professor Norio Shimakura
The author was supported in part by Grant-in-Aid for Scientific Research, Ministry of Education, Culture, Sports, Science
and Technology, Japan (No. 13640187). 相似文献
928.
Teimuraz Pirashvili 《Central European Journal of Mathematics》2003,1(2):169-183
In this paper we consider duplexes, which are sets with two associative binary operations. Dimonoids in the sense of Loday
are examples of duplexes. The set of all permutations carries a structure of a duplex. Our main result asserts that it is
a free duplex with an explicitly described set of generators. The proof uses a construction of the free duplex with one generator
by planary trees. 相似文献
929.
Yong Lee Kazuhiko Hosomi Hiroyuki Uchiyama Toshio Katsuyama Shinya Kominami Tomoyoshi Mishima 《Optical Review》2003,10(1):38-42
An InGaAsP slab-type asymmetric-coupled-waveguide-based dispersion compensator with a mode selector has been designed and fabricated. The mode selector is necessary to select either a symmetric [with a positive group-velocity dispersion (GVD)] or antisymmetric (with a negative GVD) supermode. These supermodes exist simultaneously in the dispersion-compensation region of the device. Pulse-compression experiments were used to test the dispersion compensator, evaluating the function of the mode selector. A theoretical study of the experimental results shows that the mode selector obtains a very strong selectivity (nearly 100%) for the antisymmetric supermode. 相似文献
930.
Synchronized whistlers recorded at Varanasi 总被引:1,自引:0,他引:1
Some interesting events of synchronized whistlers recorded at low latitude station Varanasi during magnetic storm period of
the year 1977 are presented. The dynamic spectrum analysis shows that the component whistlers are Eckersley whistlers having
dispersion 10 s1/2 and 30 s1/2. An attempt has been made to explain the dynamic spectra using lightning discharge generated from magnetospheric sources 相似文献