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1.
2.
We establish the existence and stability of multidimensional transonic shocks for the Euler equations for steady potential compressible fluids. The Euler equations, consisting of the conservation law of mass and the Bernoulli law for the velocity, can be written as a second-order, nonlinear equation of mixed elliptic-hyperbolic type for the velocity potential. The transonic shock problem can be formulated into the following free boundary problem: The free boundary is the location of the transonic shock which divides the two regions of smooth flow, and the equation is hyperbolic in the upstream region where the smooth perturbed flow is supersonic. We develop a nonlinear approach to deal with such a free boundary problem in order to solve the transonic shock problem. Our results indicate that there exists a unique solution of the free boundary problem such that the equation is always elliptic in the downstream region and the free boundary is smooth, provided that the hyperbolic phase is close to a uniform flow. We prove that the free boundary is stable under the steady perturbation of the hyperbolic phase. We also establish the existence and stability of multidimensional transonic shocks near spherical or circular transonic shocks.
3.
J. B. Lewis E. L. Baldeschwieler L. D. Tabern E. F. Shelberg D. Hillis S. Cromer I. F. Bingham S. Givaudon M. Aubert M. R. Moutte A. Andant P. Lambert J. Lecomte J. Tausz H. Wolf B. Gordon W. Dachnow I. Perrier M. Lobunetz M. O. Chaikin C. Engler D. Holde 《Analytical and bioanalytical chemistry》1940,119(7-8):307-310
4.
[3,3]-Sigmatropic rearrangements of allyl tetronates and allyl tetramates to give 3-allyltetronic or -tetramic acids, respectively, proceed within 20-60 min under microwave irradiation (300 W, 130-190 °C). Consecutive (homo)sigmatropic [1,5] H-shifts such as oxa-ene reactions are promoted less effectively, which allows the isolation of Claisen intermediates of sigmatropic domino sequences, in contrast to conventional heating. 相似文献
5.
P. Murzyn C. R. Pidgeon P. J. Phillips J. -P. Wells N. T. Gordon T. Ashley J. H. Jefferson T. M. Burke J. Giess M. Merrick B. N. Murdin C. D. Maxey 《Physica E: Low-dimensional Systems and Nanostructures》2004,20(3-4):220
We have made direct pump–probe measurements of spin lifetimes in long wavelength narrow-gap semiconductors at wavelengths between 4 and 10 μm and from 4 to 300 K. In particular, we measure remarkably long spin lifetimes, τs300 ps, even at 300 K for epilayers of degenerate n-type InSb. In this material the mobility is approximately constant between 77 and 300 K, and we find that τs is approximately constant in this temperature range. In order to determine the dominant spin relaxation mechanism we have investigated the temperature dependence of τs in non-degenerate lightly n-type Hg0.78Cd0.22Te of approximately the same band gap as InSb, and find that τs varies from 356 ps at 150 K to 24 ps at 300 K. Our results, both in magnitude and temperature dependence of τs, imply that the Elliott–Yafet model dominates in these materials. 相似文献
6.
Gordon W. Rewcastle Hamish S. Sutherland Claudette A. Weir Adrian G. Blackburn William A. Denny 《Tetrahedron letters》2005,46(50):8719-8721
A novel two-step synthesis of isonitrosoacetanilides [2-(hydroxyimino)-N-phenylacetamides] has been developed, involving the initial acylation of aniline derivatives with 2,2-diacetoxyacetyl chloride, followed by reaction with hydroxylamine hydrochloride. The method works equally well with a variety of different aniline derivatives, including those with poor aqueous solubility and those containing electron rich ortho-substituents, neither of which react well under traditional conditions. 相似文献
7.
M. W. Alexejewa A. G. Pukirew A. Tschetajew J. A. Feldman E. Allisson D. A. Webb Sh. Murahashi S. Sabetay M. Nicloux H. Kreipe E. Flotow L. Malaprade und Y. R. Naves 《Fresenius' Journal of Analytical Chemistry》1940,120(7-8):271-275
Ohne Zusammenfassung 相似文献
8.
It is shown that data on the dissociation rate of deuterium obtained in an experiment at the Sudbury Neutrino Observatory provides evidence that the Continuous Spontaneous Localization wavefunction collapse model should have mass–proportional coupling to be viable. 相似文献
9.
Carl E. Gordon 《Geometriae Dedicata》1992,42(2):187-203
The symmetric group on k symbols is made to operate on a certain set of matrices in such a way that its orbits are in one-to-one correspondence with the orbits of the k-arcs of an N-dimensional projective space under the group of projectivities. This leads to a formula for the number of such orbits. 相似文献
10.
Inhibition of the reduction of Cr(VI) at the magnetite–water interface by calcium carbonate coatings
The effect of calcium carbonate coatings on the reduction of aqueous chromate on the magnetite(1 1 1) surface has been investigated using a combination of synchrotron based X-ray photoemission spectroscopy (PES) and X-ray absorption near edge structure (XANES) spectroscopy, along with laboratory-based powder X-ray diffraction (XRD) and scanning electron microscopy (SEM). CaCO3 coatings (dominantly calcite with minor quantities of aragonite and vaterite) of thicknesses ranging from 10 Å to 20 m were grown on magnetite(1 1 1) surfaces by exposure to supersaturated aqueous solutions followed by evaporation of the solution—a process that mimics pore-water evaporation in vadose zones leading to the formation of caliche and calcium carbonate coatings on mineral grains. Coating thicknesses were determined from attenuation of the Fe 2p photoemission signal by the carbonate coating. For coatings less than 15 Å thick, Cr 2p photoemission and Cr LII, LIII-edge XANES spectra show that chromate is reduced by the underlying magnetite surface; however, as the minimum coating thickness increases beyond 15 Å, the magnetite surface becomes passivated and further chromate reduction ceases. Our findings suggest that carbonate coatings on natural magnetite grains can significantly reduce or eliminate their ability to reduce Cr(VI), which is a toxic and highly mobile environmental contaminant. 相似文献