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971.
972.
Christian Bär 《Communications in Mathematical Physics》1997,188(3):709-721
We prove that the nodal set (zero set) of a solution of a generalized Dirac equation on a Riemannian manifold has codimension
2 at least. If the underlying manifold is a surface, then the nodal set is discrete. We obtain a quick proof of the fact that
the nodal set of an eigenfunction for the Laplace-Beltrami operator on a Riemannian manifold consists of a smooth hypersurface
and a singular set of lower dimension. We also see that the nodal set of a Δ-harmonic differential form on a closed manifold
has codimension 2 at least; a fact which is not true if the manifold is not closed. Examples show that all bounds are optimal.
Received: 28 October 1996 / Accepted: 3 March 1997 相似文献
973.
A. A. Maksimenko I. D. Sadekov A. G. Maslakov O. E. Kompan A. I. Yanovskii Yu. T. Struchkov V. I. Minkin 《Journal of Structural Chemistry》1991,32(3):404-405
Scientific-Research Institute of Physical and Organic Chemistry, Rostov State University. A. N. Nesmeyanov Institute of Heteroorganic Compounds, Academy of Sciences of the USSR. Translated from Zhurnal Strukturnoi Khimii, Vol. 32, No. 3, pp. 104–106, May–June, 1991. 相似文献
974.
Laser gas-assisted material processing finds wide application in industry. The modelling of heating, elastic response of the substrate material, and the wave analysis gives insight into the laser workpiece interaction. In the present study, laser gas-assisted heating of steel is considered. The normal component of the thermal stress is taken as the source of load for the flexural wave generation in the material. The flexural wave generated is simulated and the wave characteristics are analyzed at four locations at the workpiece surface. The numerical scheme employing a control volume approach is introduced when solving the governing equations of flow and heat transfer while finite element and spectran element methods are used when solving the stress and wave equations. It is found that the normal component of the stress is tensile. The dispersion effect of the workpiece material, interference of the reflected beam, and partial overlapping of second mode of the travelling wave enable to identify a unique pattern in the travelling wave in the substrate. 相似文献
975.
Keith B. Oldham 《Journal of Solid State Electrochemistry》1997,1(1):36-44
This study concerns an infinite plane whose smoothness is marred by a single defect: either a groove or a ridge. The blemished
plane serves as an electrode supporting a diffusion-controlled steady-state process. By using a convenient coordinate transformation,
the local current density at all points on the surface is determined exactly. The results are found to confirm intuitive expectations.
Thus, compared with normal values on the plane remote from a groove, the electron transfer rate is diminished within the groove
but enhanced along its margins. Similarly, an abnormally large transfer rate is encountered high on the ridge but the rate
is subnormal on its lower flanks. The total current is demonstrated to be unchanged by the presence of the blemish.
Received: 27 September 1996 / Accepted: 11 March 1997 相似文献
976.
977.
We estimate the possible influence of spectral line profile (Lorentz profile, Van Vleck–Weisskopf profile, and profile obtained by solving kinetic equation) on the rotation part of the dielectric permittivity of water-vapor monomers. Spectral regions corresponding to long-wavelength (static) and high-frequency (optical) limiting cases as well as regions in close proximity to resonances of various intensities are considered. The studied effects are compared with the corresponding effects on water-vapor absorption coefficient, which are related to factors determining the line-shape structure. 相似文献
978.
The structural phase transition from orthorhombic (T) phase to tetragonal (T′) phase in substituted La2−x
R
x
CuO4 (R = Pr, Nd, Sm, Eu and Gd) and T′ to T-phase in Pr2−x
M
x
CuO4−y
(M = Sr, Ca) has been studied by X-ray diffraction technique. The T-phase of La2CuO4 is transferred to T′ phase abruptly atx=0.8, 0.4, 0.4, 0.3 and 0.4 respectively for substitution of Pr, Nd, Sm, Eu and Gd for La in La2CuO4 without evidence of the T* phase. The T′ structure of Pr2CuO4 (x = 0.0) gets transformed to the T* structure at 30% Ca doping (x=0.6) and then to the T structure at 50% Ca doping (x=1.0), while for Sr-contentx=0.0, 0.4 and 1.0 it shows T′, T* and T structure respectively. 相似文献
979.
V. I. Khromov V. V. Kharlamov A. M. Chekmarev G. A. Andropova B. A. Mamet A. S. Plachinda 《Hyperfine Interactions》1991,67(1-4):565-567
The iron containing corrosion products from water heat-carrier and deposits of the second circuit of the nuclear power plant were investigated by means of absorption Mössbauer spectroscopy. The nonstoichiometric magnetite and paramagnetic (superparamagnetic) iron oxide particles were found to be the main corrosion products. The fraction of the magnetically ordered phase varied in the range 0–100% depending on the location in the second circuit. 相似文献
980.
G. M. Luke L. P. Le B. J. Sternlieb Y. J. Uemura J. H. Brewer R. Kadono R. F. Kiefl S. R. Kreitzman T. M. Riseman C. L. Seaman Y. Dalichaouch M. B. Maple J. D. Garrett 《Hyperfine Interactions》1991,64(1-4):517-522
We have performed both zero field and high transverse field measurements at dilution refrigerator temperatures on a number of heavy electron systems, examining the superconducting and magnetic properties of these interesting materials. Among the materials studied to date are UBe13, URu2Si2 and U6Fe. The magnetic field penetration depth in the superconducting state of UBe13 is greater than 10000 Å, as no increase in the transverse field relaxation rate is observed belowT c . A sharp increase in the precession frequency is seen, starting atT c . This frequency shift shows little temperature dependence at low temperature; we found no clear evidence for unconventional superconductivity in this material. Zero field measurements in URu2Si2 show the weak antiferromagnetic transition at 17.5 K. Finally, we we found no clear evidence for unconventional superconductivity in this material. Zero field measurements in URu2Si2 show the weak antiferromagnetic transition at 17.5 K. Finally, we have observed relaxation in high transverse field due to the formation of a flux lattice in U6Fe, a material where the electron effective mass is rather lighter than in other heavy fermion systems. The relaxation exhibits a sharp onset atT c=3.9 K, and is flat at low temperatures as expected for a conventional superconductor. 相似文献