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961.
I. N. Sergeev 《Journal of Mathematical Sciences》2006,135(1):2764-2793
The definition of the characteristic frequencies of zeroes and changes of sign for solutions is given. It is equal to the
upper medium (with respect to the time half-axis) of their number on the half-interval of length π. We also define the main frequencies for a linear homogeneous equation of order n. These main frequencies for an equation with constant coefficients coincide with the absolute values of the imaginary parts
of the roots of the corresponding characteristic polynomial. It is proved that for the second-order equation the main frequencies
are the same for all solutions and that they are stable with respect to uniformly small and infinitely small perturbations
of the coefficients. For the third-order equation they can be different, and for any of the main frequencies an example of
nonstability is given.
__________
Translated from Trudy Seminara imeni I. G. Petrovskogo, No. 25, pp. 249–294, 2005. 相似文献
962.
Julia K Pruns Jens-Peter Vietzke Manfred Strassner Claudius Rapp Ulrich Hintze Wilfried A K?nig 《Rapid communications in mass spectrometry : RCM》2002,16(3):208-211
A new solvent-free sample preparation method using silver trifluoroacetate (AgTFA) was developed for the analysis of low molecular weight paraffins and microcrystalline waxes by laser desorption/ionization time-of-flight mass spectrometry (LDI-TOFMS). Experiments show that spectral quality can be enhanced by dispersing AgTFA directly in liquid paraffins without the use of additional solvents. This preparation mixture is applied directly to the MALDI probe. Solid waxes could be examined by melting prior to analysis. The method also provides sufficiently reproducible spectra that peak area ratios between mono- and bicyclic alkane peaks indicated variations in the cycloalkane content of paraffin samples. Dehydrogenation of hydrocarbons observed during the desorption/ionization process was studied by analysis of alkane standards. 相似文献
963.
964.
Zarubitskii O. G. Budnik V. G. Omel'chuk A. A. Melekhin V. T. Opanasyuk V. P. Zakharchenko N. F. 《Russian Journal of Applied Chemistry》2002,75(4):558-561
Electrochemical separation of lead-silver alloys into the constituents by thin-layer electrolysis in molten electrolytes, with bismuth as metal separator, is studied. It is proposed to determine the extent of component recovery by potentiometry. 相似文献
965.
G. Dattoli 《Journal of Mathematical Analysis and Applications》2002,269(2):716-725
Bilateral generating functions are those involving products of different types of polynomials. We show that operational methods offer a powerful tool to derive these families of generating functions. We study cases relevant to products of Hermite polynomials with Laguerre, Legendre and other polynomials. We also propose further extensions of the method which we develop here. 相似文献
966.
We indicate bases for spinor representations of the groups O(3), SO(3), and SU(2) in which the representation matrices are real-valued. The matrix entries in these bases are calculated. We describe the transformation of classical orthogonal harmonic polynomials in three-dimensional space by these matrix entries. 相似文献
967.
J. C. Fabris S. V. B. Gonçalves P. E. de Souza 《General Relativity and Gravitation》2002,34(12):2111-2126
The mass power spectrum for a Universe dominated by the Chaplygin gas is evaluated numerically from scales of the order of the Hubble horizon to 100 Mpc. The results are compared with a pure baryonic Universe and a cosmological constant model. In all three cases, the spectrum increases with k, the wavenumber of the perturbations. The slope of the spectrum is higher for the baryonic model and smaller for the cosmological constant model, the Chaplygin gas interpolating these two models. The results are analyzed in terms of the sound velocity of the Chaplygin gas and the moment the Universe begins to accelerate. 相似文献
968.
Stability of a Model of Relativistic Quantum Electrodynamics 总被引:1,自引:0,他引:1
The relativistic “no pair” model of quantum electrodynamics uses the Dirac operator, D(A) for the electron dynamics together with the usual self-energy of the quantized ultraviolet cutoff electromagnetic field
A– in the Coulomb gauge. There are no positrons because the electron wave functions are constrained to lie in the positive
spectral subspace of some Dirac operator, D, but the model is defined for any number, N, of electrons, and hence describes a true many-body system. In addition to the electrons there are a number, K, of fixed nuclei with charges ≤Z. If the fields are not quantized but are classical, it was shown earlier that such a model is always unstable (the ground
state energy E=−∞) if one uses the customary D(0) to define the electron space, but is stable (E > − const.(N+K)) if one uses D(A) itself (provided the fine structure constant α and Z are not too large). This result is extended to quantized fields here, and stability is proved for α= 1/137 and Z≤ 42. This formulation of QED is somewhat unusual because it means that the electron Hilbert space is inextricably linked
to the photon Fock space. But such a linkage appears to better describe the real world of photons and electrons.
Received: 8 September 2001 / Accepted: 18 March 2002 相似文献
969.
M. A. Alsaleh 《Journal of Mathematical Sciences》2002,111(6):3814-3819
970.
In this paper, a two-dimensional finite volume unstructured mesh method (FVUM) based on a triangular background interpolation mesh is developed for analysing the evolution of the saltwater intrusion into single and multiple coastal aquifer systems. The model formulation consists of a ground-water flow equation and a salt transport equation. These coupled and non-linear partial differential equations are transformed by FVUM into a system of differential/algebraic equations, which is solved using backward differentiation formulas of order one through five. Simulation results are compared with previously published solutions where good agreement is observed. 相似文献