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61.
In the present paper, we find a class of linear homogeneous differential equations of order n + 1 (n > 1) whose fundamental system of solutions is constructed from the fundamental system of solutions of a second-order differential
equation. The spectral properties of differential operators generated by these differential expressions are investigated.
In particular, sufficient conditions are obtained for the coefficients of a second-order differential equation under which
the case of maximal deficiency indices is realized.
Dedicated to the memory of B. M. Levitan 相似文献
62.
N. S. Simonović 《Few-Body Systems》2006,38(2-4):139-145
In agreement with the Kohn theorem the relative motion (rel) of three electrons in a two-dimensional parabolic trap separates
from the centre-of-mass (CM) motion. By introducing new coordinates the Hamiltonian for relative motion in the approximation
of non-interacting electrons can be taken to the normal form. The eigenstates of the normalized Hamiltonian are products of
the Fock-Darwin states for normal modes. The energy levels for relative motion are obtained by diagonalizing the exact Hamiltonian
in the eigenbasis for the non-interacting case. In this basis the interaction matrix elements can be obtained in the analytical
form. Since the rank of the Hamiltonian matrix is significantly reduced, the calculations are faster and more accurate than
those for the full (CM + rel) motion. This advantage is especially important for the calculations of excited states and the
analysis of energy spectra. 相似文献
63.
S. Meenakshi B.K. Godwal I. Orgzall S. Tkachev 《Journal of Physics and Chemistry of Solids》2006,67(8):1660-1667
We report the results of an X-ray diffraction study of CdAl2Se4 and of Raman studies of HgAl2Se4 and ZnAl2Se4 at room temperature, and of CdAl2S4 and CdAl2Se4 at 80 K at high pressure. The ambient pressure phase of CdAl2Se4 is stable up to a pressure of 9.1 GPa above which a phase transition to a disordered rock salt phase is observed. A fit of the volume pressure data to a Birch-Murnaghan type equation of state yields a bulk modulus of 52.1 GPa. The relative volume change at the phase transition at ∼9 GPa is about 10%. The analysis of the Raman data of HgAl2Se4 and ZnAl2Se4 reveals a general trend observed for different defect chalcopyrite materials. The line widths of the Raman peaks change at intermediate pressures between 4 and 6 GPa as an indication of the pressure induced two stage order-disorder transition observed in these materials. In addition, we include results of a low temperature Raman study of CdAl2S4 and CdAl2Se4, which shows a very weak temperature dependence of the Raman-active phonon modes. 相似文献
64.
Benjamin J. K. Evans Susan M. Scott Antony C. Searle 《General Relativity and Gravitation》2002,34(10):1675-1684
We have developed a new tool for numerical work in General Relativity: GRworkbench. We discuss how GRworkbench's implementation of a numerically-amenable analogue to Differential Geometry facilitates the development of robust and chart-independent numerical algorithms. We consider, as an example, geodesic tracing on two charts covering the exterior Schwarzschild space-time. 相似文献
65.
K. C. Shin 《Communications in Mathematical Physics》2002,229(3):543-564
We study the eigenvalue problem with the boundary conditions that decays to zero as z tends to infinity along the rays , where is a real polynomial and . We prove that if for some we have for all , then the eigenvalues are all positive real. We then sharpen this to a larger class of polynomial potentials.
In particular, this implies that the eigenvalues are all positive real for the potentials when with , and with the boundary conditions that decays to zero as z tends to infinity along the positive and negative real axes. This verifies a conjecture of Bessis and Zinn-Justin.
Received: 16 January 2002 / Accepted: 1 May 2002 Published online: 6 August 2002 相似文献
66.
K. Wieand 《Probability Theory and Related Fields》2002,123(2):202-224
Let U be an n × n random matrix chosen from Haar measure on the unitary group. For a fixed arc of the unit circle, let X be the number of eigenvalues of M which lie in the specified arc. We study this random variable as the dimension n grows, using the connection between Toeplitz matrices and random unitary matrices, and show that (X -E [X])/(\Var (X))1/2 is asymptotically normally distributed. In addition, we show that for several fixed arcs I
1
, ..., I
m
, the corresponding random variables are jointly normal in the large n limit.
Received: 15 November 2000 / Revised version: 27 September 2001 / Published online: 17 May 2002 相似文献
67.
Olaf Hansen 《Mathematical Methods in the Applied Sciences》2002,25(12):1075-1090
In this article we study the radiosity operator along an edge between two adjacent half‐planes. First we show that the radiosity operator is invertible in a whole scale of anisotropic Sobolev spaces. In the absence of any shadows we are able to derive regularity properties of the solution, which depend only on the angle between the half‐planes, the reflectivity coefficients and the right‐hand side. This work can be considered as a supplement to the article of Rathsfeld (Mathematical Methods in the Applied Sciences 1999; 22 : 217–241). Copyright © 2002 John Wiley & Sons, Ltd. 相似文献
68.
Kasper K. Berthelsen Jesper Møller 《Bulletin of the Brazilian Mathematical Society》2002,33(3):351-367
This primer provides a self-contained exposition of the case where spatial birth-and-death processes are used for perfect
simulation of locally stable point processes. Particularly, a simple dominating coupling from the past (CFTP) algorithm and
the CFTP algorithms introduced in [13], [14], and [5] are studied. Some empirical results for the algorithms are discussed.
Received: 30 June 2002 相似文献
69.
A stability theorem is proved for mappings with bounded distortion over John domains in the Heisenberg group furnished with the Carnot–Caratheodory metric. 相似文献
70.
We investigate the linear stability of the Bickley jet in the framework of the beta-plane approximation. Because singular inviscid neutral modes exist in the retrograde case , it is necessary to add viscosity to interpret them. One of these modes was found in closed form by Howard and Drazin [1] . However, its critical point is at the center of the jet and it was therefore not possible for these authors to ascertain the relationship of this mode to the stability problem or to discuss how to continue the eigenfunction across the singularity.
The viscous critical layer problem associated with this singularity is considerably more difficult than the usual one (which leads to integrals of the Airy function) because and, consequently, a second-order turning point is involved. Our analysis shows that the Howard–Drazin mode is degenerate in the domain where it is valid as a limit of the viscous problem (wavenumber α2 ≤ 9/2 ), that is, it corresponds to both an odd and an even mode. This conclusion is confirmed by direct numerical solution of the Orr–Sommerfeld equation which shows, in addition, that viscosity is destabilizing along portions of the stability boundary. For a retrograde jet, instability is found to occur beyond the inviscid critical value of β, that is, in the region where the flow would be stable according to the Rayleigh–Kuo condition. 相似文献
The viscous critical layer problem associated with this singularity is considerably more difficult than the usual one (which leads to integrals of the Airy function) because and, consequently, a second-order turning point is involved. Our analysis shows that the Howard–Drazin mode is degenerate in the domain where it is valid as a limit of the viscous problem (wavenumber α