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21.
John M. Davis Ian A. Gravagne 《Journal of Mathematical Analysis and Applications》2007,332(2):1291-1307
In this work, we reexamine the time scale Laplace transform as defined by Bohner and Peterson [M. Bohner, A. Peterson, Dynamic Equations on Time Scales: An Introduction with Applications, Birkhäuser, Boston, 2001; M. Bohner, A. Peterson, Laplace transform and Z-transform: Unification and extension, Methods Appl. Anal. 9 (1) (2002) 155-162]. In particular, we give conditions on the class of functions which have a transform, develop an inversion formula for the transform, and further, we provide a convolution for the transform. The notion of convolution leads to considering its algebraic structure—in particular the existence of an identity element—motivating the development of the Dirac delta functional on time scales. Applications and examples of these concepts are given. 相似文献
22.
Mark Israelit 《Foundations of Physics》2002,32(6):945-961
A spatially closed universe undergoing at present accelerated expansion, having a non-vanishing cosmological constant, and filled with luminous- and dark matter is described in terms of the Integrable Weyl–Dirac theory. It is shown that, during the dust-dominated period, dark matter and the quintessence pressure, the latter giving rise to acceleration: both are created by the Dirac gauge function. The behavior of two models: a nearly flat one and a well closed are considered in appropriate gauges, and plausible scenarios are obtained. The outcome of the present paper, together with results of a previous work,(31) provide a geometrically based, classical, singularity-free model of the universe, that has originated from a pure geometric Weyl–Dirac entity, passed a prematter period, the radiation-dominated era, and continues its development in the present dust period. 相似文献
23.
Hubert Kalf 《Journal of Differential Equations》2004,205(2):408-423
We show that the point spectrum of the standard Coulomb-Dirac operator H0 is the limit of the point spectrum of the Dirac operator with anomalous magnetic moment Ha as the anomaly parameter tends to 0. For negative angular momentum quantum number κ, this holds for all Coulomb coupling constants c for which H0 has a distinguished self-adjoint realisation. For positive κ, however, there are some exceptional values for c, and in general an index shift between the eigenvalues of H0 and the limits of eigenvalues of Ha appears, accompanied with additional oscillations of the eigenfunctions of Ha very close to the origin. 相似文献
24.
25.
Influence of relaxation effects on probabilities of the 2s2p35S2-2s22p2 3P1,2 intercombination transitions in NII
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Transition probabilities of the 2s2p^3 {}^5S_2-2s^22p^2 {}^3P_{1,2} intercombination transitions in NII have been calculated by using a large-scale multiconfiguration Dirac-Fock method. In the calculation the most important effects of relativity, correlation, and relaxation are considered. From the calculated transition probabilities, the lifetime of the 2s2p^3 {}^5S_2 metastable state is derived. The result is in excellent agreement with the latest experimental result. In the meantime the influence of anomalously strong relaxation effects on probabilities of the 2s2p^3 {}^5S_2-2s^22p^2 {}^3P_{1,2} lines in NII have been found. 相似文献
26.
本文考虑了R^n 1空间中椭圆函数和准椭圆函数的一些性质,然后分别讨论了周期和准周期Riemann边值问题,给出了解的表达式和可解条件。 相似文献
27.
The Dirac equation is solved for two novel terms which describe the interaction energy between the half-integral spin of a
fermion and the classical, circularly polarized, electromagnetic field. A simple experiment is suggested to test the new terms
and the existence of radiation-induced fermion resonance. 相似文献
28.
David Fryberger 《Foundations of Physics Letters》1990,3(4):379-386
Issues raised by W. A. Rodrigues, Jr. are discussed.1. This is not a new result; see,e.g., Rohrlich.(3)
2. A typographical error in Eq. (77) is corrected here: The productj A in the right-hand parentheses was erroneously transcribed in Ref. (2) as
A.3. I define electromagnetic fieldF = A to be that generated by electric charges and the magnetoelectric fieldG = M to be that generated by magnetic monopoles:F F +5
G.
4. Rodrigues, on the other hand, takes the position that the importance of the Lagrangian formulation should be downgraded if not discarded altogether: ... it is redundant to look for Lagrangians.(1)
5. In fact, he reformulates it using the language of differential forms.6. It is interesting to observe that this bilinear form has the additional virtue of being appropriate for dealing with the monopolecharge parity question, which was pointed out long ago.(14)
7. In fact, even mathematics looks to Nature for its authority.(16) There is evidence that Rodrigues does not understand this concept.(17) 相似文献
29.
A variational method for solving the time-independent single-particle Dirac equation in the Coulomb field of two nuclei is
described. A minimax variational principle and basis functions that have the proper analytic behavior, i.e. behave like r
γ,γ non-integer, in the neighborhood of a nucleus, are used. A momentum space integration scheme for computing the necessary
two-center integrals is described. Results are given for a standard test problem on two nuclei with Z=90 with an internuclear separation of 2.0/Z. The results confirm those of a previous calculation [F.A. Parpia and A.K. Mohanty, Chem Phys Lett 238: 209 (1995)].
Received: 13 May 1998 / Accepted: 22 June 1998 / Published online: 28 August 1998 相似文献
30.
At the special value of the reduced inverse temperature=2, the equilibrium statistical mechanics of a two-dimensional Coulomb gas confined to the surface of a sphere is an exactly solvable problem, just as it was for the Coulomb gas in a plane. The thermodynamic quantities and all the correlation functions can be calculated. Use is made of an isomorphism between the classical Coulomb gas and the free Fermi field theory associated with the Dirac operator on the sphere.Laboratory associated with the Centre National de la Recherche Scientifique. 相似文献