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131.
132.
Young Ja Park 《Proceedings of the American Mathematical Society》2004,132(7):2075-2083
A logarithmic Sobolev trace inequality is derived. Bounds on the best constant for this inequality from above and below are investigated using the sharp Sobolev inequality and the sharp logarithmic Sobolev inequality.
133.
D. Baleanu 《Czechoslovak Journal of Physics》2003,53(11):971-976
The variational formulation of the Schrödinger field was investigated and the applicability of the chain method was analyzed. Using Batalin-Fradkin-Tyutin formalism a gauge invariant theory was constructed. 相似文献
134.
135.
136.
Myron W. Evans 《Foundations of Physics Letters》2003,16(6):513-547
A generally covariant wave equation is derived geometrically for grand unified field theory. The equation states most generally that the covariant d'Alembertian acting on the vielbein vanishes for the four fields which are thought to exist in nature: gravitation, electromagnetism, weak field and strong field. The various known field equations are derived from the wave equation when the vielbein is the eigenfunction. When the wave equation is applied to gravitation the wave equation is the eigenequation of wave mechanics corresponding to Einstein's field equation in classical mechanics, the vielbein eigenfunction playing the role of the quantized gravitational field. The three Newton laws, Newton's law of universal gravitation, and the Poisson equation are recovered in the classical and nonrelativistic, weak-field limits of the quantized gravitational field. The single particle wave-equation and Klein-Gordon equations are recovered in the relativistic, weak-field limit of the wave equation when scalar components are considered of the vielbein eigenfunction of the quantized gravitational field. The Schrödinger equation is recovered in the non-relativistec, weak-field limit of the Klein-Gordon equation). The Dirac equation is recovered in this weak-field limit of the quantized gravitational field (the nonrelativistic limit of the relativistic, quantezed gravitational field when the vielbein plays the role of the spinor. The wave and field equations of O(3) electrodynamics are recovered when the vielbein becomes the relativistic dreibein (triad) eigenfunction whose three orthonormal space indices become identified with the three complex circular indices (1), (2), (3), and whose four spacetime indices are the indices of non-Euclidean spacetime (the base manifold). This dreibein is the potential dreibein of the O(3) electromagnetic field (an electromagnetic potential four-vector for each index (1), (2), (3)). The wave equation of the parity violating weak field is recovered when the orthonormal space indices of the relativistic dreibein eigenfunction are identified with the indices of the three massive weak field bosons. The wave equation of the strong field is recovered when the orthonormal space indices of the relativistic vielbein eigenfunction become the eight indices defined by the group generators of the SU (3) group. 相似文献
137.
本文利用比较原理以及一种特殊变换研究了一类非线性退化方程的混合问题,得到了这类复杂问题解的渐进性质。 相似文献
138.
Antonio Vitolo 《Journal of Differential Equations》2003,194(1):166-184
This paper is concerned with the maximum principle for second-order linear elliptic equations in a wide generality. By means of a geometric condition previously stressed by Berestycki-Nirenberg-Varadhan, Cabré was very able to improve the classical ABP estimate obtaining the maximum principle also in unbounded domains, such as infinite strips and open connected cones with closure different from the whole space. Now we introduce a new geometric condition that extends the result to a more general class of domains including the complements of hypersurfaces, as for instance the cut plane. The methods developed here allow us to deal with complete second-order equations, where the admissible first-order term, forced to be zero in a preceding result with Cafagna, depends on the geometry of the domain. 相似文献
139.
Mathematical Notes - 相似文献
140.
K. L. Janssens B. Partoens F. M. Peeters 《Physica E: Low-dimensional Systems and Nanostructures》2004,21(2-4):349
We investigated theoretically the influence of strain on the exciton in both single and three vertically coupled self-assembled quantum dot systems in the presence of a perpendicular magnetic field. For the single disk, we find that the heavy-hole exciton is the ground state, while for the system of three stacked disks, the light hole state was found to be lower in energy. Results for the diamagnetic shift were compared with experimental results. 相似文献