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991.
The general Dirac equation in 1+1 dimensions with a potential with a completely general Lorentz structure is studied. Considering mixed vector–scalar–pseudoscalar square potentials, the states of relativistic fermions are investigated. This relativistic problem can be mapped into a effective Schrödinger equation for a square potential with repulsive and attractive delta-functions situated at the borders. An oscillatory transmission coefficient is found and resonant state energies are obtained. In a special case, the same bound energy spectrum for spinless particles is obtained, confirming the predictions of literature. We showed that existence of bound-state solutions is conditioned by the intensity of the pseudoscalar potential, which possess a critical value. 相似文献
992.
In this work we apply the Dirac method in order to obtain the classical relations for a particle on an ellipsoid. We also determine the quantum mechanical form of these relations by using Dirac quantization. Then by considering the canonical commutation relations between the position and momentum operators in terms of curved coordinates, we try to propose the suitable representations for momentum operator that satisfy the obtained commutators between position and momentum in Euclidean space. We see that our representations for momentum operators are the same as geometric one. 相似文献
993.
994.
K. Guerlebeck In this paper, we consider the following nonlinear Dirac equation By applying the variant generalized weak linking theorem for strongly indefinite problem developed by Schechter and Zou, we prove the existence of nontrivial and ground state solutions for the aforementioned system under conditions weaker than those in Zhang et al. (Journal of Mathematical Physics, 2013). John Wiley & Sons, Ltd. 相似文献
995.
The synergism of lithium bromide and antimony trioxide on the flame-retardancy of a cotton fabric (woven, plain 150 g m2) has been investigated in this study. The impregnations of cotton fabric with suitable individual additives and/or their
appropriate admixed formulation were carried out. The flammability test has also been fulfilled using described procedure,
in the earlier published articles. Their outcomes comply with thermogravimetry’s data. Moreover the latest mentioned outcomes
support the catalytic effect of this synergism. Explanation of the data could be in favor of existing flame-retardation’s
theories. Ultimately this synergism is in compliance with the green chemistry and economical viewpoints. 相似文献
996.
997.
Frederik Witt 《Advances in Mathematics》2008,219(6):1972-2005
We investigate a new 8-dimensional Riemannian geometry defined by a generic closed and coclosed 3-form with stabiliser PSU(3), and which arises as a critical point of Hitchin's variational principle. We give a Riemannian characterisation of this structure in terms of invariant spinor-valued 1-forms, which are harmonic with respect to the twisted Dirac operator ? on Δ⊗Λ1. We establish various obstructions to the existence of topological reductions to PSU(3). For compact manifolds, we also give sufficient conditions for topological PSU(3)-structures that can be lifted to topological SU(3)-structures. We also construct the first known compact example of an integrable non-symmetric PSU(3)-structure. In the same vein, we give a new Riemannian characterisation for topological quaternionic Kähler structures which are defined by an Sp(1)⋅Sp(2)-invariant self-dual 4-form. Again, we show that this form is closed if and only if the corresponding spinor-valued 1-form is harmonic for ? and that these equivalent conditions produce constraints on the Ricci tensor. 相似文献
998.
Zhixin Cheng 《Journal of Mathematical Analysis and Applications》2008,340(1):558-568
Schonbek [M.E. Schonbek, Convergence of solutions to nonlinear dispersive equations, Comm. Partial Differential Equations 7 (1982) 959-1000] obtained the strong convergence of uniform bounded approximate solutions to hyperbolic scalar equation under the assumption that the flux function is strictly convex. While in this paper, by constructing four families of Lax entropies, we succeed in dealing with the non-convexity with the aid of the well-known Bernstein-Weierstrass theorem, and obtaining the strong convergence of uniform L∞ or bounded viscosity solutions for scalar conservation law without convexity. 相似文献
999.
Charles L. Epstein 《Journal of Geometric Analysis》2008,18(2):341-368
In this article we build on the framework developed in Ann. Math. 166, 183–214 ([2007]), 166, 723–777 ([2007]), 167, 1–67 ([2008]) to obtain a more complete understanding of the gluing properties for indices of boundary value problems for the Spin ℂ-Dirac operator with sub-elliptic boundary conditions. We extend our analytic results for sub-elliptic boundary value problems
for the Spin ℂ-Dirac operator, and gluing results for the indices of these boundary problems to Spin ℂ-manifolds with several pseudoconvex (pseudoconcave) boundary components. These results are applied to study Stein fillability
for compact, 3-dimensional, contact manifolds.
This material is based upon work supported by the National Science Foundation under Grant No. 0603973, and the Francis J.
Carey term chair. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author
and do not necessarily reflect the views of the National Science Foundation. 相似文献
1000.
Hartmut Pecher 《NoDEA : Nonlinear Differential Equations and Applications》2008,15(3):279-294
The 1D Cauchy problem for the Dirac-Klein-Gordon system is shown to be locally well-posed for low regularity Dirac data in
and wave data in for under certain assumptions on the parameters r and s, where , generalizing the results for p = 2 by Selberg and Tesfahun. Especially we are able to improve the results from the scaling point of view with respect to
the Dirac part.
相似文献