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51.
The Lorentz-violating isotropic modified Maxwell theory minimally coupled to standard Dirac theory is characterized by a single real dimensionless parameter which is taken to vanish for the case of the standard (Lorentz-invariant) theory. A finite domain of positive and negative values of this Lorentz-violating parameter is determined, in which microcausality and unitarity hold. The main focus of this article is on isotropic modified Maxwell theory, but similar results for an anisotropic nonbirefringent case are presented in Appendix A. 相似文献
52.
53.
We introduce Lorentz spaces and with variable exponents. We prove several basic properties of these spaces including embeddings and the identity . We also show that these spaces arise through real interpolation between and . Furthermore, we answer in a negative way the question posed in 12 whether the Marcinkiewicz interpolation theorem holds in the frame of Lebesgue spaces with variable integrability. 相似文献
54.
In the paper we construct a system of bounded functions which generates an uncomplemented subspace in the Lorentz space Λ(α)
for all α∈(0,1). Lower bounds of the norms of the projector onto such subspaces are obtained.
Translated fromMatematicheskie Zametki, Vol. 68, No. 1, pp. 57–65, July, 2000. 相似文献
55.
Anna Kamińska Anca M. Parrish 《Journal of Mathematical Analysis and Applications》2010,366(1):389-390
In this note we state the accurate formulas of convexity and concavity constants in Lorentz spaces, correcting the formulas from Kamińska and Parrish (2008) [2]. 相似文献
56.
V. Majerník 《Foundations of Physics Letters》1997,10(4):357-370
We propose a spacetime scheme representing the union of the real and non-real spacetime as a possible geometrical framework
for Caldirola’s idea, that the bradyonic motion can be regarded as a light-like motion in an additional extra space. The playground
of all physical processes is the union space. However, the physical processes in union space are differently projected on
the real and non-real spacetime. The waves linked with luxons in union space are projected on the real spacetime so that they
propagate here always with the velocity of light. The waves linked with bradyons in union space are projected on the non-real
spacetime so that they propagate here with the velocity of light. The wave linked with a bradyon in union space, which is
projected on the real spacetime, is here described by the Schroedinger and Dirac equations. There is proposed a symmetry which
demands that the physical world is in its law the same whether it is seen from real or non-real spacetime. We discuss some
consequences of this symmetry in the theory of elementary particles. 相似文献
57.
David E. Edmunds Bohumí r Opic 《Proceedings of the American Mathematical Society》2003,131(3):745-754
We give new characterizations of Lorentz spaces by means of certain quasi-norms which are shown to be equivalent to the classical ones.
58.
We consider the Cauchy problem of Navier-Stokes equations in weak Morrey spaces. We first define a class of weak Morrey type spaces Mp*,λ(Rn) on the basis of Lorentz space Lp,∞ = Lp*(Rn)(in particular, Mp*,0(Rn) = Lp,∞, if p > 1), and study some fundamental properties of them; Second,bounded linear operators on weak Morrey spaces, and establish the bilinear estimate in weak Morrey spaces. Finally, by means of Kato's method and the contraction mapping principle, we prove that the Cauchy problem of Navier-Stokes equations in weak Morrey spaces Mp*,λ(Rn) (1<p≤n) is time-global well-posed, provided that the initial data are sufficiently small. Moreover, we also obtain the existence and uniqueness of the self-similar solution for Navier-Stokes equations in these spaces, because the weak Morrey space Mp*,n-p(Rn) can admit the singular initial data with a self-similar structure. Hence this paper generalizes Kato's results. 相似文献
59.
N. I. Chernov 《Journal of statistical physics》1994,74(1-2):11-53
In 1981 Bunimovich and Sinai established the statistical properties of the planar periodic Lorentz gas with finite horizon. Our aim is to extend their theory to the multidimensional Lorentz gas. In that case the Markov partitions of the Bunimovich-Sinai type, the main tool of their theory, are not available. We use a crude approximation to such partitions, which we call Markov sieves. Their construction in many dimensions is essentially different from that in two dimensions; it requires more routine calculations and intricate arguments. We try to avoid technical details and outline the construction of the Markov sieves in mostly qualitative, heuristic terms, hoping to carry out our plan in full detail elsewhere. Modulo that construction, our proofs are conclusive. In the end, we obtain a stretched-exponential bound for the decay of correlations, the central limit theorem, and Donsker's Invariance Principle for multidimensional periodic Lorentz gases with finite horizon. 相似文献
60.
Karin Melnick 《Geometriae Dedicata》2007,126(1):131-154
We prove results toward classifying compact Lorentz manifolds on which Heisenberg groups act isometrically. We give a general
construction, leading to a new example, of codimension-one actions – those for which the dimension of the Heisenberg group
is one less than the dimension of the manifold. The main result is a classification of codimension-one actions, under the
assumption they are real-analytic. 相似文献