特殊Lorentz变换的一种新的导出方法

利用光速不变原理，在尽可能少的条件下，导出了特殊Ｌｏｒｅｎｔｚ变换公式，避开了在以往的特殊Ｌｏｒｅｎｔｚ变换公式的推导中所添加的那些除光速不变原理以外的种种限制，简化推导步骤，以利于扩大其应用领域．     

Strong solutions of the Navier–Stokes equations based on the maximal Lorentz regularity theorem in Besov spaces

We show existence and uniqueness theorem of local strong solutions to the Navier–Stokes equations with arbitrary initial data and external forces in the homogeneous Besov space with both negative and positive differential orders which is an invariant space under the change of scaling. If the initial data and external forces are small, then the local solutions can be extended globally in time. Our solutions also belong to the Serrin class in the usual Lebesgue space. The method is based on the maximal Lorentz regularity theorem of the Stokes equations in the homogeneous Besov spaces. As an application, we may handle such singular data as the Dirac measure and the single layer potential supported on the sphere.     

Optimal Gaussian Sobolev embeddings

A reduction theorem is established, showing that any Sobolev inequality, involving arbitrary rearrangement-invariant norms with respect to the Gauss measure in Rn, is equivalent to a one-dimensional inequality, for a suitable Hardy-type operator, involving the same norms with respect to the standard Lebesgue measure on the unit interval. This result is exploited to provide a general characterization of optimal range and domain norms in Gaussian Sobolev inequalities. Applications to special instances yield optimal Gaussian Sobolev inequalities in Orlicz and Lorentz(-Zygmund) spaces, point out new phenomena, such as the existence of self-optimal spaces, and provide further insight into classical results.     

Some Aspects of LrW1 (G) n L(p, q, W2dμ)(G)

Let G be a locally compact Abelian group with Haar measure. The authors discuss some basic properties of LrW1 (G) n L(p, q, W2dμ)(G) spaces. Then the necessary conditions for compact embeddings of the spaces LrW1 ( Rd) N L(p, q, W2dμ)( Rd) are showed.     

Dual of two dimensional Lorentz sequence spaces

In [M. Kato and L. Maligranda, On James and Jordan–von Neumann constants of Lorentz sequence spaces, J. Math. Anal. Appl. 258 (2001) 457–465], it is an open problem to compute the James constant of the dual space of two dimensional Lorentz sequence space d⁽²⁾(w,q). In this paper, we shall determine the dual norm of d⁽²⁾(w,q) and completely compute the James constant of d⁽²⁾(w,q).     

TiAlON系薄膜材料的椭偏研究

 对新型太阳能用薄膜材料TiAlON材料进行了椭偏研究。采用Cauchy,Lorentz和Tauc Lorentz模型对绝缘性TiAlON薄膜的椭偏测量结果进行了模拟,得到了薄膜的光学常数。通过比较色散模型及薄膜结构在不同波段的应用情况,说明Tauc Lorentz模型更适合于从紫外到近红外宽光谱的拟合。结果表明光谱椭偏术可以作为表征TiAlON材料系的可靠手段,是进一步表征多层膜系光学性质的基础。     

推导纵向相对论多普勒效应的新方法

基于狭义相对论的洛伦兹变换和同时的相对性,本文给出了一个推导长度收缩和纵向相对论多普勒效应的新方法。该方法可更直观理解在两个惯性系中观测一个纵向光波的波长与观测沿纵向静止于某个系中杆的长度的本质区别。     

狭义相对论中同时性的研究

本文对狭义相对论中＂同时性＂的基础和＂尺缩钟慢＂效应的本质进行了深入探讨.＂绝对同时＂和＂绝对静止＂一样是不存在的,＂同时＂和＂静止＂都具有相对性.以此为出发点,本文对一个不能直接应用＂尺缩钟慢＂效应解决的物理问题进行了深入研究.结果表明只要找到与正在发生的事件始终保持相对静止的惯性参考系,我们就可以引入＂固有时间＂的概念,再结合＂尺缩钟慢＂效应得到相应事件相对于地面参考系的时间变化规律.     

GABOR ANALYSIS OF THE SPACES M(p,q,w)(R~d) AND S(p,q,r,w,ω)(R~d)

Let g be a non-zero rapidly decreasing function and w be a weight function. In this article in analog to modulation space, we define the space M(p, q, w)(Rd) to be the subspace of tempered distributions f ∈ S′(Rd) such that the Gabor transform Vg(f) of f is in the weighted Lorentz space L(p, q, wdμ) (R2d). We endow this space with a suitable norm and show that it becomes a Banach space and invariant under time frequence shifts for 1 ≤ p, q ≤ ∞. We also investigate the embeddings between these spaces and the...     

Rashba coupling induced by Lorentz symmetry breaking effects

The arising of a Rashba‐like coupling, a Zeeman‐like term and a Darwin‐like term induced by Lorentz symmetry breaking effects in the non‐relativistic quantum dynamics of a spin‐1/2 neutral particle interacting with external fields is studied. Moreover, the influence of a Rashba‐like coupling induced by a Lorentz symmetry violation background on the Tan–Inkson potential [W.‐C. Tan and J. C. Inkson, Semicond. Sci. Technol. 11 , 1635 (1996)] is discussed.