An orthonormal beam family of super Lorentz-Gauss （SLG） beam model is proposed to describe the higher-order mode beams with high divergence, which are generated by a high power diode laser. Here we consider the simp...An orthonormal beam family of super Lorentz-Gauss （SLG） beam model is proposed to describe the higher-order mode beams with high divergence, which are generated by a high power diode laser. Here we consider the simplest case of the SLG beams, where there are four mutually orthogonal SLG beams, namely SLG00, SLG01, SLG10, and SLGll beams. The SLG00 beam is just the Lorentz-Gauss beam. Based on the Collins integral formula and the Hermite-Gaussian expansion of a Lorentz function, an analytical expression for the Wigner distribution function （WDF） of an SLG11 beam through a paraxial ABCD optical system is derived. The properties of the WDF of an SLG11 beam propagating in free space are demonstrated. The normalized WDFs of an SLG11 beam at the different spatial points are depicted in several observation planes. The influence of the beam parameter on the WDF of an SLGI 1 beam in free space is analyzed at different propagation distances. The second-order moments of the WDF of an SLG11 beam in free space are also examined. This research reveals the propagation properties of an SLGll beam from another perspective. The WDFs of SLG01 and SLG10 beams can be easily obtained by using the WDFs of Lorentz-Gauss beam and the SLG11 beam.展开更多
In this paper, we apply function parameters to real interpolation of Lorentz- Orlicz martingale spaces. Some new interpolation theorems are formulated which generalize some known results in Lorentz spaces An introduce...In this paper, we apply function parameters to real interpolation of Lorentz- Orlicz martingale spaces. Some new interpolation theorems are formulated which generalize some known results in Lorentz spaces An introduced by Sharpley.展开更多
关于算子Tf(x)=integral from n=0 to x (φ(t/x))f(t)dt的双权Lorentz模不等式,我们给出了充分和必要条件,其中φ:(0,1)→(0,∞)是非增且满足φ(ab)≤D(φ(a)+φ(b))0<a,b<1,D为常数。该算子包含了Riemann-Liouville分数次积分及...关于算子Tf(x)=integral from n=0 to x (φ(t/x))f(t)dt的双权Lorentz模不等式,我们给出了充分和必要条件,其中φ:(0,1)→(0,∞)是非增且满足φ(ab)≤D(φ(a)+φ(b))0<a,b<1,D为常数。该算子包含了Riemann-Liouville分数次积分及Hardy算子。展开更多
The properties of a wave equation for a six-component wave function of a photon are re-analyzed. It is shown that the wave equation presents all the properties required by quantum mechanics, except for the ones that a...The properties of a wave equation for a six-component wave function of a photon are re-analyzed. It is shown that the wave equation presents all the properties required by quantum mechanics, except for the ones that are linked with the definition of the position operator. The situation is contrasted with the three-component formulation based on the Riemann-Silberstein wave function. The inconsistency of the latter with the principles of quantum mechanics is shown to arise from the usual interpretation of the wave function. Finally, the Lorentz invariance of the six-component wave equation is demonstrated explicitly for Lorentz boosts and space inversion.展开更多
In this study,the effects of high magnetic field gradients on the segregation of alloying elements,crystallized phases,and particles in alloys during solidification process and corresponding microstructures were discu...In this study,the effects of high magnetic field gradients on the segregation of alloying elements,crystallized phases,and particles in alloys during solidification process and corresponding microstructures were discussed.It was confirmed that applying an external high magnetic field gradient during solidification process is an effective processing route for controlling segregation in alloys and then fabricating functional materials which have special mierostruetures and properties.Such controlling and fabrication were realized by controlling the migration of the alloying elements, crystallized phases,and particles in the liquid matrix on the basis of the Lorentz and magnetic forces.展开更多
We use Lorentz polynomials to give an efficient way to prove Daubechies＇ results on the existence of spline type orthogonal scaling functions and to evaluate a class of Daubechies scaling functions in a unified appro...We use Lorentz polynomials to give an efficient way to prove Daubechies＇ results on the existence of spline type orthogonal scaling functions and to evaluate a class of Daubechies scaling functions in a unified approach.展开更多
基金Project supported by the National Natural Science Foundation of China (Grant No.10974179)the Natural Science Foundation of Zhejiang Province,China(Grant No.Y1090073)
文摘An orthonormal beam family of super Lorentz-Gauss （SLG） beam model is proposed to describe the higher-order mode beams with high divergence, which are generated by a high power diode laser. Here we consider the simplest case of the SLG beams, where there are four mutually orthogonal SLG beams, namely SLG00, SLG01, SLG10, and SLGll beams. The SLG00 beam is just the Lorentz-Gauss beam. Based on the Collins integral formula and the Hermite-Gaussian expansion of a Lorentz function, an analytical expression for the Wigner distribution function （WDF） of an SLG11 beam through a paraxial ABCD optical system is derived. The properties of the WDF of an SLG11 beam propagating in free space are demonstrated. The normalized WDFs of an SLG11 beam at the different spatial points are depicted in several observation planes. The influence of the beam parameter on the WDF of an SLGI 1 beam in free space is analyzed at different propagation distances. The second-order moments of the WDF of an SLG11 beam in free space are also examined. This research reveals the propagation properties of an SLGll beam from another perspective. The WDFs of SLG01 and SLG10 beams can be easily obtained by using the WDFs of Lorentz-Gauss beam and the SLG11 beam.
基金supported by National Natural Science Foundation of China(Grant No.11201354)Hubei Province Key Laboratory of Systems Science in Metallurgical Process(Wuhan University of Science and Technology)(Y201321)National Natural Science Foundation of Pre-Research Item(2011XG005)
文摘In this paper, we apply function parameters to real interpolation of Lorentz- Orlicz martingale spaces. Some new interpolation theorems are formulated which generalize some known results in Lorentz spaces An introduced by Sharpley.
文摘关于算子Tf(x)=integral from n=0 to x (φ(t/x))f(t)dt的双权Lorentz模不等式,我们给出了充分和必要条件,其中φ:(0,1)→(0,∞)是非增且满足φ(ab)≤D(φ(a)+φ(b))0<a,b<1,D为常数。该算子包含了Riemann-Liouville分数次积分及Hardy算子。
文摘The properties of a wave equation for a six-component wave function of a photon are re-analyzed. It is shown that the wave equation presents all the properties required by quantum mechanics, except for the ones that are linked with the definition of the position operator. The situation is contrasted with the three-component formulation based on the Riemann-Silberstein wave function. The inconsistency of the latter with the principles of quantum mechanics is shown to arise from the usual interpretation of the wave function. Finally, the Lorentz invariance of the six-component wave equation is demonstrated explicitly for Lorentz boosts and space inversion.
基金Item Sponsored by the National Natural Science Foundation of China (Grant Nos.51006020 and 51174056) the Fundamental Research Funds for the Central Universities (Grant Nos.N090109001+3 种基金N100409008and N100609001) the National Basic Research Program of China (Grant Nos.2011CB612206 and 2011CB610405) the Wuhan National High Magnetic Field Center (Grant No.WHMFCK2011006)
文摘In this study,the effects of high magnetic field gradients on the segregation of alloying elements,crystallized phases,and particles in alloys during solidification process and corresponding microstructures were discussed.It was confirmed that applying an external high magnetic field gradient during solidification process is an effective processing route for controlling segregation in alloys and then fabricating functional materials which have special mierostruetures and properties.Such controlling and fabrication were realized by controlling the migration of the alloying elements, crystallized phases,and particles in the liquid matrix on the basis of the Lorentz and magnetic forces.
文摘We use Lorentz polynomials to give an efficient way to prove Daubechies＇ results on the existence of spline type orthogonal scaling functions and to evaluate a class of Daubechies scaling functions in a unified approach.
