区间上单峰扩张自映射周期轨道的超旋转对

设f是区间I=[0,1]上的单峰扩张自映射, k ∈N,m≥2,λm,k是方程x(k-1)m(xm- 1)Q(x,m 1) (x(k-1)m-1)Q(x,m)=0在(1, ∞)上的唯一实根,其中Q(x,m)=(xm- 2xm-1 1).本文证明:若f的扩张常数λ≥λm,k,则f有超旋转对为(k,km 1)的周期轨道. 此外,还指出,当1<λ<λm,k时,在区间上存在单峰扩张自映射具有扩张常数λ却无超旋转对为(k,km 1)的周期轨道.     

Bifurcations of heteroclinic loops

By generalizing the Floquet method from periodic systems to systems with exponential dichotomy, a local coordinate system is established in a neighborhood of the heteroclinic loop Γ to study the bifurcation problems of homoclinic and periodic orbits. Asymptotic expressions of the bifurcation surfaces and their relative positions are given. The results obtained in literature concerned with the 1-hom bifurcation surfaces are improved and extended to the nontransversal case. Existence regions of the 1-per orbits bifurcated from Γ are described, and the uniqueness and incoexistence of the 1-hom and 1-per orbit and the inexistence of the 2-hom and 2-per orbit are also obtained. Project supported by the National Natural Science Foundation of China (Grant No. 19771037) and the National Science Foundation of America # 9357622. This paper was completed when the first author was visiting Northwestern University.     

Exchange-enhanced spin-splitting in a two-dimensional electron gas in the presence of the Rashba spin–orbit interaction

We present a theoretical study on how many-body effects can affect the spin-splitting of a two-dimensional electron gas in the presence of the Rashba spin–orbit interaction. The standard Hartree–Fock approximation and Green's function approach are employed to calculate the energy spectrum and density of states of a spin-split two-dimensional electron gas (2DEG). We find that the presence of the exchange interaction can enhance significantly the spin-splitting of a 2DEG on top of the Rashba effect. The physical reasons behind this important phenomenon are discussed.     

The relativistic energy spectrum of hydrogen

The exact eigenfunctions of the spin‐orbit‐coupling operators for a relativistic binary system are calculated. Concerning the eigenvalue problem and the radial part of the wavefunction of the bound state, we provide corrections for our previous calculations [1] that contained some sign errors.     

氢原子中电子椭圆轨道的简单处理

对氢原子或类氢离子中电子的椭圆轨道和能量给出了一个简单的处理方法．     

Electron spin filtering in all-semiconductor tunneling structures

In this work we briefly review the present day perspectives for exploiting conventional non-magnetic semiconductor nano-technology to design high speed spin-filter devices. In recent theoretical investigations a high spin polarization has been predicted for the ballistic tunneling current in semiconductor single- and double-barrier asymmetric tunnel structures of III–V semiconductors with strong Rashba spin–orbit coupling. We show in this paper that the polarization in the tunneling can probability be sufficiently increased for producing realistic single-barrier structures by including of the Dresselhaus term into consideration.     

一致凸Banach空间中渐近非扩张映象的几乎轨道的渐近行为

设Ｘ是有Ｆｒéｃｈｅｔ可微范数的一致凸Ｂａｎａｃｈ空间，Ｃ是Ｘ的有界闭凸子集，Ｔ：Ｃ→Ｃ是一个渐近非扩张映象．证明了，如果｛ｘ_ｎ：ｎ≥１｝是Ｔ的几乎轨道，则序列｛ｘ０｝弱几乎收敛到集合∩from∞to(ｎ＝１)ｃｏ｛ｘ_i：ｉ≥ｎ｝∩Ｆ（Ｔ）的唯一点，其中，Ｆ（Ｔ）是Ｔ的不动点集．     

Geometric Analysis and Symbol Calculus: Fourier Transform Magnetic Resonance Imaging and Wavelets

Due to its unequalled advantages, the magnetic resonance imaging (MRI) modality has truly revolutionized the diagnosis and evaluation of pathology. Because many morphological anatomic details that may not be visualized by other high tech imaging methods can now be readily shown by diagnostic MRI, it has already become the standard modality by which all other clinical imaging techniques are measured. The unique quantum physical basis of the MRI modality combined with the imaging capabilities of current computer technology has made this imaging modality a target of interdisciplinary interest for clinicians, physicists, biologists, engineers, and mathematicians. Due to the fact that MRI scanners perform corticomorphic processing, this modality is by far more complex than all the other high tech clinical imaging techniques. The purpose of this paper is to outline a phase coherent wavelet approach to Fourier transform MRI. It is based on distributional harmonic analysis on the Heisenberg nilpotent Lie group G and the associated symplectically invariant symbol calculus of pseudodifferential operators. The contour and contrast resolution of MRI scans which is controlled by symplectic filter bank processing gives the noninvasive MRI modality superiority over X-ray computed tomography (CT) in soft tissue differentiation.     

Single-cavity 8 MeV race-track microtron

This paper describes the operational details of the single-cavity race track microtron of this laboratory. The machine is capable of providing electrons of 8 MeV energy at 1 mA peak current. Important parameters of the machine and beam handling system are studied and the results are reported.     

人造卫星相对论中间轨道的积分

由于激光技术可使人造卫星轨道测量精度大大提高,因此轨道计算必须考虑广义相对论效应.本文将中间轨道理论推广到考虑广义相对论效应的人造卫星轨道计算中,给出了相对论中间轨道的积分,并导出了以轨道参数为变量的相对论摄动运动方程.