Automatic compensation of magnetic field for a rubidium space cold atom clock

When the cold atom clock operates in microgravity around the near-earth orbit, its performance will be affected by the fluctuation of magnetic field. A strategy is proposed to suppress the fluctuation of magnetic field by additional coils, whose current is changed accordingly to compensate the magnetic fluctuation by the linear and incremental compensation. The flight model of the cold atom clock is tested in a simulated orbital magnetic environment and the magnetic field fluctuation in the Ramsey cavity is reduced from 17 nT to 2 nT, which implied the uncertainty due to the second order Zeeman shift is reduced to be less than 2×10^（-16）. In addition, utilizing the compensation, the magnetic field in the trapping zone can be suppressed from 7.5 μT to less than 0.3 μT to meet the magnetic field requirement of polarization gradients cooling of atoms.

The Erosion Effect of Kapton Film in a Ground-based Atomic Oxygen Irradiation Simulator

In order to investigate the effect of space environmental factors on spacecraft materials, a ground-based simulation facility for space atomic oxygen（AO） irradiation was developed in our laboratory. Some Kapton film samples were subjected to AO beam generated by this facility. The Kapton films before and after AO exposure were analyzed comparatively using optical microscopy, scanning electronic microscopy, atomic force microscopy, high-precision microbalance, and X-ray photoelectron spectroscopy. The experimental results indicate that the transmittance of Kapton film will be reduced by AO irradiation notably, and its color deepens from pale yellow to brown. Surface roughness of the AO-treated sample is already increased obviously after AO irradiation for 5 hours, and exhibits a flannel-like appearance after 15 hours’ exposure in AO beam. The imide rings and benzene rings in kapton molecule are partially decomposed, and some new bonds form during AO irradiation. The mass loss of kapton film increases linearly with the increase of AO fluence, which is resulted from the formation of volatile products, such as CO, CO2 and NOx. The breakage in structure and degradation in properties of AO-treated Kapton film can be attributed to the integrated effect ofimpaction and oxidization of AO beam. The test results agree well with the space flight experimental data.

WEAK TYPE（H^1 ,L^1） ESTIMATE FOR COMMUTATOR OF MARCINKIEWICZ INTEGRAL

Let μΩ,b be the commutator generalized by the n-dimensional Marcinkiewicz integral μΩ and a function b∈ BMO（R^n）. It is proved that μΩ,bis bounded from the Hardy space H^1 （R^n） into the weak L^1（R^n） space.

Real-variable characterizations of anisotropic product Musielak-Orlicz Hardy spaces

Let A :=(A_1, A_2) be a pair of expansive dilations and φ : R^n×R^m×[0, ∞) → [0, ∞) an anisotropic product Musielak-Orlicz function. In this article, we introduce the anisotropic product Musielak-Orlicz Hardy space H~φ_A(R^n× R^m) via the anisotropic Lusin-area function and establish its atomic characterization, the g-function characterization, the g_λ~*-function characterization and the discrete wavelet characterization via first giving out an anisotropic product Peetre inequality of Musielak-Orlicz type. Moreover, we prove that finite atomic decomposition norm on a dense subspace of H~φ_A(R^n× R^m) is equivalent to the standard infinite atomic decomposition norm. As an application, we show that, for a given admissible triplet(φ, q, s), if T is a sublinear operator and maps all(φ, q, s)-atoms into uniformly bounded elements of some quasi-Banach spaces B, then T uniquely extends to a bounded sublinear operator from H~φ_A(R^n× R^m) to B. Another application is that we obtain the boundedness of anisotropic product singular integral operators from H~φ_A(R^n× R^m) to L~φ(R^n× R^m)and from H~φ_A(R^n×R^m) to itself, whose kernels are adapted to the action of A. The results of this article essentially extend the existing results for weighted product Hardy spaces on R^n× R^m and are new even for classical product Orlicz-Hardy spaces.

Global Well-posedness and Global Attractor for Two-dimensional Zakharov-Kuznetsov Equation

The initial value problem for two-dimensional Zakharov-Kuznetsov equation is shown to be globally well-posed in H^s(R^2)for all 5/7<s<1 via using I-method in the context of atomic spaces.By means of the increment of modified energy,the existence of global attractor for the weakly damped,forced Zakharov-Kuznetsov equation is also established in H^s(R^2)for10/11<s<1.

Boundedness of Calderon-Zygmund operators with finite non-doubling measures

Let μ be a nonnegative Radon measure on Rd which satisfies the polynomial growth condition that there exist positive constants Co and n ∈ （0,d） such that, for all x ∈ Rd and r 〉 0, μ（B（x, r））≤ Corn, where B（x, r） denotes the open ball centered at x and having radius r. In this paper, we show that, if μ（Rd） 〈∞, then the boundedness of a Calderdn-Zygmund operator T on L2（μ） is equivalent to that of T from the localized atomic Hardy space h1（μ） to L1,∞（μ） or from h1（μ） to L1（μ）.