Variational formulas of higher order mean curvatures

In this paper, we establish the first variational formula and its Euler-Lagrange equation for the total $2p$-th mean curvature functional $\mathcal {M}_{2p}$ of a submanifold $M^n$ in a general Riemannian manifold $N^{n+m}$ for $p=0,1,...,[\frac{n}{2}]$. As an example, we prove that closed complex submanifolds in complex projective spaces are critical points of the functional $\mathcal {M}_{2p}$, called relatively $2p$-minimal submanifolds, for all $p$. At last, we discuss the relations between relatively $2p$-minimal submanifolds and austere submanifolds in real space forms, as well as a special variational problem.Comment: 13 pages, to appear in SCIENCE CHINA Mathematics 201

Anisotropic but nodeless superconducting gap in the presence of spin density wave in iron-pnictide superconductor NaFe1-xCoxAs

The coexisting regime of spin density wave (SDW) and superconductivity in the iron pnictides represents a novel ground state. We have performed high resolution angle-resolved photoemission measurements on NaFe1-xCoxAs (x = 0.0175) in this regime and revealed its distinctive electronic structure, which provides some microscopic understandings of its behavior. The SDW signature and the superconducting gap are observed on the same bands, illustrating the intrinsic nature of the coexistence. However, because the SDW and superconductivity are manifested in different parts of the band structure, their competition is non-exclusive. Particularly, we found that the gap distribution is anisotropic and nodeless, in contrast to the isotropic superconducting gap observed in an SDW-free NaFe1-xCoxAs (x=0.045), which puts strong constraints on theory.Comment: 5 pages, 4 figures + supplementary informatio

Differential Regulation of Extracellular Matrix and Soluble Fibulin-1 Levels by TGF-β<inf>1</inf> in Airway Smooth Muscle Cells

Fibulin-1 (FBLN-1) is a secreted glycoprotein that is associated with extracellular matrix (ECM) formation and rebuilding. Abnormal and exaggerated deposition of ECM proteins is a hallmark of many fibrotic diseases, such as chronic obstructive pulmonary disease (COPD) where small airway fibrosis occurs. The aim of this study was to investigate the regulation of FBLN-1 by transforming growth factor beta 1 (TGF-β1) (a pro-fibrotic stimulus) in primary human airway smooth muscle (ASM) cells from volunteers with and without COPD. Human ASM cells were seeded at a density of 1×104 cells/cm2, and stimulated with or without TGF-β1 (10 ng/ml) for 72 hours before FBLN-1 deposition and soluble FBLN-1 were measured. Fold change in FBLN-1 mRNA was measured at 4, 8, 24, 48, 72 hours. In some experiments, cycloheximide (0.5 μg/ml) was used to assess the regulation of FBLN-1 production. TGF-β1 decreased the amount of soluble FBLN-1 both from COPD and non-COPD ASM cells. In contrast, the deposition of FBLN-1 into the ECM was increased in ASM cells obtained from both groups. TGF-β1 did not increase FBLN-1 gene expression at any of the time points. There were no differences in the TGF-β1 induced FBLN-1 levels between cells from people with or without COPD. Cycloheximide treatment, which inhibits protein synthesis, decreased both the constitutive release of soluble FBLN-1, and TGF-β1 induced ECM FBLN-1 deposition. Furthermore, in cycloheximide treated cells addition of soluble FBLN-1 resulted in incorporation of FBLN-1 into the ECM. Therefore the increased deposition of FBLN-1 by ASM cells into the ECM following treatment with TGF-β1 is likely due to incorporation of soluble FBLN-1 rather than de-novo synthesis. © 2013 Chen et al

Novel annular flow electromagnetic measurement system for drilling engineering

Downhole micro-flux control drilling technology can effectively solve drilling accidents, such as kick and loss in narrow density window drilling scenarios. Using a downhole annular flow measurement system to obtain real-time information of downhole annular flow is the core and foundation of downhole micro-flux control drilling technology. The research work of electromagnetic flowmeters in recent years creates a challenge for downhole annular flow measurement. This paper proposes a new method for an annular flow measurement system based on the electromagnetic induction principle. First, the annular flow measuring principle, the weight function, the density of virtual current, and the magnetic field of the annular flow electromagnetic measurement system are described. Second, the basic design of the annular flow electromagnetic measurement system is described. Third, model simulation and dynamic experiments on an annular flow electromagnetic measurement system are carried out. The simulation and experimental results show a linear relationship between the system output and the annular flow rate, and also verify the correctness of annular flow electromagnetic measurement theory