Optimal Control of the Stretching Process of Solar Arrays on a Spacecraft Using a Genetic Algorithm

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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