Variational Problems of Surfaces in a Sphere

Let x : M → S~(n+p)(1) be an n-dimensional submanifold immersed in an(n + p)-dimensional unit sphere S~(n+p)(1).In this paper, we study n-dimensional submanifolds immersed in S~(n+p)(1) which are critical points of the functional S(x) =∫_M~S~((n/2) dv), where S is the squared length of the second fundamental form of the immersion x.When x : M → S~(2+p)(1) is a surface in S~(2+p)(1), the functional S(x) =∫_M~(S~(n/2) dv) represents double volume of image of Gaussian map.For the critical surface of S(x), we get a relationship between the integral of an extrinsic quantity of the surface and its Euler characteristic.Furthermore, we establish a rigidity theorem for the critical surface of S(x).     

High‐TC Ferromagnetic Semiconductor‐Like Behavior and Unusual Electrical Properties in Compounds with a 2×2×2 Superstructure of the Half‐Heusler Phase

Heusler phases, including the full‐ and half‐Heusler families, represent an outstanding class of multifunctional materials on account of their great tunability in compositions, valence electron counts (VEC), and properties. Here we demonstrate a systematic design of a series of new compounds with a 2×2×2 superstructure of the half‐Heusler unit cell in X–Y–Z (X=Fe, Ru, Co, Rh, Ir; Y=Zn, Mn; Z=Sn, Sb) systems. Their structures were solved by using both powder and single‐crystal X‐ray diffraction, and also directly observed by using high‐angle annular dark‐field imaging in a scanning transmission electron microscope (HAADF‐STEM). The VEC values of these new compounds span a wide and continuous range comparable to those for the full‐ and half‐Heusler families, thereby implying tunability in compositions and physical properties in the superstructure. In fact, we observed abnormal electrical properties and a ferromagnetic semiconductor‐like behavior with a high and tunable Curie temperature in these superstructures.     

多孔活性自燃金属的光谱辐射特性研究

多孔活性金属材料因为内部存在大量的孔隙，大大地增加了与空气的接触面积，使得其在空气中的燃烧较为猛烈，燃烧温度迅速上升。其燃烧过程属于固体燃烧的范畴，较为复杂。以镁为例，通过建立燃烧模型，来研究多孔活性金属的光谱辐射特性。首先，建立氧气总消耗量与活性金属剩余质量的关系，研究氧气在活性金属孔隙内的扩散浓度关系，通过求解活性金属热平衡方程得到活性金属燃烧过程中温度与时间的关系式，进而得到活性金属的峰值光谱辐射强度表达式；然后，将模型计算的仿真结果与红外热像仪测得的实验结果对比，结果表明，模型的计算结果与实验结果相一致，误差在了10%以内；最后，通过建立的燃烧模型来研究活性金属燃烧规律以及其光谱辐射特性，解决了高空、高速下的活性金属光谱辐射强度难以实验获得的问题，大大减小了实验成本与时间。分别对比不同时间活性金属箔片在1～3，3～5以及8～12 μm波段下的辐射强度，得出活性金属燃烧时的辐射强度主要集中在3～5 μm波段的结论。研究结果表明：自燃金属最大燃烧温度随高度的增加逐渐下降，随气流速度的增加先增加后减小，在速度为30 m·s-1时，温度达到最大；自燃金属的光谱辐射强度在2～6 μm波段达到最大。该模型也可以用来研究其他活性金属的燃烧特性。     

High‐energy collision‐induced dissociation of [M+Na]+ ions desorbed by fast atom bombardment of ceramides isolated from the starfish Distolasterias nipon

Ten ceramides and four cerebrosides were extracted from the starfish Distolasterias nipon by solvent extraction, silica gel column chromatography and reversed‐phase high‐performance liquid chromatography. Structural identification was conducted using tandem mass spectrometry of monosodiated ions desorbed by fast atom bombardment. The complete structures of four cerebrosides were determined by a previously reported method. The high‐energy collision‐induced dissociation (CID) spectral characteristics of ceramides with various structures depend on the number and positions of double bonds on both the N‐acyl and sphingoid chains, the presence of a hydroxyl group or a double bond at the C‐4 position of the sphingoid chain and the presence of an α‐hydroxy group on the N‐acyl chain. The high‐energy CID of the monosodiated ion, [M+Na]⁺, of each ceramide molecular species generated abundant ions, providing information on the composition of the fatty acyl chains and sphingoid long‐chain bases. Each homologous ion series along the fatty acyl group and aliphatic chain of the sphingoid base was used for locating the double‐bond positions of both chains and hydroxyl groups on the sphingoid base chain. The double‐bond positions were also confirmed by the m/z values of abundant allylic even‐ and odd‐electron ions, and the intensity ratio of the T ion peak relative to the O ion peak. This technique could determine the complete structures of ceramides and cerebrosides in an extract mixture and has great potential for determining other sphingolipids isolated from various biological sources. Copyright © 2013 John Wiley & Sons, Ltd.     

A new two‐dimensional manganese(II) coordination polymer based on thiophene‐3,4‐dicarboxylic acid

A novel manganese coordination polymer, poly[(μ₅‐thiophene‐3,4‐dicarboxylato)manganese(II)], [Mn(C₆H₂O₄S)]_n, was synthesized hydrothermally using 3,4‐thiophenedicarboxylate (3,4‐tdc²⁻) as the organic linker. The asymmetric unit of the complex contains an Mn²⁺ cation and one half of a deprotonated 3,4‐tdc²⁻ anion, both residing on a twofold axis. Each Mn²⁺ centre is six‐coordinated by O atoms of bridging/chelating carboxylate groups from five 3,4‐tdc²⁻ anions, forming a slightly distorted octahedron. The Mn²⁺ centres are bridged by 3,4‐tdc²⁻ anions to give an infinite two‐dimensional layer which incorporates one‐dimensional Mn–O gridlike chains, and in which the 3,4‐tdc²⁻ anion adopts a novel hexadentate chelating and μ₅‐bridging coordination mode. The fully deprotonated 3,4‐tdc²⁻ anion exhibits unexpected efficiency as a ligand towards the Mn²⁺ centres, which it coordinates through all of its carboxylate O atoms to provide the novel coordination mode. The IR spectrum of the complex is also reported.