关于凸曲面的几个定义的关系

本文讨论了凸曲面的几种定义及其关系，发现有的定义是局部凸的定义，有的是整体凸的定义，有的则对于局部凸和整体凸都适合，最后给出了各种定义之间互推的证明，对于局部凸和整体凸定义之间不能推证的，则说明了原因．     

Conjugacy relationship between M-convex and L-convex functions in continuous variables

By extracting combinatorial structures in well-solved nonlinear combinatorial optimization problems, Murota (1996,1998) introduced the concepts of M-convexity and L-convexity to functions defined over the integer lattice. Recently, Murota–Shioura (2000, 2001) extended these concepts to polyhedral convex functions and quadratic functions in continuous variables. In this paper, we consider a further extension to more general convex functions defined over the real space, and provide a proof for the conjugacy relationship between general M-convex and L-convex functions.Mathematics Subject Classification (1991): 90C10, 90C25, 90C27, 90C35This work is supported by Grant-in-Aid of the Ministry of Education, Culture, Sports, Science and Technology of Japan     

Local homology and dimensional full-valuedness

A natural criterion for dimensional full-valuedness of locally compact spaces with finitely generated local homology is given.     

Minkowski-type and Alexandrov-Type Theorems for Polyhedral Herissons

Classical H. Minkowski theorems on existence and uniqueness of convex polyhedra with prescribed directions and areas of faces as well as the well-known generalization of H. Minkowski uniqueness theorem due to A.D. Alexandrov are extended to a class of nonconvex polyhedra which are called polyhedral herissons and may be described as polyhedra with injective spherical image.     

Nitrate ion association with Nd3+

The overall stability constantsK ₁ andK ₂ of NdNO ₃ ²⁺ and Nd(NO₃) ₂ ⁺ complexes were determined (K ₁=1.77;K ₂=1.28) using an extraction method with tri-n-butyl phosphate as the extractant. The ratio ₁/₂ of the stepwise stability constants is discussed. It was established that the Nd(NO₃) ₂ ⁺ complex was an outer-sphere ion pair.

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Die Assoziation von Nitrat-Ion mit Nd³⁺

Zusammenfassung Mittels einer Extraktionsmethode wurden die StabilitätskonstantenK ₁ undK ₂ von NdNO ₃ ²⁺ - und Nd(NO₃)⁺-Komplexen bestimmt (K ₁=1.77;K ₂=1.28; Tri-n-butylphosphat als Extraktionsmittel). Das Verhältnis ₁/₂ der stufenweisen Stabilitätskonstanten wird diskutiert. Es stellte sich heraus, daß der Nd(NO₃)⁺-Komplex als ein Outer-Shere-Ionenpaar vorliegt.

     

次级键与晶体中锑(III)螯合物配位多面体研究

考虑立体活性孤对电子附近次级键配位原子的贡献, 对文献报道的三十个氨基多羧酸锑(III)螯合物的晶体结构中配位多面体描述进行了全面的修正. 配位多面体的几何构型指定采用了单位球内截多面体的两面角判据及其相关的ANVPDA程序. 所有配位多面体几何构型的修正均得到了键价计算的有力支持.     

次级键与晶体中锑(III)螯合物配位多面体研究

考虑立体活性孤对电子附近次级键配位原子的贡献,对文献报道的三十个氨基多羧酸锑(III)螯合物的晶体结构中配位多面体描述进行了全面的修正.配位多面体的几何构型指定采用了单位球内截多面体的两面角判据及其相关的ANVPDA程序.所有配位多面体几何构型的修正均得到了键价计算的有力支持.     

Hollow polyhedron structure of amorphous Ni-Co-S/Co(OH)_2 for high performance supercapacitors

In power storage technology,ion exchange is widely used to modify the electronic structures of electrode materials to stimulate their electrochemical properties.Here,we proposed a multistep ion exchange(cation exchange and anion exchange) strategy to synthesize amorphous Ni-Co-S and β-Co(OH)_2 hybrid nanomaterials with a hollow polyhedron structures.The synergistic effects of different components and the remarkable superiorities of hollow structure endow Ni-Co-S/Co(OH)_2 electrode with outstanding electrochemical performance,including ultra-high specific capacity(1440.0 C/g at 1 A/g),superior capacitance retention rate(79.1% retention at 20 A/g) and long operating lifespan(81.4% retention after5000 cycles).Moreover,the corresponding hybrid supercapacitor enjoys a high energy density of 58.4 Wh/kg at the power density of 0.8 kW/kg,and a decent cyclability that the capacitances are maintained at80.8% compared with the initial capacitance.This research presents a high-performance electrode material and provides a promising route for the construction of electrode materials for supercapacitors with both structural and component advantages.     

船舶与海洋平台结构冰载荷的高性能扩展多面体离散元方法

船舶与海洋平台结构的冰载荷是寒区海洋工程结构物设计中的关键参数,而离散元方法是有效计算结构冰载荷的重要手段. 本文采用基于闵可夫斯基和原理的扩展多面体离散元方法模拟船舶与海洋平台结构的相互作用过程. 其中,构造扩展多面体的近似包络函数并建立了基于优化模型的快速接触搜索算法;考虑单元间粘结作用的刚度软化过程建标识码元间的粘结-破碎模型. 同时,发展了 CPU-GPU 协同异构环境下的高性能并行算法. 为分析海冰与海洋结构作用中的冰载荷,采用ISO标准验证了扩展多面体离散元分析结构冰载荷的准确性. 采用离散元方法计算了船舶结构的冰载荷,研究了船舶结构表明的线载荷分布特点,并采用船舶结构冰阻力经验公式验证了计算结果的合理性. 采用离散元方法计算了平整冰区与多桩腿平台结构的相互作用,分析各桩腿上的冰载荷特点. 针对碎冰区的海冰管理过程,采用离散元方法分析了船舶结构绕行过程中的船舶和海洋平台结构冰载荷. 本文方法可有效应用于海洋结构冰载荷分析,能为极地船舶与海洋平台结构的设计和安全运行提供科学的分析手段.