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.     

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.     

Penalty Virtual Element Method for the 3D Incompressible Flow on Polyhedron Mesh

In this paper, a penalty virtual element method (VEM) on polyhedral mesh for solving the 3D incompressible flow is proposed and analyzed. The remarkable feature of VEM is that it does not require an explicit computation of the trial and test space, thereby bypassing the obstacle of standard finite element discretizations on arbitrary mesh. The velocity and pressure are approximated by the practical significative lowest equal-order virtual element space pair (Xh,Qh) which does not satisfy the discrete inf-sup condition. Combined with the penalty method, the error estimation is proved rigorously. Numerical results on the 3D polygonal mesh illustrate the theoretical results and effectiveness of the proposed method.     

BaY2F8晶体生长基元与结晶机理的探讨

本文通过对BaY2F8晶体结构的分析,从晶体的生长基元为负离子配位多面体理论出发,对自然冷却条件下BaY2F8晶体自发结晶习性进行了研究,提出了以Ba2+为中心的近八配位十二面体和以Y3+为中心的近八配位十二面体是晶体生长的基元.并根据自发结晶的BaY2F8的XRD,说明了BaY2F8晶体的{200}、{130}、{021}、{330}、{-111}、{111}、{221}、{002}等面族比较发育的原因.本文证实了仲维卓的负离子配位多面体理论对BaY2F8晶体生长的适用性,并对探索新的BaY2F8单晶生长方法有参考作用.     

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.     

Volumetric coefficients,internal pressure,and cohesion energy density of <Emphasis Type="Italic">n</Emphasis>-alcohols

Changes in the thermal expansion coefficient and isothermal compressibility in homological series of n-alcohols at 298 K are discussed. It is shown that only methanol exhibits abnormal behavior. Volumetric coefficients of hypothetical solvents such as pseudo-water and pseudo-methanol are determined. Internal pressure values of liquids are calculated. The internal pressure of pseudo-water exceeds that of water, whereas the situation is opposite for the cohesion energy density.