A shape-optimization technique for the capillary surface problem

Summary The problem of the construction of an equilibrium surface taking the surface tension into account leads to Laplace-Young equation which is a nonlinear elliptic free-boundary problem. In contrast to Orr et al. where an iterative technique is used for direct solution of the equation for problems with simple geometry, we propose here an alternative approach based on shape optimization techniques. The shape of the domain of the liquid is varied to attain the optimality condition. Using optimal control theory to derive expressions for the gradient, a numerical scheme is proposed and simple model problems are solved to validate the scheme.     

Stability properties of collocation methods

Lower bounds for are given for which equidistant s-point collocation methods areA()-stable for arbitrarys.     

Normal subgroups and elementary theories of lattice-ordered groups

We show that any lattice-ordered group (l-group) G can be l-embedded into continuously many l-groups H _i which are pairwise elementarily inequivalent both as groups and as lattices with constant e. Our groups H _i can be distinguished by group-theoretical first-order properties which are induced by lattice-theoretically nice properties of their normal subgroup lattices. Moreover, they can be taken to be 2-transitive automorphism groups A(S _i ) of infinite linearly ordered sets (S _i , ) such that each group A(S _i ) has only inner automorphisms. We also show that any countable l-group G can be l-embedded into a countable l-group H whose normal subgroup lattice is isomorphic to the lattice of all ideals of the countable dense Boolean algebra B.     

Dual vectors and lower bounds for the nearest lattice point problem

We prove that given a point outside a given latticeL then there is a dual vector which gives a fairly good estimate for how far from the lattice the vector is. To be more precise, there is a set of translated hyperplanesH _i, such thatL _iH_i andd( _iH_i)(6n ²+1)^–1 d( ,L).Supported by an IBM fellowship.     

高压下C60晶体玻璃化行为的理论研究

通过构造C_(60)分子间的相互作用，研究了在不同压力下C_(60)晶体中的取向有序结构．利用计算出来的两个取向之间的能量差和相隔势驿，研究了热平衡时取向占有几率和玻璃化转变温度的压力相关性．结果与实验符合．     

掺C60有机玻璃的吸收光谱研究

研究了Ｃ６０分别在有机玻璃（ＰＭＭＡ）和正己烷中的吸收光谱，发现Ｃ６０在有机玻璃中的吸收峰同在正己烷中相互对应，同时前者的吸收峰相对于后者峰宽变大，峰位产生红移，分析了产生这种现象的原因。     

Solvent-free Synthesis of Dihydrofuran-fused [60]Fullerene Derivatives by High-speed Vibration Milling

Solvent-free organic reactions have been attracting great interest of chemists due to the elimination of the usage of harmful organic solvents,low costs,and simplicity in the procedure1.Solvent-free mechanochemical reactions of fullerenes were explored and are significant for the reactions of fullerenes because the low solubility of fullerenes in common organic solvents requires large quantity of organic solvents and some novel fullerene reactions could only occur in the solid-state reaction2.…     

卟啉类光敏剂在染料敏化太阳能电池中的应用

染料敏化太阳能电池结合了染料光敏剂和无机半导体的优势，具有较宽的光谱响应范围，制造工艺简单、成本较低，对环境友好，应用前景广阔，因而备受人们的关注。本文以卟啉配合物为主线，介绍光敏太阳能电池的基本构造和光电原理，从改善电池性能的角度，综述了各种卟啉类光敏剂在染料太阳能电池中的应用，讨论了卟啉配合物及其超分子结构对光电转化率的影响机理。     

On a characterization of the normal distribution by means of identically distributed linear forms

Let X₁, X₂,…, be independent, identically distributed random variables. Suppose that the linear forms L₁ = Σ_j=1^∞a_jX_j and L₂ = Σ_j=1^∞b_jX_j exist with probability one and are identically distributed; necessary and sufficient conditions assuring that X₁ is normally distributed are presented. The result is an extension of a theorem of Linnik (Ukrainian Math. J.5 (1953), 207–243, 247–290) concerning the case that the linear forms L₁ and L₂ have a finite number of nonvanishing components. This proof only makes use of elementary properties of characteristic functions and of meromorphic functions.     

On copowers of an ordered skew field

It is shown that the double of an ordered skew fieldE over a subfieldK, which is its own bicentralizer, can again be ordered, and a corresponding result for groups is deduced.