Negative compressibility property in hinging open-cell Kelvin structure

A new three-dimensional(3 D) cellular model based on hinging open-cell Kelvin structure is proposed for its negative compressibility property. It is shown that this model has adjustable compressibility and does exhibit negative compressibility for some certain conformations. And further study shows that the images of compressibility are symmetrical about the certain lines, which indicates that the mechanical properties of the model in the three axial directions are interchangeable and the model itself has a certain geometric symmetry. A comparison of the Kelvin model with its anisotropic form with the dodecahedron model shows that the Kelvin model has stronger negative compressibility property in all three directions.Therefore, a new and potential method to improve negative compressibility property can be derived by selecting the system type with lower symmetry and increasing the number of geometric parameters.     

Surface of Ru/Fe2O3 catalysts used in water-gas shift reaction studied by auger electron spectrometry

Summary Carbon deposits on the surface ofRu/Fe₂O₃ catalysts used in the water-gas shift reaction have been investigated by Auger Electron Spectrometry. A correlation has been found between the thickness of the carbon deposit and the catalytic activity in WGSR. The carbon deposit covers the metallic active centers and blocks their contact with reagents. The dotting of the iron oxide support with sodium has been found to reduce the amount of carbon deposit. .      

双掺(Tm3+,Tb3+)LiYF4激光器1.5 μm波长激光阈值分析

由速率方程推出了双掺（Tm^3 ,Tb^3 ）离子准四能级系统的激光阈值解析式，讨论了Tm^3 和Tb^3 离子之间的相互作用。分析了1.5μm波长附近的激光阈值和Tm^3 、Tb^3 离子的掺杂原子数分数及晶体长度的关系。结果表明，对于对应Tm^3 离子^3H4→^3F4跃迁的约1.5μm波长的激光，激活离子Tm^3 的掺杂原子数分数过大时，交叉弛豫作用将使系统阈值迅速增加。Tb^3 离子的加入，一方面能抽空激光下能级，起到降低阈值的作用；另一方面亦减少了激光上能级的寿命，使阈值升高。故Tb^3 离子有最佳掺杂原子数分数。对于Tm原子数分数为y=0.01的Tm:LiYF4晶体，Tb^3 离子的最佳掺杂原子数分数为0.002左右，同时表明，激光阈值与晶体长度有关。最佳晶体长度与Tm^3 、Tb^3 离子的掺杂原子数分数以及晶体的衍射损耗和吸收损耗有关。     

Inner derivations and norm equality

We characterize when the norm of the sum of two bounded operators on a Hilbert space is equal to the sum of their norms.

     

Efficient Collocation Schemes for Singular Boundary Value Problems

We discuss an error estimation procedure for the global error of collocation schemes applied to solve singular boundary value problems with a singularity of the first kind. This a posteriori estimate of the global error was proposed by Stetter in 1978 and is based on the idea of Defect Correction, originally due to Zadunaisky. Here, we present a new, carefully designed modification of this error estimate which not only results in less computational work but also appears to perform satisfactorily for singular problems. We give a full analytical justification for the asymptotical correctness of the error estimate when it is applied to a general nonlinear regular problem. For the singular case, we are presently only able to provide computational evidence for the full convergence order, the related analysis is still work in progress. This global estimate is the basis for a grid selection routine in which the grid is modified with the aim to equidistribute the global error. This procedure yields meshes suitable for an efficient numerical solution. Most importantly, we observe that the grid is refined in a way reflecting only the behavior of the solution and remains unaffected by the unsmooth direction field close to the singular point.     

Optimality of the double exponential formula – functional analysis approach –

Summary. In the light of the functional analysis theory we establish the optimality of the double exponential formula. The argument consists of the following three ingredients: (1) introduction of a number of spaces of functions analytic in a strip region about the real axis, each space being characterized by the decay rate of their elements (functions) in the neighborhood of the infinity; (2) proof of the (near-) optimality of the trapezoidal formula in each space introduced in (1) by showing the (near-) equality between an upper estimate for the error norm of the trapezoidal formula and a lower estimate for the minimum error norm of quadratures; (3) nonexistence theorem for the spaces, the characterizing decay rate of which is more rapid than the double exponential. Received September 15, 1995 / Accepted December 14, 1995     

Diastereoselective Alkylation of (Diene-Aldehyde)Fe(CO)3 Complexes with Functionalized Zinc-Copper Reagents NuCu(CN)Znl

Addition of functionalized zinc-copper reagents to the title complexes proceeds in a highly diastereoselective fashion to afford dienol complexes. The relative configurations of adducts 3d were determined by single X-ray diffraction analysis.     

Numerical integration of ordinary differential equations on manifolds

Summary This paper is concerned with the problem of developing numerical integration algorithms for differential equations that, when viewed as equations in some Euclidean space, naturally evolve on some embedded submanifold. It is desired to construct algorithms whose iterates also evolve on the same manifold. These algorithms can therefore be viewed as integrating ordinary differential equations on manifolds. The basic method “decouples” the computation of flows on the submanifold from the numerical integration process. It is shown that two classes of single-step and multistep algorithms can be posed and analyzed theoretically, using the concept of “freezing” the coefficients of differential operators obtained from the defining vector field. Explicit third-order algorithms are derived, with additional equations augmenting those of their classical counterparts, obtained from “obstructions” defined by nonvanishing Lie brackets.