A posteriori error analysis of a cell-centered finite volume method for semilinear elliptic problems

In this paper, we conduct a goal-oriented a posteriori analysis for the error in a quantity of interest computed from a cell-centered finite volume scheme for a semilinear elliptic problem. The a posteriori error analysis is based on variational analysis, residual errors and the adjoint problem. To carry out the analysis, we use an equivalence between the cell-centered finite volume scheme and a mixed finite element method with special choice of quadrature.     

Perfluoropentaphenylborole: A New Approach to Lewis Acidic,Electron‐Deficient Compounds

Zirconocene is the key : A new synthetic method, which utilizes zirconocene‐mediated coupling of alkynes, has been developed for the preparation of a new class of highly Lewis acidic boroles (see scheme). Such compounds hold potential for applications in catalysis and the field of electron‐deficient organic materials.

     

K3(Sc0.875Nb0.125)Nb2O9H1.75: a new scandium niobate with a unique cage structure

Potassium scandium niobate hydroxide, K₃(Sc_0.875Nb_0.125)Nb₂O₉H_1.75, is a new scandium niobate with a unique cage structure. The structure contains two non‐equivalent K⁺ sites (3m and m2 site symmetry), one disordered Sc³⁺/Nb⁵⁺ site (m site symmetry), one Nb⁵⁺ site (3m site symmetry), two O²⁻ sites (m and mm2 site symmetry) and one H⁺ site (m site symmetry). Both scandium and niobium have octahedral environments, which combine to form cages around potassium. One K atom lies in a cube‐like cage built of seven octahedra, while the other K atom is encapsulated by an eight‐membered trigonal face‐bicapped prism. The cages form sheets that extend along the ab plane.     

不同pH值下合成的双中孔和六方中孔SiO_2的表征(英文)

在相同的反应体系中当ｐｈ值从约９．５调变至１１时分别合成出双中孔ＳｉＯ２和六方中孔ＳｉＯ２材料,并用ＸＲＤ、Ｎ２吸附、ＴＥＭ、ＴＧ／ＤＴＡ和ＦＴＩＲ等测试手段对合成产物进行了表征。实验结果表明,双中孔ＳｉＯ和六 方中孔ＳｉＯ２是合成中必然出现的两种不同的中孔物相。与六方中孔ＳｉＯ２相比,双中孔ＳｉＯ２也具有典型中孔 材料的特征ＸＲＤ谱图,虽然仅呈现一个易让人产生不完全晶化误解的相对较宽的单ＸＲＤ衍射峰（ｄ＝５．２ｎｍ）,但它却给出一种独特的Ｎ２吸附等温线和窄的双峰中孔孔径分布曲线。由于孔壁的无定形及表面活性剂分子与ＳｉＯ２骨架间相似的相互作用,两类材料给出类似的ＦＴＩＲ谱图和ＴＧ／ＤＴＡ曲线。然而,在双中孔ＳｉＯ２的ＦＴＩＲ谱图中９６０ｃｍ处峰强度的微小变化可能意味着在锻烧脱除模板剂后双中孔ＳｉＯ２较六方中孔ＳｉＯ２具有更高的骨架聚合度。     

Subnormal operators and the Kaplansky density theorem

We show that if S is a pure subnormal operator, then the minimal normal extension can be written as with . We also extend the Kaplansky density theorem by proving that if is a unital -algebra of operators, then every subnormal contraction in is a (SOT) limit of normal contractions in . We prove similar results for subnormal tuples. Received: 26 July 1998 / in final form: 30 March 1999     

A pulsed-leak valve for use with ion trapping mass spectrometers

A pulsed-leak valve that allows the introduction of a prolonged, flat, and controllable pulse of gas is described. Test results from the valve that utilized a Fourier transform ion cyclotron resonance mass spectrometer with Ar and C₂H₆ as the sample gases indicate that the valve functions as expected and yields basically rectangular pressure profiles in the cell region. The rise and fall times are similar to those of just the stand-alone pulsed valve and are believed to be determined mainly by the design of the vacuum system, rather than the design of the pulsed-leak valve. Kinetic data for the reaction of Nb⁺ with C₂H₆, acquired with the use of the pulsed-leak valve to introduce the C₂H₆ gas, demonstrates the practical application of this valve for kinetic and other analogous studies. Use of the pulsed-leak valve greatly reduces the loss of the reactant ion signal during the cooling period.     

Tangent Fermions: Dirac or Majorana Fermions on a Lattice Without Fermion Doubling

Methods to discretize the Hamiltonian of a topological insulator or topological superconductor, without giving up on the topological protection of the massless excitations (respectively, Dirac fermions or Majorana fermions) are reviewed. The method of tangent fermions, pioneered by Richard Stacey, is singled out as being uniquely suited for this purpose. Tangent fermions propagate on a $2+1$ dimensional space-time lattice with a tangent dispersion: ${\tan }^2(\mathit{\epsilon }/2)={\tan }^2(k_x/2)+{\tan }^2(k_y/2)$ in dimensionless units. They avoid the fermion doubling lattice artefact that will spoil the topological protection, while preserving the fundamental symmetries of the Dirac Hamiltonian. Although the discretized Hamiltonian is nonlocal, as required by the fermion-doubling no-go theorem, it is possible to transform the wave equation into a generalized eigenproblem that is local in space and time. Applications that are discussed include Klein tunneling of Dirac fermions through a potential barrier, the absence of localization by disorder, the anomalous quantum Hall effect in a magnetic field, and the thermal metal of Majorana fermions.     

Tetracopper σ-Bound μ-Acetylide and -Diyne Units Stabilized by a Naphthyridine-based Dinucleating Ligand

Reactions of a dicopper(I) tert-butoxide complex with alkynes possessing boryl or silyl capping groups resulted in formation of unprecedented tetracopper(I) μ-acetylide/diyne complexes that were characterized by NMR and UV/Vis spectroscopy, mass spectrometry and single-crystal X-ray diffraction. These compounds possess an unusual μ₄-η¹:η¹:η¹:η¹ coordination mode for the bridging organic fragment, enforced by the rigid and dinucleating nature of the ligand utilized. Thus, the central π system remains unperturbed and accessible for subsequent reactivity and modification. This has been corroborated by addition of a fifth copper atom, giving rise to a pentacopper acetylide complex. This work may provide a new approach by which metal-metal cooperativity can be exploited in the transformation of acetylide and diyne groups to a variety of substrates, or as a starting point for the controlled synthesis of copper(I) alkyne-containing clusters.