AuI-Catalyzed Haloalkynylation of Alkenes

The formal insertion of alkenes into aromatic chloro- and bromoalkynes takes place under cationic gold catalysis. This haloalkynylation reaction can be performed with cyclic, gem-disubstituted and monosubstituted alkenes, using BINAP, triazolo[4,3-b]isoquinolin-3-ylidene ligands or SPhos, respectively. The products were isolated in moderate to excellent yields and with complete diastereo- and regioselectivity; the halogen atom bonding the more substituted carbon of the alkene. Preliminary experiments showed that the enantioselective haloalkynylation of cyclopentene can be performed with (S)-BINAP to afford the insertion products with moderate to good enantioselectivities.     

Time‐resolved in situ tomography for the analysis of evolving metal‐foam granulates

An experimental setup has been developed that allows for capturing up to 25 tomograms s^?1 using the white X‐ray beam at the experimental station EDDI of BESSY II, Berlin, Germany. The key points are the use of a newly developed, precise and fast rotation stage, a very efficient scintillator and a fast CMOS camera. As a first application, the foaming of aluminium alloy granules at 923 K was investigated in situ. Formation and growth of bubbles in the liquid material were observed and found to be influenced by the limited thermal conductivity in the bulk granules. Changes that took place between two tomographic frames separated in time by 39 ms could be detected and analysed quantitatively.     

Laplacian Operators and Radon Transforms on Grassmann Graphs

Let Ω be a vector space over a finite field with q elements. Let G denote the general linear group of automorphisms of Ω and let us consider the left regular representation associated with the natural action of G on the set X of linear subspaces of Ω. In this paper we study a natural basis B of the algebra End_G(L ₂(X)) of intertwining maps on L ₂(X). By using a Laplacian operator on Grassmann graphs, we identify the kernels in B as solutions of a basic hypergeometric difference equation. This provides two expressions for these kernels. One in terms of the q-Hahn polynomials and the other by means of a Rodrigues type formula. Finally, we obtain a useful product formula for the mappings in B. We give two different proofs. One uses the theory of classical hypergeometric polynomials and the other is supported by a characterization of spherical functions in finite symmetric spaces. Both proofs require the use of certain associated Radon transforms.     

Hardy-type estimates for Dirac operators

We prove some Hardy type inequalities related to the Dirac operator by elementary methods, for a large class of potentials, which even includes measure valued potentials. Optimality is achieved by the Coulomb potential. When potentials are smooth enough, our estimates provide some spectral information on the operator.     

Towards the Evaluation of the Relevant Degrees of Freedom in Nonlinear Partial Differential Equations

We investigate an operator renormalization group method to extract and describe the relevant degrees of freedom in the evolution of partial differential equations. The proposed renormalization group approach is formulated as an analytical method providing the fundamental concepts of a numerical algorithm applicable to various dynamical systems. We examine dynamical scaling characteristics in the short-time and the long-time evolution regime providing only a reduced number of degrees of freedom to the evolution process.     

Xe对NO(X)微分截面和非弹性散射中的碰撞诱导旋转准直

本文对NO(X)-Xe碰撞系统在碰撞能量为519 cm^-1,测量了完全?-双峰分解的微分截面和碰撞引起的旋转准直力矩. 同时结合初始量子态选择,使用六极杆的非均质电场,借助量子态分辨的测量,利用(1+1'')共振增强的多光子电离和速度离子成像. 结果显示,微分截面以及偏振相关的微分截面均显示与从头算势能面上进行的量子力学散射计算[J. K?os etal. J. Chem. Phys. 137, 014312 (2012)]一致. 通过与准经典轨迹、硬壳势能的量子力学散射以及运动近端模型的比较,评估了势能对所测微分截面和碰撞引起的旋转准直力矩的影响.     

A smoothing method for mathematical programs with equilibrium constraints

Received May 3, 1996 / Revised version received November 19, 1997 Published online January 20, 1999