Low energy positron scattering from atoms in and on solids observed with low energy positron diffraction and reemission microscopy

The present status of low energy positron diffraction (LEPD) and positron reemission microscopy (PRM) is reviewed in the context of unanswered questions regarding the elastic scattering of positrons in the 1–300 eV energy range from atoms in solids and at solid surfaces. Recent LEPD studies yield an agreement between theoretical and experimental diffraction intensities for semiconductors that has never been equalled in electron diffraction studies. This situation is discussed in terms of the repulsive interaction between the positron and the embedded atomic potential and the lack of exchange with the nonspherically distributed valence electrons. The scattering of re-emitted positrons in PRM from atoms chemisorbed or physisorbed on the re-emitting surface has not yet received the same theoretical attention as scattering from embedded atoms in LEPD. Possible ways in which positron scattering from overlying atomic structures manifests itself in PRM as well as positron re-emission holography are discussed, both from the practical viewpoint of observing these structures and in the context of fundamental questions regarding the positron re-emission process itself.     

Phospha-palladacycles and N-heterocyclic carbene palladium complexes: efficient catalysts for CC-coupling reactions

Due to the great importance of palladium-catalyzed Heck-type reactions in scientific and industrial chemistry, a lot of publications and reviews have been published during the last years describing this matter under different aspects. This article presents a summary of catalytic applications of palladium complexes with phosphorus ligands containing a metallated sp³-carbon centre (“palladacycles”) or with N-heterocyclic carbene ligands in C-C and C-N coupling reactions of aryl halides including recent results of mechanistic discussions about their role in the catalytic cycle.     

Solving Sequences of Refined Multistage Stochastic Linear Programs

Multistage stochastic programs with continuous underlying distributions involve the obstacle of high-dimensional integrals where the integrands' values again are given by solutions of stochastic programs. A common solution technique consists of discretizing the support of the original distributions leading to scenario trees and corresponding LPs which are – up to a certain size – easy to solve. In order to improve the accuracy of approximation, successive refinements of the support result in rapidly expanding scenario trees and associated LPs. Hence, the solvability of the multistage stochastic program is limited by the numerical solvability of sequences of such expanding LPs. This work describes an algorithmic technique for solving the large-scale LP of refinement ν based on the solutions at the previous ν?1 refinements. Numerical results are presented for practical problem statements within financial applications demonstrating significant speedup (depending on the size of the LP instances).     

Synthese und Struktur von γ-Halogenpropyl-octa(silasesquioxanen)

Synthesis and Structures of γ-Halopropyl-octa(silasesquioxanes) As a more rapid and versatile synthetic approach, we have studied the FeCl₃-catalyzed hydrolytic polycondensation of suited trichlorosilanes in a biphasic system which yields e.g. the new octa(silasesquioxane) (BrCH₂CH₂CH₂)₈Si₈O₁₂.     

On the Asymptotics of Fekete-Type Points for Univariate Radial Basis Interpolation

Suppose that K ^d is compact and that we are given a function fC(K) together with distinct points x_iK, 1in. Radial basis interpolation consists of choosing a fixed (basis) function g : ⁺→ and looking for a linear combination of the translates g(|x−x_j|) which interpolates f at the given points. Specifically, we look for coefficients c_j such that has the property that F(x_i)=f(x_i), 1in. The Fekete-type points of this process are those for which the associated interpolation matrix [g(|x_i−x_j|)]_1i,jn has determinant as large as possible (in absolute value). In this work, we show that, in the univariate case, for a broad class of functions g, among all point sequences which are (strongly) asymptotically distributed according to a weight function, the equally spaced points give the asymptotically largest determinant. This gives strong evidence that the Fekete points themselves are indeed asymptotically equally spaced.