Massenspektrometrische untersuchung organischer stickstoffverbindungen - XVI: Elektronenstossinduzierte fragmentierungen von α-pyridiyl-ω-phenylalkanonen und α-phenyl-ω-pyridylalkanen

The electron impact induced fragmentations of twelve pyridine derivatives are discussed. The fragmentation pattern of these compounds is strongly influenced by the number of methylene groups as well as the position of substitution in the pyridine nucleus. By means of mass spectrometry a differentiation between the 2-pyridyl and the 4-pyridyl derivatives is possible and this fact could be important with respect to an analytical identification of the compounds.     

Means and Følner Condition on Polynomial Hypergroups

We investigate summing sequences in the context of polynomial hypergroups. It will be shown that the summing sequence ${(S_{n})_{n\in\mathbb{N}_{0}}}We investigate summing sequences in the context of polynomial hypergroups. It will be shown that the summing sequence (S_n)_{n ? \mathbbN0}{(S_{n})_{n\in\mathbb{N}_{0}}}, where S _n = {0, 1, . . . , n}, is equivalent to the growth condition (H) of the Haar weights h(n). This condition is also sufficient for the existence of means which satisfy a strong form of translation invariance. Furthermore we give exact representations of the unique translation invariant mean on the space of weakly almost periodic sequences for a large class of polynomial hypergroups.     

Affine Slice for the Coadjoint Action of a Class of Biparabolic Subalgebras of a Semisimple Lie Algebra

In this article, we give a simple explicit construction of an affine slice for the coadjoint action of a certain class of biparabolic (also called seaweed) subalgebras of a semisimple Lie algebra over an algebraically closed field of characteristic zero. In particular, this class includes all Borel subalgebras.     

Approximation with Bernstein–Szegö polynomials

We present approximation kernels for orthogonal expansions with respect to Bernstein–Szegö polynomials. Theconstruction is derived from known results for Chebyshev polynomials of the first kind and does not pose any restrictions on the Bernstein–Szegö polynomials.     

WavePacket: A Matlab package for numerical quantum dynamics. III. Quantum-classical simulations and surface hopping trajectories

WavePacket is an open-source program package for numerical simulations in quantum dynamics. Building on the previous Part I (Schmidt and Lorenz, Comput. Phys. Commun. 2017, 213, 223] and Part II (Schmidt and Hartmann, Comput. Phys. Commun. 2018, 228, 229] which dealt with quantum dynamics of closed and open systems, respectively, the present Part III adds fully classical and mixed quantum-classical propagation techniques to WavePacket. There classical phase-space densities are sampled by trajectories which follow (diabatic or adiabatic) potential energy surfaces. In the vicinity of (genuine or avoided) intersections of those surfaces, trajectories may switch between them. To model these transitions, two classes of stochastic algorithms have been implemented: (1) Tully's fewest switches surface hopping and (2) Landau–Zener-based single switch surface hopping. The latter one offers the advantage of being based on adiabatic energy gaps only, thus not requiring nonadiabatic coupling information any more. The present work describes the MATLAB version of WavePacket 6.1.0, which is essentially an object-oriented rewrite of previous versions, allowing to perform fully classical, quantum-classical and quantum-mechanical simulations on an equal footing, that is, for the same physical system described by the same WavePacket input. The software package is hosted and further developed at the Sourceforge platform, where also extensive Wiki-documentation as well as numerous worked-out demonstration examples with animated graphics are available. © 2019 Wiley Periodicals, Inc.     

High‐temperature catalysts for the production of α‐olefins based on iron(II) and iron(III) tridentate bis(imino)pyridine complexes modified by nitrilo group

Series of Fe(II) and Fe(III) tridentate bis(imino)pyridine complexes without nitrilo groups 2–6 and with nitrilo groups 7–13 were synthesized. According to X‐ray analysis, the introduction of nitrilo groups in para‐ and ortho‐positions tends to result in shorter axial Fe? N bonds. Both types of complexes, 2–6 and 9–13 , afforded very productive catalysts for the production of α‐olefins with higher K values and better linearity of Schultz–Flory distribution α‐olefins than the parent methyl substituted Fe(II) complex 1 . Noticeably, the complexes functionalized with a para‐nitrilo group 9–13 tend to make α‐olefins with higher K values of the Schultz–Flory distribution, more ideal distributions, and less of the heavier insoluble fractions of α‐olefins than corresponding nonsymmetrically substituted complexes without para‐nitrilo groups 2–6 . Statistically significant correlations were obtained between % solids of total α‐olefins and the blocked solid angle fraction in the +z hemisphere ( = 51.3%, p = 0.012) and between catalyst productivity and total blocked solid angle fraction ( = 43.5%, p = 0.023). The modest values of show that, while steric effects are significant, they are not the sole factor determining catalyst performance. © 2007 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 46: 585–611, 2008     

Multi-Component Ginzburg-Landau Theory: Microscopic Derivation and Examples

This paper consists of three parts. In part I, we microscopically derive Ginzburg–Landau (GL) theory from BCS theory for translation-invariant systems in which multiple types of superconductivity may coexist. Our motivation are unconventional superconductors. We allow the ground state of the effective gap operator \({K_{T_c}+V}\) to be n-fold degenerate and the resulting GL theory then couples n order parameters. In part II, we study examples of multi-component GL theories which arise from an isotropic BCS theory. We study the cases of (a) pure d-wave order parameters and (b) mixed (s + d)-wave order parameters, in two and three-dimensions. In part III, we present explicit choices of spherically symmetric interactions V which produce the examples in part II. In fact, we find interactions V which produce ground state sectors of \({K_{T_c}+V}\) of arbitrary angular momentum, for open sets of of parameter values. This is in stark contrast with Schrödinger operators \({-\nabla^2+V}\), for which the ground state is always non-degenerate. Along the way, we prove the following fact about Bessel functions: At its first maximum, a half-integer Bessel function is strictly larger than all other half-integer Bessel functions.     

Uniqueness of Radial Solutions for the Fractional Laplacian

We prove general uniqueness results for radial solutions of linear and nonlinear equations involving the fractional Laplacian (?Δ)^s with s ? (0,1) for any space dimensions N ≥ 1. By extending a monotonicity formula found by Cabré and Sire , we show that the linear equation has at most one radial and bounded solution vanishing at infinity, provided that the potential V is radial and nondecreasing. In particular, this result implies that all radial eigenvalues of the corresponding fractional Schrödinger operator H = (?Δ)^s + V are simple. Furthermore, by combining these findings on linear equations with topological bounds for a related problem on the upper half‐space , we show uniqueness and nondegeneracy of ground state solutions for the nonlinear equation for arbitrary space dimensions N ≥ 1 and all admissible exponents α > 0. This generalizes the nondegeneracy and uniqueness result for dimension N = 1 recently obtained by the first two authors and, in particular, the uniqueness result for solitary waves of the Benjamin‐Ono equation found by Amick and Toland .© 2016 Wiley Periodicals, Inc.