On the order of composite multistep methods for ordinary differential equations

Summary In this paper, a general class ofk-step methods for the numerical solution of ordinary differential equations is discussed. It is shown that methods with order of consistencyq have order of convergence (q+1) if a very simple condition is satisfied. This result gives a new aspect to previous results of Spijker; it also serves as a starting point for a new theory of cyclick-step methods, completing an approach of Donelson and Hansen. It facilitates the practical determination of high-order cyclick-step methods, especially of stiffly stable,k-step methods.     

A note on mixed A-reflexive groups

This paper presents a Warfield-type characterization of A-reflexive groups in the case that A is a mixed abelian group of torsion-free rank 1.     

Intermediates of N-Heterocyclic Carbene (NHC) Dimerization Probed in the Gas Phase by Ion Mobility Mass Spectrometry: C−H⋅⋅⋅:C Hydrogen Bonding Versus Covalent Dimer Formation

N-Heterocyclic carbenes (NHCs, :C ) can interact with azolium salts ( C−H⁺ ) by either forming a hydrogen-bonded aggregate ( CHC⁺ ) or a covalent C−C bond ( CCH⁺ ). In this study, the intramolecular NHC–azolium salt interactions of aromatic imidazolin-2-ylidenes and saturated imidazolidin-2-ylidenes have been investigated in the gas phase by traveling wave ion mobility mass spectrometry (TW IMS) and DFT calculations. The TW IMS experiments provided evidence for the formation of these important intermediates in the gas phase, and they identified the predominant aggregation mode (hydrogen bond vs. covalent C−C) as a function of the nature of the interacting carbene–azolium pairs.     

Donor-Flexible Bis(pyridylidene amide) Ligands for Highly Efficient Ruthenium-Catalyzed Olefin Oxidation

An exceptionally efficient ruthenium-based catalyst for olefin oxidation has been designed by exploiting N,N′-bis(pyridylidene)oxalamide (bisPYA) as a donor-flexible ligand. The dynamic donor ability of the bisPYA ligand, imparted by variable zwitterionic and neutral resonance structure contributions, paired with the redox activity of ruthenium provided catalytic activity for Lemieux–Johnson-type oxidative cleavage of olefins to efficiently prepare ketones and aldehydes. The ruthenium bisPYA complex significantly outperforms state-of-the-art systems and displays extraordinary catalytic activity in this oxidation, reaching turnover frequencies of 650 000 h⁻¹ and turnover numbers of several millions.     

Hybrid Plasmonic–Aerogel Materials as Optical Superheaters with Engineered Resonances

Solar radiation is a versatile source of energy, convertible to different forms of power. A direct path to exploit it is the generation of heat, for applications including passive building heating, but it can also drive secondary energy-conversion steps. We present a novel concept for a hybrid material which is both strongly photo-absorbing and with superior characteristics for the insulation of heat. The combination of that two properties is rather unique, and make this material an optical superheater. To realize such a material, we are combining plasmonic nanoheaters with alumina aerogel. The aerogel has the double function of providing structural support for plasmonic nanocrystals, which serve as nanoheaters, and reducing the diffusion rate of the heat generated by them, resulting in large local temperature increases under a relatively low radiation intensity. This work includes theoretical discussion on the physical mechanisms impacting the system's balanced thermal equilibrium.     

Transverse momentum distributions of neutral pions from central and peripheral16O+Au collisions at 200A·GeV

The production of neutral pions by the interaction of 200A·GeV p and¹⁶O projectiles with a Au target has been studied in the pseudorapidity range 1.5≦η≦2.1. Transverse momentum spectra have been measured between 0.4 GeV/c and 3.6 GeV/c and their dependence on the centrality of the collision has been investigated. The peripheral-collision spectra display a marked change of slope with a hard component starting at about 1.8 GeV/c, in contrast to central-collision data. The data are discussed in comparison to p+p and α+α data from the ISR.     

Torus Knots and the Topological Vertex

We propose a class of toric Lagrangian A-branes on the resolved conifold that is suitable to describe torus knots on S ³. The key role is played by the \({SL(2, \mathbb{Z})}\) transformation, which generates a general torus knot from the unknot. Applying the topological vertex to the proposed A-branes, we rederive the colored HOMFLY polynomials for torus knots, in agreement with the Rosso and Jones formula. We show that our A-model construction is mirror symmetric to the B-model analysis of Brini, Eynard and Mariño. Compared to the recent proposal by Aganagic and Vafa for knots on S ³, we demonstrate that the disk amplitude of the A-brane associated with any knot is sufficient to reconstruct the entire B-model spectral curve. Finally, the construction of toric Lagrangian A-branes is generalized to other local toric Calabi–Yau geometries, which paves the road to study knots in other three-manifolds such as lens spaces.     

Parametrically shaped femtosecond pulses in the nonlinear regime obtained by reverse propagation in an optical fiber

We present the experimental realization of a method to generate predetermined, arbitrary pulse shapes after transmission through an optical fiber in the nonlinear regime. The method is based on simulating the reverse propagation of the desired pulse shape in the fiber. First, linear and nonlinear parameters of a single-mode step-index fiber required for the simulation are determined. The calculated pulse shapes are then generated in a pulse shaper.     

Palladation of diimidazolium salts at the C4 position: access to remarkably electron-rich palladium(II) centers

Palladation of C2-protected diimidazolium salts with Pd(OAc)2 afforded complexes comprising C4-bound N-heterocyclic dicarbene ligands. The reactivity of these complexes towards Lewis acids (AgBF4, AgOAc) and Br?nsted acids (H2SO4, H3PO4, HOAc) revealed that abnormal C4 bonding of the carbenes markedly increases the nucleophilicity of the coordinated palladium center as compared to C2 bonding. Despite its formal +2 charge, the palladium center in these complexes is best described as a Lewis base. The abnormal carbene bonding mode induces new reaction patterns such as the formation of a Pd-Ag adduct. Based on metallation studies including the palladation of a dissymmetric diimidazolium salt, a rationale for the selective activation of the C4-H bond in the diimidazolium precursor salts is proposed.