Partially Commutative Moment Problems

Partially commutative tensor algebras occur naturally in the algebraic formulation of Wightman field theory. A state on an algebra of this type leads via GNS-construction to a partially commutative family of hermitean operators on Hilbert space. We discuss the question when these operators can be extended to self adjoint operators preserving the commutation properties and state a necessary and sufficient condition for the existence of such an extension in terms of a positivity property of the state.     

Bose-Einstein condensate coupled to a nanomechanical resonator on an atom chip

We theoretically study the coupling of Bose-Einstein condensed atoms to the mechanical oscillations of a nanoscale cantilever with a magnetic tip. This is an experimentally viable hybrid quantum system which allows one to explore the interface of quantum optics and condensed matter physics. We propose an experiment where easily detectable atomic spin flips are induced by the cantilever motion. This can be used to probe thermal oscillations of the cantilever with the atoms. At low cantilever temperatures, as realized in recent experiments, the backaction of the atoms onto the cantilever is significant and the system represents a mechanical analog of cavity quantum electrodynamics. With high but realistic cantilever quality factors, the strong coupling regime can be reached, either with single atoms or collectively with Bose-Einstein condensates. We discuss an implementation on an atom chip.     

Material Discrimination in Nanoparticle Hetero-Aggregates by Analysis of Scanning Transmission Electron Microscopy Images

Hetero-contacts are interfaces between different materials at the nanoscale leading to novel functional properties. In hetero-aggregates, primary particles of at least two different materials are mixed at primary particle or cluster level. Double flame spray pyrolysis (DFSP) is a versatile technique for the controlled synthesis of such materials. Characterization of hetero-aggregates by scanning transmission electron microscopy (STEM) requires acquisition and evaluation of many aggregate images in order to derive statistically significant results. Usually, STEM energy dispersive X-ray spectroscopy (EDXS) is used to acquire elemental maps providing the material distribution of the primary particles within hetero-aggregates. However, the acquisition of a single EDXS map takes up to several minutes. For this reason, determination of material types of primary particles from the intensity in high-angle annular dark field STEM images alone is desirable. These images can be acquired within a couple of seconds. In the present work, a method is suggested which allows for achieving this objective. It can be applied to distinguish materials with a significant difference in their atomic number and hence sufficient material contrast in the STEM images.     

CH Oxidation of Ingenanes Enables Potent and Selective Protein Kinase C Isoform Activation

Ingenol derivatives with varying degrees of oxidation were prepared by two‐phase terpene synthesis. This strategy has allowed access to analogues that cannot be prepared by semisynthesis from natural ingenol. Complex ingenanes resulting from divergent C? H oxidation of a common intermediate were found to interact with protein kinase C in a manner that correlates well with the oxidation state of the ingenane core. Even though previous work on ingenanes has suggested a strong correlation between potential to activate PKCδ and induction of neutrophil oxidative burst, the current study shows that the potential to activate PKCβII is of key importance while interaction with PKCδ is dispensable. Thus, key modifications of the ingenane core allowed PKC isoform selectivity wherein PKCδ‐driven activation of keratinocytes is strongly reduced or even absent while PKCβII‐driven activation of neutrophils is retained.     

Photo‐Wolff Rearrangement of 2‐Diazo‐1,2‐naphthoquinone: Stern–Volmer Analysis of the Stepwise Reaction Pathway

2‐Diazo‐1,2‐naphthoquinone (1) and its derivatives are the photoactive components in Novolak photoresists. A femtosecond infrared study has established that the photoreaction of 1 proceeds largely by a concerted Wolff rearrangement yielding the ketene 1H‐inden‐1‐ylidene‐methanone (3) within 300 fs after excitation, but earlier trapping studies gave evidence for a minor reaction path via a carbene intermediate 1‐oxo‐2(1H)‐naphthalenylidene (2) with a lifetime of about 10 ps. Here, we provide a quantitative assessment of the stepwise pathway by Stern–Volmer analysis of the trapping of 2 by methanol to yield 2‐methoxy‐1‐naphthol (4). We conclude that the lifetime of the carbene 2 is at least 200 ps. Moreover, [3 + 2]cycloaddition of 2 and acetonitrile yielding 2‐methylnaphth[2,1‐d]oxazole (5) was observed. A comparison of the yields of 5 formed upon photolysis and upon thermolysis of 1 in acetonitrile provides evidence that a substantial part of the hot nascent carbene 2 formed photolytically rearranges to the ketene 3 during its vibrational relaxation (hot ground‐state reaction).     

Ruthenium‐Catalyzed C?C Bond Cleavage in Lignin Model Substrates

Ruthenium–triphos complexes exhibited unprecedented catalytic activity and selectivity in the redox‐neutral C C bond cleavage of the β‐O‐4 lignin linkage of 1,3‐dilignol model compounds. A mechanistic pathway involving a dehydrogenation‐initiated retro‐aldol reaction for the C C bond cleavage was proposed in line with experimental data and DFT calculations.     

Explicit constructions and properties of generalized shift-invariant systems in $L^{2}(\mathbb {R})$

Generalized shift-invariant (GSI) systems, originally introduced by Hernández et al. and Ron and Shen, provide a common frame work for analysis of Gabor systems, wavelet systems, wave packet systems, and other types of structured function systems. In this paper we analyze three important aspects of such systems. First, in contrast to the known cases of Gabor frames and wavelet frames, we show that for a GSI system forming a frame, the Calderón sum is not necessarily bounded by the lower frame bound. We identify a technical condition implying that the Calderón sum is bounded by the lower frame bound and show that under a weak assumption the condition is equivalent with the local integrability condition introduced by Hernández et al. Second, we provide explicit and general constructions of frames and dual pairs of frames having the GSI-structure. In particular, the setup applies to wave packet systems and in contrast to the constructions in the literature, these constructions are not based on characteristic functions in the Fourier domain. Third, our results provide insight into the local integrability condition (LIC).     

A novel class of organo- (hydro-) gelators based on ascorbic acid

A library of novel, lipid-modified derivatives of ascorbic acid was shown to exhibit highly attractive properties as surfactants, emulsifiers, oil soluble antioxidants, and highly effective gelators in organic solvents and especially water. In these systems, intermolecular hydrogen bonding and van der Waals forces act synergistically to induce gelation as confirmed by spectroscopic studies. The morphology of the formed gel has been characterized by scanning electron microscopy.     

The Brauer-Manin obstruction for sections of the fundamental group

We introduce the notion of a Brauer-Manin obstruction for sections of the fundamental group extension and establish Grothendieck’s section conjecture for an open subset of the Reichardt-Lind curve.     

Striking stability of a substituted silicon(II) bis(trimethylsilyl)amide and the facile Si-Me bond cleavage without a transition metal catalyst

Silicon(II) bis(trimethylsilyl)amide (LSiN(SiMe(3))(2), L= PhC(NtBu)(2)) (2) has been synthesized by the reaction of LSiHCl(2) with KN(SiMe(3))(2) in 1:2 molar ratio in high yield where 1 equiv of the latter functions as a dehydrochlorinating agent. 2 exhibits a high stability up to 154 °C and can be handled in open air for a short period of time without any appreciable decomposition. An amazing five-membered cyclic silene (3) results from the cleavage of one Si-Me bond of 2 with an adamantyl phosphaalkyne. 3 is the first example of a heavy cyclopentene derivative which consists of four different elements, C, N, Si, and P. Both compounds are characterized by multinuclear NMR spectroscopy, EI-mass spectrometry, and single crystal X-ray diffraction studies.