α-Chlor-nitrone IV: Zur Stereochemie der λ-Lacton-Synthese und eine Methode zum Aufbau von α-Methyliden-λ-lactonen aus Olefinen. Über synthetische Methoden, 8. (vorläufige) Mitteilung

The Ag⁺-induced reaction between N-cyclohexyl-α-chloro-propionaldonitrone and the two diastereomeric 2-butenes in liquid SO₂ is a stereospecific cis-addition. The use of N-cyclo-hexyl-α,β-dichloro-propionaldonitrone in this type of reaction provides a preparative route from olefines to α-methylidene-butyrolactones.     

Excitation energies through the locally renormalized equation-of-motion formalism: singles and doubles model

The stationary conditions obtained from approximate coupled-cluster functional derived from the numerator-denominator connected expansion (NDC) [K. Kowalski and P. Piecuch, J. Chem. Phys. 122, 074107 (2005)] are employed to calculate the linear response of cluster amplitudes. A simple scheme that involves singly and doubly excited amplitudes, termed locally renormalized equation-of-motion approach with singles and doubles (LR-EOMCCSD), is compared with other excited-state methods that include up to two-body operators in the wave function expansion. In particular, the impact of the local denominators on the excitation energies is discussed in detail. Several benchmark calculations on the CH(+), C(2), N(2), O(3), and ClOCl molecules are presented to illustrate the performance of the LR-EOMCCSD approach.     

An Approach to Wavelet Isomorphisms of Function Spaces Via Atomic Representations

Both wavelet and atomic decomposition techniques are essential tools in the study of function spaces nowadays, but they both have their advantages and disadvantages. The celebrated bridge between both concepts was given by the compactly supported Daubechies wavelets which can be interpreted as atoms. In this paper we deal with the converse direction, that is, we present a fairly general approach how to construct compactly supported wavelets when an atomic decomposition is known already. The main idea is Taylor’s expansion combined with our new, so-called \(\varkappa \)-convergence assumption in the admitted sequence spaces. We finally exemplify our main result and collect some known and new settings where such a wavelet decomposition is obtained, e.g., in spaces of Besov or Triebel–Lizorkin type with a doubling weight.     

Exact and approximation methods for dependability assessment of tram systems with time window

The transportation system examined in this paper is the city tram one, where failed trams are replaced by reliable spare ones. If failed tram is repaired and delivered, then it comes back on work. There is the time window that failed tram has to be either replaced (exchanged) by spare or by repaired and delivered within. Time window is therefore paramount to user perception of transport system unreliability. Time between two subsequent failures, exchange time, and repair together with delivery time, respectively, are described by random variables A, E, and D. A/E/D is selected as the notation for these random variables. There is a finite number of spare trams. Delivery time does not depend on the number of repair facilities. Hence, repair and delivery process can be treated as one with infinite number of facilities. Undesirable event called hazard is the event: neither the replacement nor the delivery has been completed in the time window. The goal of the paper is to find the following relationships: hazard probability of the tram system and mean hazard time as functions of number of spare trams. For systems with exponential time between failures, Weibull exchange and exponential delivery (so M/W/M in the proposed notation) two accurate solutions have been found. For systems with Weibull time between failures with shape in the range from 0.9 to 1.1, Weibull exchange and exponential delivery (i.e. W/W/M) a method yielding small errors has been provided. For the most general and difficult case in which all the random variables conform to Weibull distribution (W/W/W) a method returning moderate errors has been given.     

Contrast mechanisms in photothermal scanning tunneling microscopy

By irradiation of the tunneling junction of a scanning tunneling microscope with intensity-modulated laser light a gap-width modulation due to thermal expansion of tip and sample was produced. Photothermal images were obtained by spatial mapping of the resulting modulation of the tunneling current or its logarithm. The various mechanisms responsible for the observed contrast are discussed quantitatively. In case of a highly corrugated gold film on mica the contrast arises mainly from either the current variations caused by the non-zero reaction time of the current control loop or from a geometry factor. In both cases the images reflect certain properties of the sample topography. On the other hand, for a liquid-crystal film adsorbed on graphite a contrast on a molecular scale was found which is attributed to variations of the effective barrier height.     

Directed Supramolecular Surface Assembly of SNAP‐tag Fusion Proteins

Supramolecular assembly of proteins on surfaces and vesicles was investigated by site‐selective incorporation of a supramolecular guest element on proteins. Fluorescent proteins were site‐selectively labeled with bisadamantane by SNAP‐tag technology. The assembly of the bisadamantane functionalized SNAP‐fusion proteins on cyclodextrin‐coated surfaces yielded stable monolayers. The binding of the fusion proteins is specific and occurs with an affinity in the order of 10⁶ M ^?1 as determined by surface plasmon resonance. Reversible micropatterns of the fusion proteins on micropatterned cyclodextrin surfaces were visualized by using fluorescence microscopy. Furthermore, the guest‐functionalized proteins could be assembled out of solution specifically onto the surface of cyclodextrin vesicles. The SNAP‐tag labeling of proteins thus allows for assembly of modified proteins through a host–guest interaction on different surfaces. This provides a new strategy in fabricating protein patterns on surfaces and takes advantage of the high labeling efficiency of the SNAP‐tag with designed supramolecular elements.