Counting BPS States on the Enriques Calabi-Yau

We study topological string amplitudes for the FHSV model using various techniques. This model has a type II realization involving a Calabi-Yau threefold with Enriques fibres, which we call the Enriques Calabi-Yau. By applying heterotic/type IIA duality, we compute the topological amplitudes in the fibre to all genera. It turns out that there are two different ways to do the computation that lead to topological couplings with different BPS content. One of them gives the standard D0-D2 counting amplitudes, and from the other one we obtain information about bound states of D0-D4-D2 branes on the Enriques fibre. We also study the model using mirror symmetry and the holomorphic anomaly equations. We verify in this way the heterotic results for the D0-D2 generating functional for low genera and find closed expressions for the topological amplitudes on the total space in terms of modular forms, and up to genus three. This model turns out to be much simpler than the generic B-model and might be exactly solvable.     

In Situ Generated Gold Nanoparticles on Active Carbon as Reusable Highly Efficient Catalysts for a C −C Stille Coupling

Gold nanoparticle catalysts are important in many industrial production processes. Nevertheless, for traditional C ?C cross‐coupling reactions they have been rarely used and Pd catalysts usually give a superior performance. Herein we report that in situ formed gold metal nanoparticles are highly active catalysts for the cross coupling of allylstannanes and activated alkylbromides to form C ?C bonds. Turnover numbers up to 29 000 could be achieved in the presence of active carbon as solid support, which allowed for convenient catalyst recovery and reuse. The present study is a rare case where a gold metal catalyst is superior to Pd catalysts in a cross‐coupling reaction of an organic halide and an organometallic reagent.     

Analytical Investigations of Bacterial Cellulose

The cultivation of the bacterium Acetobacter xylinus AX 5 was carried out in the common Hestrin-Schramm medium containing D -glucose as C-source and citric acid as buffer component. HPLC studies proved to be convenient methods to investigate the stability and interactions of these constituents in the starting culture liquid. Within the initial sterilization step and limited by the citric acid, up to 6% of the D -glucose was partially isomerized to D-fructose and degraded to dark-yellow products. In static culture, A. xylinus AX 5 produces cellulose extracellularly on the surface of this medium. Solid-state NMR spectroscopy represents a suitable analytical method to characterize the supramolecular structure of the bacterial cellulose in never-dried, air-dried, and freeze-dried states. It could be demonstrated that the drying process reduces the degree of crystallinity in the range of about 12% without changes in the Iα/β ratio of these cellulose modifications.     

ConFlo III - an interface for high precision delta(13)C and delta(15)N analysis with an extended dynamic range

A newly developed interface coupling a CHN combustion device (elemental analyser 'EA') to an isotope ratio mass spectrometer is described and evaluated. The purpose of the device is to extend the dynamic range of delta(13)C and delta(15)N analysis from less than 2 orders of magnitude to more than 3 orders of magnitude. Carbon isotope ratio measurements of atropine as a model compound have been performed analysing between 1 μg to 5 mg C with acceptable to excellent precision (0.6 to 0.06 per thousand, delta-notation). The correction due to the blank signal is critical for sample amounts smaller than 4 μg C. The maximum sample weight is determined by the combustion capacity of the EA. Larger sample amounts are measured using dilution of a small part of the EA effluent with helium. The dilution mechanism works virtually free of isotope fractionation. Copyright 1999 John Wiley & Sons, Ltd.     

Preparative and 1H NMR Investigation on Regioselective Silylation of Starch Dissolved in Dimethyl Sulfoxide

Reaction of starch 1 dissolved in dimethyl sulfoxide (DMSO) with bulky thexyldimethylchlorosilane (TDSCl) in the presence of pyridine leads to regioselectively functionalized silyl ethers with a degree of substitution (DS) up to 1.8. The control of the DS_Si, of the regioselectivity, and of the reaction pathway is described in detail. The reaction proceeds homogeneously up to DS_Si of 0.6. With ongoing silylation the polymers form a separate phase incorporating the silylating agent to form TDS‐starches with DS_Si values higher than 1.0. After peracetylation of the silyl starches, the substitution pattern has been characterized not only in the anhydroglucose repeating units (AGU) but also in the non‐reducing terminal end groups (TEG) by means of two‐dimensional ¹H NMR techniques. Up to DS_Si 1.0, a very high regioselective functionalization of the primary 6‐OH groups in the AGU as well as in the TEG is detectable. With increasing silylation (DS_Si > 1.0), the subsequent silylation takes place at the 2‐OH groups of the AGU and at the 3‐OH groups of the TEG. These results are compared with our own investigations on the silylation of starch in the reaction system N‐methylpyrrolidone (NMP)/ammonia and on the silylation of cellulose in N,N‐dimethylacetamide (DMA)/LiCl/pyridine solution.     

DC- and RF-GD-OES measurements of adsorbed organic monolayers on copper

Our direct current (DC)- and radiofrequency glow discharge optical emission spectroscopy (RF-GD-OES) measurements of adsorbed organic monolayers were inspired by the work of Shimizu et al., who presented the first example of depth profile analysis of an adsorbed monolayer by RF-GD-OES in 2004. The great potential of RF-GD-OES for analyses of layers with thicknesses in the subnanometer range was surprising. Shimizu et al. discussed not only the qualitative detection of atoms of the organic monolayer (C, H, N, S), but also the determination of the different orientation of the molecules relative to the surface due to a significant peak sequence. This latter assumption was questioned in the analytical community. We intend to demonstrate the potential of the GD-OES technique for surface analysis in terms of reliability and reproducibility by using an advanced vacuum instrumentation and presputtering with silicon. It will be shown that comparable measurements can be reproduced not only with RF-GD-OES but, above all, also with DC-GD-OES. The experimental steps to adsorb thiourea molecules on a copper substrate are described in detail. Further experiments with other organic molecules, e.g. benzotriazole (BTA) or benzothiazole (BTH), disprove the predicted correlation between the orientation of the molecules relative to the surface and the occurrence of peak separation. Ultimately, a quantification of compounds of the organic monolayer in the case of adsorbed thiourea is achieved.      

A note on fundamental,non-fundamental,and robust cycle bases

In many biological systems, robustness is achieved by redundant wiring, and reflected by the presence of cycles in the graphs connecting the systems’ components. When analyzing such graphs, cyclically robust cycle bases of are of interest since they can be used to generate all cycles of a given 2-connected graph by iteratively adding basis cycles. It is known that strictly fundamental (or Kirchhoff) bases, i.e., those that can be derived from a spanning tree, are not necessarily cyclically robust. Here we note that, conversely, cyclically robust bases (even of planar graphs) are not necessarily fundamental. Furthermore, we present a class of cubic graphs for which cyclically robust bases can be explicitly constructed.     

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.     

Electrochemical texturing of Al-doped ZnO thin films for photovoltaic applications

The processes during chemical and electrochemical etching of Al-doped ZnO are investigated utilizing a scanning flow cell setup with online detection of dissolved Zn ions. The rate of chemical dissolution was found to be a linear function of buffer and proton concentration in near neutral pH solutions according to a transport limited reaction. In contrast, electrochemical etching is limited by the kinetics of the reaction and increases linearly with the imposed current density. Due to this fundamental difference, the dissolution of Zn can be either uniform over the whole surface or highly localized at active sites like grain boundaries. A combined approach of chemical etching and the well-controllable galvanostatic dissolution thus allows a fine adjustment of the ZnO:Al surface texture for applications in silicon thin film photovoltaic cells in order to improve their overall energy conversion efficiency.