Higher order derived functors and the Adams spectral sequence

Classical homological algebra studies chain complexes, resolutions, and derived functors in additive categories. In this paper we define higher order chain complexes, resolutions, and derived functors in the context of a new type of algebraic structure, called an algebra of left cubical balls  . We show that higher order resolutions exist in these algebras, and that they determine higher order Ext-groups. In particular, the _Em$E_m$-term of the Adams spectral sequence (m>2)$(m>2)$ is such a higher Ext-group, providing a new way of constructing its differentials.     

4-(Dimethylamino)pyridine as a powerful auxiliary reagent in the electroless synthesis of gold nanotubes

Gold nanotubes of small particle sizes down to 5 nm and high aspect ratios were synthesized in ion track etched polycarbonate following a rational reaction design. 4-(Dimethylamino)pyridine (DMAP) was employed to adjust the electroless deposition by interfering with the autocatalytically active gold surface. Modification of the pH value and DMAP concentration led to a wide range of products which were characterized by SEM, TEM, and EDS. Filigree nanotubes of 10-15 nm wall thickness and 5.0 ± 2.1 nm grain size were obtained as well as robust and free-standing structures proving homogeneous deposition along the whole template length of 30 μm. Template-supported gold nanotubes were applied in the UV-vis monitored reduction of 4-nitrophenol by sodium borohydride under pseudo-first-order conditions. They proved to be a reliable microfluidic system of excellent catalytic activity coming up with an apparent rate constant of 1.3 × 10(-2) s(-1). Despite a high flow rate, the reaction showed 99% conversion after a distance of just 60 μm.     

Nanofibers resulting from cooperative electrostatic and hydrophobic interactions between peptides and polyelectrolytes of opposite charge

We investigated whether cationic peptides that contain hydrophobic side chains were able to stabilize themselves via hydrophobic interactions between neighboring peptide molecules upon electrostatic binding to oppositely charged polyelectrolytes. The interaction mechanism was examined through a model system consisting of the anionic polyelectrolyte alginate and the cationic decapeptide ozarelix. The interaction resulted in the formation of highly ordered complexes that were noticeable upon visual inspection. These complexes were then investigated by microscopic techniques and shown to exhibit a branched network structure. Cryogenic-temperature transmission electron microscopy (cryo-TEM) and negative staining TEM revealed that the molecular interactions between alginate and ozarelix led to the formation of nanofibers. The rodlike nanofibers had a diameter distribution of 4-8 nm. Isothermal titration calorimetry was used to determine the thermodynamic parameters of the alginate-ozarelix interaction. The binding constant was found to be on the order of 10(6) M(-1), indicating a high binding affinity. The interaction of the peptide with the polyelectrolyte triggered profound changes in the conformation of ozarelix, which was confirmed by UV spectroscopy and circular dichroism. On the basis of these experimental results, a theoretical modeling study of the alginate-ozarelix interaction was conducted to gain a better molecular-level understanding of the complex structure. It revealed that, upon binding of ozarelix to alginate, new intermolecular and intramolecular aromatic interactions between the ozarelix molecules occurred. These interactions changed the conformation of the peptide, a modification in which the aromatic side chains played a major role. Our results indicate that the cationic peptides interact with the polyanions via electrostatic interactions, but are additionally stabilized via hydrophobic interactions. This binding mode may serve as a powerful tool to extend the duration of drug release in hydrogel drug delivery systems.     

Ring-closing metathesis of sulfoximine-substituted N-tethered trienes: modular asymmetric synthesis of medium-ring nitrogen heterocycles

A synthesis of sulfoximine-substituted medium-ring nitrogen heterocycles (MRNHs) having a high degree of substitution has been developed. Its key steps are the modular asymmetric synthesis of sulfoximine-substituted N-tethered trienes and their Ru-catalyzed ring-closing metathesis (RCM) reaction. The highly substituted N-tethered trienes were obtained enantio- and diastereopure through 1) the diastereoselective aminoalkylation of sulfoximine-substituted allyltitanium complexes with N-tert-butylsulfonyliminoester, 2) N-allylation of homoallylic N-sulfonyl amines, 3) allylation, hydroxylalkylation, and formylation of α-lithioalkenylsulfoximines, and 4) allylation of α-formylalkenylsulfoximines. The Ru-catalyzed RCM reaction of the sulfoximine-substituted 1,7,10- and 1,7,12-trienes stereoselectively afforded the corresponding nine-, ten-, and eleven-membered MRNHs in good yields. An interesting difference in reactivity was noted in the case of a sulfoximine-substituted 1,7,10-triene and its corresponding 1,10-diene. While the triene readily underwent a RCM reaction, the diene reacted only in the presence of Ti(OiPr)(4) under formation of the corresponding MRNH. The feasibility of a removal of the sulfoximine auxiliary and the N-sulfonyl protecting group from the MRNHs were demonstrated through reduction and cleavage, respectively, of a nine-membered heterocycle, both of which proceeded readily and gave the corresponding cyclic alkene and amine, respectively.     

Performance evaluation of numerical methods for the Maxwell–Liouville–von Neumann equations

The Maxwell–Liouville–von Neumann (MLN) equations are a valuable tool in nonlinear optics in general and to model quantum cascade lasers in particular. Several numerical methods to solve these equations with different accuracy and computational complexity have been proposed in related literature. We present an open-source framework for solving the MLN equations and parallel implementations of three numerical methods using OpenMP. The performance measurements demonstrate the efficiency of the parallelization.     

The net distribution of elements in multiphase polymer materials via element-specific electron microscopy

Applications of the Electron Spectroscopic Imaging technique (ESI) within the field of multiphase polymer materials are discussed. Imaging with elastically scattered electrons as well as imaging with electrons with defined energy loss are presented. From the latter the net distribution of elements can be derived. Several examples are given: Glassy diblock copolymers polystyrene-block-poly(2-vinyl pyridine), polyethylenes, interpenetrating networks, interdiffusion couples, blends of polystyrene and polystyrene-graft-poly(oxyethylene), carbon black reinforced natural rubber, and epitactic growth of poly(1-pentenylene) on isotactic poly (propylene) surface. Visualization of the rigid amorphous phase in polyethylene is presented, as well as electron spectroscopic diffraction (ESD) of oriented PE. One of the features of ESI is due to the fact that discrimination between true morphology and artefacts is possible in an unbiased manner, even for minor details: Heavy metal staining is abandonable, and structural analysis by one element may be proved by analysis with other elements, which may be present in the sample or which may be added by chemical reaction or interaction with groups within the molecules.