Atomic-scale friction on stepped surfaces of ionic crystals

We report on high-resolution friction force microscopy on a stepped NaCl(001) surface in ultrahigh vacuum. The measurements were performed on single cleavage step edges. When blunt tips are used, friction is found to increase while scanning both up and down a step edge. With atomically sharp tips, friction still increases upwards, but it decreases and even changes sign downwards. Our observations extend previous results obtained without resolving atomic features and are associated with the competition between the Schw?bel barrier and the asymmetric potential well accompanying the step edges.     

Microwave absorption studies of MgB2 superconductor

Microwave absorption studies have been carried out on MgB₂ superconductor using a standard X-band EPR spectrometer. The modulated low-field microwave absorption signals recorded for polycrystalline (grain size ∼ 10 μm) samples suggested the absence of weak-link character. The field dependent direct microwave absorption has been found to obey a ✓H dependence with two different slopes, which indicated a transition from strongly pinned lattice to flux flow regime.     

A Laboratory Study of Heterogeneous Catalysis in Ultrahigh Vacuum

A surface science experiment has been developed that can be used in both the undergraduate and graduate curriculum. Students study the mechanism of carbon monoxide oxidation using a platinum foil catalyst, and they also get hands-on experience with ultrahigh vacuum equipment. Using temperature programmed desorption, students study the desorption of carbon monoxide and oxygen from platinum foil in vacuum. The study allows students to determine that the Langmuir-Hinshelwood reaction mechanism operates in this catalytic system.     

On modified Picard and Gauss—Weierstrass singular integrals

We introduce a certain modification of the Picard and Gauss—Weierstrass singular integrals and prove approximation theorems for them. Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 57, No. 11, pp. 1577–1584, November, 2005.     

1,3‐Bis(ethylamino)‐2‐nitrobenzene, 1,3‐bis(n‐octylamino)‐2‐nitrobenzene and 4‐ethylamino‐2‐methyl‐1H‐benzimidazole

1,3‐Bis(ethylamino)‐2‐nitrobenzene, C₁₀H₁₅N₃O₂, (I), and 1,3‐bis(n‐octylamino)‐2‐nitrobenzene, C₂₂H₃₉N₃O₂, (II), are the first structurally characterized 1,3‐bis(n‐alkylamino)‐2‐nitrobenzenes. Both molecules are bisected though the nitro N atom and the 2‐C and 5‐C atoms of the ring by twofold rotation axes. Both display intramolecular N—H...O hydrogen bonds between the amine and nitro groups, but no intermolecular hydrogen bonding. The nearly planar molecules pack into flat layers ca 3.4 Å apart that interact by hydrophobic interactions involving the n‐alkyl groups rather than by π–π interactions between the rings. The intra‐ and intermolecular interactions in these molecules are of interest in understanding the physical properties of polymers made from them. Upon heating in the presence of anhydrous potassium carbonate in dimethylacetamide, (I) and (II) cyclize with formal loss of hydrogen peroxide to form substituted benzimidazoles. Thus, 4‐ethylamino‐2‐methyl‐1H‐benzimidazole, C₁₀H₁₃N₃, (III), was obtained from (I) under these reaction conditions. Compound (III) contains two independent molecules with no imposed internal symmetry. The molecules are linked into chains via N—H...N hydrogen bonds involving the imidazole rings, while the ethylamino groups do not participate in any hydrogen bonding. This is the first reported structure of a benzimidazole derivative with 4‐amino and 2‐alkyl substituents.     

Tree-width and dimension

Over the last 30 years, researchers have investigated connections between dimension for posets and planarity for graphs. Here we extend this line of research to the structural graph theory parameter tree-width by proving that the dimension of a finite poset is bounded in terms of its height and the tree-width of its cover graph.     

Robust partial least squares model for prediction of green tea antioxidant capacity from chromatograms

In this paper a robust version of the partial least squares model (partial robust M-regression, PRM) was built to predict the total antioxidant capacity of green tea extracts. In order to construct a calibration model, chromatograms obtained by a fast high-performance liquid chromatographic method on a monolithic silica column were related with the total antioxidant capacity of green tea extracts as determined by the Trolox antioxidant capacity method. Since natural samples are the subject of the study, some outlying samples are present in the data, as shown in an earlier work. Therefore, to construct reliable calibration models, they were detected and removed prior to modeling. With the applied robust partial least squares approach, where a weighting scheme is embedded to down-weight the negative influence of outliers upon the model it is possible to construct a robust calibration model, without prior identification of outlying objects. It was shown that a robust model, allowing satisfactory prediction for test samples, can be used in controlling green tea antioxidant capacity based on their chromatograms. The constructed robust partial least squares model was shown to have virtually the same fit and predictive power as the classical partial least squares model when outlying samples were removed from the data.