A surface containing a line and a circle through each point is a quadric

We prove that a surface in 3-dimensional Euclidean space containing a line and a circle through each point is a quadric. We also give some particular results on the classification of surfaces containing several circles through each point.     

Heterocyclization of electrophilic alkenes with tetranitromethane revisited: regiochemistry and the mechanism of nitroisoxazole formation

Revised regiochemistry for the heterocyclization of electrophilic alkenes with tetranitromethane (TNM) in the presence of triethylamine, providing rapid access to nitroisoxazoles, is reported. The formation of 5-nitroisoxazoles previously incorrectly assigned as 3-nitro regioisomers, has now been established unambiguously by X-ray crystallography. Empirical computations with ACD/CNMR Predictor, based both on hierarchical ordering of spherical environments (HOSE) and an algorithm of artificial neural networks (ANN), and also Density Functional Theory computations of the ¹³C NMR chemical shifts for the 3- versus 5-nitroisoxazoles are shown to consistently match the spectra of the experimentally observed 5-regioisomers.     

Counting master integrals: Integration by parts vs. differential reduction

The techniques of integration by parts and differential reduction differ in the counting of master integrals. This is illustrated using as an example the two-loop sunset diagram with on-shell kinematics. A new algebraic relation between the master integrals of the two-loop sunset diagram that does not follow from the standard integration-by-parts technique is found.     

Superacid mediated hydroxyalkylation reaction of 1,2,3‐indanetrione: a theoretical study

Energies of mono‐ and multiprotonation for 1,2,3‐indanetrione and ninhydrin in triflic acid (TFSA) media were estimated at PBE0/aug‐cc‐pvtz//6‐31+G** level of theory. The reactivity of formed intermediates in the reaction of aromatic electrophilic substitution has been studied at the same level of theory. It appears that the basicity of carbonyl groups in 1,2,3‐indanetrione is extremely low due to mutual influences of carbonyl groups. Carbonyl 2 is the least basic but the most reactive in accordance with experiment. Calculations demonstrated that monoprotonated intermediates are the principal reactive species in the reaction of hydroxyalkylation of 1,2,3‐indanetrione in TFSA. A new isomerization mechanism of 2,2‐diaryl‐1,3‐indanediones to 3‐(diarylmethylene)isobenzofuranones in TFSA media has been proposed. Copyright © 2010 John Wiley & Sons, Ltd.     

Efficient entry into hydrazinopeptide-like structures via sequential Ugi reactions

Novel types of hydrazinopeptide-like units containing five elements of diversity have been prepared in two steps using sequential Ugi reactions.     

A computational DFT analysis of OH chemisorption on catalytic Pt(111) nanoparticles

In this article, various energies and geometries of pure platinum nanoparticles and those of platinum nanoparticles with adsorbed OH were investigated. Fourteen different platinum clusters of 3–40 atoms were studied using spin-unrestricted density functional theory (DFT) with a double numerical plus polarization basis set. This range of sizes gave enough information for establishing the general trends that were the primary goal of the study. Three different shapes of platinum clusters were presented, and the effect of cluster size on binding energy, total energy, and HOMO–LUMO energy gap was investigated. Subsequently, same calculations were performed for those selected Pt clusters with OH adsorbate on the surface. The results show that the stability of both the pure clusters and the clusters with adsorbed OH molecule increases with an increase of cluster size. This fact indicates that direct influence of the size of Pt cluster on the reaction rate is possible, and the understanding of how cluster size would affect binding energy is important. As expected, the effect of cluster size on total energy of molecule was shown to be a linear function independent of cluster type. We also found that optimized (stable) Pt clusters were bigger in size than that of the initial clusters, or clusters with bulk geometry.     

Synthesis,structure and properties of N-aminosaccharin – A selective inhibitor of human carbonic anhydrase I

Previously unknown N-aminosaccharin was prepared in good yield via the one-step direct amination of saccharin sodium salt with hydroxylamine-O-mesitylenesulfonic acid (MSH) and its reactivity investigated. N-aminosaccharin and its derivatives were tested against hCA isoforms and the parent compound was identified to be a selective, low micromolar inhibitor (K_i = 8.8 μM) of hCA I. These findings provide a ligand-efficient starting point for the design of potent hCA I inhibitors – a promising drug target for retinal/cerebral edema treatment.