Unitals which meet Baer subplanes in 1 moduloq points

We prove that a parabolic unitalU in a translation plane of orderq ² with kernel containing GF(q) is a Buekenhout-Metz unital if and only if certain Baer subplanes containing the translation line of meetU in 1 moduloq points. As a corollary we show that a unital 16-03 in PG(2,q ²) is classical if and only if it meets each Baer subplane of PG(2,q ²) in 1 moduloq points.     

The preparation of 2,6-diaminopyrazine, 2,6-diazidopyrazine and some of their derivatives

A much improved synthesis of the heretofore difficultly obtainable 2,6-diaminopyrazine (4) was afforded by the low-pressure catalytic hydrogenation (palladium on carbon) of 2,6-diazido-pyrazine (2) ; reaction of 2,6-dichloropyrazine (1) and sodium azide gave 2 in 84% yield. The outcome of the reduction was found to be solvent dependent: 1,2-dimethoxyethane containing aqueous ammonia gave 4 in 83% yield; 1,2-dimethoxyethane alone gave 5-aminotetrazolo[1,5-a]-pyrazine (3) in 26% yield. Additional alternative syntheses of 3 and 4 are described. A number of acyl and azo derivatives of 4 were prepared. Reactions of 2 with dimethyl acetylenedicarboxylate and ethyl acetate (base catalyzed) leading to vic-triazole derivatives are also described.     

Vibrations and thermodynamics of clusters of polycyclic aromatic hydrocarbon molecules: the role of internal modes

The vibrational spectra of clusters of coronene molecules are theoretically calculated using a mixed quantum/classical scheme, each molecule being described by a tight-binding Hamiltonian, the intermolecular forces being provided by explicit Lennard-Jones and point charge sites. The normal modes of vibrations are shown to exhibit significant variations upon clustering. In particular, for large clusters intra- and intermolecular modes tend to mix and fill the mid-infrared range. We also calculate the heat capacity of the (C24H12)8 cluster as a function of temperature, emphasizing the isomerizations that take place during melting. Quantum delocalization effects, as obtained from the Pitzer-Gwinn semiclassical approximation, are important enough to wash out all signatures of the structural transitions on the caloric curve. On the basis of a simple two-state model we estimate that clusters containing about 300 molecules are required for melting to be detected on the caloric curve.     

Estimating entropies from molecular dynamics simulations

While the determination of free-energy differences by MD simulation has become a standard procedure for which many techniques have been developed, total entropies and entropy differences are still hardly ever computed. An overview of techniques to determine entropy differences is given, and the accuracy and convergence behavior of five methods based on thermodynamic integration and perturbation techniques was evaluated using liquid water as a test system. Reasonably accurate entropy differences are obtained through thermodynamic integration in which many copies of a solute are desolvated. When only one solute molecule is involved, only two methods seem to yield useful results, the calculation of solute-solvent entropy through thermodynamic integration, and the calculation of solvation entropy through the temperature derivative of the corresponding free-energy difference. One-step perturbation methods seem unsuitable to obtain entropy estimates.     

Linked Supramolecular Building Blocks for Enhanced Cluster Formation

Methylene‐bridged calix[4]arenes have emerged as extremely versatile ligand supports in the formation of new polymetallic clusters possessing fascinating magnetic properties. Metal ion binding rules established for this building block allow one to partially rationalise the complex assembly process. The ability to covalently link calix[4]arenes at the methylene bridge provides significantly improved control over the introduction of different metal centres to resulting cluster motifs. Clusters assembled from bis‐calix[4]arenes and transition metal ions or 3d‐4f combinations display characteristic features of the analogous calix[4]arene supported clusters, thereby demonstrating an enhanced and rational approach towards the targeted synthesis of complex and challenging structures.     

Synthesis of novel β-lactams bearing an anthraquinone moiety,and evaluation of their antimalarial activities

A novel series of β-lactams bearing an anthraquinone moiety have been synthesized from imines derived from anthraquinone-2-carbaldehyde and ketenes by a [2+2] cycloaddition reaction. The cycloadducts were fully characterized and evaluated for their antimalarial activities against Plasmodium falciparum K14 resistant strain and showed moderate to excellent EC₅₀ values varying from 9 to 50 μM.     

Acetalization of glycerol using mesoporous MoO3/SiO2 solid acid catalyst

Acetalization of glycerol with various aldehydes has been carried out using mesoporous MoO₃/SiO₂ as a solid acid catalyst. A series of MoO₃/SiO₂ catalysts with varying MoO₃ loadings (1–20 mol%) were prepared by sol–gel technique using ethyl silicate-40 and ammonium heptamolybdate as silica and molybdenum source respectively. The sol–gel derived samples were calcined at 500 °C and characterized using various physicochemical characterization techniques. The XRD of the calcined samples showed the formation of amorphous phase up to 10 mol% MoO₃ loading and at higher loading of crystalline α-MoO₃ on amorphous silica support. TEM analyses of the materials showed the uniform distribution of MoO₃ nanoparticles on amorphous silica support. Raman spectroscopy showed the formation of silicomolybdic acid at low Mo loading and a mixture of α-MoO₃ and polymolybdate species at high Mo loadings. Moreover the Raman spectra of intermediate loading samples also suggest the presence of β-MoO₃. Acetalization of glycerol with benzaldehyde was carried out using series of MoO₃/SiO₂ catalysts with varying MoO₃ loadings (1–20 mol%). Among the series, MoO₃/SiO₂ with 20 mol% MoO₃ loadings was found to be the most active catalyst in acetalization under mild conditions. Maximum conversion of benzaldehyde (72%) was obtained in 8 h at 100 °C with 60% selectivity for the six-membered acetal using 20% MoO₃/SiO₂. Interestingly with substituted benzaldehydes under same reaction conditions the conversion of aldehydes decreased with increase in selectivity for six-membered acetals. These results indicate the potential of this catalyst for the acetalization of glycerol for an environmentally benign process.     

Depth notions for orthogonal regression

Global depth, tangent depth and simplicial depths for classical and orthogonal regression are compared in examples, and properties that are useful for calculations are derived. The robustness of the maximum simplicial depth estimates is shown in examples. Algorithms for the calculation of depths for orthogonal regression are proposed, and tests for multiple regression are transferred to orthogonal regression. These tests are distribution free in the case of bivariate observations. For a particular test problem, the powers of tests that are based on simplicial depth and tangent depth are compared by simulations.