Line-bundle-valued ternary quadratic forms over schemes

We study degenerations of rank 3 quadratic forms and of rank 4 Azumaya algebras, and extend what is known for good forms and Azumaya algebras. By considering line-bundle-valued forms, we extend the theorem of Max-Albert Knus that the Witt-invariant—the even Clifford algebra of a form—suffices for classification. An algebra Zariski-locally the even Clifford algebra of a ternary form is so globally up to twisting by square roots of line bundles. The general, usual and special orthogonal groups of a form are determined in terms of automorphism groups of its Witt-invariant. Martin Kneser’s characteristic-free notion of semiregular form is used.     

Growth and characteristics of reactive pulsed laser deposited molybdenum trioxide thin films

Molybdenum trioxide thin films were prepared by reactive pulsed laser deposition on Corning 7059 glass substrates. The influence of oxygen partial pressure and deposition temperature on the structure, surface morphology and optical properties of these films was studied to understand the growth mechanism of MoO₃ thin films. The films formed at 473 K in an oxygen partial pressure of 100 mTorr exhibited predominantly a (0k0) orientation, corresponding to an orthorhombic layered structure of α-MoO₃. The evaluated optical band gap of the films was 3.24 eV. The crystallite size increased with increase of deposition temperature. The films formed at an oxygen partial pressure of pO₂=100 mTorr and at a deposition temperature greater than 700 K exhibited both (0k0) and (0kl) orientations, representing α-β mixed phases of MoO₃. The films formed at an oxygen partial pressure less than 100 mTorr were found to be sub-stoichiometric with α-β mixed phases. The investigation revealed the growth of polycrystalline and single-phase orthorhombic-layered-structure α-MoO₃ thin films with composition nearly approaching the nominal stoichiometry at moderate substrate temperatures in an oxygen partial pressure of 100 mTorr. Received: 9 April 2001 / Accepted: 6 August 2001 / Published online: 17 October 2001     

Understanding guest and pressure‐induced porosity through structural transition in flexible interpenetrated MOF by Raman spectroscopy

Interpenetrating metal organic frameworks are interesting functional materials exhibiting exceptional framework properties. Uptake or exclusion of guest molecules can induce sliding in the framework making it porous or non‐porous. To understand this dynamic nature and how framework interaction changes during sliding, metal organic framework (MOF) 508 {Zn(BDC)( 4,4′‐Bipy)_0.5 · DMF(H₂O)_0.5} was selected for study. We have investigated structural transformation in MOF‐508 under variable conditions of temperature, pressure and gas loading using Raman spectroscopy and substantiated it with IR studies and density functional theory (DFT) calculations. Conformational changes in the organic linkers leading to the sliding of the framework result in changes in Raman spectra. These changes in the organic linkers are measured as a function of high pressure and low temperature, suggesting that the dynamism in MOF‐508 framework is driven by ligand conformation change and inter‐linker interactions. The presence of Raman signatures of adsorbed CO₂ and its librational mode at 149 cm⁻¹ suggests cooperative adsorption of CO₂ in the MOF‐508 framework, which is also confirmed from DFT calculations that give a binding energy of 34 kJ/mol. Copyright © 2015 John Wiley & Sons, Ltd.     

Four oxoindole‐linked α‐alkoxy‐β‐amino acid derivatives

Four structures of oxoindolyl α‐hydroxy‐β‐amino acid derivatives, namely, methyl 2‐{3‐[(tert‐butoxycarbonyl)amino]‐1‐methyl‐2‐oxoindolin‐3‐yl}‐2‐methoxy‐2‐phenylacetate, C₂₄H₂₈N₂O₆, (I), methyl 2‐{3‐[(tert‐butoxycarbonyl)amino]‐1‐methyl‐2‐oxoindolin‐3‐yl}‐2‐ethoxy‐2‐phenylacetate, C₂₅H₃₀N₂O₆, (II), methyl 2‐{3‐[(tert‐butoxycarbonyl)amino]‐1‐methyl‐2‐oxoindolin‐3‐yl}‐2‐[(4‐methoxybenzyl)oxy]‐2‐phenylacetate, C₃₁H₃₄N₂O₇, (III), and methyl 2‐[(anthracen‐9‐yl)methoxy]‐2‐{3‐[(tert‐butoxycarbonyl)amino]‐1‐methyl‐2‐oxoindolin‐3‐yl}‐2‐phenylacetate, C₃₈H₃₆N₂O₆, (IV), have been determined. The diastereoselectivity of the chemical reaction involving α‐diazoesters and isatin imines in the presence of benzyl alcohol is confirmed through the relative configuration of the two stereogenic centres. In esters (I) and (III), the amide group adopts an anti conformation, whereas the conformation is syn in esters (II) and (IV). Nevertheless, the amide group forms intramolecular N—H...O hydrogen bonds with the ester and ether O atoms in all four structures. The ether‐linked substituents are in the extended conformation in all four structures. Ester (II) is dominated by intermolecular N—H...O hydrogen‐bond interactions. In contrast, the remaining three structures are sustained by C—H...O hydrogen‐bond interactions.     

Effect of heterocyclic ring system on formation of dimeric quinolones under catalyst-free conditions: a green approach

The intermediate-dependent green and efficient synthesis of dimeric quinolones 4a–l and 7a–l by the Knoevenagel condensation followed by Michael-type addition of 4-hydroxy-1-methylquinolin-2(1H)-one 1a, b to indole-3-aldehydes 2a–f and aromatic aldehydes 5a–l in water through the condensed compound 3a–l under catalyst-free conditions is described. This reaction was found to be environmentally friendly, has easy-workup and shorter reaction times giving good yields of the product without the need for its isolation using column chromatography.     

Integrated quality by design (QbD) and design of experiments (DoE) approach for UFLC determination of telaprevir in rat serum

An ultrafast liquid chromatographic bioanalytical method was developed and validated for the determination of telaprevir in Wistar albino rat serum. Principles of quality by design (QbD) were implemented for enhancing the bioanalytical liquid–liquid extraction of telaprevir from rat serum. A Box–Behnken design was utilized in the studies by selecting extraction time, centrifugation speed, and vortex time as the critical method variables for evaluating their effect on the critical analytical attribute, i.e., %recovery of telaprevir. Chromatographic separation was achieved within a run time of 10?min using a C-18 column and mobile phase comprising of methanol:borate buffer of pH 9 (90:10 v/v) flowing at 1.2?mL/min. Photodiode array detection was performed at 270?nm. Results of validation studies were satisfactory. The method was linear over a concentration of 25–10,000?ng/mL. Limit of detection for the developed method was 10?ng/mL. Further, design of experiments (DoE) used for inter-day accuracy and precision study suggested superior method reliability. This integrated QbD- and DoE-based approach ensured the development of a validated and reliable analytical method for optimum bioanalysis of telaprevir in biological matrix.     

Quotient and product sets of thin subsets of the positive integers

We study the cardinalities of A/A and AA for thin subsets A of the set of the first n positive integers. In particular, we consider the typical size of these quantities for random sets A of zero density and compare them with the sizes of A/A and AA for subsets of the shifted primes and the set of sums of two integral squares.     

Flow past an axisymmetric body embedded in a saturated porous mediumÉcoulement derrière un corps à symétrie axiale plongé dans un milieu poreux saturé

The problem of viscous fluid past an axisymmetric body embedded in a fluid saturated porous medium is studied using the Brinkman's extension. A general formula for the drag on the body is derived in the form of a limit of an expression involving the stream function characterizing the flow. The flow past an axisymmetric approximate sphere is also considered. The stream function in this case is obtained in terms of Bessel functions and Gegenbauer's functions. The drag acting on the body is evaluated by using the formula derived. Its variation is studied with respect to geometric and permeability parameters. The special cases of flow past a sphere and a spheroid are obtained from the present analysis. To cite this article: D. Srinivasa Charya, J.V. Ramana Murthy, C. R. Mecanique 330 (2002) 417–423.     

Synthesis and Antimicrobial Activity of Amido Sulfonamido Methane Linked Bisoxazoles,Bisthiazoles, and Bisimidazoles

A new class of amido sulfonamido methane linked bisoxazoles, bisthiazoles, and bisimidazoles were prepared adopting simple and versatile synthetic methodologies. The lead compounds were assayed for antimicrobial activity.