Computation of limit periodic continued fractions. A survey

Over the last 20 years a large number of algorithms has been published to improve the speed and domain of convergence of continued fractions. In this survey we show that these algorithms are strongly related. Actually, they essentially boil down to two main principles.We also prove some results on asymptotic expansions of tail values of limit periodic continued fractions.Dedicated to Luigi Gatteschi on his seventieth birthdayThis research was partially supported by The Norwegian Research Council and by the HMC project ROLLS, under contract CHRX-CT93-0416.     

Application of hydrophilic ionic liquids as co-solvents in chloroperoxidase catalyzed oxidations

The effect of hydrophilic ionic liquids (ILs) on the activity of chloroperoxidase (CPO) was checked through kinetic and stereochemical studies. The possibility to employ this enzyme in synthesis has been demonstrated investigating the chemo- and stereoselectivity of oxidation of phenyl methylsulfide in several citrate buffer-IL mixtures.     

Pediatric Laryngotracheal Stenosis and Airway Reconstruction: A Review of Voice Outcomes, Assessment, and Treatment Issues

Laryngotracheal stenosis is defined as a congenital or acquired narrowing of the airway. Congenital causes may include subglottic membranous or cartilaginous narrowing. Acquired causes may include trauma due to prolonged endotracheal or tracheal intubation or laryngotracheal injury. Although advances have been made over the past 30 years in reconstructive surgeries to improve airway patency in these patients, long-term laryngeal function for voice production is not well defined in this population. This review examines causes, symptoms and signs, and methods for diagnosing laryngotracheal stenosis. Surgical management procedures are briefly summarized. The current literature on voice outcomes is summarized. The predominant voice characteristics in the population are presented, although results are challenged by the heterogeneity of voice presentation and paucity of data from instrumental measures. Considerations for subjective and instrumental assessment, measures of quality of life, instrumental methods, and treatment options specific to the needs of this population are discussed. Research strategies to identify long-term outcomes of surgical and behavioral treatments in this population are posed.     

Competing kinetic pathways in the bromine addition to allylic ethers in 1,2‐dichloroethane: Opposite temperature effects

The kinetics of the electrophilic bromination of three allylic ethers in a nonprotic solvent, 1,2‐dichloroethane, has been investigated. Two of them followed a prevalent second‐order pathway, while the third one exhibited a classical, clean third order. The second‐order pathway in the first two olefins is attributed to electrophilic assistance of the ethereal oxygen to the attacking bromine molecule. In the molecular bromination of 2,4‐cis‐dimethyl‐8‐oxabicyclo[3.2.1]‐6‐octen‐3‐cis‐ol, opposite temperature dependences were found for the two different kinetic pathways. An exoergonic process for the second‐order reaction was explained by the lesser stability of the bromiranium–bromide ionic intermediate, compared to the bromiranium–tribromide in the third‐order profile. © 2007 Wiley Periodicals, Inc. 39: 197–203, 2007     

Implementation of some higher-order convection schemes on non-uniform grids

A generalized formulation is applied to implement the quadratic upstream interpolation (QUICK) scheme, the second-order upwind (SOU) scheme and the second-order hybrid scheme (SHYBRID) on non-uniform grids. The implementation method is simple. The accuracy and efficiency of these higher-order schemes on non-uniform grids are assessed. Three well-known bench mark convection-diffusion problems and a fluid flow problem are revisited using non-uniform grids. These are: (1) transport of a scalar tracer by a uniform velocity field; (2) heat transport in a recirculating flow; (3) two-dimensional non-linear Burgers equations; and (4) a two-dimensional incompressible Navier-Stokes flow which is similar to the classical lid-driven cavity flow. The known exact solutions of the last three problems make it possible to thoroughly evaluate accuracies of various uniform and non-uniform grids. Higher accuracy is obtained for fewer grid points on non-uniform grids. The order of accuracy of the examined schemes is maintained for some tested problems if the distribution of non-uniform grid points is properly chosen.     

Self-organized ZnAl2O4 nanostructures grown on -sapphire

Self-organized ZnAl₂O₄ nanostructures with the appearance (in SEM) of high aspect ratio horizontal nanowires are grown on uncatalysed c-sapphire by vapour phase transport. The nanostructures grow as three equivalent crystallographic variants on c-sapphire. Raman and cathodoluminescence spectroscopy confirm that the nanostructures are not ZnO and TEM shows that they are the cubic spinel, zinc aluminate, ZnAl₂O₄, formed by the reaction of Zn and O with the sapphire substrate.     

Indirect boundary element method for unsteady linearized flow over prolate and oblate spheroids and hemispheroidal protuberances

The indirect boundary element method was used to study the hydrodynamics of oscillatory viscous flow over prolate and oblate spheroids, and over hemispheroidal bodies hinged to a plate. Analytic techniques, such as spheroidal coordinates, method of images, and series representations, were used to make the numerical methods more efficient. A novel method for computing the hydrodynamic torque was used, since for oscillatory flow the torque cannot be computed directly from the weightings. Instead, a Green's function for torque was derived to compute the torque indirectly from the weightings. For full spheroids, the method was checked by comparing the results to exact solutions at low and high frequencies, and to results computed using the singularity method. For hemispheroids hinged to a plate, the method for low frequencies was checked by comparing the results to previous results, and to exact solutions at high frequencies. Copyright © 2004 John Wiley & Sons, Ltd.     

Synthesis,characterization and coordination chemistry of the new tetraazamacrocycle 4,10-dimethyl-1,4,7,10-tetraazacyclododecane-1,7-bis(methanephosphonic acid monoethyl ester) dipotassium salt

A new potentially hexadentate tetraazamacrocycle based on the cyclen skeleton has been synthesized and fully characterized. The macrocycle 4,10-dimethyl-1,4,7,10-tetraazacyclododecane-1,7-bis(methanephosphonic acid monoethyl ester) dipotassium salt (Me2DO2PME) contains mutually trans monoethyl ester phosphonate acid substituents on two nitrogen atoms, and trans methyl substituents on the other two nitrogen atoms. The protonation constants of this macrocycle and the stability constants of its complexes with Cu2+, Zn2+, Gd3+ and Ca2+ ions have been determined by pH potentiometric titrations. The protonation sequence of the macrocycle has been studied by 1H, 31P[1H] and 13C[1H] NMR spectroscopy: the first and second protonation steps take place at the methyl-substituted nitrogen atoms, while the third protonation involves one oxygen from a phosphonate group. Upon protonation, all the CH2 ring protons become magnetically inequivalent on the NMR time scale due to a slow conformational rearrangement, most likely occasioned by the formation of multiple hydrogen bonds within the macrocyclic ring. Me2DOPM forms neutral, mononuclear complexes with all the metals investigated. The presence of hydroxo complexes was observed for Ca2+ and Zn2+ at high pH values. Structural information on the neutral complex [Cu(Me2DO2PME)] has been obtained by a solution X-Band EPR study. It is proposed that Me2DO2PME binds Cu2+ in a distorted octahedral structure using all of its donor atoms, i.e. the four nitrogen atoms and the two phosphonate oxygen atoms. The redox chemistry of [Cu(Me2DO2PME)] in dimethyl sulfoxide and water has been studied by electrochemical measurements. Cyclic voltammetry in DMSO shows the complex to undergo a quasireversible one-electron reduction step leading to an unstable CuI species.     

Structures of new secofriedelane and friedelane acids from Calophyllum inophyllum of French Polynesia

Three new friedelane-type triterpenoids, 3,4-secofriedelan-3,28-dioic acid (1), 27-hydroxyacetate canophyllic acid (2) and 3-oxo-27-hydroxyacetate friedelan-28-oic acid (3), were isolated from the leaves of Calophyllum inophyllum (Clusiaceae) grown in French Polynesia. Their structures were established by the concerted application of 2D NMR techniques including gs-COSY, gs-HMQC and gs-HMBC.