Algebras of quotients of path algebras

Leavitt path algebras are shown to be algebras of right quotients of their corresponding path algebras. Using this fact we obtain maximal algebras of right quotients from those (Leavitt) path algebras whose associated graph satisfies that every vertex connects to a line point (equivalently, the Leavitt path algebra has essential socle). We also introduce and characterize the algebraic counterpart of Toeplitz algebras.     

Determination of trace amounts of cobalt in water by solid-phase spectrophotometry after preconcentration on a nitroso R salt chelating resin

A sensitive method for the determination of microamounts of cobalt by ion-exchanger spectrophotometry has been developed. The chromogenic agent, Nitroso-R-Salt (NRS), was loaded on an anionic-exchange resin (Amberlite CG-400). The absorbance of the NRS-cobalt complex on the chelating resin was measured at 508 nm. The best conditions for the preconcentration of cobalt on the resin before the spectrophotometric determination were a pH value of 6, temperature of 80 °C, and heating times of 45 or 90 min for 50 and 400 ml of sample, respectively. The detection limits were 27 ng/ml (50-ml samples) and 1.8 ng/ml (400-ml samples). Interference by other metals was investigated. The method is useful for determination of cobalt in natural waters.     

UV spectrophotometric flow-injection assay of tetracycline antibiotics retained on Sephadex QAE A-25 in drug formulations

A flow injection analysis system with solid phase spectrophotometric transduction has been developed for the assay of tetracycline (TC), doxycicline (DTC), oxycicline (OTC) and chlortetracycline (CTC). The packing material of the flow-through cell consists of Sephadex QAE A-25 resin on which tetracyclines are temporarily retained. The carrier itself acts as the desorbing solution. The measurements of the intrinsic absorbance of tetracyclines (1000 μl of sample volume) were made at 380 nm (TC, DTC and OTC) and 387 nm (CTC). The detection limits were found to be 0.069 (TC and OTC), 0.081 (DTC) and 0.121 (CTC) μg ml⁻¹ and the linear dynamic range extended between 0.5 and 12 (TC, DTC and OTC) and 1–20 μg ml⁻¹ (CTC). The relative standard deviations (n=10) ranged between 0.7 and 1.2%. A study of the potentially interfering species was carried out. Using the proposed method, tetracyclines were satisfactorily determined without any interference from excipients in pharmaceutical preparations.     

Localized modes on an Ablowitz-Ladik nonlinear impurity

We study localized modes on a single Ablowitz-Ladik impurity embedded in the bulk or at the surface of a one-dimensional linear lattice. Exact expressions are obtained for the bound state profile and energy. Dynamical excitation of the localized mode reveals exponentially-high amplitude oscillations of the spatial profile at the impurity location. The presence of a surface increases the minimum nonlinearity to effect a dynamical selftrapping.     

Comparing Metrics at Large: Harmonic vs Quo-Harmonic Coordinates

To compare two space-times on large domains, and in particular the global structure of their manifolds, requires using identical frames of reference and associated coordinate conditions. In this paper we use and compare two classes of time-like congruences and corresponding adapted coordinates: the harmonic and quo-harmonic classes. Besides the intrinsic definition and some of their intrinsic properties and differences we consider with some detail their differences at the level of the linearized approximation of the field equations. The hard part of this paper is an explicit and general determination of the harmonic and quo-harmonic coordinates adapted to the stationary character of three well-know metrics, Schwarzschild's, Curzon's and Kerr's, to order five of their asymptotic expansions. It also contains some relevant remarks on such problems as defining the multipoles of vacuum solutions or matching interior and exterior solutions.     

Local Rings of Rings of Quotients

The aim of this paper is to characterize those elements in a semiprime ring R for which taking local rings at elements and rings of quotients are commuting operations. If Q denotes the maximal ring of left quotients of R, then this happens precisely for those elements if R which are von Neumann regular in Q. An intrinsic characterization of such elements is given. We derive as a consequence that the maximal left quotient ring of a prime ring with a nonzero PI-element is primitive and has nonzero socle. If we change Q to the Martindale symmetric ring of quotients, or to the maximal symmetric ring of quotients of R, we obtain similar results: an element a in R is von Neumann regular if and only if the ring of quotients of the local ring of R at a is isomorphic to the local ring of Q at a. Partially supported by the Ministerio de Educación y Ciencia and Fondos Feder, jointly, trough projects MTM2004-03845, MTM2007-61978 and MTM2004-06580-C02-02, MTM2007-60333, by the Junta de Andalucía, FQM-264, FQM336 and FQM02467 and by the Plan de Investigación del Principado de Asturias FICYT-IB05-017.     

Desirability functions as response in a d‐optimal design for evaluating the extraction and purification steps of six tranquillizers and an anti‐adrenergic by liquid chromatography‐tandem mass spectrometry

Internal standards can be added at different stages of an analytical procedure. When they are added at the beginning of a multiresidue method and their behavior is not exactly the same as that of the analytes, the intended correction for small variations within the analytical process could not be achieved. Because of this, in the present work, the use of d ‐optimal designs together with desirability functions is proposed to state the experimental response under study. The overall desirability function used relates two analytical criteria: to assess a similar chemical behavior of each analyte in relation to its internal standard and to avoid a significant reduction of the absolute peak area of the internal standards. This strategy has been applied to the analysis of the effect of four factors related to the extraction and purification steps of six tranquillizers and a β‐blocker from pig muscle analyzed by liquid chromatography–tandem mass spectrometry. The effect of those factors has been evaluated by means of an ad hoc d ‐optimal design consisting of only 11 experiments. The resulting levels of the four factors that enable to achieve the greatest overall desirability have also been compared with those obtained when either the standardized or absolute peak area has been considered as response. Differences in both the significant factors and their optimum levels have been observed. It is noticeable that the experimental effort necessary to study the effect of the factors has been reduced by more than 50% thanks to the d ‐optimal design. Copyright © 2015 John Wiley & Sons, Ltd.     

Additive Differential Pulse Voltammetry for the Study of Slow Charge Transfer Processes at Spherical Electrodes

The application of additive differential pulse voltammetry to the study of the kinetics of a charge transfer process is studied. A simple analytical solution is presented, valid for spherical electrodes of any size and for electrode processes of any reversibility. From this solution, valuable diagnostic criteria for the elucidation of the electrochemical reversibility are established based on the variation of the ADPV signal with the duration of the potential pulses, the electrode radius and the pulse height. Working curves for the determination of the kinetic parameters are also given. The value of the ADPV technique is experimentally demonstrated by studying the kinetics of the reduction of 3‐nitrophenolate^? and europium³⁺ at mercury hemispherical microelectrodes.