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.     

Reactions of difluorocarbene with conjugated polyfluorodienes

Heating 2-chloroperfluoro-1,3-butadiene or perfluoro-1,3-pentadiene with excess hexafluoropropylene oxide leads to the formation of the corresponding cyclopentenes.Translated from Izvestiya Akademii Nauk SSSR, Seriya Khimicheskaya, No. 6, pp. 1430–1431, June, 1990.     

The least square nucleolus is a general nucleolus

This short note proves that the least square nucleolus (Ruiz et al. (1996)) and the lexicographical solution (Sakawa and Nishizaki (1994)) select the same imputation in each game with nonempty imputation set. As a consequence the least square nucleolus is a general nucleolus (Maschler et al. (1992)). Received: December 1998/Revised version: July 1999     

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.     

Fractal signature methods for profiling of processed surfaces

A new approach to surface profiling of structural materials that evolves from the concept of fractal signature is put forward. This approach has been developed and advantageously applied for acquisition of low-contrast targets. It is based on the fractal theory, and fractal signatures and fractal dimensions (which are intimately related to both the object’s topology and evolutionary processes in dynamic systems) are used as estimating parameters. The experimental data obtained prove the existence of fractal clusters on the processed surface microrelief. Quantitative characterization of these clusters is given.     

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.