Quotient probabilistic normed spaces and completeness results

We introduce the concept of quotient in PN spaces and give some examples. We prove some theorems with regard to the completeness of a quotient.     

Talbot self-imaging in fractional Fourier planes of real and complex orders

A study of Talbot self-imaging associated with fractional Fourier transforms (FRFTs) of real and complex orders, as realised by bulk lenses, is presented. Self-images of a periodic object, corresponding to different orders, can be observed in different FRFT planes, herein called Talbot-FRFT planes. The spatial scaling factor of the self-images is shown to be a harmonic function of the FRFT order.     

Implementation of recycling routes for scanning probe microscopy tips.

In this work, effective, yet simple, recycling mechanisms for used scanning probe microscopy (SPM) tips were implemented. Comprising a tip profile characterization methodology and specific cleaning procedures, which decontaminate SPM tips whether the contamination nature is known or not, such routes were optimized during numerous tests with brand new, previously used, and already discarded categories of SPM tips. The results show that if the used tip suffered contamination only, but no physical damages, during its scanning lifetime, it becomes readily available for reutilization after the cleansing process, characterizing a recycling route. On the other hand, if the tip went through wear and breakages during its utilization, it still can be decontaminated, but may not be directly reutilized due to its inadequate physical profile. Nevertheless, the methodology developed in this work may yet be applied as part of a more complex recycling route.     

Thermal reactions of tributyltin hydride with alpha-azido esters: unexpected intervention of tin triazene adducts under both nonradical and radical conditions

Thermal reaction of various alpha-azido esters with Bu(3)SnH in refluxing benzene results in smooth production of 3-(tributylstannyl)-1-triazene adducts affording cyclized 1,2,3-triazol-4-ones in preference to reduced amines and thence provides a new useful method for the preparation of these triazole derivatives. In the presence of AIBN the occurrence of triazene products still remains important or even exclusive and, consequently, generation of the expected stannylaminyl radicals is seriously limited. With 2-azidomalonates and alpha-azido-beta-keto esters stannyltriazenes can similarly occur in the absence of the radical initiator, but in the latter cases the ensuing triazenes undergo preferential cyclization onto the ketone moiety to give reactive hydroxytriazolines. Contrary to alpha-azido esters, in the presence of AIBN alpha-azido-beta-keto esters as well as azidomalonates give rise only to the usual stannylaminyl radicals. A possible explanation for the different behavior of the mono- and dicarbonyl azides in the presence of AIBN is put forward.     

Intramolecular cyclization of acyl radicals onto the azido group: a new radical approach to cyclized lactams

[reaction: see text] Aryl- and alkyl-derived azidoacyl radicals, generated from thiolesters by intramolecular homolytic substitution at the sulfur, can undergo five- and six-membered cyclization onto the azido moiety to give cyclized lactams.     

Determination of sulfametoxazole, sulfadiazine and associated compounds in pharmaceutical preparations by capillary zone electrophoresis

A capillary zone electrophoresis method is presented to separate sulfadiazine, sulfamethoxazole, trimethoprim, bromhexine and guaiacol by using a fused-silica capillary (60.2 cm x 75 microm I.D.). The separation was carried out at 30 kV and 25 degrees C in a 15 mM phosphate buffer adjusted to pH 6.2 as electrolyte. Under these conditions, the run time was 6 min and the limits of quantification were about 1 mg/l for every component. The method was applied to pharmaceutical preparations and the results provided recoveries close to 100%.     

Development and validation of an analytical methodology for the determination of p,p′-DDT, p,p′-DDE and p,p′-DDD in fish oil pills

An analytical methodology was proposed and validated to be applied to the determination of p,p′-DDT and its metabolites p,p′-DDE and p,p′-DDD in fish oil. The analytical procedure presented in this paper involves a single-step clean up process prior to the analysis. A solution of 1,2,3,4-tetrachloronaphtalene was used as internal standard.The analytical technique used was gas chromatography coupled to an electron capture detector. Details on the validation process are provided.The limits of detection ranged from 2.6 to 4.7 pg μL^− 1. The BCR 598 standard reference material (cod liver oil) was used to evaluate the performance of the methodology with satisfactory recoveries for all the compounds.The analytes were determined in three different fish oil pills sold in Spain as a supplementary vitamin support. The sum of p,p′-DDT and metabolites was from 13.2 to 51.3 ng g^− 1, the dominant compound being p,p′-DDE.     

A priori error estimates for numerical methods for scalar conservation laws. Part I: The general approach

In this paper, we construct a general theory of a priori error estimates for scalar conservation laws by suitably modifying the original Kuznetsov approximation theory. As a first application of this general technique, we show that error estimates for conservation laws can be obtained without having to use explicitly any regularity properties of the approximate solution. Thus, we obtain optimal error estimates for the Engquist-Osher scheme without using the fact (i) that the solution is uniformly bounded, (ii) that the scheme is total variation diminishing, and (iii) that the discrete semigroup associated with the scheme has the -contraction property, which guarantees an upper bound for the modulus of continuity in time of the approximate solution.

     

Detection of soil pollution by hydrocarbons using headspace-mass spectrometry and identification of compounds by headspace-fast gas chromatography-mass spectrometry

The direct coupling of a headspace sampler with a mass spectrometer is proposed as a screening tool for the rapid detection of soil pollution by hydrocarbons from petroleum and derivatives. The samples are subjected to the headspace generation process, with no prior treatment, and the volatiles generated are introduced directly into the mass spectrometer, thereby obtaining a fingerprint of the sample analysed. Suitable treatment of the signal by chemometric techniques allows unequivocal characterisation of the different types of sample. The use of fast gas chromatography with a mass spectrometer detector coupled to the headspace sampler allows identification of the major hydrocarbons present in the mineral and organic polluted samples, interpretation of the results obtained, and demonstrates the analytical potential of headspace-mass spectrometry coupling.