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.     

Vibronic intensities in centrosymmetric coordination compounds of the rare earths Part II. A vibronic crystal field-closure-ligand polarisation model and applications to the PrCl6 and UBr6 complex ions in octahedral symmetry

A symmetry adapted formalism to evaluate the vibronic intensities induced by the ungerade vibrational modes in centrosymmetric coordination compounds of the rare earths is put forward and applied to several selected electronic transitions of the PrCl³⁻₆ and UCl²⁻₆ complex ions in octahedral symmetry. This current model is based upon a modified symmetry adapted version of the combined vibronic crystal field-closure-ligand polarisation approach. This model differs from that developed in Part I of this series, in that for the vibronic crystal field contribution to the total transition dipole moment, the closure procedure is employed rather than the utilisation of a truncated basis set for the central metal intermediate electronic states. A criterion is introduced to choose an appropriate set of phases for both the electronic and the vibrational coordinates so that to ensure the right sign for the interference term (which couples together both the vibronic crystal field and the vibronic ligand polarisation contributions to the total transition dipole moment). We have focused our attention on the modulation of the intermolecular force field and a version of a modified general valence force field has been adopted. The reasons for using this formalism rather than the superposition model (SM) are fully discussed in the text. Finally, it is shown that the agreement with experiment is satisfactory for most of the components of the transitions studied, despite the apparent simplicity of our model calculation. General master equations applicable to any f^N electronic configurations are derived to show the utility and flexibility of this current formalism.     

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%.     

Vibronic intensities in centrosymmetric lanthanide complex ions. I

Summary A theoretical model to calculate the vibronic intensities induced by the odd vibrational modes in centrosymmetric lanthanide complexes is developed and applied to octahedral complex ions, LnX ₆ ^3– , such as occur in the hexachloroelpasolites Cs₂NaLnCl₆. Both the crystal field and the ligand polarisation contributions are evaluated using a standard set of symmetry coordinates. For the crystal field term a truncated expansion of the intermediates states is employed rather than the more conventional closure approximation. Special care is necessary to ensure that the phases of the contributions are correctly determined since the cross-term between the ligand polarisation and crystal field contributions is signed. General equations applicable to anyf ⁿ complex ion are derived and an example of their application to the PrCl ₆ ^3– ion is given The agreement with experiment is satisfactory.     

Emission studies of pyrene solutions

Emission spectra of pyrene in hexane have been obtained over a temperature range (from 130 to 260 K) that has not been explored before for concentrations ranging from 10^?4 mole/? to 2 × 10^?2 mole/?. A conventional and new approximation which does not depend on the experimental set-up response functions has been used for evaluating pyrene excimer association energy W_DM and other pyrene parameters. In both methods W_DM agrees quite satisfactorlly, at all concentrations used, with that reported in the literature and obtained by other techniques. However, both approximation fail to yield the right values of the rate parameters at concentrations ? 2 g/?. This set the upper limit of sample solubility to be at C = 2g/? for our range of temperature. Furthermore, the new approximation can probably be used at higher concentration (for higher range of temperature) and even may be used for other organic molecules. There was also no difference in the ratio of the excimer (I_D) to monomer (I_M) quantum yields when an intense laser beam was used as a source of excitation rather than a super-pressure Hg-lamp. This suggested that the concentrations we used might not be large enough. As a result, the laser beam would not create enough density of excited molecules to affect the ratio of I_D/I_M.     

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.