Section Pseudophrys is a taxonomically critical species complex that has a history of circumscriptional uncertainty, suggesting the need for further evaluation. Its taxonomy in the Iberian Peninsula has been controversial, with treatments ranging from three species and three subspecies to ten species. Extensive observations in the field and analysis of morphological characters based on 50 populations sampled show that most of the characters used by previous authors for distinguishing the species are variable among or even within populations. In the present study, representatives from the Iberian Peninsula and Morocco were investigated using morphometric and molecular (nuclear ribosomal ITS sequences) analyses. Seventeen floral characters and, in addition, four ratios, were measured from 642 live plants belonging to 50 populations of representatives of sect. Pseudophrys ( Ophrys arnoldii , O. bilunulata , O. dianica , O. fusca and O. lupercalis ). To determine characters distinguishing different species and to examine their circumscription, we performed morphometric analyses on three different subsets of sect. Pseudophrys , one with all the currently recognized species, another containing the closely related O. bilunulata and O. dianica , and finally the populations of O. arnoldii and O. lupercalis . These populations were treated as Operational Taxonomic Units (OTUs) and studied using cluster analysis, principal component analysis (PCA) and canonical discriminant analysis (CDA); box plots of selected quantitative characters were also made. Finally, variation in nrITS sequences among eight members of sect. Pseudophrys was analysed phylogenetically. Our results indicate that sect. Pseudophrys is monophyletic and well supported. We maintain the recognition of all taxa studied except O. arnoldii , and do not recognize any new taxa based on our examinations of the different populations of O. lupercalis .
Abstract. We shall prove an equiconvergence theorem between Fourier-Bessel expansions of functions in certain weighted Lebesgue spaces and the classical cosine Fourier expansions of suitable related functions. These weighted Lebesgue spaces arise naturally in the harmonic analysis of radial functions on euclidean spaces and we shall use the equiconvergence result to deduce sharp results for the pointwise almost everywhere convergence of Fourier integrals of radial functions in the Lorentz spaces LP'q(W). Also we shall briefly apply the above approach to the study of the harmonic analysis of radial functions on noneuclidean hyperbolic spaces.
In 1869 Hermann Hankel proved what is by now known as Hankel's inversion formula for Fourier-Bessel expansions:Revisiting [Hankel] we shall prove an equiconvergence theorem between FourierBessel expansions of functions in certain weighted Lebesgue spaces and the classical cosine Fourier expansions of suitable related functions. These weighted Lebesgue spaces arise naturally in the harmonic analysis of radial functions on euclidean spaces and we shall use the equiconvergence result to deduce sharp results for the pointwise almost everywhere convergence of Fourier in-
A sequential flow injection method for simultaneous chloride and fluoride determination in waters with potentiometric detection is described. The method is based on the simultaneous chloride and fluoride potentiometric detection using two ion selective electrodes in two serial flow-through cells. The necessary ionic strength adjustment is obtained by mixing the TISAB solution with the sample by diffusion during the propelling process to the detection cells. The new method was applied successfully to drinking water samples.
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