Axioms ◽  
2021 ◽  
Vol 10 (2) ◽  
pp. 107
Author(s):  
Juan Carlos García-Ardila ◽  
Francisco Marcellán

Given a quasi-definite linear functional u in the linear space of polynomials with complex coefficients, let us consider the corresponding sequence of monic orthogonal polynomials (SMOP in short) (Pn)n≥0. For a canonical Christoffel transformation u˜=(x−c)u with SMOP (P˜n)n≥0, we are interested to study the relation between u˜ and u(1)˜, where u(1) is the linear functional for the associated orthogonal polynomials of the first kind (Pn(1))n≥0, and u(1)˜=(x−c)u(1) is its Christoffel transformation. This problem is also studied for canonical Geronimus transformations.


Foods ◽  
2020 ◽  
Vol 9 (6) ◽  
pp. 710 ◽  
Author(s):  
Jean Paul Formosa ◽  
Frederick Lia ◽  
David Mifsud ◽  
Claude Farrugia

Maltese honey has been produced, marketed, and sold as an exclusive local gourmet food product for countless years. Yet, thus far, no study has evaluated the individuality of this local food product. The evaluation of the parameters and properties which characterise the provenance and floral source of honey have been the subject of various studies worldwide, owing to the price and potential beneficial properties of this food product. Models analysing the potential of attenuated total reflection mid-infrared (ATR-FT-MIR) spectroscopy in discriminating and classifying local honey from that of foreign origin were investigated using 21 Maltese honey samples and 49 honey samples collected from abroad (Sicily, Greece, Sweden, Italy, France, Estonia and other samples of mixed geographical origin). Through a combination of spectroscopic techniques, spectral transformations, variable selection and partial least squares discriminant analysis (PLS-DA), chemometric models which successfully classified the provenance of local and non-local honey were developed. The results of these models were also corroborated with other classification and pattern recognition techniques, such as linear discriminate analysis (LDA), support vector machines (SVM) and feed-forward artificial neural networks (FF-ANN).


2012 ◽  
Vol 82 (282) ◽  
pp. 1057-1068 ◽  
Author(s):  
Kenier Castillo ◽  
Francisco Marcellán

2008 ◽  
Vol 49 (1-4) ◽  
pp. 169-185 ◽  
Author(s):  
Luis Garza ◽  
Javier Hernández ◽  
Francisco Marcellán

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