Second structure relation for semiclassical orthogonal polynomials

Classical orthogonal polynomials are characterized from their orthogonality and by a first or second structure relation. For the semiclassical orthogonal polynomials (a generalization of the classical ones), we find only the first structure relation in the literature. In this paper, we establish a second structure relation. In particular, we deduce it by means of a general finite-type relation between a semiclassical polynomial sequence and the sequence of its monic derivatives.     

Mineral salts removal and lithium traces determination in highly concentrated solutions and natural brines

The usual methods, of lithium traces determination, refer in particular to the aqueous solutions whose dry residues do not exceed 7 g L⁻¹. Flame spectrometry or atomic absorption is used for the determination of the considered element.In the case of natural brines, the total dissolved salt ranges from 250 to 350 g L⁻¹. Consequently the determination of lithium traces in this kind of solutions, by the above mentioned spectroscopic methods, may be disturbed due to interferences phenomena. So, a preparatory processing step of the samples is needed.In order to prevent the mentioned phenomena, the total or partial removal of mineral salts, by adding appropriate organic solvent, is carried out. Accordingly, it is significant to make sure that the total quantity of lithium remains in the solution.Therefore, the experimental conditions (sulfate ion removal, solvent ratio and solid-liquid contact time) are optimized. After that the different experimental steps are arranged to make sure the lithium determination, by flame spectrometry, practicable.Finally, the established method is applied firstly to determine Li⁺ in some natural brines and secondly to estimate the lithium reserves in the Tunisian natural brines deposits.     

Purification and properties of two laccase isoenzymes produced byBotrytis cinerea

Laccases produced by five strains ofBotrytis cinerea were studied. Extraction and purification have been performed in order to compare the enzymatic characteristics both, physicochemically and kinetically. Two strains produced isoenzymes of laccase. These two molecular forms of laccase had different isoelectric points (2.6 and 2.8) and sugar content (86 and 91%). The optimum reactional pH was found to be very similar for both enzymes, in contrast to the temperature sensitivity, which is very different.     

On the cut polytope

The cut polytopeP _C (G) of a graphG=(V, E) is the convex hull of the incidence vectors of all edge sets of cuts ofG. We show some classes of facet-defining inequalities ofP _C (G). We describe three methods with which new facet-defining inequalities ofP _C (G) can be constructed from known ones. In particular, we show that inequalities associated with chordless cycles define facets of this polytope; moreover, for these inequalities a polynomial algorithm to solve the separation problem is presented. We characterize the facet defining inequalities ofP _C (G) ifG is not contractible toK ₅. We give a simple characterization of adjacency inP _C (G) and prove that for complete graphs this polytope has diameter one and thatP _C (G) has the Hirsch property. A relationship betweenP _C (G) and the convex hull of incidence vectors of balancing edge sets of a signed graph is studied.