Notes on the non-autonomous Lyness equation

We prove that the solutions of the non-autonomous Lyness equation x_n+1=(x_n+b_n)/x_n−1, b_n>0, x₀>0, x₁>0, are bounded away from zero and infinity if the sequence b_n is monotonic. We also give an example to show that the solutions need not be bounded even when the sequence b_n attains only two values.     

Synthesis of protected derivatives of O-phosphotyrosine incorporation in a heptapeptide

The solid phase synthesis of the phosphopeptide Leu-Arg-Arg-Ala-Tyr(P)-Leu-Gly is reported via the stepwise incorporation of the protected phosphoamino acid Nα -tert-butyloxycarbonyl-O-dimethyl-phosphono-L-tyrosine.     

On the supposed equilibrium Ph6Pb2Ph4Pb+Ph2Pb in solution

The reaction between pentadeuteriophenyllithium and hexaphenyldilead combined with new measurements of isotopic exchange between Ph₆Pb₂ (labelled with RaD) and Ph₄Pb, have shown that the dilead compound is undissociated in solution. These results cast doubt upon the previously reported equilibrium: Ph₆Pb₂Ph₄Pb+Ph₂Pb.     

Synthesis of new 1,2,3-triazolo[1,2-a]benzotriazole derivatives or substituted 2,3-benzo-1,3a,6,6a-tetraazapentalenes. II

This paper continues the synthesis of new 1,2,3-triazolo[1,2-a]benzotriazoles or 2,3-benzo-1,3a,6,6a-tetrazapentalenes to submit to biological assays. The derivatives were obtained by deoxycyclization reactions of appropriate nitrophenyl-1,2,3-triazole derivatives and by thermal decomposition of appropriate azidophenyl-1,2,3-triazoles (Schemes 1 and 2). Some attempts to extend these synthetic routes to the preparation of 1,2,4-triazolo[1,2-a]benzotriazoles (Scheme 3) and 1,2,3-triazolo[1,2-b]-4H-1,2,3-benzo-triazines (Scheme 4) completely failed.     

A generalised London formula for dispersion coefficients

A generalised London formula is presented for the one-centre calculation of dispersion coefficients of spherically symmetric atoms in S-states in terms of the static multipole polarisabilities and the related orbital excitation energies of the individual atoms. The results obtained for the C₆, C₈, C₁₀ coefficients for H₂ and for the C₆ coefficients for He₂, Li₂, Be₂ and their mixtures are highly encouraging.     

New 1,2,3‐triazolo[4,5‐e]1,2,4‐triazolo[4,3‐c]pyrimidine derivatives II

The 7‐chloro‐3‐(2‐chlorobenzyl)‐ and 7‐chloro‐3‐(2‐fluorobenzyl)‐1,2,3‐triazolo[4,5‐d]pyrimidines ( 1 and 4 ), by nucleophilic replacement with some hydrazides, gave the corresponding 7‐hydrazidoderivatives ( 2a‐e and 5a‐e ). These, by heating in Dowtherm, underwent an intramolecular cyclization to form the new tricyclic 7‐substituted‐3‐(2‐chlorobenzyl)‐ and 3‐(2‐fluorobenzyl)‐1,2,3‐triazolo[4,5‐e]1,2,4‐triazolo[4,3‐c]pyrimidines ( 3a‐d and 6a‐d ). The 7‐hydrazino‐3‐(2‐chlorobenzyl)‐ and 7‐hydrazino‐3‐(2‐fluorobenzyl)‐triazolo‐pyrimidines ( 9a and 9b ) were also prepared via the corresponding mercapto ( 7a and 7b ) and thiomethyl ( 8a and 8b ) derivatives.     

Determination of metal concentration in fat supplements for swine nutrition by atomic absorption spectroscopy

The presence of some essential and toxic metals in fat supplements for swine diet was investigated. Collected samples represented a relevant production of the Italian industry. In particular, some samples were enriched with antioxidants or waste cooking oils. The method for the determination of Ca, Cu, Cd, Fe, Mg, Mn, Ni, Pb, and Zn in fat samples was developed by means of a certified reference material (CRM 186) and a representative fatty sample (RFS). All samples were digested in closed vessels in a microwave oven and then analyzed by flame atomic absorption or graphite furnace atomic absorption spectrometry. The entire analytical method provided a satisfactory repeatability and reproducibility confirmed by agreement between the experimental recovery data obtained for the CRM 186 sample and, with the method of standard additions, for the RFS material. The samples generally showed a small amount of metals compared with the recommended daily intake for the essential elements. On the other hand, some samples contained a significant concentration, from an analytical point of view, of Cd, Ni, and Pb. Principal component analysis (PCA) was applied to inspect the experimental data obtained from samples analysis. Basically no differences were detected in terms of metal concentration among the fat supplements analyzed.     

Can simple enones be useful partners for the catalytic stereoselective alkylation of indoles?

A new catalytic system for the first example of enantioselective Friedel-Crafts-type (FC) addition of indoles to simple enones is described. The use of an equimolar amount of chiral [Al(salen)Cl] and 2,6-lutidine (10 mol %) was found to be effective in promoting the conjugate addition of indoles to (E)-arylcrotyl ketones, furnishing the corresponding beta-indolyl ketones in excellent yield and high enantioselectivity (ee up to 89%). The role of the base was investigated through spectroscopic as well as computational analyses, which suggested that in situ formation of a new chiral (base.[Al(salen)]) complex was operating under our reaction conditions. In particular, a stable cationic [Al(salen)] hexacoordinate trans complex with the additive base and the enone is suggested as being responsible for the stereocontrolled reaction. Finally, detailed monitoring of the reaction course was carried out showing that a conventional FC pathway induced by [Al(salen)Cl] acting as a Lewis acid is operating.     

1,2,3-Triazolo[4,5-d]-1,2,4-triazolo[4,3-b]pyridazines

Some new 1,2,3-triazolo[4,5-d]-1,2,4-triazolo[4,3-b]pyridazines were prepared starting from the corresponding 1,2,3-triazolo[4,5-d]pyridazines via the formation of the 1,2,4-triazole ring, by condensation of an appropriate monocarbon fragment with the 4-hydrazino substituent and the nitrogen atom in the 5 position of the heterocycle. Condensation of 4-phenylhydrazino substituted derivatives with formic acid gave zwitterionic compounds.