Fluorinated heterocyclic compounds. An expedient route to 5-perfluoroalkyl-1,2,4-triazoles via an unusual hydrazinolysis of 5-perfluoroalkyl-1,2,4-oxadiazoles: first examples of an ANRORC-like reaction in 1,2,4-oxadiazole derivatives

The hydrazinolysis reaction of 5-perfluoroalkyl-1,2,4-oxadiazoles has been investigated. Nucleophilic addition of the reagent to the C(5)-N(4) double bond of the oxadiazole ring, followed by ring-opening and then ring-closure involving the beta-nitrogen atom of the hydrazino moiety and the C(3) of the oxadiazole ring, explains the formation of 5-perfluoroalkyl-1,2,4-triazoles as final products. Useful applications in synthesis of this uncommon hydrazinolysis can be claimed.     

On-line determination of trace levels of palladium by flame atomic absorption spectrometry

A preconcentration method is developed for the on-line determination of palladium in complex matrices with flame atomic absorption spectrometry (FAAS). The flow system comprised of a minicolumn filled with polyamine Metalfix-Chelamine resin which is highly selective for Pt(IV), Au(III) and Pd(II). Best preconcentration conditions are established by testing different resin quantities, sample and eluent solution volumes, and adsorption and elution steps flow rates. Sample volumes of 4.7 ml of palladium solutions resulted in an enrichment factor of twenty at the optimum hydrodynamic conditions. This value can be increased by injecting larger volumes of sample solution. The method is sensitive, easy to operate and permitted the determination of sub-mg l⁻¹ levels of palladium with a detection limit of 0.009 mg l⁻¹. The resin was used up to 60 times in consecutive retention-elution cycles without any appreciable deterioration in its performance. The applicability of this method was tested by determining the palladium content in synthetic geological samples as well as in the pellet-type used car catalyst reference material.     

Softening the long-wavelength electromagnetic response of finite quantal systems

The long wavelength electromagnetic response of finite quantal systems depend on the spill-out of fermions from the surface of the system as well as on its deformation, as testified by the analysis of results obtained for fullerenes C₆₀, C₇₀, C₉₀, C₁₁₀ and C₂₈H_n, as well as for alkali metal clusters, in particular Na₈. Similar results are also found in the study of the electromagnetic response of atomic nuclei.     

Tetra-2,3-pyrazinoporphyrazines with externally appended pyridine rings. 3. A new highly electron-deficient octacationic macrocycle: tetrakis-2,3-[5,6-di{2-(N-methyl)pyridiniumyl}pyrazino]porphyrazine, [(2-Mepy)8TPyzPzH(2)]8+

A new octacationic macrocycle, tetrakis-2,3-[5,6-di{2-(N-methyl)pyridiniumyl}pyrazino]porphyrazine, was obtained in its hydrated form as the water-soluble iodide salt. This compound, abbreviated as [(2-Mepy)(8)TPyzPzH(2)](I(8)).8H(2)O (2-Mepy = 2(N-methyl)pyridiniumyl moiety), was obtained by demetalation of the corresponding Mg(II) complex, [(2-Mepy)(8)TPyzPzMg(H(2)O)](I(8)).5H(2)O, which in turn was prepared from its corresponding neutral hydrated species tetrakis-2,3-[5,6-di(2-pyridyl)pyrazino]porphyrazinato(monoaquo)magnesium(II), [Py(8)TPyzPzMg(H(2)O)].4H(2)O, by reaction with CH(3)I in N,N-dimethylformamide. The quaternization reactions by using CH(3)I or methyl p-toluenesulfonate were also conducted on the monomeric precursor 2,3-dicyano-5,6-di(2-pyridyl)-1,4-pyrazine, [(CN)(2)Py(2)Pyz], with formation of the monoquaternized ion [(CN)(2)Py(2-Mepy)Pyz](+) neutralized by iodide and p-toluenesulfonate anions. Single-crystal X-ray work allowed elucidation of the structure of the two salt-like species. The diquaternized ion [(CN)(2)(2-Mepy)(2)Pyz](2+) could also be obtained as a p-toluenesulfonate salt, but attempts at direct macrocyclization of this dicationic species were unsuccessful. The iodide salt [(2-Mepy)(8)TPyzPzH(2)](I(8)).8H(2)O is water-soluble, with different solubilities depending on the range of pH explored. It was established that the macrocycle [(2-Mepy)(8)TPyzPzH(2)](8+) undergoes facile deprotonation and behaves as a strong acid. Aggregation phenomena are observed for both the octacation [(2-Mepy)(8)TPyzPzH(2)](8+) and its corresponding centrally deprotonated species [(2-Mepy)(8)TPyzPz](6+). Nevertheless, both cationic moieties exist in their monomeric form under specific experimental conditions. UV-visible monitored titrations with NaOH provide information about the type of protonation/deprotonation equilibria which are complicated by the occurrence of aggregation phenomena.     

On the massive sine-Gordon equation in the first few regions of collapse

We study the ultraviolet stability problem for the two-dimensional Yukawa interaction :cos:d in the region , where . The results have a natural Coulomb gas interpretation, because the counterterms do not depend on the field.Partially supported by C.N.R.S. trough the University of Paris VI     

Optimal and sub-optimal stopping rules for the Multistart algorithm in global optimization

In this paper the problem of stopping the Multistart algorithm for global optimization is considered. The algorithm consists of repeatedly performing local searches from randomly generated starting points. The crucial point in this algorithmic scheme is the development of a stopping criterion; the approach analyzed in this paper consists in stopping the sequential sampling as soon as a measure of the trade-off between the cost of further local searches is greater than the expected benefit, i.e. the possibility of discovering a better optimum.Stopping rules are thoroughly investigated both from a theoretical point of view and from a computational one via extensive simulation. This latter clearly shows that the simple1-step look ahead rule may achieve surprisingly good results in terms of computational cost vs. final accuracy.The research of the second author was partially supported by Progetto MPI 40% Metodi di Ottimizzazione per le Decisioni.