On the capacity of boolean graph formulæ

In a recent paper we have solved several well-known combinatorial problems treating them as special cases of our generalization of Shannon's notion of graph capacity. We present a new simple formalism to deal with all such problems in a unified manner, considering graphs or families of graphs as special formulæ the variables of which are pairs of vertices of their common vertex sets. In all of these problems, the maximum size of a set ofn-length sequences from a fixed alphabet is to be determined under various restrictions on the element pairs present in the same coordinate of any two sequences from the set. For sufficiently homogeneous formulæ capacity becomes computable.New applications include generalizations of our result on the maximum number of pairwise qualitatively independentk-partitions of ann-set from independence to various forms of qualitative dependence.Work partially supported by the Italian Ministry of the University and Scientific Research, Project: Algoritmi, Modelli di Calcolo e Strutture Informative.     

3-nitrocoumarins as dienophiles in the Diels-Alder reaction in water. An approach to the synthesis of nitrotetrahydrobenzo[c]chromenones and dihydrodibenzo[b,d]furans

The [4 + 2] cycloadditions of 3-nitrocoumarin (1a), 6-chloro-3-nitrocoumarin (1b), and 6-, 7-, and 8-hydroxy-3-nitrocoumarins (1c, 5, and 6) with (E)-piperylene (7), isoprene (8), 2,3-dimethyl-1,3-butadiene (9), 2-methoxy-1,3-butadiene (10), 2,3-dimethoxy-1,3-butadiene (11), and cyclopentadiene (12) were investigated in aqueous medium, in organic solvent and under solventless conditions. The reactions performed in water occurred in heterogeneous phase but were faster than those executed in toluene or dichloroethane (DCE). 1a-c, 5, and 6 behaved as 2pi components in the Diels-Alder cycloadditions with 7-10 and 12, and exo adducts were preferentially or exclusively produced. Surprisingly 1a, behaved as a 4pi component in the cycloaddition in water with 11 and 4-substituted 3-nitrochromanones 20 and 21 were isolated. The cycloadditions of hydroxy-3-nitrocoumarins 1c, 5, and 6 with 1,3-diene 9 did not work in water or in organic solvent, but did work under solventless conditions. Nitrotetrahydrobenzo[c]chromenones 13-16, 24, and 25, originating from the normal electron-demand Diels-Alder reactions, were converted into dihydrodibenzo[b,d]furans 27-31 in water, via one-pot Nef-cyclodehydration reactions.     

TBAF-catalyzed synthesis of 5-substituted 1H-tetrazoles under solventless conditions

Tetrabutylammonium fluoride (TBAF) is an efficient catalyst in the [3 + 2] cycloaddition reaction of organic nitriles 1 with trimethylsilyl azide (TMSN(3)) in solventless conditions. The corresponding 5-substituted 1H-tetrazoles 2 were obtained under mild conditions and in 80-97% yields.     

Copper and iron interactions with angiotensin-converting enzyme inhibitors. A study by fast-atom bombardment tandem mass spectrometry

Fast atom bombardment, combined with high-energy collision-induced tandem mass spectrometry, has been used to investigate gas-phase metal-ion interactions with captopril, enalaprilat and lisinopril, all angiotensin-converting enzyme inhibitors.Suggestions for the location of metal-binding sites are presented. For captopril, metal binding occurs most likely at both the sulphur and the nitrogen atom. For enalaprilat and lisinopril, binding preferably occurs at the amine nitrogen. Copyright 1999 John Wiley & Sons, Ltd.     

Polymerized mixed aggregates containing gadolinium complex and CCK8 peptide

Two novel amphiphilic unimers containing an aliphatic hydrophobic chain (PDA) with two C≡C triple bonds and hydrophilic heads presenting the chelating agent DTPAGlu and the CCK8 bioactive peptide, respectively, have been prepared by solid phase synthesis. Aggregates obtained by mixing together PDA-DTPAGlu, or its Gd(III) complex, and PDA-L2-CCK8 in 70/30 molar ratio before and after a polymerization process carried out by UV irradiation have been structurally characterized by means of small angle neutron scattering. The relaxivity properties of aggregates containing Gadolinium complexes have also been investigated. Elongated mixed micelles have been observed, in which the relaxivity value r _1p for each Gadolinium complex, measured at 20 MHz and 298 K, is around 12 mM^–1 s^–1.     

Quasi-stadium laser diodes with an unstable resonator condition

We have observed lasing in a complicated eigenmode of a quasi-stadium laser diode with an unstable resonator consisting of two curved end mirrors obeying an unstable resonator condition and two straight sidewall mirrors. The laser was fabricated by application of a reactive-ion-etching technique to a molecular beam epitaxy-grown graded-index separate-confinement heterostructure single-quantum-well GaAs/AlGaAs structure. The far-field pattern shows that the lasing mode corresponds to the complicated lowest-loss mode obtained numerically by an extended Fox-Li method.     

Polystyryl-supported TBD as an efficient and reusable catalyst under solvent-free conditions

Polystyryl supported-TBD (PSTBD) is an efficient and reusable heterogeneous basic catalyst under solvent-free conditions for a variety of organic transformations such as 1,2-epoxide ring-opening, aldol-type condensation and Michael addition.