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.     

Narrow band quantitative and multivariate electroencephalogram analysis of peri-adolescent period

ABSTRACT: BACKGROUND: The peri-adolescent period is a crucial developmental moment of transition from childhood to emergent adulthood. The present report analyses the differences in Power Spectrum (PS) of the Electroencephalogram (EEG) between late childhood (24 children between 8 and 13 years old) and young adulthood (24 young adults between 18 and 23 years old). RESULTS: The narrow band analysis of the Electroencephalogram was computed in the frequency range of 0--20 Hz. The analysis of mean and variance suggested that six frequency ranges presented a different rate of maturation at these ages, namely: low delta, delta-theta, low alpha, high alpha, low beta and high beta. For most of these bands the maturation seems to occur later in anterior sites than posterior sites. Correlational analysis showed a lower pattern of correlation between different frequencies in children than in young adults, suggesting a certain asynchrony in the maturation of different rhythms. The topographical analysis revealed similar topographies of the different rhythms in children and young adults. Principal Component Analysis (PCA) demonstrated the same internal structure for the Electroencephalogram of both age groups. Principal Component Analysis allowed to separate four subcomponents in the alpha range. All these subcomponents peaked at a lower frequency in children than in young adults. CONCLUSIONS: The present approaches complement and solve some of the incertitudes when the classical brain broad rhythm analysis is applied. Children have a higher absolute power than young adults for frequency ranges between 0-20 Hz, the correlation of Power Spectrum (PS) with age and the variance age comparison showed that there are six ranges of frequencies that can distinguish the level of EEG maturation in children and adults. The establishment of maturational order of different frequencies and its possible maturational interdependence would require a complete series including all the different ages.     

A new look at XRD patterns of archaeological ceramic bodies

In this paper, the general rules of phase transformations in calcareous clay bodies during firing were used to estimate the equivalent firing temperature (EFT) of seventeenth century polychrome Persian haft rang tiles based on their X-ray diffraction (XRD) patterns. The novelty of this work is, however, that it handles the XRD patterns of archaeological clay bodies with principal component analysis (PCA) in order to have a new look at their firing and thermal behaviour. Statistically handling the XRD patterns, different clusters were discriminated in the clay bodies whose mineralogical composition showed various proportions of amorphous and quartz contents. The results showed interesting trends in the different clusters in terms of the EFT, quartz content and the density of the bodies. The present work uses PCA to have a new look at XRD patterns of archaeological clay bodies and, moreover, to interpret the PCA results in order to estimate the EFT of a large number of archaeological clay bodies.     

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.     

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.