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.     

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.     

Experimental and Computational Study of the Thermal Decomposition of 3‐Methyl‐3‐buten‐1‐ol in m‐Xylene Solution

An experimental study of the thermal decomposition of a β‐hydroxy alkene, 3‐methyl‐3‐buten‐1‐ol, in m‐xylene solution, has been carried out at five different temperatures in the range of 513.15–563.15 K. The temperature dependence of the rate constants for the decomposition of this compound in the corresponding Arrhenius equation is given by ln k (s^?1) = (25.65 ± 1.52) ? (17,944 ± 814) (kJ·mol^?1)·T^?1. A computational study has been carried out at the M05–2X/6–31+G(d,p) level of theory to calculate the rate constants and the activation parameters by the classical transition state theory. There is a good agreement between the experimental and calculated rate constants and activation Gibbs energies. The bonding characteristics of reactant, transition state, and products have been investigated by the natural bond orbital analysis, which provides the natural atomic charges and the Wiberg bond indices. Based on the results obtained, the mechanism proposed is a one‐step process proceeding through a six‐membered cyclic transition state, being a concerted and slightly asynchronous process. The results have been compared with those obtained previously by us (Struct Chem 2013, 24, 1811–1816) for the thermal decomposition of 3‐buten‐1‐ol, in m‐xylene solution. We can conclude that in the compound studied in this work, 3‐methyl‐3‐buten‐1‐ol, the effect of substitution at position 3 by a weakly activating CH₃ group is the stabilization of the transition state formed in the reaction and therefore a small increase in the rate of thermal decomposition.     

Structural and Kinetic Aspects of Blood Plasma Protein Adsorption on the Surface of Hydrophobic Polymers

Abstract

Due to the wide use of polymers in medicine, researchers are required to solve a very important problem–to understand the interaction between materials of nonphysiological origin and the surrounding biological liquids, and tissues, particularly blood.     

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.