Solvable set/hyperset contexts: I. Some decision procedures for the pure,finite case

Hereditarily finite sets and hypersets are characterized both as algorithmic data structures and by means of a first-order axiomatization which, despite being rather weak, suffices to make the following two problems decidable:

• (1) Establishing whether a conjunction r of formulae of the form: ? y₁ ?? y_m((y₁?W₁& ?&y_m ?W_m) ←q), with q quantifier-free and involving only the relators =, ? and propositional connectives, and each y_i distinct from all w_j's, is satisfiable.
• (2) Establishing whether a formula of the form ? y q, q quantifier-free, is satisfiable.

Concerning (1), an explicit decision algorithm is provided; moreover, significantly broad subproblems of (1) are singled out in which a classification — that we call the ‘syllogistic decomposition’ of r — of all possible ways of satisfying the input conjunction r can be obtained automatically. For one of these subproblems, carrying out the decomposition results in a finite family of syntactic substitutions that generate the space of all solutions to r. In this sense, one has a unification algorithm. Concerning (2), a technique is provided for reducing it to a subproblem of (1) for which a decomposition method is available. The algorithmic complexity of the problems under study is highlighted; a generalization of the decidability results to a theory where sets are blended with free Herbrand functors is announced. © 1996 John Wiley & Sons, Inc.     

Determination of low levels of free fibres of chrysotile in contaminated soils by X-ray diffraction and FTIR spectroscopy

A new analytical method for the determination of low levels (0.01–1 wt%) of free fibres of chrysotile in contaminated clayey, sandy and sandy-organic soils is described. The detection limit of 0.01 wt% is reached with an enrichment of free fibres of chrysotile in the sample using a standard laboratory elutriator for sedimentation analysis. The chrysotile quantitative determination is performed both by X-ray powder diffraction, using the internal standard and reference intensity ratio methods, and by Fourier-transform infrared absorption spectroscopy. The procedure can be successfully applied to different soils after removal, by a thermal treatment, of the matrix components which can interfere. This straightforward method fulfils the request of public institutions and private companies for an appropriate quantitative determination of chrysotile-free fibres in contaminated soils.     

Preparation and self-assembly of chiral porphyrin diads on the gold electrodes of quartz crystal microbalances: a novel potential approach to the development of enantioselective chemical sensors

Porphyrin diad 1 was synthesized by reaction of the acyl chloride of porphyrin 2 and trans-1,2-dithiane-4,5-diol. The Co complex of this diad was studied as a potential enantioselective receptor for chiral recognition in solution and in the solid state. In solution both enantiomers of limonene induce significant changes in the visible and circular dichroism (CD) spectra of [Co2(1)], while a different behavior is observed in the case of the enantiomeric pair of trans-1,2-diaminocyclohexane. A different efficiency of [Co2(1)] chiral recognition is obtained for these compounds, with a remarkable degree of enantiodiscrimination observed in the case of limonene. Self-assembled monolayers of [Co2(1)] were deposited onto the gold electrodes of quartz crystal microbalances to be used as sensing materials of nanogravimetric sensors operating in the gas phase. The enantiodiscrimination properties of these sensors towards the enantiomeric pairs of chiral analytes have been studied. While in the case of analytes bearing donor ligand atoms we did not observe a remarkable enantioselectivity, a significant degree of chiral discrimination was observed in the case of limonene; this result is particularly encouraging for the potential development of enantioselective chemical sensors for use in an array configuration.     

Subphthalocyanines as narrow band red-light emitting materials

A series of new light emitting subphthalocyanines, lower homologues of phthalocyanines, were synthesized having color points covering the red-orange region of the visible spectrum. Additionally, they were found to be of potential use as narrow band emitters for red-light emitting diodes.     

The hydrophobic effect in aqueous solutions of nonelectrolytes. I. Self-interactions of alkylureas

In order to clarify some aspects of the hydrophobic interactions, the enthalpies of dilution of monoethylurea, 1,3-dimethylurea, and 1,3-diethylurea have been determined calorimetrically at 25°C. The calorimetric data, expressed in terms of excess enthalpy, permit the evaluation of the pair and triplet interaction coefficients. The analyses of these and of the analogous coefficientsg _xx andg _xxx, derived from osmotic data, indicate a driving force favorable to the interactions among the hydrated solute molecules. Nevertheless, the positive values of theh _xx andh _xxx coefficients seem to suggest that the source of the effect is a rearrangement of the water molecules rather than a direct association of the solute molecules. There are evidences of a strict correlation between the enthalpic and the entropic effects. Preliminary data were presented at the International Conferences on Chemical Thermodynamics at Baden (1973) and Montpellier (1975). The experimental part was carried out at the Istituto Chimico of the University of Trieste. To whom correspondence should be addressed.     

The riboflavin—dihydroriboflavin system in acidic medium on mercury: Part II. A polarographic investigation

Polarographic current—potential characteristics and current—time curves for the reduction of riboflavin (RF) to dihydroriboflavin (DRF) in 0.01 M HClO₄ + 0.09 M NaClO₄ have been examined in detail. It has thus been shown that the RF adsorption prewave is due to the formation of two overlapping adsorbed monolayers of DRF molecules. Lateral interactions of RF molecules between themselves, of DRF molecules between themselves and of RF with DRF molecules in the first adsorbed monolayer are weak, whereas vertical interactions between overlapping DRF molecules are relatively strong. This explains the abrupt increase in the slope of the RF adsorption prewave and its shift towards more positive potentials as soon as the second adsorbed monolayer of DRF starts to form. The so-called “normal” wave for RF reduction has a half-wave potential E^II_{$\text{1}\text{2}$} = ?0.180 V/SCE, practically coinciding with the formal potential of the RF/DRF couple, and a slope corresponding to a reversible two-electron reduction unaffected by semiquinone formation. The shape of polarographic mean current vs. potential curves has been accounted for through an approximate solution of the corresponding diffusional problem.     

The CuII−CuI−Cu0(Hg) system in the presence of benzotriazole: Part II. A chronocoulometric investigation

Both the oxidation of Cu⁰ at dropping amalgam electrodes immersed in solutions of benzotriazole (BTA) and the reduction of Cu^II at a dropping mercury electrode from BTA solutions have been investigated by the single potential-step chronocoulometric technique. The dependence of the charge Q(t) flowing as a consequence of a given potential jump E_i→E_f upon the initial and final potentials E_i and E_f, as well as upon the time t elapsed from the instant of the potential jump provides direct evidence for the presence of a single adsorbed monolayer of a Cu^I compound on a mercury electrode immersed in a Cu^II solution containing BTA, at applied potentials positive to ≈?0.4 V/SCE. Analogous measurements carried out at dropping amalgam electrodes reveal the presence of a single adsorbed monolayer of a Cu^I compound, or else of an adsorbed multilayer, depending on the potential range investigated. The results of the chronocoulometric measurements are in agreement with those of the polarographic measurements of Part I.     

Synthesis, characterization, biocide and toxicological activities of di-n-butyl- and diphenyl-tin(IV)-salicyliden-beta-amino alcohol derivatives

The one pot reaction of salicylaldehyde 1, beta-amino alcohols 2a-2c, and di-n-butyltin(IV) oxide 3a or diphenyltin(IV) oxide 3b produced five diorganotin(IV) compounds, 4a-4c, 5a, and 5c, in good yields. All compounds were characterized by IR, (1)H, (13)C, and (119)Sn NMR spectroscopy, and elemental analysis; furthermore, compounds 4b, 4c, 5a, and 5c were characterized by X-ray diffraction analysis. After the structural characterization, all of the compounds were tested in vitro against Bacillus subtilis (Gram-positive, strain ATCC 6633), Escherichia coli (Gram-negative, strain DH5alpha), Pseudomonas aeruginosa (Gram-negative, strain BH3), Desulfovibrio longus (strain DSM 6739), and Desulfomicrobium aspheronum (strain DSM 5918) to assess their antimicrobial activity. Compounds 4 and 5 demonstrated a wide range of bactericidal activities against the tested aerobic (one Gram-positive and two Gram-negative subtypes) and anaerobic bacteria (two sulfate-reducing bacteria, SRB). Compound 5 had better bactericidal performances than compound 4. For all of the compounds, the acute toxicity was measured using luminescent bacteria toxicity (LBT-Microtox) tests to track their further environmental impact. According to these results and in order to fulfill environmental regulations, the toxicity of the compounds studied herein can be modulated through the proper selection of the disubstituted tin(IV) moiety.     

The static dielectric constant of solutions of water inn-alcohols at 15, 25, 35, and 45°C

Dielectric constants (measured at 1 MHz) are reported for solutions of water (concentration range 0 to 0.2 mole fraction) in 1-propanol at 25°C, and in 1-butanol, 1-pentanol, and 1-hexanol at 15, 25, 35, and 45°C. These results, together with literature values for solutions of water in methanol, ethanol, 1-heptanol, and 1-octanol, show that water interacts with alcohols in at least two ways: (1) it can participate in the formation of dynamic hydrogen-bonded chains, thereby raising the polarizability; (2) it can form relatively stable structures such as H₂O(ROH)₄ which have zero net dipole moment and consequently diminish volume polarizability. For C _n H _2n+1 OH alcohols,n≥4, most of the initially added water forms complexes: consequently, addition of water to these alcohols lowers the dielectric constant.     

Topological Space of the Chemical Elements and its Properties

We carried out a mathematical study of 72 chemical elements taking advantage of the chemotopological method. We selected 128 properties to define the elements (physico-chemical, geochemical and chemical properties). Then, we looked for correlated properties and we reduced the number of them to 90. In this way we defined each element as a 90-tuple. Afterwards, we applied principal component analysis and cluster analysis (4 similarity functions and 5 grouping methodologies). Then, we calculated a consensus tree for the 20 dendrograms generated by the CA. Afterwards, we extracted the similarity relationships from the consensus tree and built up a basis for a topology on the set of chemical elements. Finally, we calculated some topological properties (closures, derived sets, boundaries, interiors and exteriors) of several subsets of chemical elements. We found that alkali metals, alkaline earth metals and noble gases appear not related to the rest of the elements. Also, we found that the boundary of non-metals are the semimetals with a stair-shape on the periodic table