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.     

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.     

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     

Polyoxometalates as Inorganic Building Blocks of Multifunctional Molecular Materials

The use of polyoxometalates (pOM's) as inorganic component in the synthesis of new molecular hybrid materials is presented. Here we show that the combination of organic molecules of the tetrathiafulvalene (TTF) type or perylene (per) with POM's yields new radical salts with unprecedented structures that present interesting magnetic and/or electrical properties or coexistence of both. The first true metallic radical salt containing a POM has been prepared and characterized. We also describe the recent results obtained by combining magnetic POM's with the organometallic cation decamethylferrocene.     

Ferromagnetism and chirality in two-dimensional cyanide-bridged bimetallic compounds

The combination of hexacyanoferrate(III) anions, [Fe(CN)(6)](3)(-), with nickel(II) complexes derived from the chiral ligand trans-cyclohexane-1,2-diamine (trans-chxn) affords the enantiopure layered compounds [Ni(trans-(1S,2S)-chxn)(2)](3)[Fe(CN)(6)](2).2H(2)O (1) and [Ni(trans-(1R,2R)-chxn)(2)](3)[Fe(CN)(6)](2).2H(2)O (2). These chiral systems behave as ferromagnets (T(c) = 13.8 K) with a relatively high coercive field (H(c) = 0.17 T) at 2 K. They also exhibit an unusual magnetic behavior at low temperatures that has been attributed to the dynamics of the magnetic domains in the ordered phase.     

Mechanism of Formation of Peroxocarbonates RhOOC(O)O(Cl)(P)(3) and Their Reactivity as Oxygen Transfer Agents Mimicking Monooxygenases. The First Evidence of CO(2) Insertion into the O-O Bond of Rh(eta(2)-O(2)) Complexes

Extended labeling experiments have shown that formation of rhodium peroxocarbonate from CO(2) and [RhCl(eta(2)-O(2))(P)(3)] (P is PEt(2)Ph or PEtPh(2)) proceeds through O-O bond cleavage and CO(2) insertion. O-transfer to ancillary phosphine ligand to give R(3)P=O selectively (>85%) involves the Rh-linked O atom of the peroxo group of RhCl(CO(4))(P)(3).