Smoothing minimally supported frequency wavelets: Part II

The main purpose of this paper is to give a procedure to “mollify” the low-pass filters of a large number ofMinimally Supported Frequency (MSF) wavelets so that the smoother functions obtained in this way are also low-pass filters for an MRA. Hence, we are able to approximate (in the L ² -norm) MSF wavelets by wavelets with any desired degree of smoothness on the Fourier transform side. Although the MSF wavelets we consider are bandlimited, this may not be true for their smooth approximations. This phenomena is related to the invariant cycles under the transformation x ↦2x (mod2π). We also give a characterization of all low-pass filters for MSF wavelets. Throughout the paper new and interesting examples of wavelets are described.     

Limiting Partial Molar Volumes of Electrolytes in 2-Methyl-2-Butanol <Emphasis Type="Bold">+</Emphasis> Water Mixtures at 298.15 K

Partial molar volumes at infinite dilution, V⁰₂, of alkali–metal halides (LiCl, NaCl KCl RbCl CsCl, NaBr, KBr, KI), tetra-n-alkylammonium bromides, R₄NBr (R=Me, Et, n-Pr, n-Bu, n-Pen), NaBPh₄, and Ph₄PCl have been determined in binary solvent mixtures of water with 2-methyl-2-butanol covering the water-rich region and the alcohol-rich region at 298.15 K. V⁰₂ for alkali–metal halides show relatively little dependence on the solvent composition. However, in the case of hydrophobic electrolytes the observed effects are more pronounced. A good linear dependence between V⁰₂(R₄NBr) and the molecular weight of the tetra-n-alkylammonium cation is found. Limiting single-ion volumes have been obtained using the assumption that V⁰(Ph₄P⁺)–V⁰(BPh^–₄)=2.0 cm³-mol^–1. The trends in the single-ion volumes are discussed in both solvent regions.     

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.     

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.