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.     

Excess enthalpies of aqueous ternary solutions of urea and polyols at 25°C

The heats of dilution of nine ternary solutions of urea and polyols have been determined at 25°C. Excess enthalpies and their virial coefficients h _xy have been evaluated and compared with the data reported in the literature for mono- and polyfunctional alcohols and other oxygenated nonelectrolytes. The group additivity approach of Savage and Wood was applied and the contributions to the enthalpy coefficients, due to the water mediated interactions between urea and the functional groups –CH₂–, –OH, and –O– were determined. On the other hand, by using empirical combination rules among the cross- and self-enthalpic interaction coefficients it is possible to emphasize the large differences in the behavior (even in the presence of urea) of the polyols (and in particular of cyclitols) and of saccharides.     

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.     

Reversible colorimetric probes for mercury sensing

The selectivity and sensitivity of two colorimetric sensors based on the ruthenium complexes N719 [bis(2,2'-bipyridyl-4,4'-dicarboxylate)ruthenium(II) bis(tetrabutylammonium) bis(thiocyanate)] and N749 [(2,2':6',2' '-terpyridine-4,4',4' '-tricarboxylate)ruthenium(II) tris(tetrabutylammonium) tris(isothiocyanate)] are described. It was found that mercury ions coordinate reversibly to the sulfur atom of the dyes' NCS groups. This interaction induces a color change in the dyes at submicromolar concentrations of mercury. Furthermore, the color change of these dyes is selective for mercury(II) when compared with other ions such as lead(II), cadmium(II), zinc(II), or iron(II). The detection limit for mercury(II) ions--using UV-vis spectroscopy--in homogeneous aqueous solutions is estimated to be approximately 20 ppb for N719 and approximately 150 ppb for N749. Moreover, the sensor molecules can be adsorbed onto high-surface-area mesoporous metal oxide films, allowing reversible heterogeneous sensing of mercury ions in aqueous solution. The results shown herein have important implications in the development of new reversible colorimetric sensors for the fast, easy, and selective detection and monitoring of mercuric ions in aqueous solutions.     

Fitting complex potential energy surfaces to simple model potentials: application of the simplex-annealing method

A stochastic method of optimization, which combines simulated annealing with simplex, is implemented to fit the parameters of a simple model potential. The main characteristic of the method is that it explores the whole space of the parameters of the model potential, and therefore it is very efficient in locating the global minimum of the cost function, in addition to being independent of the initial guess of the parameters. The method is employed to fit the complex intermolecular potential energy surface of the dimer of water, using as a reference the spectroscopic quality anisotropic site-site potential of Feller et al. The simple model potential chosen for its reparameterization is the MCY model potential of Clementi et al. The quality of the fit is assessed by comparing the geometry of the minimum, the harmonic frequencies, and the second virial coefficients of the parameterized potential with the reference one. Finally, to prove more rigorously the robustness of this method, it is compared with standard nonstochastic methods of optimization.     

Estudios sobre ácidos hidroxámicos

Résumé On propose un procédé de microdosage des groupements méthoxyles dans les pectines, qui repose sur la libération de ces groupements par saponification de l'hydroxylamine alcoolique dans un appareil, sur leur transformation en formiates de méthyle et sur leur distillation. Le formiate de méthyle forme ainsi l'acide formhydroxamique que l'on dose par colorimétrie à l'état de chélate avec le fer-III.On réalise l'hydrolyse de la pectine à 100° C en tube scellé. On fait réagir avec l'acide formique en excès, une partie aliquote de l'hydrolysat dans le micro-appareil de distillation déjà décrit. Le procédé convient pour 1 à 3 mg de pectine et la durée des opérations est de deux heures et demies. Sa spécificité est satisfaisante bien que le groupe éthoxyle puisse gêner. Son action est d'ailleurs peu vraisemblable, puisqu'il ne fait pas partie de la molécule de pectine. Les résultats du procédé sont en générale un peu plus bas que ceux des méthodes volumétriques servant à ce dosage. On a étudié la reproductibilité pour les esters méthyliques et l'on a mis en évidence une erreur par défaut de 2 à 4%. Les plus petites quantités de groupes méthoxyles que l'on puisse doser sont de 20g. Le procédé recommandé est une application particulière de méthodes applicables de façon générale au dosage des esters méthyliques dans les substances organiques. Ce sera l'objet d'une autre communication de cette série.

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Summary A micromethod is given for determining methoxyl groups in pectins. It is based of the liberation of these groups by saponification, conversion into methyl formate, and distillation of the latter into a receiver containing alcoholic hydroxylamine. The methyl formate reacts to give formhydroxamic acid, which is determined colorimetrically as iron(III) chelate.The hydrolysis of the pectin is conducted at 100° C in a sealed tube. An aliquot part of the hydrolysate is brought into reaction with excess formic acid in a microdistillation apparatus that was described previously. The procedure is suitable for 1 to 3 mg pectin and requires 21/2 hours for all partial operations. The specificity is satisfactory, even though ethoxyl may interfere. However, this latter is not likely to be encountered since ethoxyl has not been shown to be a constituent of the pectin molecule. The results given by the procedure are in general inferior to those of volumetric methods. The reproducibility was tested on methyl esters and showed a minus error of 2 to 4%. The smallest amount of methoxyl which can be determined in this way is 20g. The method proposed here is a special application of a method which can be applied in general to the determination of methyl esters in organic substances, which will be the subject of a later paper in this series.

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Zusammenfassung Es wird ein Mikroverfahren zur Bestimmung der Methoxylgruppen in Pektinen angegeben, das auf der Freisetzung dieser Gruppen durch Verseifung, deren Umwandlung in Methylformiat und dessen Destillation in eine Vorlage von alkoholischem Hydroxylamin beruht. Das Methylformiat bildet damit Formhydroxamsäure, die als Eisen(III)-chelat kolorimetrisch bestimmt wird.Die Hydrolyse des Pektins wird bei 100° C in einem verschlossenen Rohr ausgeführt. Einen aliquoten Teil des Hydrolysates läßt man in einem schon früher beschriebenen Mikrodestillationsapparat mit überschüssiger Ameisensäure reagieren. Das Verfahren eignet sich für 1 bis 3 mg Pektin und erfordert für alle Teiloperationen 2^1/2 Stunden. Seine Spezifität ist befriedigend, obwohl Äthoxyl stören kann. Dessen Einwirkung ist jedoch wenig wahrscheinlich, da es nicht als Bestandteil des Pektinmoleküls nachgewiesen ist. Die Ergebnisse des Verfahrens sind im allgemeinen niedriger als die Resultate volumetrischer Methoden. Die Reproduzierbarkeit wurde an Methylestern überprüftund zeigte einen Minusfehler von 2 bis 4%. Die Mindestmenge bestimmbares Methoxyl beträgt 20g. Das vorgeschlagene Verfahren ist eine spezielle Anwendung einer allgemein für die Bestimmung von Methylestern in organischen Substanzen anwendbaren Methode, die Gegenstand einer weiteren Mitteilung dieser Serie sein wird.

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Resumen Se indica una microtécnica de valoración de metoxilos en pectinas, basada en la liberación del radical metilo éster por saponificación; en su conversion en formiato de metilo y en su simultanea destilación y recepción en hidroxilamina alcalinizada. El formiato de metilo se transforma así en ácido formohidroxámico, cuya determinación fotocolorimétrica se realiza como quelato férrico.Estas operaciones requieren efectuar la hidrólisis de la pectina en tubo cerrado y a 100° C, y en tomar una alícuota del hidrolizado, que se pasa con un exceso de ácido fórmico al aparato de microdestilación, detallado en comunicaciones anteriores. El método permite operar con 1 a 3 mg de pectina y todas las operaciones insumen unas dos y media horas. La técnica presenta condiciones satisfactorias de especificidad, pudiendo interferir los radicales etoxilos, cosa poco probable, pues no son reconocidos como componente de la molécula de pectina. Los resultados obtenidos, comparados con los del método titrimétrico, son por lo general inferiores a éste y su reproducibilidad, verificada con ésteres metílicos, tiene errores por defecto de un 2 a 4%. La cantidad mínima de metoxilo valorado alcanza a 20g. La técnica que se indica, es una aplicacion particular de otra de carácter general, aplicable a la valoración de ésteres metílicos en sustancias orgánicas, que será motivo de otra futura comunicación de esta serie.

     

A furan ring expansion approach to the synthesis of novel pyridazino-psoralen derivatives

A convenient preparation of the parent tetrahydrobenzodifuran 2 was developed from resorcinol. The oxidation of one or both furan rings of this key intermediate was accomplished with DDQ and the resulting benzodifuran was subsequently reacted with 3,6-dimethoxycarbonyl-1,2,4,5-tetrazine to afford the expected pyridazino-psoralen derivative in good yield. This simple method allowed the efficient preparation of a pyridazino-psoralen derivative with a formyl group at C-7, which was introduced by directed ortho-lithiation in the intermediate 2. An aminoalkyl side-chain was also introduced to the tetracyclic skeleton through the aldehyde functionality in a reductive amination process, which was accompanied by an unprecedented reduction of the pyridazine ring.