19F NMR chemical shifts of n-F-alkyl compounds

The examination of ¹⁹F chemical shifts for ca. 650 F-alkylated compounds of general formula CF₃(CF₂)_nCF₂X led to the following conclusions: the CF₂ groups α to X are very sensitive to the nature of X, and are spread over a range of 85 ppm. The effect of the length of the F-alkyl chain decreases rapidly, so that δCF₂(α) can already be considered as characteristic of X for n = 1 or 2 for most practical purposes. Solvent effects (in 9 different solvents having ε = 1.8 to 52.1) were found to be rather small except for the F-alkyl iodides. A chart which indicates the domain in which the CF₂(α) resonance signal is to be expected is given for 42 different series of F-alkylated compounds; it is expected to provide the synthetic chemist with a useful tool for the identification and characterization of such compounds.     

Dilute solution properties of a polyurethane. I. Linear polymers

A linear polyurethane of high molecular weight was prepared in solution by the polyaddition of equimolar amounts of ethylene glycol and methylene bis(4-phenyl isocyanate). The polymer was fractionated by using a direct sequential extraction procedure, with a solvent–nonsolvent system consisting of N,N′-dimethylformamide (DMF) and acetone (A). The resulting fractions were characterized by viscosity and lightscattering measurements. The relationship between the intrinsic viscosity and molecular weight was found in DMF at 25°C. to be [η] = 3.64 × 10^?4M^0.71. The unperturbed polymer chain dimensions were determined from intrinsic viscosity measurements carried out under experimentally determined theta conditions.     

Dynamical systems theory for music dynamics

We show that, when music pieces are cast in the form of time series of pitch variations, the concepts and tools of dynamical systems theory can be applied to the analysis of temporal dynamics in music. (i) Phase space portraits are constructed from the time series wherefrom the dimensionality is evaluated as a measure of the global dynamics of each piece. (ii) Spectral analysis of the time series yields power spectra ( approximately f(-nu)) close to red noise (nu approximately 2) in the low frequency range. (iii) We define an information entropy which provides a measure of the local dynamics in the musical piece; the entropy can be interpreted as an evaluation of the degree of complexity in the music, but there is no evidence of an analytical relation between local and global dynamics. These findings are based on computations performed on eighty sequences sampled in the music literature from the 18th to the 20th century. (c) 1995 American Institute of Physics.     

On the nilpotent * - Fourier transform

LetG be a nilpotent Lie group. The adapted nilpotent Fourier transform was introduced by D. Arnal and J. C. Cortet,:L(G) C (V,L(^2d )), whereL(G) is the Schwartz space ofG andV × ^2k is aG-invariant Zariski open set ing ^* the dual of the Lie algebra ofG. We prove the surjectivity of this transformation, which allows us to extend it to distribution spaces.     

Invariant measures for the2D-defocusing nonlinear Schrödinger equation

Consider the2D defocusing cubic NLSiu _t+u–u|u|²=0 with Hamiltonian . It is shown that the Gibbs measure constructed from the Wick ordered Hamiltonian, i.e. replacing ||⁴ by ||⁴ :, is an invariant measure for the appropriately modified equationiu _t + u‒ [u|u ²–2(|u|² dx)u]=0. There is a well defined flow on thesupport of the measure. In fact, it is shown that for almost all data the solutionu, u(0)=, satisfiesu(t)–e ^it C _Hs (), for somes>0. First a result local in time is established and next measure invariance considerations are used to extend the local result to a global one (cf. [B2]).     

k-spaces and Borel filters on the set of integers

We say that a countable, Hausdorff, topological space with one and only one accumulation point is a point-space. For such a space, we give several properties which are equivalent to the property of being a k-space. We study some free filters on the set of integers and we determine if the associated point-spaces are k-spaces or not. We show that the filters of Lutzer-van Mill-Pol are k-filters. We deduce that, for each countable ordinal , there exists a free filter of true additive class (Baire's classification) and a free filter of true multiplicative class for which the associated point-spaces are k-spaces but not , the existence being true in the additive case for . In particular, we answer negatively a question raised in J. Calbrix, C. R. Acad. Sci. Paris 305 (1987), 109--111.

     

Some geometric aspects of the calculus of fractions

We give necessary and sufficient conditions on class S of maps of a category C so that a good calculus of fractions is possible in C[S ^-1], and a geometric characterization of the communitative diagrams in the category of fractions. These conditions are also described simply in terms of Grothendiek topologies.We characterize the categories which arise in this manner by the fact that the functor C C[S ^-1] is uniformly flat and give some applications of this result.     

The Boolean Prime Ideal Theorem Plus Countable Choice Do Not Imply Dependent Choice

Two Fraenkel-Mostowski models are constructed in which the Boolean Prime Ideal Theorem is true. In both models, AC for countable sets is true, but AC for sets of cardinality 2 and the 2m = m principle are both false. The Principle of Dependent Choices is true in the first model, but false in the second. Mathematics Subject Classification: 03E25, 03E35, 04A25.     

Chemo- and regioselective synthesis of 2-alkylidenetetrahydrofurans bearing a chiral sulfur atom by domino reactions of sulfoximines

The addition of the dianion of Johnson’s sulfoximine to α,ω-halogenoesters evolves by an intramolecular heterocyclization to provide a direct access to 2-alkylidenetetrahydrofurans bearing a chiral sulfur atom via domino addition-elimination/S_N reactions.     

Etudes sur les fibres naturelles et de synthèse

Résumé Nous avons mesuré, en fonction de la température, le degré de gonflement dans l'eau de fibres de collagène amorphes qui ont été tannées différemment, ceci dans le but de pouvoir déterminer, pour chaque degré de tannage (pontage chimique) la chaleur de mélange du collagène amorphe sec avec l'eau de gonflement. En utilisant la théorie relative au gonflement des réseaux polymériques amorphes dans un excès de diluant, on a pu montrer que le paramètre thermodynamiqueχ ₁ caractéristique du système collagène-eau (paramètre deFlory-Huggins) varie avec la composition du réseau gonflé. Par contre, le paramètre ?enthalpique? correspondantϰ ₁=− =−0,34 est indépendant de cette composition. La chaleur de mélangeΔH _mél/V ₀ d'un cm³ de collagène amorphe sec avec l'eau de gonflement peut être calculée pour les différents degrées de tannage. Elle a le signe deϰ ₁, i. e. elle est négative et est donnée par:ΔH _mél/V ₀=RT gK₁(1−v₂ ^éq). Sa valeur absolue est donc d'autant moins importante que le degré de tannage des fibres est poussé; v₂ ^éq augmente en effet avec la concentration en liens intermoléculaires introduits dans les échantillons. La variation d'enthalpie accompagnant la transformation d'une fibre de collagène cristalline sèche en fibre amorphe gonflée (enthalpie de rétraction dans l'eau) diminuée de la chaleur de mélange correspondant au gonflement de la fibre amorphe sèche dans l'eau donne la chaleur de fusion du collagène sec. Cette quantité est égale à:ΔH/V ₀=28±1,5 cal./cm³ et est indépendante du degré de tannage comme on doit s'y attendre.

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Summary We have measured the temperature dependence of the swelling of amorphous collagen fibres of different degrees of tanning in an excess of water. This was done for the purpose of determining the heat of mixing of amorphous dry collagen with the equilibrium swelling water for each degree of tanning (chemical crosslinking). Using the theory of swelling of polymeric networks in an excess of diluent we were able to show that the parameterχ ₁ of the system collagen-water (Flory-Huggins parameter) is a function of the composition of the swollen network. On the other hand, the energy parameterϰ ₁=− =−0,34 is found to be concentration independent. The heat of mixingΔH _mél/V ₀ of 1 cm³ of dry amorphous collagen with the equilibrium swelling water can be calculated for the different degrees of tanning. It has the same sign asϰ ₁, i. e. is negative, and is given byΔH _mél/V ₀=RTϰ ₁ (1−v₂ ^éq). Its absolute value decreases therefore with increasing degrees of tanning, sincev ₂ ^éq increases with the density of the cross-links in the sample. The change in heat content on transforming 1 cm³ of dry crystalline collagen fibre into amorphous swollen fibre (heat of shrinking in water), decreased by the heat of swelling of the dry amorphous fibre in water, gives the heat of fusion of dry collagen. This latter equalsΔH/V ₀=28±1.5 cal/cm³ and is, as expected, independent of the degree of tanning.

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Zusammenfassung Um die Mischungsw?rme des amorphen trockenen Kollagens mit dem Quellungswasser zu bestimmen, wurde die Temperaturabh?ngigkeit des Quellungsgrades von verschieden stark gegerbten amorphen Kollagenfasern gemessen. Auf Grund der Theorie der Quellung von amorphen polymeren Netzwerken in einem überschu? von Quellungsmittel konnte gezeigt werden, da? der thermodynamische (Flory- Huggins) Parameterχ ₁ für das System Kollagen-Wasser vom Quellungsgrad des Netzwerkes abh?ngt. Hingegen ist der Enthalpieparameterϰ ₁=− =−0,34 davon unabh?ngig. Die Mischungsw?rmeΔH _mél/V₀ eines cm³ trockenen amorphen Kollagens mit dem Quellungswasser kann für verschiedene Gerbungsgrade (Vernetzungsgrade) berechnet werden. Sie hat das gleiche Vorzeichen wieϰ ₁ d. h. ist negativ, und gehorcht der Gleichung:ΔH _mél/V ₀=RTϰ ₁ (1−v₂ ^éq). Der Betrag der Mischungsw?rme ist um so kleiner, je h?her der Gerbungsgrad der Faser ist; in der Tat w?chstv ₂ ^éq mit der Konzentration der Vernetzungspunkte an. Wenn von der Enthalpie?nderung, welche mit dem übergang von einer trockenen kristallinen Faser zu einer gequollenen amorphen verbunden ist, (Schrumfungsenthalpie im Wasser), die oben definierte QuellungsenthalpieΔH _mél/V ₀ abgezogen wird, so bleibt die Schmelzw?rme des trockenen Kollagens übrig. Diese Schmelzw?rme betr?gt:ΔH/V ₀=28±1,5 cal./cm³ und ist, wie zu erwarten, vom Vernetzungsgrad (Gerbungsgrad) des Fadens unabh?ngig.

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Travail effectué au Laboratoire de Chimie-Physique de l'Université de Liège, Liège (Belgique).