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.     

Cocycle d'Euler etK2

In this paper we construct a canonical 2-cocycle on the groupP SL(2,k) with values in the Witt groupW(k) of the fieldk. This allows us to produce anatural homomorphism :H ₂(SL(2,k); Z)I ²(k), whereI ²(k) is the square of the fundamental ideal. We prove that this homomorphism is in fact a lift of Milnor's symbol.

     

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).     

Synthèse de nouveaux types de dérivés C-glycosyliques à partir de sucres acétyléniques ou de leurs équivalents synthétiques partiels

Synthesis of Novel Types of C-Glycosyl-derivatives from Acetylenic Sugars or Partial Synthetic Equivalents thereof The concept of synthetic equivalent is not unequivocal and, for example, α-fluoroenamines may behave in some cases as synthetic equivalents of ynamines and, in other situations, quite differently. Some uses of these α-fluoroenamines, ‘partial synthetic equivalents’ of ynamines, for the synthesis of C-glycosyl derivatives of coumarins, chromones, quinolines, quinolones, thietenes and isoxazoles are described. We also report the preparation of a series of mono- and diglycosylthiophenes by reacting HS^? with mono- and diglycosylbutadiynes. Acetylenic sugar derivatives have also been used for the synthesis of a diglycosylazaphosphorine and a spirooxolenone.     

Studies on the 4-benzoylpyridine-3-carboxamide entity as a fragment model of the Isoniazid-NAD adduct

An ortho-metallation-electrophilic substitution sequence was employed as a key step to build the 4-benzoylpyridine framework. It was found that 4-benzoylpyridine-3-carboxamide and an N-pyridyl alkylated derivative both exist in a unique cyclized hemiamidal structure, not in the usually expected keto-amide open form. These structures represent fragment models of the Isoniazid-NAD adducts involved in the mechanism of action of the antituberculous drug Isoniazid.     

Bicyclic aziridines as intermediates in the photolysis of polycyclic aromatic azides.

According to the subsequent treatment, azepines $\text{16}$, $\text{17}$, $\text{19}$ or 1,2-dihydro derivatives $\text{18}$ and $\text{20}$ are obtained in the photolysis in basic medium of β-anthracenic azides $\text{7b}$ and $\text{7c}$ and provide strong evidence for the intermediate formation of bicyclic aziridines.     

Bit-string methods for selective compound acquisition

Selective compound acquisition programs need to ensure that the compounds that are chosen do not contain undesirable functionality. This is easy to achieve if a supplier is prepared to provide unambiguous structure representations for the compounds that they have available: this paper discusses selection techniques that can be used when a supplier is prepared to make available only fragment bit-string representations for the compounds in their catalog. Experiments with three databases and three types of bit-string show that a simple k-nearest-neighbor searching method provides a surprisingly effective, although far from perfect, way of selecting compounds when only bit-string representations are available. A second approach, based on the use of a fragment weighting scheme analogous to those used in substructural analysis studies, proved to be noticeably less effective in operation.     

Nachweis von C (15)-epimeren Coleonen C und D in der Natur und ihre Bedeutung für den sterischen Verlauf der Bildung des Spirocyclopropanrings

Natural Occurrence of C(15)-Epimeric Coleons C and D and its Significance to the Stereochemistry of the Formation of a Spirocyclopropanring In a previous paper some evidence was presented for a predominant occurrence of epimeric coleons ((15S)-coleon C ((15 S)- 1a ), and (15S)-coleon D ((15S)- 2a )) in Plectranthus lanuginosus [1], The proposed structures have now been proven by careful comparison of their physical data with those of the already described C(15)-epimers whose structures were deduced by X-ray analysis of a derived cis-diketone 3 [5], Examination of the epimeric purity of coleons possessing a 2-hydroxy-1-methylethyl side-chain (coleons C , D , H , I , I ′ and derivatives) isolated from seven different species (Coleus, Plectranthus and Solenostemon) has shown that these coleons always occur as a mixture of C(15)-epimers, although in most cases with one predominant epimer. The consequences for the stereochemistry of the postulated in vivo formation of the methyl-substituted spirocyclopropane substructure is discussed.