Questioni di algebra universale in una categoria astratta

Riassunto Allo scopo di studiare alcuni problemi di algebra universale in una categoriaK, si definiscono, relativamente ad un oggetto diK, alcuni concetti di solito riferiti ad un insieme, quali quello di relazione binaria (in particolare di equivalenza), composizione di corrispondenze, nucleo di un morfismo.

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Summary In order to study some problems of Universal Algebra in a categoryK, some set theoretic concepts are generalized to objects ofK.

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Lavoro eseguito nell'ambito dell'attività dei Gruppi di Ricerca Matematici del C.N.R. (programma n. 8), nell'anno 1969.     

Problemi al contorno con condizioni omogenee per le equazioni quasi-ellittiche

Summary We are concerned with non-variational boundary value problems, with omogeneus boundary conditions, for linear partial differential equations of quasi-elliptic type in a bounded domain Θ in Rⁿ. It is well known that some of difficulties which arise in treating such problems, in comparison with ? regular ? elliptic problems, are connected with the presence of angular points in Θ: let us point out withB. Pini [32] that ? a bounded domain for which it is possible to assign a correct boundary value problem for a quasi-elliptic but not elliptic equation always has angular points ?. We suppose Θ is a cartesian product of a finite number of open sets and, in order to overcome the difficulties attached to the presence of angular points in Θ, taking as a model the two previous papers[33], [34] devoted to elliptic problems with singular data, we investigate the problem within suitable Sobolev weight spaces, connected with the angular points of Θ and included in the ones we have studied in[35]. Within such spaces we get existence and uniqueness theorems.

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Lavoro eseguito con contributo del C. N. R.

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Entrata in Redazione il 30 ottobre 1971.     

Una proprietà delle famiglie numerabili di catene sopra un albero

Riassunto Si studia qui un problema relativo alla distribuzione delle famiglie di catene sopra insiemi ordinati particolarmente regolari che vengono qui chiamati ?alberi?: si stabilisce un teorema d'isomorfismo e se ne mostra, attraverso corollari immediati, il significato topologico.

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Résumé On étudie ici un problème concernant la situation des familles dénombrables de cha?nes sur des ensembles ordonnés particulièrement réguliers, qu'on appelle ?arbres?: on établit un théorème d'isomorphisme dont on montre, par des considérations très simples, la signification topologique.

     

Secondary mechanical relaxation effects in some cycloalkyl side groups containing polymers

Summary The dynamic mechanical properties at acoustic and low-ultrasonic frequencies (6–60 kHz) have been determined in polycyclopentylmethacrylate (PCPMA), polycyclohexylmethacrylate (PCHMA), polycyclohepthylmethacrylate (PCHpMA), polycyclooctylmethacrylate (PCOcMA), polycyclohexylacrylate (PCHA), polyvinylhexahydrobenzoate (PVHHBz), polyvinylcyclohexylether (PVCHE) and polyvinylcyclohexane (PVCH) Measurements were carried out by an electrostatic method (flexural vibrations) over the temperature range 60 °K to room temperature. All polymers, except for polyvinylcyclohexane, exhibit a γ-relaxation, connected with internal motion of the cycloalkyl ring, whose activation parameters depend exclusively on the nature of the ring. PVCHMA, PVCHA, PVHHBz, PVCHE and PVCH exhibit a further secondary relaxation effect (δ-process) at lower temperature, whose position on the temperature scale, strength (peak height) and activation parameters depend on the nature of the units to which the cyclohexyl ring is attached. The δ-process is attributed to some complex motion of the whole cyclohexyl ring, involving oscillatory rotation of the same around simple bonds which link it to the backbone chain. Contrarily to the δ-process of the phenyl side group containing polymers, the δ-process of the polymers here examined seems to be more sensibly dependent on intramolecuar effects.

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Zusammenfassung Es wurden die dynamischen Eigenschaften im akustischen und im Bereich langsamer Ultraschallfrequenzen (6–60 kHz) untersucht für Polycyclopentylmethacrylat (PCPMA), Polycyclohexylmethacrylat (PCHMA), Polycycloheptylmethacrylat (PCHpMA), Polycyclooctylmethacrylat (PCOcMA), Polycyclohexylacrylat (PCHA), Polyvinylhexahydrobenzoat (PVHHBz) Polyvinylcyclohexyl?ther (PVCHE) und Polyvinylcyclohexan (PVCH). Die Untersuchungen wurden mit einer elektrostatischen Methode (Biegeschwingung) über den Temperaturbereich von 60 °K bis Raumtemperatur durchgeführt. Alle Polymeren, au?er Polyvinylcyclohexanen, zeigen eine γ-Relaxation verbunden mit internen Bewegungen des Cycloalkylrings, deren Aktivierungsparameter wesentlich von der Natur des Rings abh?ngen. PVCHMA, PVCHA, PVHHBz, PVCHE und PVCH zeigen einen weiteren sekund?ren Relaxationseffekt (δ-Proze?) bei tieferen Temperaturen, dessen Lage in der Temperaturskala, St?rke (Peakh?he) und Aktivierungsparameter von der Natur der Einheiten abh?ngen, an welchen der Cyclohexylring h?ngt. Der δ- Proze? wird irgendeiner komplexen Bewegung des ganzen Cyclohexylrings zugeschrieben, eingeschlossen oszillatorische Rotation desselben um die Einfachbindung, die ihn mit der Hauptkette verbindet. Anders als der δ-Proze? der Phenylseitengruppen enthaltenden Polymerenketten scheint der hier untersuchte δ-Proze? emfindlicher von intramolekularen Effekten abzuh?ngen.

     

Sulle trilinearità tra rette

Sunto Si dà una definizione di trilinearità tra spaz? grafici indi si studiano le trilinearità tra rette complesse, considerando in particolare le trilinearità complete. Si dimostra come i var? casi proiettivamente distinti si possano ottenere intersecando la varietà diSegre, prodotto di tre rette, mediante spaz? lineari ad essa opportunamente tangenti. A Enrico Bompiani in occasione del suo Giubileo scientifico     

Properties of iodine complexes of monosubstituted polyacetylenes

Iodine complexes of six monosubstituted polyacetylenes with methyl, ethyl, propyl, pentyl, t-butyl, and phenyl substituents have been characterized by electronic spectroscopy. UV spectra allow the determination of the nature and the amount of active species, and photoelectronic spectra confirm the nature of these species. These measurements indicate the presence of iodine in the I and I₂ forms. The concentration of I is low (0.12–4.0 mol%), and it depends on the nature of the substitutent, but this amount does not decrease when the films are left under vacuum. On the other hand, the adsorption of ε high concentration of iodine is possible; this adsorption is governed by a diffusion mechanism and is reversible. Iodine doping leads to a cis-to-trans isomerization of the polymers, except for poly(3-3-dimethyl-1-butyne), which can be isomerized to the cis or to the trans form, depending on the solvent employed. Electrical properties of polymer I complexes are also reported. Conductivities of about 10^?4 Ω^?1 cm^?1 are obtained for all polymers in the presence of an excess of iodine.     

Definition of a multicenter bond index

The tensor character of the first-order density matrix leads to the definition of an MO multicenter bond index for closed-shell systems. It is here applied to three-center bonds. Satisfactory results are obtained for compounds involving secondary bonds, strong and normal hydrogen bonds; the index for the peptide bond is found to be similar to that of strong hydrogen bonds.On leave of absence from Inst. de Física, UFBA, 40000 Salvador, BA, Brasil.     

Computer Automated Structure Evaluation (CASE) of the teratogenicity of retinoids with the aid of a novel geometry index

Summary The CASE (Computer Automated Structure Evaluation) program, with the aid of a geometry index for discriminating cis and trans isomers, has been used to study a set of retinoids tested for teratogenicity in hamsters. CASE identified 8 fragments, the most important representing the non-polar terminus of a retinoid with an additional ring system which introduces some rigidity in the isoprenoid side chain. The geometry index helped to identify relevant fragments with an all-trans configuration and to distinguish them from irrelevant fragments with other configurations.     

The stereochemistry of the 6-membered ring of cedranone

Evidence from the coupling constants and solvent shifts of the protons in cedranone rules out the boat and chair conformations of the cyclohexanone ring. Linear correlation of the solvent shifts of the C-15 methyl protons of cedranone with those of the α-methyl groups of fenchone indicates a nearly planar conformation of the cedranone ring. Site factor analysis of the ASIS effect of the methyl protons of cedranone provides conclusive evidence of a quasi-chair conformation of the 6-membered ring.