Comparative borazarobenzenes calculations following different methods

Borazarobenzenes are studied with different approaches, some treating only electrons and others including all valence electrons. The importance of the total net electronic density for interpreting the chemical behaviour of the molecules is stressed. All methods agree in assigning fairly high values to dipole moments. Disagreeing conclusions about other properties in the different methods are analyzed.

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Zusammenfassung Die Borazarobenzol-Isomeren werden mit verschiedenen Methoden untersucht, die entweder nur die -Elektronen oder alle Valenzelektronen behandeln. Die Wichtigkeit der Gesamt-Elektronen-dichte für die Erklärung des chemischen Verhaltens der Moleküle wird hervorgehoben. Alle Methoden stimmen in dem Ergebnis recht hoher Werte für die Dipolmomente überein. Unterschiedliche Ergebnisse bei der Anwendung der verschiedenen Methoden werden analysiert.

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Résumé On étude les borazarobenzènes suivant de diverses méthodes; les unes traitent seulement les électrons et les autres impliquent tous les électrons de valence. On souligne l'importance des charges nettes totales pour interpréter le comportement chimique des molécules. Toutes les méthodes s'accordent en attribuer des valeurs assez hautes au moment dipolaire. On analyse des conclusions discordantes sur d'autres propriétés prévues par les différents méthodes.

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One of us (M. G.) wishes to thank the Consiglio Nazionale delle Ricerche for making possible his stay in Italy.     

A convenient synthesis of 2-chromonecarboxylic acids

Knoevenagel condensation of the β-ketosulfinyl intermediate II with butyl glyoxylate afforded the butyl 2-hydroxy-4-(2-hydroxyphenyl)-3-methylsulfinyl-4-oxobutyrates (III). Compounds III are versatile intermediates for the synthesis of either 2-chromonecarboxylates (V) or 2-carboxy-methylene-3-coumaranone esters (VII).     

The Synthesis of (S)-(+)-2-Amino-3-(1-adamantyl)-propionic Acid (L-(+)-Adamantylalanine,Ada) as a ‘Fat’ or ‘Super’ Analogue of Leucine and Phenylalanine

Because of its overall steric resemblance to the phenylalanine analogue, carboranylalanine, the title compound was prepared by the modified Strecker synthesis of Patel & Worsley. The use of (S)-(?)-α-methylbenzylamine in the synthesis, the positive trend of [α]_D with increasing protonation, and the thin-layer chromatographic behaviour of synthetic diastereomeric dipeptides are strong indications that the configuration at the asymmetric carbon atom is S (natural L ). Its optical purity was ascertained by purification via the quinine and ephedrine salts of t-butoxy-carbonyl-adamantylalanine. The new amino acid shall be used for studies of structure-activity relationships of phenylalanine and leucine residues in biologically active peptides. In addition, a convenient synthesis in excellent yield of the starting material, 2-(1-adamantyl)-ethanal, by Pfitzner-Moffat oxidation of 2-(1-adamantyl)-ethanol is described.     

Conjunction,succession, determination and causation

The principles of regular (invariable or stochastic) conjunction, of retarded action, determination, and causality, are stated exactly and analyzed. To this end, the concepts of system, property, state, and event, as well as those of conjunction (of events and of properties) are first elucidated. Four types of determination are distinguished and analyzed and it is shown that only one of them qualifies as a causal nexus, the others being deterministic (in the large sense) but noncausal. The overall conclusion is that, while the principles of regular conjunction, retarded action and determination are both distinct and universal, the causal principle is just a restricted version of the principle of determinacy.     

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