On the spectrum of the sum of generators for a finitely generated group

Let Γ be a finitely generated group. In the group algebra ℂ[Γ], form the averageh of a finite setS of generators of Γ. Given a unitary representation π of Γ, we relate spectral properties of the operator π(h) to properties of Γ and π. For the universal representationπ _un of Γ, we prove in particular the following results. First, the spectrum Sp(π _un (h)) contains the complex numberz of modulus one iff Sp(π _un (h)) is invariant under multiplication byz, iff there exists a character such that η(S)={z}. Second, forS ⁻¹=S, the group Γ has Kazhdan’s property (T) if and only if 1 is isolated in Sp(π _un (h)); in this case, the distance between 1 and other points of the spectrum gives a lower bound on the Kazhdan constants. Numerous examples illustrate the results.     

An in vitro investigation of human enamel wear by restorative dental materials

A radiometric method was applied to assess enamel wear by another enameland by restorative materials. The radioactive enamel was submitted to wearin a machine which allows sliding motion of an antagonistic surface in contactwith the radioactive enamel. The enamel wear was evaluated by measuring thebeta-activity of ³²P transferred to water from this irradiatedtooth. Results obtained indicated that dental porcelains cause pronouncedenamel wear when compared with that provoked by another natural enamel orby resin materials. Resin materials caused less enamel wear than another naturalenamel. Vickers microhardness data obtained for antagonistic materials showeda correlation with the wear caused to the enamel.     

Construction of functional porphyrin polystyrene nano-architectures by ATRP

A series of mono-functionalized metallo-porphyrin polystyrenes have been synthesized using atom transfer radical polymerization and their self-assembling behavior was studied by electron microscopy showing that the polystyrene tail-length influences the aggregate architecture.     

A configuration interaction study of phosphine using bonded functions

A computational study is made of the effect of basis set upon the energy, properties and inversion barrier of the phosphine molecule. The calculations are performed at both the SCF and CI level. The flexibility of the double zeta basis is discussed in the light of the results.     

Struktur von 7,11-Diphenyl-2,4-diazaspiro[5,5]undecan-1,3,5,9-tetraonen durch LIS-NMR

A semi-quantitative method for determining distances between a possible coordination centre and protons from LIS-NMR values is developed for the title compounds3, although these have four coordination points. This makes it possible to propose structures and conformations for the isomers of3.

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Mit 4 Abbildungen

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H.-H. Otto undH. Yamamura, Ann. Chem., im Druck.     

Spectroelectrochemical characterisation of poly[Ni(saltMe)]-modified electrodes

Electrogenerated polymers based on the nickel(II) complex 2,3-dimethyl-N,N'-bis(salicylidene)butane-2,3-diaminatonickel(II), poly[Ni(saltMe)], were characterised by in situ FTIR and UV/Vis spectroscopy and ex-situ EPR spectroscopy in order to gain insights into film structure, electronic states and charge conduction. The role of the nickel ions during film oxidation was probed by using EPR to study naturally abundant Ni and 61Ni-enriched polymers. The data from all the spectroscopic techniques are consistent, and clearly indicate that polymerisation and redox switching are associated with oxidative ligand based processes; coulometry suggests that one positive charge was delocalised through each monomer unit. EPR provided evidence for the non-direct involvement of the metal in polymer oxidation: the polymer is best described as a polyphenylene-type compound (conducting polymer), rather than an aggregation of nickel complexes (redox polymer), and the main charge carriers are identified as polarons. An explanation for the high electrochemical stability and conductivity of poly[Ni(saltMe)] with respect to that of poly[Ni(salen)] is proposed. based on stereochemical repulsion between monomeric units; this can impose a less compact supramolecular structure on polymers with bulkier substituents.     

Etude dilatométrique de la cristallisation et de la transformation polymorphe du polybutène — 1 isotactique

Résumé On étudie par dilatométrie la cinétique de cristallisation et de la transformation III de trois échantillons de polybutène-1 isotactique. On montre que la cristallisation de l'échantillon fondu est initiée par des germes hétérogènes, dont le nombre varie d'un échantillon à l'autre. La vitesse de cristallisation varie linéairement avec l'inverse du degré de surfusion (T ^–1), sa variation thermique étant indépendante de l'échantillon. On met en évidence l'importance de la cristallisation secondaire, qui suit le processus autocatalytique. D'autre part, la transformation III, après refroidissement, est initiée par des germes apparaissant sporadiquement dans les fibrilles lamellaires de la texture sphérulitique, et elle se propage le long de celles-ci. D'une manière générale la vitesse de transformation isotherme dépend de l'histoire thermique: on examine ici l'influence de la température de cristallisation primitive et celle d'une trempe préalable aux basses températures. Cette dernière engendre un grand nombre de germes, dont la fraction qui résiste à une élévation de température, accélère la transformation. On discute, enfin, les trois volumes de référence déterminant la cristallinité des échantillons dans les deux formes. On propose une nouvelle échelle de cristallinité, dont la cohérence est confirmée par l'invariance des valuers des coefficients de dilatation des deux formes de cristaux, déduites de la dilatation des échantillons obtenus après trempe ou cristallisation isotherme à haute température.

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Summary Kinetics of crystallization and transformation III are investigated dilatometrically with three isotactic Polybutene-1 samples. Primary autocatalytic crystallization from the supercooled melt is initiated by a heterogeneous nucleation process, the number of nucle being determined by the previous temperature of the melt. The rate of crystallization depends linearly on the reciprocal of the degree of supercooling (T ^–1) and its thermal variation is identical for the three samples investigated. The importance of the secondary cristallization, which follows the primary process, is emphasized. On the other hand, the transformation III, which occurs after cooling the semicristalline sample in the room temperature range, is initiated by nuclei appearing sporadically in the lamellar ribbons of the spherulitic texture and they grow linearly along these ribbons. In general the isothermal rate of transformation depends on the previous thermal history of the sample: the influence of the cristallization temperature and that of quenching to low temperatures are systematically investigated. Such a quenching prior to transformation generates a great number of nuclei, a fraction of which persiste even at higher temperatures and increases the rate of transformation. Reference volumes, which determine the cristallinity of PB-1 in its two forms, are discussed. A new cristallinity scale is proposed, the coherence of which is confirmed by the constant values of the expansion coefficients of the two cristalline forms, calculated from the actuel thermal expansion of the semicristalline material, the cristallinity of which varied in a large range.

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Zusammenfassung Es wird an drei isotaktischen Polybuten-1-Proben die Kinetik der Kristallisation und der Transformation von II nach I untersucht. Eine primäre autokatalytische Kristallisation aus der unterkühlten Schmelze wird durch einen heterogenen Keimbildungs-Prozeß initiiert. Die Zahl der Keime ist durch die vorausgehende Temperatur der Schmelze bedingt. Die Geschwindigkeit der Kristallisation hängt linear vom reziproken Wert der Unterkühlung ab (T ^–1) und die thermische Variation ist identisch für alle drei untersuchten Proben. Die Wichtigkeit der Sekundär-Kristallisation, die dem primären Prozeß folgt, wird betont. Andererseits wird die Transformation von II nach I, die nach Abkühlen der halb-kristallinen Probe auf Raumtemperatur eintritt, durch Keime initiiert, die verstreut in den laminaren Rippen der sphärulithischen Textur erscheinen. Sie wachsen linear längs der Rippen. Im allgemeinen hängt die isotherme Geschwindigkeit der Transformation von der thermischen Vorgeschichte der Probe ab. Der Einfluß der Kristallisations-Temperatur und der des Abschreckens zu tiefen Temperaturen werden systematisch untersucht. Ein Abschrecken vor der Transformation erzeugt eine große Zahl von Keimen, von denen ein Bruchteil auch bei höheren Temperaturen fortbesteht und die Transformations-Geschwindigkeit so erhöht. Referenz-Volumina, die die Kristallinität von PB-1 bestimmen, werden diskutiert in ihren zwei Formen. Eine neue Kristallinitäts-Skala wird vorgeschlagen, deren Zutreffen durch die konstanten Werte der Ausdehnungs-Koeffizienten der zwei Kristall-Formen, berechnet aus dem tatsächlichen Ausdehnungsverhaltens des semikristallinen Materials, dessen Kristallanteil in einem großen Bereich variierte, gesichert wird.

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Avec 12 figures en 14 détails et 8 tableaux

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Beursier del'OTAN pendant l'année 1966.     

Calculations on electric-field-induced shifts in ultraviolet absorption spectra: The significance of doubly excited configurations

Calculations on the cation-induced shifts in the UV spectrum of the terphenyl mononegative ion suggest that the spectra of the ions of alternant hydrocarbons, as compared with those of the molecules, are rather insensitive to electric field perturbations. This feature only shows up if one includes enough (doubly) excited configurations to allow for the polarization of the excited states involved in the optical transitions.

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Zusammenfassung Berechnungen über die von Kationen verursachten Verschiebungen im UV-Spektrum des mononegativen Terphenylions deuten darauf hin, daß die Spektren der Ionen alternierender Kohlenwasserstoffe im Vergleich zu denen der Molekeln gegen vom elektrischen Feld hervorgerufene Störungen ziemlich unempfindlich sind. Dies kommt nur dann zum Ausdruck, wenn man in den Berechnungen genügend (doppelt) angeregte Konfigurationen mit einbezieht, um auch die Polarisation der an den optischen Übergängen beteiligten Anregungszustände zu erfassen.

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Résumé Des calculs sur les déplacements — provoqués par le cation — dans le spectre ultraviolet de l'ion mononégatif de terphényle indiquent que les spectres des ions d'hydrocarbures alternants, à côté de ceux des molécules, sont assez insensibles aux perturbations du champ électrique. On ne trouve ce résultat que dans le cas où l'on introduit un nombre suffisant de configurations excitées (doublement) pour tenir compte de la polarisation des états excités liés aux transitions optiques.