Probability matrices, non-negative rank, and parameterization of mixture models

In this paper, we parameterize non-negative matrices of sum one and rank at most two using the least possible number of parameters. We also show how this parameterization relates to a class of statistical models, known in Probability and Statistics as mixture models for contingency tables. In particular, we show how to use this parameterization to make some optimization problems computationally easier.     

Optical activity of alternating copolymers of chiral α-olefins with alkyl acrylates

The synthesis of high-molecular-weight substantially alternating copolymers of alkyl acrylates with optically active α-olefins is reported. “Induced optical activity” on the side-chain ester chromophores, depending on the chemical structure of the chiral α-olefin, is indicated by CD measurements. Data are reported supporting the conclusion that this induced optical activity is related to a preferential chiral conformation of the macromolecules due to a cooperative effect.     

Stereoelective polymerization of racemic α-olefins: Influence of conversion and of nature of catalyst components

The dependence of stereoelectivity on conversion has been investigated by polymerizing racemic 4-methyl-1-hexene (I) and 3,7-dimethyl-1-octene (II) in the presence of catalysts prepared from TiCl₄ and bis[(S)-2-methylbutyl]-zinc(III) or tris [(S)-2-methylbutyl]aluminum (IV). The influence of the nature of transition metal halide has also been examined by polymerization of racemic I and II with catalysts obtained from III and transition metal halides as well as from TiCl₄ and optically active organometallic compounds containing phenyl groups. Stereoelectivity remains practically constant or increases slightly with increasing conversion, but it is affected by the nature of transition metal halide. Moreover a detectable variation of stereoelectivity was observed by changing the chemical structure of the alkyl group in the optically active organometallic component of the catalyst. In any case, however, stereoelectivity is not higher than 5–10%. Evidence in favor of asymmetric induction by the catalytic complex is reported and discussed.     

Some experimental aspects of DSC determination of kinetic parameters in thermal decompositions of solids

Some particular methods of collecting and treating DSC data for the determination of kinetic parameters in thermal decompositions of solids are suggested. These are mainly concerned with an extrapolation method to avoid the effect of the sample mass; with an approximate method to obtain the activation energy and the exponent of the decay-law for runs at constant temperature in which the total area under the thermal curve is not known with accuracy; and with a method to ascertain whether a particular decomposition takes place by a single mechanism or by a sequence of different mechanisms.

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Zusammenfassung Einige besondere Methoden der Sammlung und Verarbeitung von DSC-Daten zur Bestimmung kinetischer Parameter bei der thermischen Zersetzung von Festkörpern werden vorgeschlagen. Diese befassen sich hauptsächlich mit einer Extrapolationsmethode um die Wirkung der Einwaage zu vermeiden; mit einer Annäherungsmethode um die Aktivierungsenergie und den Exponenten des Zersetzungsgesetzes von Versuchen bei konstanter Temperatur zu erhalten, bei welchen die Gesamtoberfläche unter der thermischen Kurve nicht genau bekannt ist; und mit einer Methode zur Bestimmung ob eine bestimmte Zersetzung durch einen einzigen Mechanismus oder durch eine Reihenfolge verschiedener Mechanismen herbeigeführt wird.

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Résumé On propose quelques méthodes particulières pour rassembler et traiter les données de l'analyse calorimétrique différentielle (DSC) dans le but de déterminer les paramètres cinétiques de la décomposition des corps solides. Ces méthodes comportent surtout une extrapolation afin d'éviter l'influence de la prise d'essai, une approximation afin d'obtenir l'énergie d'activation et l'exposant de la loi de décomposition pour les expériences effectuées à température constante dans lesquelles la surface totale délimitée par la courbe n'est pas connue avec exactitude, et enfin un moyen de s'assurer si une décomposition particulière est due à un seul mécanisme ou à une succession de divers mécanismes.

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Work supported by the Italian Consiglio Nazionale delle Ricerche (C. N. R.). Contrac No. 71.01589.03.     

Angular distributions for (3,4)(Lambda)H bound states in the (3,4)He(e,e(')K+) reaction

The (3,4)(Lambda)H and (4)(Lambda)H hypernuclear bound states have been observed for the first time in kaon electroproduction on (3,4)He targets. The production cross sections have been determined at Q(2)=0.35 GeV2 and W=1.91 GeV. For either hypernucleus the nuclear form factor is determined by comparing the angular distribution of the (3,4)He(e,e(')K+)(3,4)(Lambda)H processes to the elementary cross section 1H(e,e K+)Lambda on the free proton, measured during the same experiment.     

High resolution spectroscopy of the 12Lambda B hypernucleus produced by the (e,e'K+) reaction

High-energy, cw electron beams at new accelerator facilities allow electromagnetic production and precision study of hypernuclear structure, and we report here on the first experiment demonstrating the potential of the (e,e'K+) reaction for hypernuclear spectroscopy. This experiment is also the first to take advantage of the enhanced virtual photon flux available when electrons are scattered at approximately zero degrees. The observed energy resolution was found to be approximately 900 keV for the (12)(Lambda)B spectrum, and is substantially better than any previous hypernuclear experiment using magnetic spectrometers. The positions of the major excitations are found to be in agreement with a theoretical prediction and with a previous binding energy measurement, but additional structure is also observed in the core excited region, underlining the future promise of this technique.     

Measurement of the electric form factor of the neutron through d-->(e-->,e(')n)p at Q2 = 0.5 (GeV/c)(2)

We report the first measurement using a solid polarized target of the neutron electric form factor G(n)(E) via d-->(e-->,e(')n)p. G(n)(E) was determined from the beam-target asymmetry in the scattering of longitudinally polarized electrons from polarized deuterated ammonia ( 15ND3). The measurement was performed in Hall C at Thomas Jefferson National Accelerator Facility in quasifree kinematics with the target polarization perpendicular to the momentum transfer. The electrons were detected in a magnetic spectrometer in coincidence with neutrons in a large solid angle segmented detector. We find G(n)(E) = 0.04632+/-0.00616(stat)+/-0.00341(syst) at Q2 = 0.495 (GeV/c)(2).