Order series of labelled posets

Order series of labelled posets are multi-analogues of the more familiar order polynomials; the corresponding multi-analogues of the related representation polynomials are calledE-series. These series can be used to describe the effect of composition of labelled posets on their order polynomials, whence their interest for us. We give a reciprocity theorem forE-series, and show that for an unlabelled poset the form of theE-series depends only upon the comparability graph of the poset. We also prove that theE-series of any labelled poset is a rational power series (in many indeterminates) and give an algorithm for computing it which runs in polynomial time when the poset is strictly labelled and of bounded width. Finally, we give an explicit product formula for theE-series of strictly labelled interval posets.This research was supported by the Natural Sciences and Engineering Research Council of Canada under operating grant #0105392.     

Study of the three-dimensional Ising model on film geometry with the cluster Monte Carlo method

Topological properties of clusters are used to extract critical parameters. This method is tested for the bulk properties ofd=2 percolation and thed=2, 3 Ising model. For the latter we obtain an accurate value of the critical temperatureJ/k _B T _c=0.221617(18). In the case of thed=3 Ising model with film geometry the critical value of the surface coupling at the special transitions is determined as J_1c/J=1.5004(20) together with the critical exponents ₁ ^m =0.237(5) and=0.461(15).     

Ab Initio versus CNDO barrier calculations

Energy barrier curves to internal rotation in P₂H₄ and P₂F₄ have been studied by the ab initio SCF-LCAO-MO method in the gaussian approximation and by the CNDO method. For P₂H₄, two stable rotamers at 75 and 180 of equal energy and separated by a barrier of only 500 cal/mole are predicted, and the cis barrier computes to be 4.1 kcal/mole. A trans-only form of P₂F₄ is the theoretical structure with only an arrest in the barrier curve at the gauche position. The CNDO method does not produce reliable information concerning the number of stable rotamers, their precise configurations, or the heights of the barriers.

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Zusammenfassung Die Kurven der Energiebarriere bei der inneren Rotation von P₂H₄ und P₂F₄ wurden nach der ab initio SCF-LCAO-MO-Methode mit einer Basis von Gaussfunktionen sowie nach der CNDO-Methode untersucht. Beim P₂H₄ ergeben sich zwei stabile Rotamere von gleicher Energie bei 75 und 180 und getrennt durch eine Barriere von nur 500 cal/mol; die cis-Barriere berechnet sich zu 4.1 kcal/mol. Eine reine trans-Form von P₂F₄ ist die theoretische Struktur mit nur einem Sattelpunkt in der Energiekurve bei der gauche-Position. Die CNDO-Methode liefert keine genügend genauen Anhaltspunkte zur Zahl der stabilen Rotameren, ihren genauen Konfigurationen oder zu den Höhen der Barrieren.

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Résumé Les courbes d'énergie donnant les barrières de rotation interne ont été étudiées pour P₂H₄ et P₂F₄ par la méthode ab-initio SCF LCAO MO en base gaussienne et par la méthode CNDO. Pour P₂H₄ on prévoit deux rotamères stables de mÊme énergie à 75 et 180 séparés par une barrière de 500 cal/mole seulement, la barrière cis calculée étant de 4,1 kcal/mole. La structure théorique de P₂F₄ est la forme «tout-trans» avec seulement un arrÊt sur la courbe dans la position gauche. La méthode CNDO ne produit pas d'informations sûres en ce qui concerne les rotamères stables tant du point de vue de leurs configurations que de celui des barrières.

     

Radiohochspannungsionophoretische Untersuchungen der Isotopenaustauschreaktionen zwischen Polythionaten,Thiosulfat und Sulfit

The isotopic exchange of³⁵S between thiosulfate/sulfite and tetrathionate/thiosulfate is examined. The kinetic data are determined. In both cases the reactions are of second order. As the isotopic exchange between tetrathionate/thiosulfate is very fast, these reaction components are used in high dilution. Furthermore, the extent of exchange during the separation is determined.      

Synthesis of sodium tantalate nanorods by alkalide reduction

NaTaO3 nanorods were synthesized with high (>90%) yield by reduction of TaCl5 with THF solutions of the alkalide K+(15C5)2Na-, followed by product annealing under dynamic vacuum at 250 and 600 degrees C. In addition to the nanorods, the product is comprised of 5-10% approximately 10-nm diameter spheroidal NaTaO3 nanocrystals. The nanorods are generally longer than 500 nm, with some exceeding 1 mum, and 10-100 nm wide, with aspect ratios that vary between 10 and 20:1. Select area electron diffraction patterns of individual nanorods indicate that each nanorod is a single crystal with its axis oriented in the [010] direction.