On Super-KMS functionals and entire cyclic cohomology

We formulate the super-KMS condition suggested by Connes and Kastler, in the context of entire cyclic cohomology of quantum algebras. We show that the Chern character of Jaffe, Lesniewski, and Osterwalder — associated by Kastler to a super-KMS functional — satisfies the entire growth condition. Hence, a super-KMS functional defines a cocycle for the entire cyclic cohomology of quantum algebras.Supported in part by the National Science Foundation.     

Liquid chromatography of the s-triazines

Summary A series of thirty s-triazine compounds have been separated using reversed-phase high-pressure liquid chromatography. A relationship between substituent activity and retention time was developed to predict molecular structure.Work partially completed at the CIBA-GEIGY Corp., McIntosh, Ala., USA.     

A class of interaction-round-a-face models and its equivalence with an ice-type model

A new model (called the Temperley-Lieb interactions model) is introduced, in two-dimensional lattice statistics, on a square lattice . The Temperley-Lieb equivalence of this model to the six-vertex, self-dual Potts, critical hard-hexagons and critical nonintersecting string models is established. A graphical equivalence of this model to the six-vertex model generalizes this equivalence to noncritical cases of the above models. The order parameters of a specialization of this model are studied.     

A rigorous control of logarithmic corrections in four-dimensional ϕ4 spin systems

Using Gawedzki and Kupiainen's rigorous block spin transformation method, we study critical phenomena in ⁴ spin systems in four dimensions. In Part I of this work we investigate in detail the renormalization group trajectory of the system not exactly at the critical point.     

Equilibrium polymerization in a solvent: Solution on the Bethe lattice

The lattice model for equilibrium polymerization in a solvent proposed by Wheeler and Pfeuty is solved exactly on a Bethe lattice (core of a Caylay tree) with general coordination numberq. Earlier mean-field results are reobtained in the limitq, but the phase diagrams show deviations from them for finiteq. Whenq=2, our results turn into the solution of the one-dimensional problem. Although the model is solved directly, without the use of the correspondence between the equilibrium polymerization model and the diluten0 model, we verified that the latter model may also be solved on the Bethe lattice, its solution being identical to the direct solution in all parameter space. As observed in earlier studies of the puren0 vector model, the free energy is not always convex. We obtain the region of negative susceptibility for our solution and compare this result with mean field and renormalization group (-expansion) calculations.     

Fields as Kolmogzrov flows

It is widely recognized that for highly unstable dynamical systems there exists a fundamental limitation on predictability and determinism. An important class of such highly unstable systems is the class of K-flow, which is further characterized by the existence of time-asymmetric objects in the form of K-partition. Our recent approach to the problem of irreversibility has shown that when the implications of the limitation on determinism arising from strong form of instability and those of the existence of K-partition are consistently taken into account, one is naturally led from the physically unrealizable deterministic evolution of phase points to an entropy-increasing stochastic Markovian evolution. Furthermore, this transition is not the result of extraneously imposed coarse graining and/or approximation schemes, but can be brought about by an invertible transformation whose existence and construction are determined by the nature of the instability of the dynamical system itself. After a brief review of this theory which also contains some relatively new remarks, we prove that classical Klein-Gordon field (both massive and massless) possess the structure of K-flow. This seems to provide the first examples of relativistic systems that are K-flows. Some of the implications of this result are briefly discussed. From a mathematical point of view, this seems to be a first step toward an ergodic theory of partial differential equations. In the process, we also provide an independant group-theoretic proof of the existence of incoming and outgoing subspaces of the scattering theory of Lax and Phillips for the wave equation.     

Michael and ring expansion reactions of 6-carboethoxy-3,5-diaryl-2-cyclohexen-1-ones

When -keto-ester1 a was reacted with dimethyl acetylenedicarboxylate ring expansion occurred to give substituted cyclooctadienones.Michael reactions of the title compounds1 with unsaturated ketones gave adducts, some of which underwent further cyclization reactions. A new route to -tetralone ring system10 via cyclization of the intermediateMichael adduct9 is described.

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Michael- und Ringerweiterungsreaktionen von 6-Carboethoxy-3,5-diaryl-2-cyclohexen-1-onen

Zusammenfassung Bei der Reaktion von -Keto-ester1 a mit Dimethyl-acetylendicarboxylat wurden unter Ringerweiterung substituierte Cyclooctadienone erhalten. DieMichael-Reaktion der Titelverbindung1 mit ungesättigten Ketonen ergab Addukte, von denen einige weitere Cyclisierungsreaktionen eingingen. Es wird ein neuer Weg zum -Tetralonsystem10 über die Cyclisierung des intermediärenMichael-Addukts9 beschrieben.

     

Reaction paths of some open-shell reactive intermediates

The intermolecular interaction energy for reacting systems in singlet, triplet and doublet states was partitioned by the perturbation expansion method into the chemically meaningful five interaction terms: the Coulomb, exchange-repulsion, induction, dispersion, and charge-transfer energies. In the local ZDO approximation, these energy terms were evaluated for the dimerization of methylenes (^1,3CH₂), the additions of carbenes (^1,3CH₂ and^1,3CF₂) as well as amino radicals (²NH₂ and²NF₂) toward ethylene, and the hydrogen abstractions by methylenes (^1,3CH₂), nitrene (³NH), and hydroxyl radical (²OH) from methane. It has been found that the reaction path is much influenced by the spinmultiplicity, and that the charge-transfer and exchange-repulsion terms play a dominant role in determining the course of reactions.     

Comparison of the Hartree-Fock,Møller-Plesset,and Hartree-Fock-Slater method with respect to electrostatic properties of small molecules

Summary The results of various quantum chemical calculations, the Hartree-Fock (HF) method, the Møller-Plesset perturbation theory (MP2), and the Hartree-Fock-Slater (HFS) method are compared. Atomic charges, dipole moments, topological properties of the electron density distribution and polarizabilities, and first hyperpolarizabilities are calculated. Atomic charges obtained with the HFS method are found to be very close to those calculated with the MP2 method, from which we conclude that the HFS method describes to some extent electron correlation effects. Performing an MP2 calculation after an HF calculation improves the molecular dipole moments considerably, yielding values close to the experimental ones. HFS calculations are computationally less demanding than MP2 and yield comparable results for the electron density distributions, dipole moments and polarizabilities.