Anti-self-dual Hermitian metrics on blown-up Hopf surfaces

Work supported in part by NSF Grant #DMS-8704401     

Tetraacylation of isobutene: first synthesis of 1,3,6,8-tetramethyl-2,7-naphthyridine

The tetxaacetylation of isobutene has been perfomed in AlCl₃/AcCl. Treatment of the crude reaction medium with liquid ammonia yields the title compound.     

Recursive interpolation,extrapolation and projection

The recursive projection algorithm derived in a previous paper is related to several well-known methods of numerical analysis such as the conjugate gradient method, Rosen's method and Henrici's. It is connected with the general interpolation problem, with extrapolation methods, with orthogonal projection on a subspace and with Fourier expansions. Several other connections and applications are presented.     

13C NMR study of dilute ternary solutions: Acetonitrile,silver nitrate and other electrolytes in water at 25°C

The ¹³C NMR chemical shifts have been measured for dilute aqueous solutions of acetonitrile in presence of various electrolytes including silver nitrate. The two formation constants of the silver ion/acetonitrile complexes have been calculated assuming an additive contribution of each possible complex configuration. Under these conditions the values obtained for the formation constants are very close to those deduced from vapour pressure or electromotive force techniques. The other systems studied are discussed in relation to the salting phenomenon in aqueous electrolyte solutions.     

Prediction properties of some extrapolation methods

Convergence acceleration methods consist in the construction of a sequence converging faster than the initial sequence. Each member of the new sequence is a guess for the limit and it is computed from a restricted number of terms of the initial sequence. It is shown herein how convergence acceleration methods can be used to predict the next (unknown) term of the initial sequence instead of its limit. Particular emphasis on Aitken's △² process and the E-algorithm is placed.     

Dérivés Alléniques du Phosphore. Influence de l'État de Coordination du Phosphore et de la Nature des Radicaux Liés au Phosphore sur les Signes de J(P?H)

The signs of the phosphorus-proton coupling constants in various allenic organophosphorus compounds have been determined by either analysis of the AB₂X spectra or double resonance. Probable absolute signs have been obtained by taking ³J(P? H) as positive. In allenic phosphine oxides, the following signs are obtained: ²J(P? H) +ve, ³J(P? H) +ve, ⁴J(P? H) ?ve, ⁵J(P? H) +ve and the ⁴J(P? H) coupling constant varies mostly with the inductive effect of the substituents bound to the phosphorus atom. In allenic phosphines, these sings are: ²J(P? H) +ve, ³J(P? H) +ve, ⁴J(P? H) ?ve and +ve and the ⁴J(P? H) coupling constant varies with both the inductive and resonance effects to the substituents. This coupling constant is negative except when the phosphorus atom is bound to groups which are electron-donating by resonance effects. These results are discussed in relation to the pπ? dπ bonding in phosphine.     

Étude théorique de l'oxime de l'acroléine

Résumé La méthode semi-empirique de Pariser-Parr-Pople est appliquée à l'étude des quatre isomères géométriques de l'oxime de l'acroléine, en utilisant les paramètres empiriques déterminés précédemment pour les oximes de la p-benzoquinone. L'analyse théorique des énergies totales permet de penser sans ambiguité que seule la forme -trans peut exister. Dans ces conditions, le spectre électronique calculé est en très bon accord avec les résultats expérimentaux.

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The Pariser-Parr-Pople's method is applied to the study of the four -geometric conforme of the oxime derived from acrolein, using empirical parameters precedently defined for the study of p- benzoquinone oximes. The theoretical analysis of total energies allow the conclusion that alone the -trans form may exist. In these conditions, the computed electronic spectrum is in good agreement with experimental data.

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Zusammenfassung Mit der PPP-Methode wurden die vier geometrischen Isomeren des Oxims des Acrolein behandelt. Dabei wurden die empirischen Parameter benutzt, die schon bei der Untersuchung des Oxims des p-Benzochinons verwandt wurden. Es ergibt sich, daß nur die -trans Form existiert und für diesen Fall auch das berechnete Elektronenspektrum mit den experimentellen Werten gut übereinstimmt.