The arithmetic of certain quartic curves

We give a sufficient condition using the Brauer?CManin obstruction under which certain quartic curves have no rational points. Using this sufficient condition, we construct two families of genus one quartic curves violating the Hasse principle explained by the Brauer?CManin obstruction.     

Alkoxyallene‐ynes: Selective Preparation of Bicyclo[5.3.0] Ring Systems Including a δ‐Alkoxy Cyclopentadienone

The development of an intramolecular rhodium(I)‐catalyzed Pauson–Khand reaction of alkoxyallene‐ynes with a proximal alkoxy group is reported. This reaction, in the presence of a [Rh(cycloocta‐1,5‐diene)Cl]₂/propane‐1,3‐diylbis(diphenylphosphane) system under a CO atmosphere, constitutes a powerful tool for selectively accessing carbo‐ and heterobicyclo[5.3.0] frameworks featuring an enol ether moiety. Through this procedure, a straightforward access to guaiane skeletons with a tertiary hydroxy group at the C10 position was achieved.     

Topography Influence on the Lake Equations in Bounded Domains

We investigate the influence of the topography on the lake equations which describe the two-dimensional horizontal velocity of a three-dimensional incompressible flow. We show that the lake equations are structurally stable under Hausdorff approximations of the fluid domain and L ^p perturbations of the depth. As a byproduct, we obtain the existence of a weak solution to the lake equations in the case of singular domains and rough bottoms. Our result thus extends earlier works by Bresch and Métivier treating the lake equations with a fixed topography and by Gérard-Varet and Lacave treating the Euler equations in singular domains.     

Optimization incentive and relative riskiness in experimental stag-hunt games

We compare the experimental results of three stag-hunt games. In contrast to Battalio et al. (Econometrica 69:749–764, 2001), our design keeps the riskiness ratio of the two strategies at a constant level as the optimization premium is increased. We define the riskiness ratio as the relative payoff range of the two strategies. We find that decreasing the riskiness ratio while keeping the optimization premium constant decreases sharply the frequency of the payoff-dominant equilibrium strategy. On the other hand an increase of the optimization premium with a constant riskiness ratio has no effect on the choice frequencies. Finally, we confirm the dynamic properties found by Battalio et al. that increasing the optimization premium favours best-response and sensitivity to the history of play.     

On a convex set with nondifferentiable metric projection

A remarkable example of a nonempty closed convex set in the Euclidean plane for which the directional derivative of the metric projection mapping fails to exist was constructed by A. Shapiro. In this paper, we revisit and modify that construction to obtain a convex set with \(C^{1,1}\) boundary which possesses the same property.     

Synthesis,Complexes and Metal Extraction Ability of R1R2NC(X)NHP(Y)(0Ph)2

Abstract

The new 1,1-disubstituted 3-diphenoxy(thio)phosphoryl-(thio)ureas, R¹R²NC(X)NHP(0Ph)₂, HA, with X,Y = O,S, were synthesized by addition of secondary mines to the corresponding P-iso(thio)cyanates. This reaction is reversible if X,Y = S. (PhO)₂P(Y)Cl reacts with H₂NC(X)NR₂ in the presence of an HCl acceptor only if X,Y a 0. Side reactions are observed. Phosphorylated derivatives of biuret were isolated from such a reaction mixture.     

Book Review

Abstract

A Guide to Organophosphorus Chemistry, by Louis D. Quin, an internationally recognized authority, published by John Wiley and Sons (http://www.wiley.com/chemistry) ISBN 0-471-31824-8, $94.95, 394pp.

Aminophosphonic and Aminophosphinic Acids: Chemistry and Biological Activity. Editors: Valery P. Kukhar (Ukrainian Academy of Sciences) and Harry R Hudson (University of North London). Published by John Wiley and Sons Ltd., Chichester, UK, on 31 March, 2000. ISBN 0 471-89149-5, 175.00 Pounds sterling, 634 pages.

Phosphorus Ylides. Chemistry and Application in Organic Synthesis, by Oleg I. Kolodiazhnyi. Published by Wiley-VCH, 1999, ISBN 3-527-29531-3, 220SF, 555 pages.     

Synthesis and Study of a Sulfur Heterocycle Fused p-Phenylene Vinylene Conducting Polymer

Abstract

Poly(benzo[1,2-b:4,5-b′]dithiophene-4,8-diyl vinylene) (1) has been prepared by the pyrolysis of the precursor polymer 2 and studied. Quantum mechanical calculations on the aromatic and quinoid monomers, oligomers and polymers indicate that 1 is a planar aromatic polymer.