(Perhalogenmethylthio)heterocyclen. XVIII . Synthese und eigenschaften von halogenierten (perhalogenmethylthio)pyrrolen

(Trifluoromethyltho)pyrroles 1-5 and (chlorodifluoromethylthio)pyrroles 6 were chlorinated by sulfuryl chloride, sulfuryl chloride/silicon dioxide, sulfuryl chloride/disulfur dichloried/aluminium trichloried to give the corresponding chloropyrroles 1a-d , 2a,b , 3a,b , 4a , 5a , and 6a-c Bromination with bromine or iodination with iodine/potassium iodide of 2, 3, 4 , and 6 yielded the derivatives 2c,d, 3c,d, 4b, 6d , and 2e, 3e, f, 4c , 6e respectively. Mixed halogenated pyrroles 3g and h were obtained from 3a and bromne or 3a and iodine/potassium iodide. During some chlorination reactions 7, 8 , and 9 were fromed in low yield asbyproducts. The ¹H-nmr, ¹⁹F-nmr and ir spectroscopic data are presented.     

Cyclobutenes by platinum-catalyzed cycloisomerization reactions of enynes

1,6-Enynes bearing (electron-rich) aryl substituents on their alkyne moiety rearrange to cyclobutene derivatives in the presence of catalytic amounts of PtCl2 in toluene. The reaction is significantly accelerated when performed under an atmosphere of CO (1 atm), most likely by increasing the electrophilicity of the metal template by temporary coordination to this pi-acidic ligand. This transformation allows the build up of considerable strain in the products as witnessed by the productive formation of tricyclic skeletons, such as 7 or 9. Moreover, these products provide evidence for the mechanistic scenario of platinum-catalyzed cycloisomerization reactions previously proposed, which are thought to proceed via organo-platinum species that mimic the reactivity of metal-complexed "nonclassical" carbocations.     

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No-arbitrage conditions,scenario trees,and multi-asset financial optimization

Many numerical optimization methods use scenario trees as a discrete approximation for the true (multi-dimensional) probability distributions of the problem’s random variables. Realistic specifications in financial optimization models can lead to tree sizes that quickly become computationally intractable. In this paper we focus on the two main approaches proposed in the literature to deal with this problem: scenario reduction and state aggregation. We first state necessary conditions for the node structure of a tree to rule out arbitrage. However, currently available scenario reduction algorithms do not take these conditions explicitly into account. State aggregation excludes arbitrage opportunities by relying on the risk-neutral measure. This is, however, only appropriate for pricing purposes but not for optimization. Both limitations are illustrated by numerical examples. We conclude that neither of these methods is suitable to solve financial optimization models in asset–liability or portfolio management.     

Implicit runge-kutta methods for differential inclusions

This paper is concerned with the application of implicit Runge-Kutta methods suitable for stiff initial value problems to initial value problems for differential inclusions with upper semicontinuous right-hand sides satisfying a uniform one-sided Lipschitz condition and a growth condition. The problems could stem from differential equations with state discontinuous right-hand sides. It is shown that there exist methods with higher order of convergence on intervals where the solution is smooth enough. Globally we get at least the order one.