Enantiodivergence in alkylation of 1-(6-methoxynaphth-2-yl)ethyl acetate by potassium dimethyl malonate catalyzed by chiral palladium-DUPHOS complex

Alkylation of racemic 1-(6-methoxynaphth-2-yl)ethyl acetate by potassium dimethyl malonate catalyzed by a chiral palladium-DUPHOS complex afforded the substitution product with 87% ee, along with 6-methoxy-2-vinylnaphthalene that arose from an elimination process, in a 43/57 substitution/elimination ratio. The reaction performed on a mixture of quasi-enantiomeric substrates provided insight into the stereochemical course of the reaction, establishing that—for a given enantiomer of the catalyst, one enantiomer of the substrate afforded mainly the substitution product whereas the other enantiomer underwent elimination.     

Probing the stereo‐electronic properties of cationic rhodium complexes bearing chiral diphosphine ligands by 103Rh NMR

¹⁰³Rh NMR represents a powerful tool to assess the global electronic and steric contribution of diphosphine ligands on [Rh(COD)(diphosphine)]⁺ complexes. In the case of DIOP, BINAP and MeDUPHOS, this approach proved to be more informative than classical CO‐stretching frequency measurements. After validation, this method has been extended to a set of seven diphosphines. ¹⁰³Rh NMR measurements on [Rh(COD)(diphosphine)]PF₆ lead to the following order of donor properties: dppe > MeBPE > MeDUPHOS > dppb > DIOP > BINAP > Tol‐BINAP. This trend has been validated by DFT in the case of DIOP, BINAP and MeDUPHOS. In conjunction, ³¹P NMR chemical shift has been shown to reflect the ring constraints of the Rh‐diphosphine scaffold. This contribution is a step towards a mechanistic investigation of the catalytic hydrogenation of unsaturated substrates by ¹⁰³Rh NMR and DFT. Copyright © 2010 John Wiley & Sons, Ltd.     

Skeletal rearrangements in the 2,3-diazanorbornene series. A fast access to highly functionalized cyclopentanes

[reaction: see text] Acid-catalyzed nucleophilic substitution of bicyclic hydrazine-epoxide involves nitrogen participation, leading to a skeletal rearrangement. This transformation enables the fast preparation of disubstituted bicyclic hydrazines in a regio- and stereoselective manner, leading to several polyfunctional diaminocyclopentanes after hydrogenolysis.     

Palladium-catalyzed cross-coupling of aryl electrophiles with dimethylalkynylaluminum reagents

[reaction: see text] Alkynyldimethylaluminum reagents are easily available from terminal alkynes and trimethylaluminum via a triethylamine-catalyzed metalation. These compounds can react with various aromatic and heterocyclic halides in the presence of palladium in a fast and efficient way. This catalyzed cross-coupling reaction provides a simple entry to numerous internal alkynes, using a readily available, inexpensive, and nontoxic metalating agent.     

A fixed point theorem in partially ordered sets and some applications to matrix equations

An analogue of Banach's fixed point theorem in partially ordered sets is proved in this paper, and several applications to linear and nonlinear matrix equations are discussed.

     

Entropy of generalized Gaussian optical fields

We consider two definitions of entropy: thermodynamic entropy and signal entropy. We compare their value for the class of generalized Gaussian fields. The first definition is well adapted to monomode stationary fields, while the second one is bounded only for multimode fields. We prove that these two notions are definitely different, for example, the real Gaussian field has a maximum signal entropy and a minimum thermodynamic entropy (among the Gaussian fields).     

Direct guanidinylation of aryl and heteroaryl halides via copper-catalyzed cross-coupling reaction

A modified Ullmann reaction using p-methoxybenzyl (PMB) guanidine as guanidinylation agent yielded various aryl and heteroaryl guanidines in good yields.     

On Finite Maximal Chains of Weak Baer Going-Down Rings

Some recent results of Ayache on going-down domains and extensions of domains that either are residually algebraic or have DCC on intermediate rings are generalized to the context of extensions of commutative rings. Given a finite maximal chain 𝒞 of R-subalgebras of a weak Baer ring T, it is shown how a “min morphism” hypothesis can be used to transfer the “going-down ring” property from R to each member of 𝒞. The integral minimal ring extensions which are min morphisms are classified. The ring extensions satisfying FCP (i.e., for which each chain of intermediate rings is finite) are characterized as the strongly affine extensions with DCC on intermediate rings. In the relatively integrally closed case, such extensions R ? T induce open immersions Spec(S) → Spec(R) for each R-subalgebra S of T.     

A branch-and-cut method for the obnoxious p-median problem

The obnoxious p-median (OpM) problem is the repulsive counterpart of the ore known attractive p-median problem. Given a set I of cities and a set J of possible locations for obnoxious plants, a p-cardinality subset Q of J is sought, such that the sum of the distances between each city of I and the nearest obnoxious site in Q is maximised. We formulate (OpM) as a {0,1} linear programming problem and propose three families of valid inequalities whose separation problem is polynomial. We describe a branch-and-cut approach based on these inequalities and apply it to a set of instances found in the location literature. The computational results presented show the effectiveness of these inequalities for (OpM). The work of the first author has been partially supported by the Coordinated Project C.A.M.P.O. and that of the third author by a short mobility grant, both of the Italian National Research Council.