Palladium-catalyzed electrophilic allylation reactions via bis(allyl)palladium complexes and related intermediates

The synthetic scope of the allyl-palladium chemistry can be extended to involve electrophilic reagents. The greatest challenge in these reactions is the catalytic generation of an allyl-palladium intermediate incorporating a nucleophilic allyl moiety. A vast majority of the published reactions that involve palladium-catalyzed allylation of electrophiles proceed via bis(allyl)palladium intermediates. The eta(1)-moiety of the bis(allyl)palladium intermediates reacts with electrophiles, including aldehydes, imines, or Michael acceptors. Recently, catalytic electrophilic allylations via mono-allylpalladium complexes were also presented by employment of so-called "pincer complex" catalysts.     

Supramolecular approaches to generate libraries of chelating bidentate ligands for homogeneous catalysis

The process of catalyst discovery and development relying on combinatorial methods has suffered so far from the difficult access to structurally diverse and large libraries of ligands, in particular the structurally more complex class of bidentate ligands. A completely new approach to streamline the difficult ligand synthesis process is to use structurally less complex monodentate ligands that self-assemble in the coordination sphere of a metal center through noncovalent attractive ligand-ligand interactions to generate bidentate, chelating ligands. When complementary attractive ligand-ligand interactions are employed, it is even possible to generate libraries of defined chelate-ligand catalysts by simply mixing two different monomeric ligands. This Minireview summarizes the first approaches and results in this new field of combinatorial homogeneous catalysis.     

Syntheses of seven-membered rings: ruthenium-catalyzed intramolecular [5+2] cycloadditions

The Ru-catalyzed intramolecular [5+2] cycloaddition of cyclopropylenynes is investigated with respect to the regio- and diastereoselectivity as well as the functional group compatibility of the reaction. Evidence for the mechanism as occurring through a ruthenacyclopentene intermediate is elucidated from 1) the study of the diastereoselectivity of the cycloaddition; 2) the effect of variation of substituents on the regioselectivity of cyclopropyl bond cleavage in 1,2-trans- and 1,2-cis-disubstituted cyclopropanes and 3) examples that clearly do not involve ruthenacyclohexene as intermediates as products still incorporate the cyclopropyl moiety. The scope and limitations of the Ru-catalyzed cycloaddition are discussed and compared with the Rh-catalyzed reaction. The potential power of this methodology towards natural product total synthesis is demonstrated by the formation of several polycyclic systems with the chosen reaction conditions and readily available cyclopropylenyne substrates.     

Exploiting non-abelian point group symmetry in direct two-electron integral transformations

Summary A simple and general scheme to exploit any discrete point group symmetry in two-electron integral transformations is introduced. It has been implemented together with integral pre-screening techniques in direct two-electron integral transformations. Its application has also been extended to subsequent MO integral processing steps like MP2 or solution of the coupled-perturbed Hartree-Fock equations (CPHF). Timings for representative applications are presented.     

Recent Progress in Direct Partial Oxidation of Methane to Methanol

The direct conversion of methane to methanol has attracted a great deal of attention for nearly a century since it was first found possible in 1902, and it is still a challenging task. This review article describes recent advancements in the direct partial oxidation of methane to methanol. The history of direct oxidation of methane and the difficulties encountered in the partial oxidation of methane to methanol are briefly summarized. Recently reported developments in gas-phase homogeneous oxidation, heterogeneous catalytic oxidation and liquid phase homogeneous catalytic oxidation of methane axe reviewed.     

Exponential stability of discrete-time systems with slowly time-varying delays

Slowly time-varying delays are seldom, but do need to be, considered in the context of discrete-time systems. This paper addresses the exponential stability issue of discrete-time systems with slowly time-varying delays. The basic idea is to transform, by utilizing the switching transformation approach, the original system with slowly time-varying delays into an equivalent switched system with special switching signal. Different types of delays correspond to different types of switching signals, and the stability issue of the original system is converted into that of a switched system. It is the first time that the method of switched homogeneous polynomial Lyapunov function is applied to general delayed systems. Some sufficient exponential stability conditions for the original system are proposed in several situations. It is numerically shown that the conservativeness of the proposed conditions reduces as the degree of the switched homogeneous polynomial Lyapunov function increases.     

On the complete solution of ∈y″=y 3

In Ref. 1, the author claimed that the problem y=y ³ is soluble only for a certain range of the parameter . An analytic approach, as adopted in the following contribution, reveals that a unique solution exists for any positive value of . The solution is given in closed form by means of Jacobian elliptic functions, which can be numerically computed very efficiently. In the limit 0+, the solutions exhibit boundary-layer behavior at both endpoints. An easily interpretable approximate solution for small is obtained using a three-variable approach.     

Meromorphic singular foliations on complex projective surfaces

Here we show that many numerical computations and bounds on the degrees of the algebraic leaves for singular meromorphic foliations on ² may be extended to large classes of foliations and complex projective surfaces.The author was partially supported by MURST and GNSAGA of CNR (Italy)     

Curvature invariants, differential operators and local homogeneity

We first prove that a Riemannian manifold with globally constant additive Weyl invariants is locally homogeneous. Then we use this result to show that a manifold whose Laplacian commutes with all invariant differential operators is a locally homogeneous space.

     

Optimal life strategies in organisms exposed to recurrent critical events

The optimal partition of energy between survival and reproduction is considered for a population subject to recurrent and potentially lethal critical events. The best strategy is found by maximizing fitness, a functional derived from the Lotka equation. The dynamics is governed by a second-order, age-varying, nonlinear system. The energy storage and the probability of survival are the state variables, while the amounts of energy placed into and withdrawn from the storage are the controls. The optimal life strategy is shown to be as follows: build up the storage at the very beginning of life, and then progressively deplete it to resist the critical events.This work was partially supported by MURST Project Ricerche sui Fondamenti della Conservazione della Natura. The authors would like to thank C. Ricci for suggesting the problem and C. Matessi for helpful discussion.