RuO4-promoted oxidative polycyclization of isoprenoid polyenes. A further insight into the stereochemistry of the process

Further studies on the RuO₄-catalyzed oxidative polycyclization of isoprenoid polyenes have been carried out. The configuration of the tris-THF product from the oxidation of geranylgeranyl acetate has been determined by a combination of spectral and chemical correlation methods. The oxidation of (E,Z)-farnesyl acetate, synthesized from nerol, has been carried out. This process stops at the first cyclization indicating that an E configuration of the Δ⁶ double bond is needed for the second cyclization to occur. The results are discussed in comparison with previous knowledge on the related Re(VII) polycyclization of polyenic bis-homoallylic alcohols.     

An RQP algorithm using a differentiable exact penalty function for inequality constrained problems

In this paper we propose a recursive quadratic programming algorithm for nonlinear programming problems with inequality constraints that uses as merit function a differentiable exact penalty function. The algorithm incorporates an automatic adjustment rule for the selection of the penalty parameter and makes use of an Armijo-type line search procedure that avoids the need to evaluate second order derivatives of the problem functions. We prove that the algorithm possesses global and superlinear convergence properties. Numerical results are reported.     

Invariant Metrics on Cohomogeneity One Manifolds

Let G be one of the connected subgroups of the orthogonal group of ⁿ which acts transitively on the unit sphere S ^n–1. We get the necessary and sufficient condition for G-invariant metrics g on ⁿ \{0} to be extendend to the origin. For n=2 this is a classical result of Berard–Bergery. The curvature tensor and the sectional curvature of any such Riemannian G-manifold ( ⁿ , g) are described in terms of the length of the Killing vector fields, as well as the second fundamental form of the regular orbits G(P)=S ^n–1. As an application we describe all G-invariant metrics which are Kähler, hyperKähler or have constant principal curvatures. Some of these results are generalized to the case of any cohomogeneity one G-manifold which, in a neighbourhood of a singular orbit, can be identified with a twisted product.     

EEG topography-specific BOLD changes: a continuous EEG-fMRI study in a patient with focal epilepsy

Blood oxygenation level dependent (BOLD) response related to interictal activity was evaluated in a patient with post-traumatic focal epilepsy at repeated continuous electroencephalogram (EEG)-functional magnetic resonance imaging examinations. Lateralized interictal EEG activity induced a main cluster of activation co-localized with the anatomical lesion. Spreading of EEG interictal activity to both frontal lobes evoked bilateral clusters of activation indicating that topography of BOLD response might depend on the spatial distribution of epileptiform activity.     

Organocatalytic,Asymmetric Eliminative [4+2] Cycloaddition of Allylidene Malononitriles with Enals: Rapid Entry to Cyclohexadiene‐Embedding Linear and Angular Polycycles

A direct aminocatalytic synthesis has been developed for the chemo‐, regio‐, diastereo‐, and enantioselective construction of densely substituted polycyclic carbaldehydes containing fused cyclohexadiene rings. The chemistry utilizes, for the first time, remotely enolizable π‐extended allylidenemalononitriles as electron‐rich 1,3‐diene precursors in a direct eliminative [4+2] cycloaddition with both aromatic and aliphatic α,β‐unsaturated aldehydes. The generality of the process is demonstrated by approaching 6,6‐, 5,6‐, 7,6‐, 6,6,6‐, and 6,5,6‐fused ring systems, as well as biorelevant steroid‐like 6,6,6,6,5‐ and 6,6,6,5,6‐rings. A stepwise reaction mechanism for the key [4+2] addition is proposed as a domino bis‐vinylogous Michael/Michael/retro‐Michael reaction cascade. The utility of the malononitrile moiety as traceless activating group of the dicyano nucleophilic substrates is demonstrated.     

Blended implicit methods for solving ODE and DAE problems,and their extension for second-order problems

The use of implicit numerical methods is mandatory when solving general stiff ODE/DAE problems. Their use, in turn, requires the solution of a corresponding discrete problem, which is one of the main concerns in the actual implementation of the methods. In this respect, blended implicit methods provide a general framework for the efficient solution of the discrete problems generated by block implicit methods. In this paper, we review the main facts concerning blended implicit methods for the numerical solution of ODE and DAE problems.     

Synthesis and x-ray characterization of the [Ir6(CO)15COEt]-Anionic Cluster

The reaction of Ir₆(CO)₁₆ with a mixture of CO, H₂, and ethylene yields the [Ir₆(CO)₁₅COEt]^- anion, which has been shown by X-ray diffraction to contain an octahedral iridium cluster bearing a —bonded acyl group; the arrangement of the 11 terminal and 4 edge-bridging carbonyl groups is different from that found in both the analogous rhodium complex and the parent Ir₆(CO)₁₆ carbonyl.     

Chemical reactions in fast atom bombardment mass spectrometry

Examples of various chemical reactions occurring in the matrix or in the selvedge region in fast atom bombardment (FAB) mass spectrometry are discussed. These are categorized as oxidations and reductions; substitutions; clusterings and additions; and sample decomposition or transformation. Some reactions observed showed significant time behaviour and in one case it was possible to determine rate constants. These data suggest that chemical reactions can be accelerated significantly by fast atom bombardment.