Highly enantioselective and regioselective copper-catalyzed 1,4 addition of grignard reagents to cyclic enynones

In this letter we describe an unusual result in terms of regioselectivity with respect to copper-catalyzed conjugate additions of various Grignard reagents to cyclic enynones. The use of Cu(OTf)(2) and NHC ligand L1 as the catalyst combination in CH(2)Cl(2) led to the unique formation of the 1,4 adduct. This selectivity does not follow the general trend previously observed in the literature using extended Michael acceptors. Moreover these reactions allowed for the creation of a quarternary stereogenic center with enantioselectivities up to 97% ee.     

Supersymmetry and its spontaneous breaking in the random field Ising model

We provide a resolution of one of the long-standing puzzles in the theory of disordered systems. By reformulating the functional renormalization group for the critical behavior of the random field Ising model in a superfield formalism, we are able to follow the associated supersymmetry and its spontaneous breaking along the functional renormalization group flow. Breaking is shown to occur below a critical dimension d(DR) ? 5.1 and leads to a breakdown of the "dimensional reduction" property. We compute the critical exponents as a function of dimension and give evidence that scaling is described by three independent exponents.     

Regularity Issues in the Problem of Fluid Structure Interaction

We investigate the evolution of rigid bodies in a viscous incompressible fluid. The flow is governed by the 2D Navier–Stokes equations, set in a bounded domain with Dirichlet boundary conditions. The boundaries of the solids and the domain have Hölder regularity C ^1,α , 0 < α ≦ 1. First, we show the existence and uniqueness of strong solutions up to the collision. A key ingredient is a BMO bound on the velocity gradient, which substitutes to the standard H ² estimate for smoother domains. Then, we study the asymptotic behaviour of one C ^1,α body falling over a flat surface. We show that a collision is possible in finite time if and only if α < 1/2.     

Construction of orthonormal bases in higher symmetry classes of tensors

We present a method for constructing an orthonormal basis for a symmetry class of tensors from an orthonormal basis of the underlying vector space. The basis so obtained is not composed of decomposable symmetrized tensors. Indeed, we show that, for symmetry classes of tensors whose associated character has degree higher than one, it is impossible to construct an orthogonal basis of decomposable symmetrized tensors from any basis of the underlying vector space. We end with an open problem on the possibility of a symmetry class having an orthonormal basis of decomposable symmetrized tensors.     

Curve graphs and Garside groups

We present a simple construction which associates to every Garside group a metric space, called the additional length graph, on which the group acts. These spaces share important features with curve graphs: they are \(\delta \)-hyperbolic, infinite, and typically locally infinite graphs. We conjecture that, apart from obvious counterexamples, additional length graphs have always infinite diameter. We prove this conjecture for the classical example of braid groups \((B_n,B_n^{+},\varDelta )\); moreover, in this framework, reducible and periodic braids act elliptically, and at least some pseudo-Anosov braids act loxodromically. We conjecture that for \(B_n\), the additional length graph is actually quasi-isometric to the curve graph of the n times punctured disk.     

Nonribosomal peptide synthesis in animals: the cyclodipeptide synthase of Nematostella

Cyclodipeptide synthases (CDPSs) are small enzymes structurally related to class-I aminoacyl-tRNA synthetases (aaRSs). They divert aminoacylated tRNAs from their canonical role in ribosomal protein synthesis, for cyclodipeptide formation. All the CDPSs experimentally characterized to date are?bacterial. We show here that a predicted CDPS from the sea anemone Nematostella vectensis is an active CDPS catalyzing the formation of various cyclodipeptides, preferentially containing tryptophan. Our findings demonstrate that eukaryotes encode active CDPSs and suggest that all CDPSs have?a similar aminoacyl-tRNA synthetase-like architecture and ping-pong mechanism. They also raise questions about the biological roles of the cyclodipeptides produced in bacteria and eukaryotes.     

Enantioselective supramolecular catalysis induced by remote chiral diols

A new method of creating libraries of chiral diphosphines is presented. Supramolecular coordination compounds based on Ti, Rh, achiral ditopic ligands, and chiral diols were synthesized by in situ mixing and used as catalysts in the asymmetric hydrogenation of (Z)-methyl 2-acetamido-3-phenylacrylate, giving ee's of up to 92%. The ditopic ligands contain a Schiff base that coordinates to the assembly metal Ti and a phosphine as a ligand for Rh. Chirality is introduced by coordination of the chiral diols to Ti. The controlling chiral center and the substrate are separated by as much as 13 ?.