A stereoselective total synthesis of the natural antibiotic (-)-8-O-methyltetrangomycin 1 is reported. The essential steps for this convergent synthesis are the transformation of a geraniol epoxide into a chiral octadiyne derivative, which was converted into a triyne. The cobalt-mediated [2+2+2] cycloaddition of the triyne led to a benz[a]anthracene system, which was oxidized with Ag(Py)(2)MnO(...

Plant volatiles (PVs) are lipophilic molecules with high vapor pressure that serve various ecological roles. The synthesis of PVs involves the removal of hydrophilic moieties and oxidation/hydroxylation, reduction, methylation, and acylation reactions. Some PV biosynthetic enzymes produce multiple products from a single substrate or act on multiple substrates. Genes for PV biosynthesis evolve b...

A novel approach of the convergent functionalisation of aryl dibromides to form NS5A type inhibitors using C-H activation is reported. The focus of investigation was to reduce the formation of homodimeric side product, as well as to investigate the scope of different aryl dibromides that were tolerated under the reaction conditions. The C-H activation methodology was found to give a viable synt...

We discuss variants of the Jacobi–Davidson method for solving the generalized complex-symmetric eigenvalue problem. The Jacobi–Davidson algorithm can be considered as an accelerated inexact Rayleigh quotient iteration. We show that it is appropriate to replace the Euclidean inner product xy in C by the bilinear form x y. The Rayleigh quotient based on this bilinear form leads to an asymptotical...

Phase retrieval seeks to recover a signal x ∈ C from the amplitude |Ax| of linear measurements Ax ∈ C. We cast the phase retrieval problem as a non-convex quadratic program over a complex phase vector and formulate a tractable relaxation (called PhaseCut) similar to the classical MaxCut semidefinite program. We solve this problem using a provably convergent block coordinate descent algorithm wh...

This work is concerned with the construction and analysis of high order product integration methods for a class of Volterra integral equations with logarithmic singular kernel. Sufficient conditions for the methods to be convergent are derived and it is shown that optimal convergence orders are attained if the exact solution is sufficiently smooth. The case of non-smooth solutions is dealt with...

Infinite determinantal measures introduced in this note are inductive limits of determinantal measures on an exhausting family of subsets of the phase space. Alternatively, an infinite determinantal measure can be described as a product of a determinantal point process and a convergent, but not integrable, multiplicative functional. Theorem 2, the main result announced in this note, gives an ex...

We study the multiple-sets split feasibility problem that requires to find a point closest to a family of closed convex sets in one space such that its image under a linear transformation will be closest to another family of closed convex sets in the image space. By casting the problem into an equivalent problem in a suitable product space we are able to present a simultaneous subgradients proj...

A convergent diastereo- and enantioselective total synthesis of anticancer and antifungal macrocyclic natural product disorazole C1 is reported. The central feature of the successful route is the application of catalytic Z-selective cross-metathesis (CM). Specifically, we illustrate that catalyst-controlled stereoselective CM can be performed to afford structurally complex Z-alkenyl-B(pin) as w...

The central problem of concern to Serrano, Boguña and Vespignani [1] can be effectively and elegantly addressed using a well-established two-stage algorithm that has been applied to internal migration flows for numerous nations and several other forms of ”transaction flow data” [2, 3, 4]. In the first stage, the N row and N column sums of the N × N matrix of weighted, directed network flows (fi...