Bound constrained interval global optimization in the COCONUT Environment

We introduce a new interval global optimization method for solving bound constrained problems. The method originates from a small standalone software and is implemented in the COCONUT Environment, a framework designed for the development of complex algorithms, containing numerous state-of-the-art methods in a common software platform. The original algorithm is enhanced by various new methods implemented in COCONUT, regarding both interval function evaluations (such as first and second order derivatives with backward automatic differentiation, slopes, slopes of derivatives, bicentered forms, evaluations on the Karush–John conditions, etc.) and algorithmic elements (inclusion/exclusion boxes, local search, constraint propagation). This resulted in a substantial performance increase as compared to the original code. During the selection of the best combination of options, we performed comparison tests that gave empirical answers to long-lasting algorithmic questions (such as whether to use interval gradients or use slopes instead), that have never been studied numerically in such detail before. The new algorithm, called coco_gop_ex, was tested against the prestigious BARON software on an extensive set of bound constrained problems. We found that in addition to accepting a wider class of bound constrained problems and providing more output information (by locating all global minimizers), coco_gop_ex is competitive with BARON in terms of the solution success rates (with the exception of a set of nonlinear least squares problems), and it often outperforms BARON in running time. In particular, coco_gop_ex was around 21 % faster on average over the set of problems solved by both software systems.     

A study of accelerated Newton methods for multiple polynomial roots

We analyze and compare several accelerated Newton methods with built in multiplicity estimates. We also introduce the concept of indicator functions and discuss the Crouse-Putt method. It is shown that many of the accelerated Newton methods not only derive from Schröder’s classic approach but are equivalent. The related computational experiments show that the built in multiplicity estimates can significantly decrease the number of Newton iterations, while the error of these estimates may significantly increase.     

Synthesis of vinca alkaloids and related compounds part 94. Epimerization of compounds with aspidospermane and D‐secoaspidospermane skeleton

The individual epimerization steps of vincadifformine ( 1 ), deethylvincadifformine isomers ( 2,3 ), their synthetic intermediates ( 4–13 ) as well as that of simpler compounds with D‐secoaspidospermane skeleton ( 15–17 ) were studied a ) in protic medium (boiling deuteroacetic acidic) and b ) under reductive (with sodium borodeuteride in boiling acetic acid, or with sodium borohydride in boiling deuteroacetic acid) conditions.     

CaL-B a highly selective biocatalyst for the kinetic resolution of furylbenzthiazole-2-yl-ethanols and acetates

A highly stereoselective enzymatic kinetic resolution of novel various substituted racemic furylbenzthiazole-2-yl-ethanols and their acetates has been developed. Both processes, the enzymatic acylation of the racemic alcohols and the enzymatic methanolysis of racemic acetates yielded highly enantiomerically enriched (ee >98%) resolution product, when CaL-B was used as a biocatalyst in acetonitrile. The absolute configuration of the obtained (R)-(+)-1-(5-(4-chlorobenzo[d]thiazol-2-yl)furan-2-yl)ethanol was determined by a detailed ¹H NMR study of rac- and (+)-1-(5-(4-chlorobenzo[d]thiazol-2-yl)furan-2-yl)ethanol Mosher derivatives.     

Synthesis of vinca alkaloids and related compounds. Part 102: Simple synthesis and ring transformation of (±)-minovincine. First synthesis of (±)-vincaminine

A molecule with an indole skeleton, containing a latent acrylic ester function—acting as a diene—readily reacted with benzoic acid (4-bromomethylene-5-oxo)hexyl ester that had been built up from pentane-2,4-dione. Dehydration of the enamine and subsequent [4+2] cycloaddition supplied epimers having the d-secoaspidospermane skeleton. These compounds directly or after epimerization gave (±)-minovincine. Oxidative ring transformation of (±)-minovincine under different conditions led to (±)-16-acetyl-16-deethylapovincamine and (±)-vincaminine.     

Existence and multiplicity results for hemivariational inequalities with two parameters

A multiplicity result of Ricceri, based on a minimax inequality, is applied to locally Lipschitz functionals and the existence of one or two non-trivial solutions for a class of two-parameter hemivariational inequalities is proved. An application is given to elliptic problems with discontinuous nonlinearities on unbounded domains.     

On spectral synthesis in varieties containing the solutions of inhomogeneous linear functional equations

As a continuation of our previous work [2] the aim of the recent paper is to investigate the solutions of special inhomogeneous linear functional equations by using spectral synthesis in translation invariant closed linear subspaces of additive/multiadditive functions containing the restrictions of the solutions to finitely generated fields. The idea is based on the fundamental work of [5]. Using spectral analysis in some related varieties we can prove the existence of special solutions (automorphisms) of the functional equation but spectral synthesis allows us to describe the entire space of solutions on a large class of finitely generated fields. It is spanned by the so-called exponential monomials which can be given in terms of automorphisms of \({\mathbb C}\) and differential operators. We apply the general theory to some inhomogeneous problems motivated by quadrature rules of approximate integration [8], see also [7, 9].     

Palladium-catalysed reactions of 6-halogeno-1,1′-binaphthyl derivatives. A detailed investigation of structure/reactivity and structure/selectivity relationships

Five 6-halogeno-binaphthyl derivatives of different structure were synthesised starting from 2,2′-dihydroxy-1,1′-binaphthyl 1. Several new 6-substituted binaphthyl compounds were obtained via the palladium-catalysed reactions of these derivatives. The reactivity of 6-iodo derivatives was much greater in most cases. In cross-coupling reactions the 6-bromo compounds were converted into the products using longer reaction times and/or higher temperatures. The reactivity difference between the two types of substrates was especially marked in aminocarbonylation and Heck reactions.