The lower estimate for linear positive operators,I

A method to prove lower estimates for linear operators is introduced. As a result the best lower estimate for certain convolution operators, for the multivariate Bernstein-Durrmeyer operators in part I and the Bernstein polynomial operators in part II (see [10]), are obtained.Communicated by Hubert Berens     

A Review on the Potential and Limitations of Recyclable Thermosets for Structural Applications

Abstract

The outstanding performance of conventional thermosets arising from their covalently cross-linked networks directly results in a limited recyclability. The available commercial or close-to-commercial techniques facing this challenge can be divided into mechanical, thermal, and chemical processing. However, these methods typically require a high energy input and do not take the recycling of the thermoset matrix itself into account. Rather, they focus on retrieving the more valuable fibers, fillers, or substrates. To increase the circularity of thermoset products, many academic studies report potential solutions which require a reduced energy input by using degradable linkages or dynamic covalent bonds. However, the majority of these studies have limited potential for industrial implementation. This review aims to bridge the gap between the industrial and academic developments by focusing on those which are most relevant from a technological, sustainable and economic point of view. An overview is given of currently used approaches for the recycling of thermoset materials, the development of novel inherently recyclable thermosets and examples of possible applications that could reach the market in the near future.     

Development and Molecular Understanding of a Pd-Catalyzed Cyanation of Aryl Boronic Acids Enabled by High-Throughput Experimentation and Data Analysis

A synthetic method for the palladium-catalyzed cyanation of aryl boronic acids using bench stable and non-toxic N-cyanosuccinimide has been developed. High-throughput experimentation facilitated the screen of 90 different ligands and the resultant statistical data analysis identified that ligand σ-donation, π-acidity and sterics are key drivers that govern yield. Categorization into three ligand groups – monophosphines, bisphosphines and miscellaneous – was performed before the analysis. For the monophosphines, the yield of the reaction increases for strong σ-donating, weak π-accepting ligands, with flexible pendant substituents. For the bisphosphines, the yield predominantly correlates with ligand lability. The applicability of the designed reaction to a wider substrate scope was investigated, showing good functional group tolerance in particular with boronic acids bearing electron-withdrawing substituents. This work outlines the development of a novel reaction, coupled with a fast and efficient workflow to gain understanding of the optimal ligand properties for the design of improved palladium cross-coupling catalysts.     

Copper‐Catalyzed Regioselective Borocarbonylative Coupling of Unactivated Alkenes with Alkyl Halides: Synthesis of β‐Boryl Ketones

The borocarbonylative coupling of unactivated alkenes with alkyl halides remains a challenge. In this communication, a Cu‐catalyzed borocarbonylative coupling of unactivated alkenes with alkyl halides for the synthesis of β‐boryl ketones has been developed. A broad range of β‐boryl ketone derivatives was prepared in moderate to excellent yields with complete regioselectivity.     

Abstract Commensurators of Groups Acting on Rooted Trees

We show that the abstract commensurator of a nearly level transitive weakly branch group H coincides with the relative commensurator of H in the homeomorphism group of the boundary of the tree on which H acts. It is also shown that the commensurator of an infinite group which is commensurable with its own nth direct power contains a Higman–Thompson group as a subgroup. Applying these results to the Grigorchuk 2-group G we show that the commensurator of G is a finitely presented infinite simple group.     

Evidence of radial-axial motion couplings in an rf stored ion cloud

Received: 21 February 1997/Revised version: 13 May 1997     

Formation of K*He exciplexes on the surface of helium nanodroplets studied in real time

Superfluid helium nanodroplets are doped with potassium atoms to form complexes with the alkali atom residing on the surface of the droplets. Dispersed laser-induced fluorescence spectra of such systems already revealed the formation of M(*)He ( M = Na,K) exciplexes upon electronic excitation [Reho et al., Faraday Discuss. 108, 161 (1997)]. By means of femtosecond pump-probe spectroscopy, this formation process now is followed in real time. We find K(*)He(n = 1) to be formed within 180 fs. Furthermore, the existence of exciplexes with n>1 is quantified suggesting that the first ring around the potassium atom contains four helium atoms.     

Development of highly potent inhibitors of the ras-targeting human acyl protein thioesterases based on substrate similarity design

A matter of common sense: A common recognition motif consisting of a negatively charged group five to six bonds away (red) from the (thio)ester functionality (green) and a positively charged tail group ten to twelve bonds away (blue) was identified in two native acyl protein thioesterase?1 (APT1) substrates. This similarity led to the design of potent inhibitors of the Ras-depalmitoylating enzyme APT1.