Computable error bounds for pointwise derivatives of a Neumann problem

In this paper we discuss the recovery of derivatives and thecomputation of rigorous and useful upper bounds for the pointwiseerror in the recovered derivatives, for finite element approximationsof the Laplace equation with Neumann boundary conditions, especiallyat points close to or on a smooth, curved boundary. We analyzethe dipole image technique for the case of curved boundaries,and show how to compute reliable recovered derivatives and errorbounds even in the limiting case of points lying on the curvedboundary. Numerical experiments show reasonably tight errorbounds for points both close to and away from a curved boundary.     

Ferromagnetic manganese "cubes": from PSII to single-molecule magnets

The reaction of Mn(O?CMe)?·2H?O with Me-saoH? (Me-saoH? = 2-hydroxyphenylethanone oxime) in MeCN forms the complex [Mn(III)?(Me-sao)?(Me-saoH)?] (1) in good yields. Replacing Me-saoH? with Naphth-saoH? (Naphth-saoH? = 2-hydroxy-1-napthaldoxime) in the presence of CH?ONa forms the complex [Mn(III)?(Naphth-sao)?(Naphth-saoH)?] (2) in low yields, while the reaction between Mn(ClO?)?·6H?O, Et-saoH? (Et-saoH?= 2-hydroxypropiophenone oxime) and NBu?OH in MeCN gives the complex [Mn(III)?(Et-sao)?(Et-saoH)?] (3) in moderate yields. All three tetrametallic cages exclusively contain Mn(III) centres arranged in a "cube"-like topology, in which the metal centres are connected by -N-O(oximate) groups. The magnetic properties of 1-3 are near identical, revealing the presence of only ferromagnetic interactions between the metal ions leading to high-spin ground states of S = 8. The complexes display frequency dependent out-of-phase signals in ac susceptibility studies and, in the case of 1 single-molecule magnetism has been observed by means of single-crystal hysteresis loop measurements.     

The effect of peripheral bipyridine ligands on the photocatalytic hydrogen production activity of Ru/Pd catalysts

A pyrazine bridged ruthenium/palladium bimetallic photocatalyst with peripheral 4,4'-dicarboxyethyl-2,2'-bipyridine ligands, EtOOC-RuPd, is reported, together with its 2,2'-bipyridine analogue. Upon irradiation with visible light, EtOOC-RuPd catalyses the production of hydrogen gas whereas the complex RuPd does not.     

Semantic contamination and mathematical proof: Can a non-proof prove?

The way words are used in natural language can influence how the same words are understood by students in formal educational contexts. Here we argue that this so-called semantic contamination effect plays a role in determining how students engage with mathematical proof, a fundamental aspect of learning mathematics. Analyses of responses to argument evaluation tasks suggest that students may hold two different and contradictory conceptions of proof: one related to conviction, and one to validity. We demonstrate that these two conceptions can be preferentially elicited by making apparently irrelevant linguistic changes to task instructions. After analyzing the occurrence of “proof” and “prove” in natural language, we report two experiments that suggest that the noun form privileges evaluations related to validity, and that the verb form privileges evaluations related to conviction. In short, we show that (what is judged to be) a non-proof can sometimes (be judged to) prove.     

Post‐Functionalization of Polymers via Orthogonal Ligation Chemistry

The establishment of advanced living/controlled polymerization protocols allows for engineering synthetic polymers in a precise fashion. Combining advanced living/controlled polymerization techniques with highly efficient coupling chemistries facilitates quantitative, modular, and orthogonal functionalization of synthetic polymer strands at their chain termini as well as side‐chain functionalization. The review highlights the current status of selected post‐functionalization techniques of polymers via orthogonal ligation chemistries, major characteristics of the specific transformation chemistry, as well as the characterization of the products.

     

Self‐assembly and Cycling of a Three‐state PdxLy Metallosupramolecular System

The use of stimuli to induce reversible structural transformations in metallosupramolecular systems is of keen interest to chemists seeking to mimic the way that Nature effects conformational changes in biological machinery. While a wide array of stimuli have been deployed towards this end, stoichiometric changes have only been explored in a handful of examples. Furthermore, switching has generally been between only two distinct states. Here we use a simple 2‐(1‐(pyridine‐4‐methyl)‐1H‐1,2,3‐triazol‐4‐yl)pyridine “click” ligand in combination with Pd^II in various stoichiometries and concentrations to quantitatively access and cycle between three distinct species: a [PdL₂]²⁺ monomer, a [Pd₂L₂]⁴⁺ dimer, and a [Pd₉L₁₂]¹⁸⁺ cage.