Synthesis,Spectroscopy, Crystal Structure Determination,and Quantum Chemical Calculations of BODIPY Dyes with Increasing Conformational Restriction and Concomitant Red‐Shifted Visible Absorption and Fluorescence Spectra

Starting from the conformationally unconstrained compound 3,5‐di‐(2‐bromophenoxy)‐4,4‐difluoro‐8‐(4‐methylphenyl)‐4‐bora‐3a,4a‐diaza‐s‐indacene ( 1 ), two BODIPY dyes ( 2 and 3 ) with increasingly rigid conformations were synthesized in outstanding total yields through palladium catalyzed intramolecular benzofuran formation. Restricted bond rotation of the phenoxy fragments leads to dyes 2 and 3 , which absorb and fluoresce more intensely at longer wavelengths relative to the unconstrained dye 1 . Reduction of the conformational flexibility in 2 and 3 leads to significantly higher fluorescence quantum yields compared to those of 1 . X‐ray diffraction analysis shows the progressively more extended planarity of the chromophore in line with the increasing conformational restriction in the series 1 → 2 → 3 , which explains the larger red shifts of the absorption and emission spectra. These conclusions are confirmed by quantum chemical calculations of the lowest electronic excitations in 1 , 1a , 2 , 2a , 3 and dyes of related chemical structures. The effect of the molecular structure on the visible absorption and fluorescence emission properties of 1 , 1a , 2 , 2a , 3 has been examined as a function of solvent by means of the new, generalized treatment of the solvent effect (J. Phys. Chem. B 2009 , 113, 5951–5960). Solvent polarizability is the primary factor responsible for the small solvent‐dependent shifts of the visible absorption and fluorescence emission bands of these dyes.     

Observation of mechanical fracture and corresponding domain structure changes of polycrystalline PbTiO3 nanotubes

PbTiO₃ (PTO) nanotubes (NTs) were synthesized at various temperatures by gas phase reaction between PbO gas and anatase TiO₂ NTs and characterized by piezoresponse force microscopy (PFM). PTO ferroelectric phase was synthesized at as low as 400 °C as evidenced by PFM domain images and piezoresponse hysteresis loop measurement. Furthermore, the PTO NTs fabricated at above 500 °C underwent mechanical fracture through development of nanocracks due to grain growth, leading to ferroelectric domains with larger size and lower aspect ratio. (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Nanoscale retention‐loss dynamics of polycrystalline PbTiO3 nanotubes

We observed the nanoscale retention dynamics of polycrystalline PbTiO₃ nanotubes using piezoresponse force microscopy. We found that the retention loss of the nanodot domains on the nanotubes showed the stretched exponential relaxation behaviors with stretched exponential factor n being less than 1 (0.523 and 0.692), which are similar to the thin films. In addition, the nanodot domains showed a diverse relaxation time constant τ due to different remnant polarization of each dot domains. (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Depolarizing differential Mueller matrices

The evolution of a polarized beam can be described by the differential formulation of Mueller calculus. The nondepolarizing differential Mueller matrices are well known. However, they only account for 7 out of the 16 independent parameters that are necessary to model a general anisotropic depolarizing medium. In this work we present the nine differential Mueller matrices for general depolarizing media, highlighting the physical implications of each of them. Group theory is applied to establish the relationship between the differential matrix and the set of transformation generators in the Minkowski space, of which Lorentz generators constitute a particular subgroup.     

Pourquoi, pour qui enseigner les mathématiques?

The evolution of education in Belgium is described from 1830 to our days. The mastery of education has always been a subject of disputes between the political forces in presence. With the flow of years, more attention is paid to social considerations and the necessity of a more democratic educational system arises. Simultaneously the pedagogical ideas change and active methods of teaching are promoted, although not always used. Different schoolsystems still coexist. However, except for philosophical and religious education, the differences between them tend to diminish. This is in particular the case for mathematics teaching whose evolution is also described with some details.     

On the p-Ranks and Characteristic Polynomials of Cyclic Difference Sets

In this paper, the p-ranks and characteristic polynomials of cyclic difference sets are derived by expanding the trace expressions of their characteristic sequences. Using this method, it is shown that the 3-ranks and characteristic polynomials of the Helleseth–Kumar–Martinsen (HKM) difference set and the Lin difference set can be easily obtained. Also, the p-rank of a Singer difference set is reviewed and the characteristic polynomial is calculated using our approach.     

New Cyclic Difference Sets with Singer Parameters Constructed from d-Homogeneous Functions

In this paper, for a prime power q, new cyclic difference sets with Singer para- meters ((q ⁿ –1/q–1), (q ^n–1–1/q–1), (q ^n–2–1/q–1)) are constructed by using q-ary sequences (d-homogeneous functions) of period q ⁿ –1 and the generalization of GMW difference sets is proposed by combining the generation methods of d-form sequences and extended sequences. When q is a power of 3, new cyclic difference sets with Singer parameters ((q ⁿ –1/q–1), (q ^n–1–1/q–1), (q ^n–2–1/q–1)) are constructed from the ternary sequences of period q ⁿ –1 with ideal autocorrelation introduced by Helleseth, Kumar, and Martinsen.     

Turning it off! Disfavouring hydrogen evolution to enhance selectivity for CO production during homogeneous CO2 reduction by cobalt–terpyridine complexes

Understanding the activity and selectivity of molecular catalysts for CO₂ reduction to fuels is an important scientific endeavour in addressing the growing global energy demand. Cobalt–terpyridine compounds have been shown to be catalysts for CO₂ reduction to CO while simultaneously producing H₂ from the requisite proton source. To investigate the parameters governing the competition for H⁺ reduction versus CO₂ reduction, the cobalt bisterpyridine class of compounds is first evaluated as H⁺ reduction catalysts. We report that electronic tuning of the ancillary ligand sphere can result in a wide range of second-order rate constants for H⁺ reduction. When this class of compounds is next submitted to CO₂ reduction conditions, a trend is found in which the less active catalysts for H⁺ reduction are the more selective towards CO₂ reduction to CO. This represents the first report of the selectivity of a molecular system for CO₂ reduction being controlled through turning off one of the competing reactions. The activities of the series of catalysts are evaluated through foot-of-the-wave analysis and a catalytic Tafel plot is provided.