Multiresolution Analysis and Radon Measures on a Locally Compact Abelian Group

A multiresolution analysis is defined in a class of locally compact abelian groups G. It is shown that the spaces of integrable functions and the complex Radon measures M(G) admit a simple characterization in terms of this multiresolution analysis.     

Identifying the underlying structure and dynamic interactions in a voting network

We analyse the structure and behaviour of a specific voting network using a dynamic structure-based methodology which draws on Q-Analysis and social network theory. Our empirical focus is on the Eurovision Song Contest over a period of 20 years. For a multicultural contest of this kind, one of the key questions is how the quality of a song is judged and how voting groups emerge. We investigate structures that may identify the winner based purely on the topology of the network. This provides a basic framework to identify what the characteristics associated with becoming a winner are, and may help to establish a homogenous criterion for subjective measures such as quality. Further, we measure the importance of voting cliques, and present a dynamic model based on a changing multidimensional measure of connectivity in order to reveal the formation of emerging community structure within the contest. Finally, we study the dynamic behaviour exhibited by the network in order to understand the clustering of voting preferences and the relationship between local and global properties.     

Super‐Resolution Imaging of the Golgi in Live Cells with a Bioorthogonal Ceramide Probe

We report a lipid‐based strategy to visualize Golgi structure and dynamics at super‐resolution in live cells. The method is based on two novel reagents: a trans‐cyclooctene‐containing ceramide lipid (Cer‐TCO) and a highly reactive, tetrazine‐tagged near‐IR dye (SiR‐Tz). These reagents assemble via an extremely rapid “tetrazine‐click” reaction into Cer‐SiR, a highly photostable “vital dye” that enables prolonged live‐cell imaging of the Golgi apparatus by 3D confocal and STED microscopy. Cer‐SiR is nontoxic at concentrations as high as 2 μM and does not perturb the mobility of Golgi‐resident enzymes or the traffic of cargo from the endoplasmic reticulum through the Golgi and to the plasma membrane.     

On hydrogen activation in the hydroformylation of olefins with Rh4(CO)12 or Co2(CO)8 as catalyst precursors

In the hydroformylation of ethylene with approximately equimolar H₂/D₂ mixtures and Rh₄(CO)₁₂ or Co₂(CO)₈ as the catalyst precursor about 50% of propionaldehyde-d₁ was formed. The propionaldehyde-d₀/d₂ ratio was ～ 3 for rhodium and ～ 2.6 for the cobalt catalyst. On the basis of the results and assuming that there is no rapid M(H)₂/M(D)₂ scrambling, activation of hydrogen through M(H)₂ or M(H)₂(olefin) complexes can be excluded.     

Enantioselective Alternating Olefin-Carbon Monoxide Copolymerization: A new concept for activity and stereoselectivity

Cationic Pd-complexes modified by dicyclohexyl{(R)-1-[(S)-2-(diphenylphosphino)ferrocenyl]ethyl}phosphine ( 1a ) give very active catalytic systems for the regioregular isotactic specific copolymerization of propene with CO. Other alk-1-enes also give stereoregular and regioregular copolymers, even if with lower productivity. The copolymers are isolated as poly(4-alkyl-tetrahydrofuran-2,2,5,5-tetrayl-2-oxy-2-methylenes) B in the solid state and give the isomeric poly(2-alkyl-1-oxopropane-1,3-diyls) A by dissolution in (CF₃)₂CHOH. Solid polymer A (R = Et) is formed back at least partially when the dissolved material is reprecipitated from MeOH. The use of the related (ferrocenyl)diphosphine ligands 1b ? e and 2 as the catalyst modifier shows that the presence of both elements of chirality and of large substituents on the P-atoms of the ligand is necessary to achieve good stereocontrol, and that the large difference in basicity between the two P-atoms is probably the reason for the good catalytic activity.