Solid Extensions of the Cesàro Operator on ℓ p and c 0

We introduce and study the largest Banach lattice (for the coordinate-wise order) which is a solid subspace of \({\mathbb{C}^\mathbb{N}}\) and to which the classical Cesàro operator \({\mathcal{C}\colon\ell^p \to \ell^p}\) (a positive operator) can be continuously extended while still maintaining its values in ? ^p . Properties of this optimal Banach lattice \({[\mathcal{C}, \ell^p]_s}\) are presented. In addition, all continuous convolution operators of \({[\mathcal{C}, \ell^p]_s}\) into itself are identified and the spectrum of \({\mathcal{C}\colon[\mathcal{C}, \ell^p]_s \to[\mathcal{C}, \ell^p]_s}\) is determined. A similar investigation is undertaken for the Cesàro operator \({\mathcal{C}\colon c_0\to c_0}\) .     

Diversified Applications of Chemically Modified 1,2‐Polybutadiene

Commercially available 1,2‐PB was transformed into a well‐defined reactive intermediate by quantitative bromination. The brominated polymer was used as a polyfunctional macroinitiator for the cationic ring‐opening polymerization of 2‐ethyl‐2‐oxazoline to yield a water‐soluble brush polymer. Nucleophilic substitution of bromide by 1‐methyl imidazole resulted in the formation of polyelectrolyte copolymers consisting of mixed units of imidazolium, bromo, and double bond. These copolymers, which were soluble in water without forming aggregates, were used as stabilizers in the heterophase polymerization of styrene and were also studied for their ionic conducting properties.

     

Silver tetrakis(hexafluoroisopropoxy)aluminate as hexafluoroisopropyl transfer reagent for the chlorine/hexafluoroisopropyl exchange in imino phosphanes

Treating 1,3-dichloro-2,4-bis[tris(trimethylsilyl)silyl]-cyclo-diphosphadiazane, [HypNPCl]₂ ((Me₃Si)₃Si = Hyp), or N-(2,4,6-tri-tert-butylphenyl)imino(chloro)phosphane, Mes^∗-NP-Cl (Mes^∗ = 2,4,6-tri-tert-butylphenyl), with Ag[Al(OCH(CF₃)₂)₄] leads to the abstraction of [OCH(CF₃)₂]⁻ from the counter ion [Al(OCH(CF₃)₂)₄]⁻ in a formal Lewis acid/Lewis base reaction. The final products Hyp₂N₂P₂(Cl)(OCH(CF₃)₂), Mes^∗-NP-OCH(CF₃)₂ and the dimeric Lewis acid [Al(OCH(CF₃)₂)₃]₂ have been characterized by means of X-ray analysis.     

Highly substituted 2,3,7,8,12,13,17,18-octaethylporphyrins with meso aryl residues

Highly substituted porphyrin-bearing meso aryl groups are useful compounds for optical applications and for studies on the interrelationship between the substituent pattern, macrocycle conformation and physical properties. They serve as biomimetic models for the function of tetrapyrroles in nature and help to elucidate modulation of cofactor properties through conformational effects. Using a sequence of lithium organic substitution reactions the synthesis of novel free base 5,10-A₂- and 5,10-AB-2,3,7,8,12,13,17,18-octaethylporphyrins bearing donating groups such as -OMe and -NMe₂ on the aryl-substituent was achieved. Larger aromatic residues (1-naphthyl, 9-anthracenyl and 9-phenanthrenyl) could be introduced into the macrocycle system as well, and these systems were used for the preparation of highly substituted porphyrins with a mixed substituent pattern. Using phenanthrenyl derivatives, the complete series of meso phenanthrenyl substituted octaethylporphyrins was successfully synthesized and the palladium complexes were prepared for photophysical investigations. Structural studies clearly showed the influence of individual substituents on the conformation of the tetrapyrrole macrocycle and conformational analyses revealed the variation of the underlying distortion modes depending on the type and arrangement of the meso substituents.     

Pure component spectral recovery and constrained matrix factorizations: concepts and applications

We present new ideas underlying a self‐modelling factor analytical method which allows to extract pure component spectra and the associated concentration profiles from a set of spectroscopic measurements. The usefulness of the method is demonstrated and compared with established tools for model problems and for a system from catalytic hydroformylation by Rhodium complexes both with overlapping component spectra. Self‐modelling methods tend to minimize the overlap of the recovered spectra, which can result in an unwanted distortion of the spectra and concentration profiles. For strongly overlapping spectra a penalty condition on a specific singular value of the absorptivity matrix factor and a global decomposition approach are appropriate tools to construct improved factorizations. Copyright © 2010 John Wiley & Sons, Ltd.     

Three‐Electrode‐Integrated Sensor into a Micropipette Tip

This work describes the construction, characterization, and application of a three‐electrode‐integrated sensor into a micropipette tip. The three electrodes (working, pseudoreference and counter) are positioned at the end of a micropipette tip. The working electrode (graphite composite or gold microfiber) is placed inside the micropipette tip and the pseudo‐reference and counter electrodes outside (diametrically opposed sides). This approach is candidate for portable applications and allows the analysis and studies in low‐volume solutions (ca. 10 µL) which are useful for waste minimization and development of clean analytical methods. In addition, the three‐electrode‐integrated sensor can be easy used as detector in flow injection system through its direct joining at the end of polyethylene tubing of the FIA system.     

Fragmentation behavior of a thiourea‐based reagent for protein structure analysis by collision‐induced dissociative chemical cross‐linking

The fragmentation behavior of a novel thiourea‐based cross‐linker molecule specifically designed for collision‐induced dissociation (CID) MS/MS experiments is described. The development of this cross‐linker is part of our ongoing efforts to synthesize novel reagents, which create either characteristic fragment ions or indicative constant neutral losses (CNLs) during tandem mass spectrometry allowing a selective and sensitive analysis of cross‐linked products. The new derivatizing reagent for chemical cross‐linking solely contains a thiourea moiety that is flanked by two amine‐reactive N‐hydroxy succinimide (NHS) ester moieties for reaction with lysines or free N‐termini in proteins. The new reagent offers simple synthetic access and easy structural variation of either length or functionalities at both ends. The thiourea moiety exhibits specifically tailored CID fragmentation capabilities—a characteristic CNL of 85 u—ensuring a reliable detection of derivatized peptides by both electrospray ionization (ESI) and matrix‐assisted laser desorption/ionization (MALDI) tandem mass spectrometry and as such possesses a versatile applicability for chemical cross‐linking studies. A detailed examination of the CID behavior of the presented thiourea‐based reagent reveals that slight structural variations of the reagent will be necessary to ensure its comprehensive and efficient application for chemical cross‐linking of proteins. Copyright © 2010 John Wiley & Sons, Ltd.     

Conservation of Orbital Symmetry can be Circumvented in Mechanically Induced Reactions

In first‐principles molecular dynamics simulations of the mechanically induced ring‐opening of substituted benzocyclobutene we observe both con‐ and disrotatory ring‐opening reactions. We show that this finding does not contradict the fundamental principle that the orbitals develop continuously in time. However, it constitutes an exception from the principle of the conservation of orbital symmetry and thus is indeed an exception from the Woodward–Hoffmann rules. In contrast, the ring‐opening of unsubstituted cyclobutene proceeds in a conrotatory fashion. This shows that the breaking of the Woodward–Hoffmann rules is significantly facilitated by the substituents.     

Duality for rectified cost functions

It is well-known that duality in the Monge–Kantorovich transport problem holds true provided that the cost function c : X × Y → [0, ∞] is lower semi-continuous or finitely valued, but it may fail otherwise. We present a suitable notion of rectification c _r of the cost c, so that the Monge-Kantorovich duality holds true replacing c by c _r . In particular, passing from c to c _r only changes the value of the primal Monge–Kantorovich problem. Finally, the rectified function c _r is lower semi-continuous as soon as X and Y are endowed with proper topologies, thus emphasizing the role of lower semi-continuity in the duality-theory of optimal transport.