The zeros of Faber polynomials generated by an -star

It is shown that the zeros of the Faber polynomials generated by a regular -star are located on the -star. This proves a recent conjecture of J. Bartolomeo and M. He. The proof uses the connection between zeros of Faber polynomials and Chebyshev quadrature formulas.

     

The frequency-domain method reveals the dimeric structure of Na,K-ATPase

Lucifer yellow and lissamine rhodamine sulfonyl hydrazine were used as the donor and the receptor, respectively, for Förster energy transfer measurements to determine the location of the subunit in the native Na,K-ATPase from pig kidney. It was found that (1) the subunits are located in one functional complex, i.e., the dimer ()₂ appears to be the functional complex of Na,K-ATPase, and (2) the subunits in the functional enzyme complex in the membrane are not located next to each other but are rather well separated. The distance between fluorophores covalently attached to the subunits was found to be 5.3 nm.     

Ethylene tetramerization: a new route to produce 1-octene in exceptionally high selectivities

Linear alpha-olefins, such as 1-hexene and 1-octene, are important comonomers in the production of linear low-density polyethylene (LLDPE). The conventional method of producing 1-hexene and 1-octene is by oligomerization of ethylene, which yields a wide spectrum of linear alpha-olefins (LAOs). While there exists several processes for producing 1-hexene via ethylene trimerization, a similar route for the selective production of 1-octene has so far been elusive. We now, for the first time, report an unprecedented ethylene tetramerization reaction that produces 1-octene in selectivities exceeding 70%, using an aluminoxane-activated chromium/((R2)2P)2NR1 catalyst system.     

Carbon Dioxide as an Alternative C1 Synthetic Unit: Activation by Transition-Metal Complexes

The carbon dioxide molecule has been of limited importance as a synthetic unit in organic chemistry. When it is coordinated to transition metals, however, completely new possibilities arise; CO₂ can bond to metal complexes in a variety of ways and can enter into insertion and coupling reactions, or become catalytically attached to other substrates. The formation of C? C bonds between carbon dioxide and unsaturated hydrocarbons under conditions of homogeneous catalysis makes available new synthetic routes to industrially interesting organic compounds.     

The dithianyl group as a synthon in porphyrin chemistry: condensation reactions and preparation of formylporphyrins under basic conditions

Vilsmeier formylation is one of the most widely used substitution reactions for the functionalization of porphyrins. However, its utility is limited by the electrophilic/acidic reaction conditions, deactivation of the aromatic system and regiochemical problems, the requirement for metal complexes and necessity for subsequent demetalation under harsh conditions, and low functional group tolerance. To overcome these limitations, the dithianyl group has been utilized as a latent formyl synthon in porphyrin chemistry. 2-Formyl-1,3-dithiane can be used directly in pyrrole condensation reactions to regioselectively yield porphyrins with up to four dithianyl residues. Likewise, 5-dithianyldipyrromethane could be prepared quantitatively as a key building block for various porphyrin condensation reactions yielding the respective free base formylporphyrins after deprotection. Additionally, dithianyllithium can be used as a reagent for the direct aromatic substitution of metallo- and free base porphyrins under nucleophilic conditions.     

Influence of substitutions on asymmetric dihydroxychlorins with regard to intracellular uptake, subcellular localization and photosensitization of Jurkat cells

The search for new efficient sensitizers for photodynamic therapy (PDT) points to improve photophysical properties like absorption in the red region and singlet oxygen quantum yield as well as to control the localization of the sensitizer within the tumour cell. Depending on their physicochemical properties and their uptake mechanism, sensitizers can reach different intracellular concentrations and localize in different subcellular compartments. Moreover, the preferential localization of a sensitizer in target organelles, like mitochondria or lysosomes, could determine the cell death mechanism after PDT. This study aimed to investigate the influence of substitutions on dihydroxychlorins with regard to intracellular uptake, subcellular localization and cell death pathway. Moreover, the effect of a liposome-based delivery system was tested. The intracellular uptake was found to be strictly dependent on the sensitizer molecular structure and the means of its delivery. The most polar sensitizer in this study (compound 3) had, depending on incubation time, an intracellular concentration 2-8 times higher than the unsubstituted chlorin 1. All investigated photosensitizers localize predominantly in lysosomes but after longer incubation times weak fluorescence intensity was also detected in mitochondria and Golgi apparatus. The cell death pathway was found to be influenced by the sensitizer intracellular concentration and the applied light doses. In general, the increasing amphiphilicity of the sensitizer molecules is correlated with an increased sensitizer uptake and an increased rate of necrotic cells after irradiation.     

Physical fabrication of colloidal ZnO nanoparticles combining wet-grinding and laser fragmentation

Combination of wet-grinding and laser fragmentation is a promising approach to advance both methods: Laser fragmentation will be more efficient when combined with mechanical treatment and wet-grinding may take advance of the abrasion-free laser process to achieve fabrication of smaller particles. By mechanical pre-treatment of zinc oxide microparticles in a stirred-media mill, the starting material is activated by generation of crystallographic defects, which strongly enhance the efficiency of subsequent laser fragmentation. Picosecond-laser irradiation of mechanically treated and untreated microparticles suspended in water yielded in colloidal zinc oxide nanoparticles. Furthermore, nanoparticle productivity and properties can be controlled by variation of anionic surfactant concentration.     

On images of locally finite derivations and E-derivations

Some cases of the LFED Conjecture, proposed by the second author [15], for certain integral domains are proved. In particular, the LFED Conjecture is completely established for the field of fractions $k(x)$ of the polynomial algebra $k[x]$, the formal power series algebra $k[[x]]$ and the Laurent formal power series algebra $k[[x]][x^{?1}]$, where $x=(x_1,x_2,\dots ,x_n)$ denotes n commutative free variables and k a field of characteristic zero. Furthermore, the relation between the LFED Conjecture and the Duistermaat–van der Kallen Theorem [3] is also discussed and emphasized.