On the uniqueness of symmetric bases in finite dimensional Banach spaces

Suppose{e _i} _i=1 ⁿ and{f _i} _i=1 ⁿ are symmetric bases of the Banach spacesE andF. Letd(E,F)≦C andd(E,l _n ² )≧n' for somer>0. Then there is a constantC _r=C_r(C)>0 such that for alla _i∈Ri=1,...,n $$C_r^{ - 1} \left\| {\sum\limits_{i = 1}^n {a_i e_i } } \right\| \leqq \left\| {\sum\limits_{i = 1}^n {a_i f_i } } \right\| \leqq C_r \left\| {\sum\limits_{i = 1}^n {a_i e_i } } \right\|$$ We also give a partial uniqueness of unconditional bases under more restrictive conditions.     

Dynamic alterations of fibronectin layers on copolymer substrates with graded physicochemical characteristics

Desorption and exchange of preadsorbed fibronectin layers in pure buffer solution and solutions of human serum albumin or fibronectin, respectively, were studied in dependence on the physicochemical characteristics of maleic acid copolymer films used as substrates. Although the preadsorbed amount of fibronectin differed only slightly, the protein was found to exhibit a significantly enhanced anchorage at the more hydrophobic polymer surface as compared to the more hydrophilic and more negatively charged polymer surface. The preadsorbed fibronectin layer was most efficiently exchanged by fibronectin (i.e., in the homodisplacement process) while pure buffer solution and human serum albumin solutions induced desorption or exchange of fibronectin to lower and similar degrees. An increase of the total adsorbed amount of protein due to additional adsorption of fibronectin or human serum albumin accompanied the partial exchange of the preadsorbed fibronectin in the displacement experiments. Evaluation of the kinetics of desorption and exchange of fibronectin at any of the substrates revealed two kinds of surface-attached protein populations--a fast desorbing species and a species with a slow desorption and exchange rate. By a multivariate regression analysis the surface characteristics of the polymer substrate were confirmed to determine the degree of protein desorption and exchange while the dynamics of the layer alteration was found to solely depend on the diffusion behavior of the proteins.     

Carbazole compounds as host materials for triplet emitters in organic light-emitting diodes: polymer hosts for high-efficiency light-emitting diodes

A carbazole homopolymer and carbazole copolymers based on 9,9'-dialkyl-[3,3']-bicarbazolyl, 2,5-diphenyl-[1,3,4]-oxadiazole and 9,9-bis(4-[3,7-dimethyloctyloxy]phenyl)fluorene were synthesized and their electrical and photophysical properties were characterized with respect to their application as host in phosphorescent polymer light-emitting diodes. It is shown that the triplet energy of a polymer depends on the specific connections between its building blocks. Without changing the composition of the polymer, its triplet energy can be increased from 2.3 to 2.6 eV by changing the way in which the different building blocks are coupled together. For poly(9-vinylcarbazole) (PVK), a carbazole polymer often used as host for high-energy triplet emitters in polymer light-emitting diodes, a large hole-injection barrier of about 1 eV exists due to the low-lying HOMO level of PVK. For all carbazole polymers presented here, the HOMO levels are much closer to the Fermi level of a commonly used anode such as ITO and/or a commonly used hole-injection layer such as PEDOT:PSS. This makes high current densities and consequently high luminance levels possible at moderate applied voltages in polymer light-emitting diodes. A double-layer polymer light-emitting diode is constructed comprising a PEDOT:PSS layer as hole-injection layer and a carbazole-oxadiazole copolymer doped with a green triplet emitter as emissive layer that shows an efficacy of 23 cd/A independent of current density and light output.     

Catalyzed Asymmetric Arylation Reactions

Addition and substitution reactions with carbon nucleophiles are fundamental processes in organic synthesis, and the development of general catalytic asymmetric variants thereof is still a major challenge today. In contrast to enantioselective alkyl transfer reactions, the corresponding arylations have not yet reached a high level of maturity. The existing protocols are either of no general applicability or are limited in terms of selectivity. This article summarizes established routes for catalytic asymmetric aryl transfer together with the latest developments in this area. The scope and limitations of this reaction are discussed.     

Formation and reactions of metal-metal bonded heterobimetallic (C5H4PR2)-bridged (Zr-Ir) and (Zr-Rh) complexes: evidence for the participation of metal hydride intermediates

Treatment of the complexes [(C(5)H(4)PR(2))(2)Zr(CH(3))(2)](b: R = isopropyl; c: R = cyclohexyl) with the reagent HIr(CO)(PPh(3))(3) (2b) yield the heterobimetallic complexes [mu-C(5)H(4)PR(2))(2)(H(3)C-Zr-Ir(CO)(PPh(3)))] (4b, 4c) with evolution of methane. The reaction of the -PPh(2) substituted analogue with initially yields an intermediate [(H(3)C)(2)Zr(mu-C(5)H(4)PPh(2))(2)Ir(H)(CO)(PPh(3))] 5a, that still contains both methyl groups at zirconium and does not contain a metal-metal bond. At room temperature, the intermediate reacts further with methane formation to eventually yield the (Zr-Ir) complex 4a. The corresponding [mu-C(5)H(4)PR(2))(2)(H(3)C-Zr-Rh(CO)(PPh(3)))] complexes 3a (R = Ph) and 3b (R = isopropyl) react cleanly with isopropyl alcohol to liberate methane and yield the corresponding [mu-C(5)H(4)PR(2))(2)(Me(2)CHO-Zr-Rh(CO)(PPh(3)))] products (7a, 7b). Carefully monitoring the reaction of with Me(2)CHOH by NMR revealed that the Zr-Rh functionality is attacked first to give the intermediate [Me(Me(2)CHO)Zr([micro sign]-C(5)H(4)PR(2))(2)Rh(H)(CO)(PPh(3))] (6b). This intermediate then reacts further to cleave off methane and re-form the (Zr-Rh) metal-metal bond to yield the product 7b. The tetrametallic mu-oxo-(Zr-Rh) metallocene derivate 11a was obtained starting from the (Zr-Rh) complex 3a and it was characterized by X-ray diffraction. It may be that this reaction is also initiated by H-OH addition to the [Zr-Rh] metal-metal bond.     

Developing soluble polymers for high-throughput synthetic chemistry

Soluble polymers have emerged as viable alternatives to resin supports across the broad spectrum of high-throughput organic chemistry. As the application of these supports become more widespread, issues such as broad-spectrum solubility and loading are becoming limiting factors and therefore new polymers are required to overcome such limitations. This article details the approach made within our group to new soluble polymer supports and specifically focuses on parallel libraries of block copolymers, de novo poly(styrene-co-chloromethylstyrene), PEG- stealth stars, and substituted poly(norbornylene)s.     

A Self‐Assembled Bicontinuous Cubic Phase with a Single‐Diamond Network

The first single‐diamond cubic phase in a liquid crystal is reported. This skeletal structure with the space group is formed by self‐assembly of bolaamphiphiles with swallow‐tailed lateral chains. It consists of bundles of π‐conjugated p‐terphenyl rods fused into an infinite network by hydrogen‐bonded spheres at tetrahedral four‐way junctions. We also present a quantitative model relating molecular architecture to the space‐filling requirements of six possible bicontinuous cubic phases, that is, the single‐ and double‐network versions of gyroid, diamond, and “plumber′s nightmare”.     

Silver-catalyzed imination of sulfoxides and sulfides

[reaction: see text] Silver salts in the presence of a chelating ligand efficiently catalyze the stereospecific imination of sulfoxides and sulfides with sulfonylamides and PhI(OAc)(2) to afford sulfoximines and sulfilimines, respectively, in good yields.