Orlicz norm estimates for eigenvalues of matrices

Let φ be a supermultiplicative Orlicz function such that the function $t \mapsto \varphi \left( {\sqrt t } \right)$ is equivalent to a convex function. Then each complexn×n matrixT=(τ _ij ) _{i, j} satisfies the following eigenvalue estimate: $\left\| {\left( {\lambda _i \left( T \right)} \right)_{i = 1}^n } \right\|_{\ell _\varphi } \leqslant C\left\| ( \right\|\left( {\tau _{ij} } \right)_{i = 1}^n \left\| {_{_{\ell _{\varphi *} } } )_{j = 1}^n } \right\|\ell _{\bar \varphi } $ . Here, ?_* stands for Young’s conjugate function of φ, ?, $\bar \varphi $ is the minimal submultiplicative function dominating φ andC>0 a constant depending only on φ. For the power function φ(t)=t ^p ,p≥2 this is a celebrated result of Johnson, König, Maurey and Retherford from 1979. In this paper we prove the above result within a more general theory of related estimates.     

3-connected planar spaces uniquely embed in the sphere

We characterize those locally connected subsets of the sphere that have a unique embedding in the sphere -- i.e., those for which every homeomorphism of the subset to itself extends to a homeomorphism of the sphere. This implies that if is the closure of an embedding of a 3-connected graph in the sphere such that every 1-way infinite path in has a unique accumulation point in , then has a unique embedding in the sphere. In particular, the standard (or Freudenthal) compactification of a 3-connected planar graph embeds uniquely in the sphere.

     

Preparation of new microgel polymers and their application as supports in organic synthesis

A series of soluble microgel polymers have been synthesized using solution-phase polymerization reactions. In a systematic manner, several variables such as monomer concentration, cross-linker content, reaction solvent and reaction time were examined, and this provided an optimal polymer with both solubility and precipitation characteristics suitable for synthetic applications. Thus, a chemically functionalized microgel polymer was synthesized, and the utility of this polymer in the synthesis of a small array of oxazole compounds has been demonstrated. The advantage of the microgel polymers produced was that they exhibited solution viscosities lower than those of conventional linear polymers even at higher concentrations, and this was found to be beneficial for their precipitation properties. Compounds prepared using the described microgel polymer supports were obtained in similar yields and purity when compared with insoluble resins, and more importantly, the soluble polymer bound intermediates could be analyzed at each step using standard NMR techniques.     

The 48 bp centromeric repeat is a functionally conserved motif in great apes and man showing protein-binding properties

The centromere-kinetochore complex is a chromosomal assembly site including repeat motifs and protein binding properties thus mediating chromosome motility and mitotic regulation. Next to the alpha-satellite DNA family as well as human satellite III DNA, contribution of other repetitive sequences has to be strongly considered in centromere function. Here, we report the identification of centromeric 48 bp motifs, isolated from chimpanzee and orang-utan using an orthologous human DNA probe. Applying Southern hybridization we show that these sequences are restricted to hominoid species. Diminishing hybrid formation in gibbons suggested that the 48 bp repeat originated approximately 25-20 million years ago. Consistently, both chimpanzee as well as human repeat probes failed to generate any hybridization signal with the monkey species Cercopithecus aethiops and Aotes trivirgatus. Sequence deviations from the consensus of human repeat monomers of 6% and 10.4% in chimpanzee and orang-utan, respectively, were found within a 16 bp region of the 48 bp repeat units. Gel mobility shift assays using chimpanzee repeat dimers as probes revealed peptide-binding properties with human and chimpanzee nuclear extracts. Species-specific DNA-protein complexes remained unaffected by competition studies and indicated the presence of at least one novel interacting protein consisting of two subunits with 90 and 95 kDa. Our data suggest that the 48 bp repeat, next to alpha-satellite DNA, provides essential sequence information for specific DNA-protein interaction and they imply phylogenetic conservation of these binding properties in primates. The complex is likely involved in the proper formation and/or function of mammalian centromeres.     

Baeyer-Villiger oxidation in compressed CO2

The aerobic Baeyer-Villiger oxidation of a wide range of ketones, both cyclic and acyclic to the corresponding esters or lactones can be efficiently carried out in compressed carbon dioxide in the presence of an aldehyde as co-reductant.     

Synthesis of a highly enantiomerically enriched silyllithium compound

The highly enantiomerically enriched silyllithium compound lithiomethylphenyl(1-piperidinylmethyl)silane (4) reacts stereospecifically with chlorosilanes, but over a period of several hours slow racemization in solution at room temperature occurs, which can be suppressed by a transmetalation reaction with MgBr2(thf)4.