Mixed methods on quadrilaterals and hexahedra

We describe a new family of discrete spaces suitable for use with mixed methods on certain quadrilateral and hexahedral meshes. The new spaces are natural in the sense of differential geometry, so all the usual mixed method theory, including the hybrid formulation, carries over to these new elements with proofs unchanged. Because transforming general quadrilaterals into squares introduces nonlinearity and because mixed methods involve the divergence operator, the new spaces are more complicated than either the corresponding Raviart-Thomas spaces for rectangles or corresponding finite element spaces for quadrilaterals. The new spaces are also limited to meshes obtained from a rectangular mesh through the application of a single global bilinear transformation. Despite this limitation, the new elements may be useful in certain topologically regular problems, where initially rectangular grids are deformed to match features of the physical region. They also illustrate the difficulties introduced into the theory of mixed methods by nonlinear transformations.     

Concise and enantioselective synthesis of the aminocyclitol core of hygromycin A

[reaction: see text] Stereoselective aminohydroxylation and dihydroxylation using osmium(VIII) oxidants enabled the short and efficient synthesis of the aminocyclitol core of hygromycin A. In addition to allowing the selective introduction of the heteroatoms N and O, the use of osmium (via an osmate ester) as a protecting group for a 1,2-glycol is also reported. This tactic allowed efficient differentiation of otherwise equivalent hydroxyl groups and allowed us to complete the synthesis in short order (14 steps) and excellent overall yield (12%).     

Efficient acyclic stereocontrol using the tethered aminohydroxylation reaction

[reaction: see text] The tethered aminohydroxylation (TA) of acyclic allylic carbamates has been achieved in a stereospecific and stereoselective manner. Unusually high levels of stereocontrol were observed in the oxidation of 1,1-disubstituted substrates.     

STUDIES OF ADHESION OF METAL PARTICLES TO SILICA PARTICLES BASED ON ZETA POTENTIAL MEASUREMENTS

The zeta-potentials of silica, copper, platinum and gold particles have been measured as a function of pH. The isoelectric points were found to be at pH 3.0, 5.8, 3.0 and 3.5, respectively. In the pH range 3.0 to 5.8 copper and silica particles are oppositely charged and accordingly the coating of silica with copper particles could be demonstrated. In the case of gold and platinum the sign of the charge is such that direct adhesion to silica particles cannot be expected and this was also demonstrated in the case of platinum.     

The DNA sequence and analysis of human chromosome 13

Chromosome 13 is the largest acrocentric human chromosome. It carries genes involved in cancer including the breast cancer type 2 (BRCA2) and retinoblastoma (RB1) genes, is frequently rearranged in B-cell chronic lymphocytic leukaemia, and contains the DAOA locus associated with bipolar disorder and schizophrenia. We describe completion and analysis of 95.5 megabases (Mb) of sequence from chromosome 13, which contains 633 genes and 296 pseudogenes. We estimate that more than 95.4% of the protein-coding genes of this chromosome have been identified, on the basis of comparison with other vertebrate genome sequences. Additionally, 105 putative non-coding RNA genes were found. Chromosome 13 has one of the lowest gene densities (6.5 genes per Mb) among human chromosomes, and contains a central region of 38 Mb where the gene density drops to only 3.1 genes per Mb.     

Observation of a multiply ionized plasma with index of refraction greater than one

We present clear experimental evidence showing that the contribution of bound electrons can dominate the index of refraction of laser-created plasmas at soft x-ray wavelengths. We report anomalous fringe shifts in soft x-ray laser interferograms of Al laser-created plasmas. The comparison of measured and simulated interferograms shows that this results from the dominant contribution of low charge ions to the index of refraction. This usually neglected bound electron contribution can affect the propagation of soft x-ray radiation in plasmas and the interferometric diagnostics of plasmas for many elements.