A New Proof of the Mullineux Conjecture

Let S _d denote the symmetric group on d letters. In 1979 Mullineux conjectured a combinatorial algorithm for calculating the effect of tensoring with an irreducible S _d-module with the one dimensional sign module when the ground field has positive characteristic. Kleshchev proved the Mullineux conjecture in 1996. In the present article we provide a new proof of the Mullineux conjecture which is entirely independent of Kleshchev's approach. Applying the representation theory of the supergroup GL(m | n) and the supergroup analogue of Schur-Weyl Duality it becomes straightforward to calculate the combinatorial effect of tensoring with the sign representation and, hence, to verify Mullineux's conjecture. Similar techniques also allow us to classify the irreducible polynomial representations of GL(m | n) of degree d for arbitrary m, n, and d.     

Double coset density in classical algebraic groups

We classify all pairs of reductive maximal connected subgroups of a classical algebraic group that have a dense double coset in . Using this, we show that for an arbitrary pair of reductive subgroups of a reductive group satisfying a certain mild technical condition, there is a dense -double coset in precisely when is a factorization.

     

Necessary conditions for constrained optimization problems with semicontinuous and continuous data

We consider nonsmooth constrained optimization problems with semicontinuous and continuous data in Banach space and derive necessary conditions without constraint qualification in terms of smooth subderivatives and normal cones. These results, in different versions, are set in reflexive and smooth Banach spaces.

     

Combinatorial 3-Manifolds with Transitive Cyclic Symmetry

In this article we give combinatorial criteria to decide whether a transitive cyclic combinatorial d-manifold can be generalized to an infinite family of such complexes, together with an explicit construction in the case that such a family exists. In addition, we substantially extend the classification of combinatorial 3-manifolds with transitive cyclic symmetry up to 22 vertices. Finally, a combination of these results is used to describe new infinite families of transitive cyclic combinatorial manifolds and in particular a family of neighborly combinatorial lens spaces of infinitely many distinct topological types.     

An L2 model for selfadjoint elliptic differential operators with constant coefficients on bounded domains

The selfadjoint realization of a second order elliptic differential expression with Dirichlet boundary conditions is shown to be unitarily equivalent to the maximal multiplication operator with the independent variable in an explicit L² model space. (© 2009 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Exhaustive computational search of ionic-charge clusters that mediate interactions between mammalian cytochrome P450 (CYP) and P450-oxidoreductase (POR) proteins

In this work, a model for the interaction between CYP2B4 and the FMN domain of rat P450-oxidoreductase is built using as template the structure of a bacterial redox complex. Amino acid residues identified in the literature as cytochrome P450 (CYP)–redox partner interfacial residues map to the interface in our model. Our model supports the view that the bacterial template represents a specific electron transfer complex and moreover provides a structural framework for explaining previous experimental data.We have used our model in an exhaustive search for complementary pairs of mammalian CYP and P450-oxidoreductase (POR) charge clusters. We quantitatively show that among the previously defined basic clusters, the 433K–434R cluster is the most dominant (32.3% of interactions) and among the acidic clusters, the 207D–208D–209D cluster is the most dominant (29%). Our analysis also reveals the previously not described basic cluster 343R–345K (16.1% of interactions) and 373K (3.2%) and the acidic clusters 113D–115E–116E (25.8%), 92E–93E (12.9%), 101D (3.2%) and 179E (3.2%).Cluster pairings among the previously defined charge clusters include the pairing of cluster 421K–422R to cluster 207D–208D–209D. Moreover, 433K–434R and 207D–208D–209D, respectively the dominant positively and negatively charged clusters, are uncorrelated. Instead our analysis suggests that the newly identified cluster 113D–115E–116E is the main partner of the 433K–434R cluster while the newly described cluster 343R–345K is correlated to the cluster 207D–208D–209D.     

Selective extraction and elution of weak bases by in-line solid-phase extraction capillary electrophoresis using a pH step gradient and a weak cation-exchange monolith

A polymer monolith bearing weak cation-exchange functionality was prepared for the purpose of demonstrating pH-selective extraction and elution in in-line solid-phase extraction-capillary electrophoresis (SPE-CE) utilising a model set of cationic analytes, namely imidazole, lutidine and 3-phenylpropanamine. Optimization of the electrolyte conditions for efficient elution of the adsorbed analytes using a moving pH boundary required that the capillary and monolith be filled with 44 mM sodium acetate at high pH (pH 6) and a low pH electrolyte of 3 mM sodium acetate pH 3 was placed in the electrolyte vials. This combination allowed the adsorbed analytes to be simultaneously eluted and focused into narrow bands, with peak widths of the eluted analytes having a baseline width of 1.2 s immediately after the monolith. Using these optimum elution conditions, the versatility of the SPE-CE approach was demonstrated by removing unwanted adsorbed components after extraction with a wash at a different pH and also by selecting a pH at which only some of the model weak bases were ionised. The analytical performance of the approach was evaluated and the relative standard deviation for peak heights, peak area and migration times were in the ranges of 1.4-5.3, 1.2-3.3 and 0.4-1.2% respectively. Analytes exhibited linear calibrations with r(2) values ranging from 0.996 to 0.999 over two orders of magnitude. Analyte pre-concentration provided excellent sensitivity, and limits of detection for the analyte used in this study were in the range 8.0-30 ng ml(-1), which was an enhancement of 63 when compared to normal hydrodynamic injection occupying 1.3% of the capillary of these bases in water.     

The neomycin biosynthetic gene cluster of Streptomyces fradiae NCIMB 8233: genetic and biochemical evidence for the roles of two glycosyltransferases and a deacetylase

An efficient protocol has been developed for the genetic manipulation of Streptomyces fradiae NCIMB 8233, which produces the 2-deoxystreptamine (2-DOS)-containing aminoglycoside antibiotic neomycin. This has allowed the in vivo analysis of the respective roles of the glycosyltransferases Neo8 and Neo15, and of the deacetylase Neo16 in neomycin biosynthesis. Specific deletion of each of the neo8, neo15 and neo16 genes confirmed that they are all essential for neomycin biosynthesis. The pattern of metabolites produced by feeding putative pathway intermediates to these mutants provided unambiguous support for a scheme in which Neo8 and Neo15, whose three-dimensional structures are predicted to be highly similar, have distinct roles: Neo8 catalyses transfer of N-acetylglucosamine to 2-DOS early in the pathway, while Neo15 catalyses transfer of the same aminosugar to ribostamycin later in the pathway. The in vitro substrate specificity of Neo15, purified from recombinant Escherichia coli, was fully consistent with these findings. The in vitro activity of Neo16, the only deacetylase so far recognised in the neo gene cluster, showed that it is capable of acting in tandem with both Neo8 and Neo15 as previously proposed. However, the deacetylation of N-acetylglucosaminylribostamycin was still observed in a strain deleted of the neo16 gene and fed with suitable pathway precursors, providing evidence for the existence of a second enzyme in S. fradiae with this activity.