Continuous bordering of matrices and continuous matrix decompositions

Summary. Let be the set of all real -matrices of rank . We prove that for there are no continuous vector fields such that the bordered matrix is regular for all . This result has some relevance for the numerical analysis of steady state bifurcation. As a by-product we show that there is no nonvanishing continuous vector field with for all , where is the set of all matrices of rank deficiency one. This implies that there is no singular value decomposition of depending continuously on in any matrix set which contains . As another application we prove that in general there is no global analytic singular value decomposition for analytic matrix valued functions of more than one real variable. Received October 6, 1993 / Revised version received July 18, 1994     

Closed bosonic strings in background gauge fields

The coupling to abelian background gauge fields of closed bosonic strings compactified on a torus is considered. There exist specific field configurations for which the theory cannot be defined consistently, in spite of the fact that the field equations of motion are then solved exactly. This critical behaviour is related to a breakdown of local and global world-sheet symmetries, as well as of spacetime unitarity. A physical interpretation of this phenomenon is proposed. The issue of spacetime duality is also discussed. This symmetry is shown to be partially broken for generic background field configurations.     

Towards supersymmetric subconstituent models

't Hooft's consistency equations for subconstituent models are generalized to supersymmetric theories and a few solutions are outlined.     

Descente infinie et hauteurp-adique sur les courbes elliptiques à multiplication complexe

Sans résumé     

Surfactant-free synthesis of amphiphilic diblock copolymer nanoparticles via nitroxide-mediated emulsion polymerization

Amphiphilic hairy nanoparticles are prepared in a one step, batch, heterogeneous polymerization of styrene or n-butyl acrylate, using a water-soluble poly(sodium acrylate) alkoxyamine macroinitiator based on the SG1 nitroxide.     

Representations of the rotation reflection symmetry group of the four-dimensional cubic lattice

The structure and representations of the rotation reflection symmetry group of the four-dimensional cubic lattice are described. Their connections with the representations of the three-dimensional lattice rotation reflection group, and with the representations of the continuous O(3) and O(4) groups are given.     

Structured Hybrid Nanoparticles via Surface‐Initiated ATRP of Methyl Methacrylate from Ordered Mesoporous Silica

Structured hybrid nanoparticles were synthesized via surface‐initiated atom transfer radical polymerization of MMA from ordered mesoporous silica (OMS) nanoparticles with various morphologies. The design of the OMS particles was adjusted to target either spherical core‐shell or cylindrical morphologies with a mean diameter below 400 nm. The polymer growth via ATRP from the silica surface was well‐controlled as demonstrated by the macromolecular characteristics of the grafted chains. Original hybrid multilayered nanoparticles composed of either a dense silica core or hollow core; an inner OMS shell showing radial orientation of the mesopores and an outer PMMA shell with controlled thickness were successfully prepared.

     

Self-Assembly Behavior and Application of Terphenyl-Cored Trimaltosides for Membrane-Protein Studies: Impact of Detergent Hydrophobic Group Geometry on Protein Stability

Amphipathic agents are widely used in various fields including biomedical sciences. Micelle-forming detergents are particularly useful for in vitro membrane-protein characterization. As many conventional detergents are limited in their ability to stabilize membrane proteins, it is necessary to develop novel detergents to facilitate membrane-protein research. In the current study, we developed novel trimaltoside detergents with an alkyl pendant-bearing terphenyl unit as a hydrophobic group, designated terphenyl-cored maltosides (TPMs). We found that the geometry of the detergent hydrophobic group substantially impacts detergent self-assembly behavior, as well as detergent efficacy for membrane-protein stabilization. TPM-Vs, with a bent terphenyl group, were superior to the linear counterparts (TPM-Ls) at stabilizing multiple membrane proteins. The favorable protein stabilization efficacy of these bent TPMs is likely associated with a binding mode with membrane proteins distinct from conventional detergents and facial amphiphiles. When compared to n-dodecyl-β-d -maltoside (DDM), most TPMs were superior or comparable to this gold standard detergent at stabilizing membrane proteins. Notably, TPM-L3 was particularly effective at stabilizing the human β₂ adrenergic receptor (β₂AR), a G-protein coupled receptor, and its complex with G_s protein. Thus, the current study not only provides novel detergent tools that are useful for membrane-protein study, but also suggests a critical role for detergent hydrophobic group geometry in governing detergent efficacy.