Regularity of harmonic maps from polyhedra to CAT(1) spaces

We determine regularity results for energy minimizing maps from an n-dimensional Riemannian polyhedral complex X into a CAT(1) space. Provided that the metric on X is Lipschitz regular, we prove Hölder regularity with Hölder constant and exponent dependent on the total energy of the map and the metric on the domain. Moreover, at points away from the \((n-2)\)-skeleton, we improve the regularity to locally Lipschitz. Finally, for points \(x \in X^{(k)}\) with \(k \le n-2\), we demonstrate that the Hölder exponent depends on geometric and combinatorial data of the link of \(x \in X\).     

A green protocol for the N-formylation of amines using molybdate sulfuric acid as a reusable solid catalyst

A novel and efficient method for the N-formylation of amines via the reaction of orthoformates and amines is developed. The reactions are mediated by a catalytic amount of molybdate sulfuric acid as a heterogeneous solid acid.     

Development and application of an analytical method for the determination of storage lipids, fatty acids and fatty alcohols in Calanus finmarchicus

A method was developed for the determination of the major storage lipids, wax ester and triglycerides, in the copepod Calanus finmarchicus. A variation of the Folch method was used to extract the lipid. The method was scaled down to enable the extraction of either pooled (-1 mg) or individual (approximately 200 microg) copepods. The major lipid classes were identified using TLC and quantified using HPLC coupled with evaporative light scattering detection. Analysis of laboratory reference materials indicated that this method underestimated the minor triglyceride component, but gave a good estimate of the major wax ester component. The fatty acid and fatty alcohol composition of the C. finmarchicus were determined following trans-esterification of the lipid extract in methanol. Fatty acids and fatty alcohols were initially identified by comparison with authentic standard and by mass spectroscopy. Using GC with flame ionisation detection the normalised area percentage of the fatty alcohols and fatty acid methyl esters was determined simultaneously in one run for either pooled or individual copepod samples. These methods were applied to C. finmarchicus collected from the Irminger Sea, North Atlantic in 2001 and 2002.     

Synthesis and structure of mycolactone E isolated from frog mycobacterium

The structure of mycolactone E, isolated from the frog pathogen Mycobacterium liflandii, was established via organic synthesis. Within the mycolactone family of metabolites, a structural variation has been seen only at the unsaturated fatty acid moiety thus far, and mycolactone E follows this observation. Interestingly, the absolute configuration of its unsaturated fatty acid matches that of the mycolactones from human mycobacteria, rather than the structurally more closely related mycolactone F from fish mycobacteria.     

Simulation and theory of flexible equilibrium polymers under poor solvent conditions

Grand canonical Monte Carlo simulation and simple statistical thermodynamic theory are used to model the aggregation and phase separation of systems of reversibly polymerizing monomers, capable of forming chains with or without the ability to cyclize into rings, with isotropic square-well attractions between nonbonded pairs of monomers. The general trend observed in simulation of chain-only systems, as predicted in a number of published theoretical works, is that the critical temperature for phase separation increases and the critical monomer density decreases with rising polymer bond strength. Introduction of the equilibrium between chains and rings into the theory lowers the predicted critical temperature and increases the predicted critical density. While the chain-only theories predict a vanishing critical density in the limit of complete polymerization, when ring formation is taken into account the predicted critical density in the same limit approaches the density of the onset of the ring-chain transition. The theoretically predicted effect of cyclization on chemical potential is in good qualitative agreement with a subset of simulation results in which chain-only systems were compared with equilibrium mixtures of rings and chains. The influence of attractions on the aggregation number and radius of gyration of chains and rings observed in simulations is also discussed.     

Isolation,purification, and full NMR assignments of cyclopamine from <Emphasis Type="Italic">Veratrum californicum</Emphasis>

Background  

The Hedgehog signaling pathway is essential for embryogenesis and for tissue homeostasis in the adult. However, it may induce malignancies in a number of tissues when constitutively activated, and it may also have a role in other forms of normal and maladaptive growth. Cyclopamine, a naturally occurring steroidal alkaloid, specifically inhibits the Hedgehog pathway by binding directly to Smoothened, an important Hedgehog response element. To use cyclopamine as a tool to explore and/or inhibit the Hedgehog pathway in vivo, a substantial quantity is required, and as a practical matter cyclopamine has been effectively unavailable for usage in animals larger than mice.     

Perceptually optimized gain function for cochlear implant signal-to-noise ratio based noise reduction

Noise reduction in cochlear implants has achieved significant speech perception improvements through spectral subtraction and signal-to-noise ratio based noise reduction techniques. Current methods use gain functions derived through mathematical optimization or motivated by normal listening psychoacoustic experiments. Although these gain functions have been able to improve speech perception, recent studies have indicated that they are not optimal for cochlear implant noise reduction. This study systematically investigates cochlear implant recipients' speech perception and listening preference of noise reduction with a range of gain functions. Results suggest an advantageous gain function and show that gain functions currently used for noise reduction are not optimal for cochlear implant recipients. Using the cochlear implant optimised gain function, a 27% improvement over the current advanced combination encoder (ACE) stimulation strategy in speech weighted noise and a 7% improvement over current noise reduction strategies were observed in babble noise conditions. The optimized gain function was also most preferred by cochlear implant recipients. The CI specific gain function derived from this study can be easily incorporated into existing noise reduction strategies, to further improve listening performance for CI recipients in challenging environments.