Smart Geodesic Tracing in GRworkbench

We have developed a new tool for numerical work in General Relativity: GRworkbench. We discuss how GRworkbench's implementation of a numerically-amenable analogue to Differential Geometry facilitates the development of robust and chart-independent numerical algorithms. We consider, as an example, geodesic tracing on two charts covering the exterior Schwarzschild space-time.     

Bengazoles C-G from the Sponge Jaspis sp. Synthesis of the Side Chain and Determination of Absolute Configuration

Five new antifungal bengazoles (C-G) were isolated and fully characterized from a marine sponge of the genus Jaspis sp. Bengazoles C-G, together with the known bengazoles A and B, comprise a homologous series of n, iso, and anteiso fatty acid esters (C(13)-C(16)) of the same heterocyclic bis(oxazolyl)methanol parent. The complete relative and absolute configurations of the bengazoles were determined by application of the modified Mosher method and interpretation of exciton coupling in the CD spectra of the tetra-p-bromobenzoate derivatives of bengazole A and that of a model tetrol synthesized in seven steps from L-fucose.     

PICOSECOND LASER SPECTROSCOPY AND OPTICALLY DETECTED MAGNETIC RESONANCE ON A MODEL PHOTOSYNTHETIC SYSTEM

Fluorescence-detected magnetic resonance of triplets in zero magnetic field (FDMR), fluorescence fading (FF) due to triplet-formation, both at 4.2 K, and prompt fluorescence decay kinetics (FDK) at room temperature have been measured for free pheophorbide- a (f-Pheo) and bound (b-Pheo) to a synthetic polypeptide (L-L ys -L-A la -L-A la )_n, dissolved in dimethylformamide (DMF). Fluorescence decay kinetics measurements of f-Pheo in DMF yielded 1-5 ns lifetimes, for b-Pheo in DMF a ~ 50 ps decay-component was found emitting at 730–750 nm. Zero-field splitting parameters |D| and |E| of the lowest triplet state T₁ were determined from FDMR spectra as (337 and 24) 10^-4 cm^-1 for f-Pheo and (359 and 25) 10^-4 cm^-1 for b-Pheo, both in DMF. Decay rate constants of the three spin levels of T¹ of b-Pheo ( K _x= 1200 50 s^-1, k _y= 440 25 s^-1, k _z= 80 5 s^-1) and relative steady-state populations (N_x= 28 2%, N_y= 47 2%, N_z= 26 2%) determined from FF curves predict a fluorescence decrease at the D–E and D + E FDMR transitions, whereas experimentally a fluorescence increase is observed. The FDMR sign-inversion results from singlet-singlet energy transfer from b-Pheo monomers to their aggregates, followed by fast intersystem crossing to T₁. These results indicate that aggregates are formed by two or more b-Pheo molecules at different positions on the folded polypeptide chain. This situation resembles that in chlorophyll-proteins, containing low-lying traps, resulting from interaction of chromophores with other chromophores and with the protein environment.     

Synthesis of periphery-functionalized dendritic molecules using polylithiated dendrimers as starting material

A general method for the functionalization of Si-Cl terminated carbosilane dendritic molecules via organolithium or organomagnesium reagents is described. Quantitative exchange of the bromine atoms of 4-bromophenyl-functionalized dendrimers affords polylithiated species that are valuable starting materials for further functionalization, e.g., into pyridyl alcohols. The latter were successfully applied as catalyst precursors in a ruthenium-mediated ring-closure metathesis reaction.     

An efficient solution for resolving iTRAQ and TMT channel cross‐talk

Isobaric tagging reagents such as isobaric tag for relative and absolute quantitation (iTRAQ) and tandem mass tag (TMT) typically have isotopic impurities that cause significant cross‐talk between channels. Here, we present an efficient solution to compensate for channel cross‐talk using linear algebra and find that it is between 20× and 120× faster than previous methods. We also find that the effects of channel cross‐talk are as important to manage as the effects of ratio compression because of precursor impurities, and we have released an open‐source tool to perform both types of calculations.     

The Hopf conjecture for manifolds with low cohomogeneity or high symmetry rank

We prove that the Euler characteristic of an even-dimensional compact manifold with positive (nonnegative) sectional curvature is positive (nonnegative) provided that the manifold admits an isometric action of a compact Lie group with principal isotropy group and cohomogeneity such that . Moreover, we prove that the Euler characteristic of a compact Riemannian manifold or with positive sectional curvature is positive if admits an effective isometric action of a torus , i.e., if the symmetry rank of is .