Rarita-Schwinger Type Operators on Spheres and Real Projective Space

In this paper we deal with Rarita-Schwinger type operators on spheres and real projective space. First we define the spherical Rarita-Schwinger type operators and construct their fundamental solutions. Then we establish that the projection operators appearing in the spherical Rarita-Schwinger type operators and the spherical Rarita-Schwinger type equations are conformally invariant under the Cayley transformation. Further, we obtain some basic integral formulas related to the spherical Rarita-Schwinger type operators. Second, we define the Rarita-Schwinger type operators on the real projective space and construct their kernels and Cauchy integral formulas.Comment: 21 pages. arXiv admin note: text overlap with arXiv:1106.358

An AT-barrier mechanically controls DNA reannealing under tension

Regulation of genomic activity occurs through the manipulation of DNA by competent mechanoenzymes. Force-clamp optical tweezers that allow the structural dynamics of the DNA molecule to be measured were used here to investigate the kinetics of mechanically-driven strand reannealing. When the force on the torsionally unconstrained lambda-phage DNA is decreased stepwise from above to below the overstretching transition, reannealing occurs via discrete shortening steps separated by exponentially distributed time intervals. Kinetic analysis reveals a transition barrier 0.58 nm along the reaction coordinate and an average reannealing-step size of approximately 750 bp, consistent with the average bp interval separating segments of more than 10 consecutive AT bases. In an AT-rich DNA construct, in which the distance between segments of more than 10 consecutive AT is reduced to approximately 210 bps, the reannealing step reduces accordingly without changes in the position of the transition barrier. Thus, the transition barrier for reannealing is determined by the presence of segments of more than 10 consecutive AT bps independent of changes in sequence composition, while the length of the reannealing strand changes according to the distance between poly-AT segments at least 10 bps long

Palladium nanoparticles supported on polyvinylpyridine: catalytic activity in Heck-type reactions and XPS structural studies

Palladium nanoparticles, obtained by metal vapour synthesis (MVS), were deposited on cross-linked polyvinylpyridine. The Pd/PVPy system showed high catalytic activity in the Heck C-C coupling reaction of iodo- and bromo-arenes (iodobenzene, bromobenzene, p-nitrobromobenzene, p-bromoacetophenone, p-(methoxy)bromobenzene) with alkyl acrylates (methyl acrylate, n-butyl acrylate, ethylhexyl trans-3-(4-methoxyphenyl)acrylate) at 100 degrees C-175 degrees C working under nitrogen atmosphere as well as in air. The catalyst is stable and the leaching of metal in solution is very low. When reused, the recovered Pd/PVPy maintains the catalytic activity of the pristine material. XPS structural studies performed on the starting catalyst as well as on the recovered one indicate the presence of a interaction between the basic nitrogen of the pyridine present in the polymer and the metal. (C) 2009 Elsevier Inc. All rights reserved